[{"data":1,"prerenderedAt":133233},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F0011-about-the-f-divergence":3,"i-ci:tag":132694,"i-mingcute:time-line":132694},{"post":4,"nextPost":132705,"prevPost":132894},{"id":5,"title":6,"body":7,"description":132690,"draft":132691,"enableCodeHighlight":132691,"enableCodeHightlight":132691,"enableComment":132692,"enableD2":132691,"enableKatex":132692,"extension":132693,"image":132628,"important":132691,"location":132694,"meta":132695,"navigation":132692,"ogImage":132694,"path":132696,"seo":132697,"stem":132698,"summary":132699,"tags":132700,"time":132703,"__hash__":132704},"blog\u002Fblog\u002F2026\u002F0011-about-the-f-divergence.md","f-散度族及其推论",{"type":8,"value":9,"toc":132627},"minimark",[10,63,177,524,527,532,752,916,992,2310,2315,3155,3822,4259,4716,5202,5206,5528,5571,5575,5711,5889,5946,6489,6661,7146,7359,7363,8414,8749,8847,8851,9092,9365,9401,9871,10026,10555,10558,10562,10664,10966,10971,11936,12604,13416,14259,14391,15320,15871,16169,16510,17044,17350,17966,19078,19898,20441,20787,21040,21278,21309,21405,21409,21441,21444,21447,21464,21467,21471,21474,21562,21798,22338,22503,23047,23050,23340,23625,24186,24189,24487,25182,25546,25550,25712,26189,26461,26857,27568,27571,28008,28011,28448,28717,29681,29934,30575,30813,30981,31168,31578,32084,32802,33528,33584,33829,34090,34507,34511,34513,34680,34749,35389,35784,36176,36185,36531,37146,37150,37152,37284,37352,37880,37887,38260,38633,39586,40435,40439,40441,40622,40938,41477,41639,42047,42110,42587,43205,44117,44308,44734,44738,44822,45163,45609,45985,46194,46466,46652,47190,47731,48157,48160,49015,49104,49373,49377,49380,49949,50416,50626,50754,51295,51508,51517,52019,52487,52491,54910,54914,55209,55213,55467,56134,56138,57095,57786,58288,58292,58644,58968,59073,59806,60679,60683,61502,61537,61788,61954,63000,63653,63659,63925,64423,64616,66806,67820,68130,68405,68917,70605,71495,73265,74028,74031,74442,74445,74448,74452,74756,75094,75860,75863,76224,76256,76745,76808,77603,77982,78030,78034,78914,79220,80362,82056,82060,83878,83884,84028,84430,84974,86101,87042,87048,87516,88201,88608,88681,88720,89118,89447,89699,90445,90510,91791,92436,96940,96947,96951,96954,98867,99126,99295,99299,99303,99306,99709,99915,100705,100831,101343,101347,101761,102019,102479,103185,103189,103250,103382,103769,104117,105347,105351,105537,105892,105895,106373,106763,107275,107558,107979,108239,108243,108246,108580,108584,108588,111548,114607,114610,114614,114667,114914,115127,115253,115614,115889,116266,116387,116392,116396,117433,117436,117440,117443,117502,117505,117509,117699,117703,117706,118235,118590,118594,118597,119169,119289,119293,119341,119744,119747,119751,119816,119820,119823,120177,120180,120184,120265,120619,120895,121053,121290,121556,121879,122251,122661,123536,124068,124338,124341,124345,124349,124700,124705,125444,125897,126235,126237,126838,127000,127006,127352,127868,127874,128448,128690,128694,129287,129678,130098,130446,130920,130924,131182,131497,131603,132137,132140,132144,132147,132624],[11,12,13,14,62],"p",{},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 ",[15,16,20,42],"span",{"className":17,"translate":19},[18],"katex","no",[15,21,24],{"className":22},[23],"katex-mathml",[25,26,28],"math",{"xmlns":27},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[29,30,31,38],"semantics",{},[32,33,34],"mrow",{},[35,36,37],"mi",{},"f",[39,40,37],"annotation",{"encoding":41},"application\u002Fx-tex",[15,43,47],{"className":44,"ariaHidden":46},[45],"katex-html","true",[15,48,51,56],{"className":49},[50],"base",[15,52],{"className":53,"style":55},[54],"strut","height:0.8889em;vertical-align:-0.1944em;",[15,57,37],{"className":58,"style":61},[59,60],"mord","mathnormal","margin-right:0.1076em;"," 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",[11,64,65,66,94,95,176],{},"用一个凸函数 ",[15,67,69,82],{"className":68,"translate":19},[18],[15,70,72],{"className":71},[23],[25,73,74],{"xmlns":27},[29,75,76,80],{},[32,77,78],{},[35,79,37],{},[39,81,37],{"encoding":41},[15,83,85],{"className":84,"ariaHidden":46},[45],[15,86,88,91],{"className":87},[50],[15,89],{"className":90,"style":55},[54],[15,92,37],{"className":93,"style":61},[59,60],"（满足 ",[15,96,98,130],{"className":97,"translate":19},[18],[15,99,101],{"className":100},[23],[25,102,103],{"xmlns":27},[29,104,105,127],{},[32,106,107,109,114,118,121,124],{},[35,108,37],{},[110,111,113],"mo",{"stretchy":112},"false","(",[115,116,117],"mn",{},"1",[110,119,120],{"stretchy":112},")",[110,122,123],{},"=",[115,125,126],{},"0",[39,128,129],{"encoding":41},"f(1)=0",[15,131,133,166],{"className":132,"ariaHidden":46},[45],[15,134,136,140,143,147,150,154,159,163],{"className":135},[50],[15,137],{"className":138,"style":139},[54],"height:1em;vertical-align:-0.25em;",[15,141,37],{"className":142,"style":61},[59,60],[15,144,113],{"className":145},[146],"mopen",[15,148,117],{"className":149},[59],[15,151,120],{"className":152},[153],"mclose",[15,155],{"className":156,"style":158},[157],"mspace","margin-right:0.2778em;",[15,160,123],{"className":161},[162],"mrel",[15,164],{"className":165,"style":158},[157],[15,167,169,173],{"className":168},[50],[15,170],{"className":171,"style":172},[54],"height:0.6444em;",[15,174,126],{"className":175},[59],"）定义的散度模板：",[15,178,181],{"className":179,"translate":19},[180],"katex-display",[15,182,184,261],{"className":183,"translate":19},[18],[15,185,187],{"className":186},[23],[25,188,190],{"xmlns":27,"display":189},"block",[29,191,192,258],{},[32,193,194,202,204,207,211,214,216,218,226],{},[195,196,197,200],"msub",{},[35,198,199],{},"D",[35,201,37],{},[110,203,113],{"stretchy":112},[35,205,206],{},"P",[35,208,210],{"mathvariant":209},"normal","∥",[35,212,213],{},"Q",[110,215,120],{"stretchy":112},[110,217,123],{},[195,219,220,224],{},[35,221,223],{"mathvariant":222},"double-struck","E",[35,225,213],{},[32,227,228,231,233,255],{},[110,229,230],{"fence":46},"[",[35,232,37],{},[32,234,235,237,253],{},[110,236,113],{"fence":46},[238,239,240,247],"mfrac",{},[32,241,242,245],{},[35,243,244],{},"d",[35,246,206],{},[32,248,249,251],{},[35,250,244],{},[35,252,213],{},[110,254,120],{"fence":46},[110,256,257],{"fence":46},"]",[39,259,260],{"encoding":41},"D_f(P\\|Q)\n=\\mathbb E_Q\\left[\nf\\left(\\frac{dP}{dQ}\\right)\\right]",[15,262,264,353],{"className":263,"ariaHidden":46},[45],[15,265,267,271,328,331,335,338,341,344,347,350],{"className":266},[50],[15,268],{"className":269,"style":270},[54],"height:1.0361em;vertical-align:-0.2861em;",[15,272,274,278],{"className":273},[59],[15,275,199],{"className":276,"style":277},[59,60],"margin-right:0.0278em;",[15,279,282],{"className":280},[281],"msupsub",[15,283,287,319],{"className":284},[285,286],"vlist-t","vlist-t2",[15,288,291,314],{"className":289},[290],"vlist-r",[15,292,296],{"className":293,"style":295},[294],"vlist","height:0.3361em;",[15,297,299,304],{"style":298},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[15,300],{"className":301,"style":303},[302],"pstrut","height:2.7em;",[15,305,311],{"className":306},[307,308,309,310],"sizing","reset-size6","size3","mtight",[15,312,37],{"className":313,"style":61},[59,60,310],[15,315,318],{"className":316},[317],"vlist-s","​",[15,320,322],{"className":321},[290],[15,323,326],{"className":324,"style":325},[294],"height:0.2861em;",[15,327],{},[15,329,113],{"className":330},[146],[15,332,206],{"className":333,"style":334},[59,60],"margin-right:0.1389em;",[15,336,210],{"className":337},[59],[15,339,213],{"className":340},[59,60],[15,342,120],{"className":343},[153],[15,345],{"className":346,"style":158},[157],[15,348,123],{"className":349},[162],[15,351],{"className":352,"style":158},[157],[15,354,356,360,403,407],{"className":355},[50],[15,357],{"className":358,"style":359},[54],"height:2.4em;vertical-align:-0.95em;",[15,361,363,367],{"className":362},[59],[15,364,223],{"className":365},[59,366],"mathbb",[15,368,370],{"className":369},[281],[15,371,373,395],{"className":372},[285,286],[15,374,376,392],{"className":375},[290],[15,377,380],{"className":378,"style":379},[294],"height:0.3283em;",[15,381,383,386],{"style":382},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[15,384],{"className":385,"style":303},[302],[15,387,389],{"className":388},[307,308,309,310],[15,390,213],{"className":391},[59,60,310],[15,393,318],{"className":394},[317],[15,396,398],{"className":397},[290],[15,399,401],{"className":400,"style":325},[294],[15,402],{},[15,404],{"className":405,"style":406},[157],"margin-right:0.1667em;",[15,408,411,420,423,426,518],{"className":409},[410],"minner",[15,412,416],{"className":413,"style":415},[146,414],"delimcenter","top:0em;",[15,417,230],{"className":418},[419,309],"delimsizing",[15,421,37],{"className":422,"style":61},[59,60],[15,424],{"className":425,"style":406},[157],[15,427,429,435,512],{"className":428},[410],[15,430,432],{"className":431,"style":415},[146,414],[15,433,113],{"className":434},[419,309],[15,436,438,442,509],{"className":437},[59],[15,439],{"className":440},[146,441],"nulldelimiter",[15,443,445],{"className":444},[238],[15,446,448,500],{"className":447},[285,286],[15,449,451,497],{"className":450},[290],[15,452,455,471,482],{"className":453,"style":454},[294],"height:1.3714em;",[15,456,458,462],{"style":457},"top:-2.314em;",[15,459],{"className":460,"style":461},[302],"height:3em;",[15,463,465,468],{"className":464},[59],[15,466,244],{"className":467},[59,60],[15,469,213],{"className":470},[59,60],[15,472,474,477],{"style":473},"top:-3.23em;",[15,475],{"className":476,"style":461},[302],[15,478],{"className":479,"style":481},[480],"frac-line","border-bottom-width:0.04em;",[15,483,485,488],{"style":484},"top:-3.677em;",[15,486],{"className":487,"style":461},[302],[15,489,491,494],{"className":490},[59],[15,492,244],{"className":493},[59,60],[15,495,206],{"className":496,"style":334},[59,60],[15,498,318],{"className":499},[317],[15,501,503],{"className":502},[290],[15,504,507],{"className":505,"style":506},[294],"height:0.8804em;",[15,508],{},[15,510],{"className":511},[153,441],[15,513,515],{"className":514,"style":415},[153,414],[15,516,120],{"className":517},[419,309],[15,519,521],{"className":520,"style":415},[153,414],[15,522,257],{"className":523},[419,309],[11,525,526],{},"它统一了 KL、JS、全变差、卡方、Hellinger 等众多散度，具有非负性、联合凸性、变分对偶表示和数据处理不等式等核心性质，是信息论和生成模型理论中的基础工具。",[528,529,531],"h2",{"id":530},"_1-定义","1. 定义",[11,533,534,535,580,581,638,639,668,669,697,698,751],{},"设 ",[15,536,538,557],{"className":537,"translate":19},[18],[15,539,541],{"className":540},[23],[25,542,543],{"xmlns":27},[29,544,545,554],{},[32,546,547,549,552],{},[35,548,206],{},[110,550,551],{"separator":46},",",[35,553,213],{},[39,555,556],{"encoding":41},"P,Q",[15,558,560],{"className":559,"ariaHidden":46},[45],[15,561,563,567,570,574,577],{"className":562},[50],[15,564],{"className":565,"style":566},[54],"height:0.8778em;vertical-align:-0.1944em;",[15,568,206],{"className":569,"style":334},[59,60],[15,571,551],{"className":572},[573],"mpunct",[15,575],{"className":576,"style":406},[157],[15,578,213],{"className":579},[59,60]," 是同一个可测空间 ",[15,582,584,609],{"className":583,"translate":19},[18],[15,585,587],{"className":586},[23],[25,588,589],{"xmlns":27},[29,590,591,606],{},[32,592,593,595,599,601,604],{},[110,594,113],{"stretchy":112},[35,596,598],{"mathvariant":597},"script","X",[110,600,551],{"separator":46},[35,602,603],{"mathvariant":597},"A",[110,605,120],{"stretchy":112},[39,607,608],{"encoding":41},"(\\mathcal X,\\mathcal A)",[15,610,612],{"className":611,"ariaHidden":46},[45],[15,613,615,618,621,626,629,632,635],{"className":614},[50],[15,616],{"className":617,"style":139},[54],[15,619,113],{"className":620},[146],[15,622,598],{"className":623,"style":625},[59,624],"mathcal","margin-right:0.1464em;",[15,627,551],{"className":628},[573],[15,630],{"className":631,"style":406},[157],[15,633,603],{"className":634},[59,624],[15,636,120],{"className":637},[153]," 上的两个概率分布，且 ",[15,640,642,655],{"className":641,"translate":19},[18],[15,643,645],{"className":644},[23],[25,646,647],{"xmlns":27},[29,648,649,653],{},[32,650,651],{},[35,652,206],{},[39,654,206],{"encoding":41},[15,656,658],{"className":657,"ariaHidden":46},[45],[15,659,661,665],{"className":660},[50],[15,662],{"className":663,"style":664},[54],"height:0.6833em;",[15,666,206],{"className":667,"style":334},[59,60]," 关于 ",[15,670,672,685],{"className":671,"translate":19},[18],[15,673,675],{"className":674},[23],[25,676,677],{"xmlns":27},[29,678,679,683],{},[32,680,681],{},[35,682,213],{},[39,684,213],{"encoding":41},[15,686,688],{"className":687,"ariaHidden":46},[45],[15,689,691,694],{"className":690},[50],[15,692],{"className":693,"style":566},[54],[15,695,213],{"className":696},[59,60]," 绝对连续（即 ",[15,699,701,720],{"className":700,"translate":19},[18],[15,702,704],{"className":703},[23],[25,705,706],{"xmlns":27},[29,707,708,717],{},[32,709,710,712,715],{},[35,711,206],{},[110,713,714],{},"≪",[35,716,213],{},[39,718,719],{"encoding":41},"P\\ll Q",[15,721,723,742],{"className":722,"ariaHidden":46},[45],[15,724,726,730,733,736,739],{"className":725},[50],[15,727],{"className":728,"style":729},[54],"height:0.7224em;vertical-align:-0.0391em;",[15,731,206],{"className":732,"style":334},[59,60],[15,734],{"className":735,"style":158},[157],[15,737,714],{"className":738},[162],[15,740],{"className":741,"style":158},[157],[15,743,745,748],{"className":744},[50],[15,746],{"className":747,"style":566},[54],[15,749,213],{"className":750},[59,60],"），记",[15,753,755],{"className":754,"translate":19},[180],[15,756,758,802],{"className":757,"translate":19},[18],[15,759,761],{"className":760},[23],[25,762,763],{"xmlns":27,"display":189},[29,764,765,799],{},[32,766,767,770,772,775,777,779,793,795,797],{},[35,768,769],{},"t",[110,771,113],{"stretchy":112},[35,773,774],{},"x",[110,776,120],{"stretchy":112},[110,778,123],{},[238,780,781,787],{},[32,782,783,785],{},[35,784,244],{},[35,786,206],{},[32,788,789,791],{},[35,790,244],{},[35,792,213],{},[110,794,113],{"stretchy":112},[35,796,774],{},[110,798,120],{"stretchy":112},[39,800,801],{"encoding":41},"t(x)=\\frac{dP}{dQ}(x)",[15,803,805,832],{"className":804,"ariaHidden":46},[45],[15,806,808,811,814,817,820,823,826,829],{"className":807},[50],[15,809],{"className":810,"style":139},[54],[15,812,769],{"className":813},[59,60],[15,815,113],{"className":816},[146],[15,818,774],{"className":819},[59,60],[15,821,120],{"className":822},[153],[15,824],{"className":825,"style":158},[157],[15,827,123],{"className":828},[162],[15,830],{"className":831,"style":158},[157],[15,833,835,839,907,910,913],{"className":834},[50],[15,836],{"className":837,"style":838},[54],"height:2.2519em;vertical-align:-0.8804em;",[15,840,842,845,904],{"className":841},[59],[15,843],{"className":844},[146,441],[15,846,848],{"className":847},[238],[15,849,851,896],{"className":850},[285,286],[15,852,854,893],{"className":853},[290],[15,855,857,871,879],{"className":856,"style":454},[294],[15,858,859,862],{"style":457},[15,860],{"className":861,"style":461},[302],[15,863,865,868],{"className":864},[59],[15,866,244],{"className":867},[59,60],[15,869,213],{"className":870},[59,60],[15,872,873,876],{"style":473},[15,874],{"className":875,"style":461},[302],[15,877],{"className":878,"style":481},[480],[15,880,881,884],{"style":484},[15,882],{"className":883,"style":461},[302],[15,885,887,890],{"className":886},[59],[15,888,244],{"className":889},[59,60],[15,891,206],{"className":892,"style":334},[59,60],[15,894,318],{"className":895},[317],[15,897,899],{"className":898},[290],[15,900,902],{"className":901,"style":506},[294],[15,903],{},[15,905],{"className":906},[153,441],[15,908,113],{"className":909},[146],[15,911,774],{"className":912},[59,60],[15,914,120],{"className":915},[153],[11,917,918,919,991],{},"为 Radon–Nikodym 导数（在离散情形就是概率质量之比，在密度存在时就是密度之比 ",[15,920,922,954],{"className":921,"translate":19},[18],[15,923,925],{"className":924},[23],[25,926,927],{"xmlns":27},[29,928,929,951],{},[32,930,931,933,935,937,939,942,945,947,949],{},[35,932,11],{},[110,934,113],{"stretchy":112},[35,936,774],{},[110,938,120],{"stretchy":112},[35,940,941],{"mathvariant":209},"\u002F",[35,943,944],{},"q",[110,946,113],{"stretchy":112},[35,948,774],{},[110,950,120],{"stretchy":112},[39,952,953],{"encoding":41},"p(x)\u002Fq(x)",[15,955,957],{"className":956,"ariaHidden":46},[45],[15,958,960,963,966,969,972,975,978,982,985,988],{"className":959},[50],[15,961],{"className":962,"style":139},[54],[15,964,11],{"className":965},[59,60],[15,967,113],{"className":968},[146],[15,970,774],{"className":971},[59,60],[15,973,120],{"className":974},[153],[15,976,941],{"className":977},[59],[15,979,944],{"className":980,"style":981},[59,60],"margin-right:0.0359em;",[15,983,113],{"className":984},[146],[15,986,774],{"className":987},[59,60],[15,989,120],{"className":990},[153],"）。",[993,994,996,1229,1636,1668,2248],"theorem",{"title":995},"定义 1.1（f-散度）",[11,997,998,999,1100,1101,1166,1167,668,1195,1223,1224,1228],{},"给定一个凸函数 ",[15,1000,1002,1036],{"className":1001,"translate":19},[18],[15,1003,1005],{"className":1004},[23],[25,1006,1007],{"xmlns":27},[29,1008,1009,1033],{},[32,1010,1011,1013,1016,1018,1020,1022,1025,1027,1030],{},[35,1012,37],{},[110,1014,1015],{},":",[110,1017,230],{"stretchy":112},[115,1019,126],{},[110,1021,551],{"separator":46},[35,1023,1024],{"mathvariant":209},"∞",[110,1026,120],{"stretchy":112},[110,1028,1029],{},"→",[35,1031,1032],{"mathvariant":222},"R",[39,1034,1035],{"encoding":41},"f:[0,\\infty)\\to\\mathbb R",[15,1037,1039,1057,1090],{"className":1038,"ariaHidden":46},[45],[15,1040,1042,1045,1048,1051,1054],{"className":1041},[50],[15,1043],{"className":1044,"style":55},[54],[15,1046,37],{"className":1047,"style":61},[59,60],[15,1049],{"className":1050,"style":158},[157],[15,1052,1015],{"className":1053},[162],[15,1055],{"className":1056,"style":158},[157],[15,1058,1060,1063,1066,1069,1072,1075,1078,1081,1084,1087],{"className":1059},[50],[15,1061],{"className":1062,"style":139},[54],[15,1064,230],{"className":1065},[146],[15,1067,126],{"className":1068},[59],[15,1070,551],{"className":1071},[573],[15,1073],{"className":1074,"style":406},[157],[15,1076,1024],{"className":1077},[59],[15,1079,120],{"className":1080},[153],[15,1082],{"className":1083,"style":158},[157],[15,1085,1029],{"className":1086},[162],[15,1088],{"className":1089,"style":158},[157],[15,1091,1093,1097],{"className":1092},[50],[15,1094],{"className":1095,"style":1096},[54],"height:0.6889em;",[15,1098,1032],{"className":1099},[59,366],"，且满足 ",[15,1102,1104,1127],{"className":1103,"translate":19},[18],[15,1105,1107],{"className":1106},[23],[25,1108,1109],{"xmlns":27},[29,1110,1111,1125],{},[32,1112,1113,1115,1117,1119,1121,1123],{},[35,1114,37],{},[110,1116,113],{"stretchy":112},[115,1118,117],{},[110,1120,120],{"stretchy":112},[110,1122,123],{},[115,1124,126],{},[39,1126,129],{"encoding":41},[15,1128,1130,1157],{"className":1129,"ariaHidden":46},[45],[15,1131,1133,1136,1139,1142,1145,1148,1151,1154],{"className":1132},[50],[15,1134],{"className":1135,"style":139},[54],[15,1137,37],{"className":1138,"style":61},[59,60],[15,1140,113],{"className":1141},[146],[15,1143,117],{"className":1144},[59],[15,1146,120],{"className":1147},[153],[15,1149],{"className":1150,"style":158},[157],[15,1152,123],{"className":1153},[162],[15,1155],{"className":1156,"style":158},[157],[15,1158,1160,1163],{"className":1159},[50],[15,1161],{"className":1162,"style":172},[54],[15,1164,126],{"className":1165},[59],"，则 ",[15,1168,1170,1183],{"className":1169,"translate":19},[18],[15,1171,1173],{"className":1172},[23],[25,1174,1175],{"xmlns":27},[29,1176,1177,1181],{},[32,1178,1179],{},[35,1180,206],{},[39,1182,206],{"encoding":41},[15,1184,1186],{"className":1185,"ariaHidden":46},[45],[15,1187,1189,1192],{"className":1188},[50],[15,1190],{"className":1191,"style":664},[54],[15,1193,206],{"className":1194,"style":334},[59,60],[15,1196,1198,1211],{"className":1197,"translate":19},[18],[15,1199,1201],{"className":1200},[23],[25,1202,1203],{"xmlns":27},[29,1204,1205,1209],{},[32,1206,1207],{},[35,1208,213],{},[39,1210,213],{"encoding":41},[15,1212,1214],{"className":1213,"ariaHidden":46},[45],[15,1215,1217,1220],{"className":1216},[50],[15,1218],{"className":1219,"style":566},[54],[15,1221,213],{"className":1222},[59,60]," 的 ",[1225,1226,1227],"strong",{},"f-散度"," 定义为",[15,1230,1232],{"className":1231,"translate":19},[180],[15,1233,1235,1342],{"className":1234,"translate":19},[18],[15,1236,1238],{"className":1237},[23],[25,1239,1240],{"xmlns":27,"display":189},[29,1241,1242,1339],{},[1243,1244,1248],"mtable",{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},"0.25em","right left","0em",[1249,1250,1251,1275],"mtr",{},[1252,1253,1254],"mtd",{},[1255,1256,1257],"mstyle",{"scriptlevel":126,"displaystyle":46},[32,1258,1259,1265,1267,1269,1271,1273],{},[195,1260,1261,1263],{},[35,1262,199],{},[35,1264,37],{},[110,1266,113],{"stretchy":112},[35,1268,206],{},[35,1270,210],{"mathvariant":209},[35,1272,213],{},[110,1274,120],{"stretchy":112},[1252,1276,1277],{},[1255,1278,1279],{"scriptlevel":126,"displaystyle":46},[32,1280,1281,1283,1285,1288,1290,1292,1294,1296,1300,1302,1305,1333,1335,1337],{},[32,1282],{},[110,1284,123],{},[110,1286,1287],{},"∫",[35,1289,944],{},[110,1291,113],{"stretchy":112},[35,1293,774],{},[110,1295,120],{"stretchy":112},[1297,1298,1299],"mtext",{}," ",[35,1301,37],{},[1297,1303,1304],{}," ⁣",[32,1306,1307,1309,1331],{},[110,1308,113],{"fence":46},[238,1310,1311,1321],{},[32,1312,1313,1315,1317,1319],{},[35,1314,11],{},[110,1316,113],{"stretchy":112},[35,1318,774],{},[110,1320,120],{"stretchy":112},[32,1322,1323,1325,1327,1329],{},[35,1324,944],{},[110,1326,113],{"stretchy":112},[35,1328,774],{},[110,1330,120],{"stretchy":112},[110,1332,120],{"fence":46},[35,1334,244],{},[35,1336,774],{},[110,1338,551],{"separator":46},[39,1340,1341],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int q(x)\\,\nf\\!\\left(\\frac{p(x)}{q(x)}\\right)dx,\n\\end{aligned}",[15,1343,1345],{"className":1344,"ariaHidden":46},[45],[15,1346,1348,1351],{"className":1347},[50],[15,1349],{"className":1350,"style":359},[54],[15,1352,1354],{"className":1353},[59],[15,1355,1357,1448],{"className":1356},[1243],[15,1358,1361],{"className":1359},[1360],"col-align-r",[15,1362,1364,1439],{"className":1363},[285,286],[15,1365,1367,1436],{"className":1366},[290],[15,1368,1371],{"className":1369,"style":1370},[294],"height:1.45em;",[15,1372,1374,1378],{"style":1373},"top:-3.45em;",[15,1375],{"className":1376,"style":1377},[302],"height:3.45em;",[15,1379,1381,1421,1424,1427,1430,1433],{"className":1380},[59],[15,1382,1384,1387],{"className":1383},[59],[15,1385,199],{"className":1386,"style":277},[59,60],[15,1388,1390],{"className":1389},[281],[15,1391,1393,1413],{"className":1392},[285,286],[15,1394,1396,1410],{"className":1395},[290],[15,1397,1399],{"className":1398,"style":295},[294],[15,1400,1401,1404],{"style":298},[15,1402],{"className":1403,"style":303},[302],[15,1405,1407],{"className":1406},[307,308,309,310],[15,1408,37],{"className":1409,"style":61},[59,60,310],[15,1411,318],{"className":1412},[317],[15,1414,1416],{"className":1415},[290],[15,1417,1419],{"className":1418,"style":325},[294],[15,1420],{},[15,1422,113],{"className":1423},[146],[15,1425,206],{"className":1426,"style":334},[59,60],[15,1428,210],{"className":1429},[59],[15,1431,213],{"className":1432},[59,60],[15,1434,120],{"className":1435},[153],[15,1437,318],{"className":1438},[317],[15,1440,1442],{"className":1441},[290],[15,1443,1446],{"className":1444,"style":1445},[294],"height:0.95em;",[15,1447],{},[15,1449,1452],{"className":1450},[1451],"col-align-l",[15,1453,1455,1628],{"className":1454},[285,286],[15,1456,1458,1625],{"className":1457},[290],[15,1459,1461],{"className":1460,"style":1370},[294],[15,1462,1463,1466],{"style":1373},[15,1464],{"className":1465,"style":1377},[302],[15,1467,1469,1472,1475,1478,1481,1488,1491,1494,1497,1500,1503,1506,1509,1513,1516,1613,1616,1619,1622],{"className":1468},[59],[15,1470],{"className":1471},[59],[15,1473],{"className":1474,"style":158},[157],[15,1476,123],{"className":1477},[162],[15,1479],{"className":1480,"style":158},[157],[15,1482,1287],{"className":1483,"style":1487},[1484,1485,1486],"mop","op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[15,1489],{"className":1490,"style":406},[157],[15,1492,944],{"className":1493,"style":981},[59,60],[15,1495,113],{"className":1496},[146],[15,1498,774],{"className":1499},[59,60],[15,1501,120],{"className":1502},[153],[15,1504],{"className":1505,"style":406},[157],[15,1507,37],{"className":1508,"style":61},[59,60],[15,1510],{"className":1511,"style":1512},[157],"margin-right:-0.1667em;",[15,1514],{"className":1515,"style":406},[157],[15,1517,1519,1525,1607],{"className":1518},[410],[15,1520,1522],{"className":1521,"style":415},[146,414],[15,1523,113],{"className":1524},[419,309],[15,1526,1528,1531,1604],{"className":1527},[59],[15,1529],{"className":1530},[146,441],[15,1532,1534],{"className":1533},[238],[15,1535,1537,1595],{"className":1536},[285,286],[15,1538,1540,1592],{"className":1539},[290],[15,1541,1544,1564,1572],{"className":1542,"style":1543},[294],"height:1.427em;",[15,1545,1546,1549],{"style":457},[15,1547],{"className":1548,"style":461},[302],[15,1550,1552,1555,1558,1561],{"className":1551},[59],[15,1553,944],{"className":1554,"style":981},[59,60],[15,1556,113],{"className":1557},[146],[15,1559,774],{"className":1560},[59,60],[15,1562,120],{"className":1563},[153],[15,1565,1566,1569],{"style":473},[15,1567],{"className":1568,"style":461},[302],[15,1570],{"className":1571,"style":481},[480],[15,1573,1574,1577],{"style":484},[15,1575],{"className":1576,"style":461},[302],[15,1578,1580,1583,1586,1589],{"className":1579},[59],[15,1581,11],{"className":1582},[59,60],[15,1584,113],{"className":1585},[146],[15,1587,774],{"className":1588},[59,60],[15,1590,120],{"className":1591},[153],[15,1593,318],{"className":1594},[317],[15,1596,1598],{"className":1597},[290],[15,1599,1602],{"className":1600,"style":1601},[294],"height:0.936em;",[15,1603],{},[15,1605],{"className":1606},[153,441],[15,1608,1610],{"className":1609,"style":415},[153,414],[15,1611,120],{"className":1612},[419,309],[15,1614],{"className":1615,"style":406},[157],[15,1617,244],{"className":1618},[59,60],[15,1620,774],{"className":1621},[59,60],[15,1623,551],{"className":1624},[573],[15,1626,318],{"className":1627},[317],[15,1629,1631],{"className":1630},[290],[15,1632,1634],{"className":1633,"style":1445},[294],[15,1635],{},[11,1637,1638,1639,1667],{},"更一般地写成关于 ",[15,1640,1642,1655],{"className":1641,"translate":19},[18],[15,1643,1645],{"className":1644},[23],[25,1646,1647],{"xmlns":27},[29,1648,1649,1653],{},[32,1650,1651],{},[35,1652,213],{},[39,1654,213],{"encoding":41},[15,1656,1658],{"className":1657,"ariaHidden":46},[45],[15,1659,1661,1664],{"className":1660},[50],[15,1662],{"className":1663,"style":566},[54],[15,1665,213],{"className":1666},[59,60]," 的期望形式",[15,1669,1671],{"className":1670,"translate":19},[180],[15,1672,1674,1808],{"className":1673,"translate":19},[18],[15,1675,1677],{"className":1676},[23],[25,1678,1679],{"xmlns":27,"display":189},[29,1680,1681,1805],{},[1243,1682,1683,1755],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,1684,1685,1707],{},[1252,1686,1687],{},[1255,1688,1689],{"scriptlevel":126,"displaystyle":46},[32,1690,1691,1697,1699,1701,1703,1705],{},[195,1692,1693,1695],{},[35,1694,199],{},[35,1696,37],{},[110,1698,113],{"stretchy":112},[35,1700,206],{},[35,1702,210],{"mathvariant":209},[35,1704,213],{},[110,1706,120],{"stretchy":112},[1252,1708,1709],{},[1255,1710,1711],{"scriptlevel":126,"displaystyle":46},[32,1712,1713,1715,1717,1723,1725],{},[32,1714],{},[110,1716,123],{},[195,1718,1719,1721],{},[35,1720,223],{"mathvariant":222},[35,1722,213],{},[1297,1724,1304],{},[32,1726,1727,1729,1731,1733,1753],{},[110,1728,230],{"fence":46},[35,1730,37],{},[1297,1732,1304],{},[32,1734,1735,1737,1751],{},[110,1736,113],{"fence":46},[238,1738,1739,1745],{},[32,1740,1741,1743],{},[35,1742,244],{},[35,1744,206],{},[32,1746,1747,1749],{},[35,1748,244],{},[35,1750,213],{},[110,1752,120],{"fence":46},[110,1754,257],{"fence":46},[1249,1756,1757,1763],{},[1252,1758,1759],{},[1255,1760,1761],{"scriptlevel":126,"displaystyle":46},[32,1762],{},[1252,1764,1765],{},[1255,1766,1767],{"scriptlevel":126,"displaystyle":46},[32,1768,1769,1771,1773,1775,1777,1779,1799,1801,1803],{},[32,1770],{},[110,1772,123],{},[110,1774,1287],{},[35,1776,37],{},[1297,1778,1304],{},[32,1780,1781,1783,1797],{},[110,1782,113],{"fence":46},[238,1784,1785,1791],{},[32,1786,1787,1789],{},[35,1788,244],{},[35,1790,206],{},[32,1792,1793,1795],{},[35,1794,244],{},[35,1796,213],{},[110,1798,120],{"fence":46},[35,1800,244],{},[35,1802,213],{},[110,1804,551],{"separator":46},[39,1806,1807],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\int f\\!\\left(\\frac{dP}{dQ}\\right)dQ,\n\\end{aligned}",[15,1809,1811],{"className":1810,"ariaHidden":46},[45],[15,1812,1814,1818],{"className":1813},[50],[15,1815],{"className":1816,"style":1817},[54],"height:5.1001em;vertical-align:-2.3em;",[15,1819,1821],{"className":1820},[59],[15,1822,1824,1922],{"className":1823},[1243],[15,1825,1827],{"className":1826},[1360],[15,1828,1830,1913],{"className":1829},[285,286],[15,1831,1833,1910],{"className":1832},[290],[15,1834,1837,1901],{"className":1835,"style":1836},[294],"height:2.8em;",[15,1838,1840,1843],{"style":1839},"top:-4.8em;",[15,1841],{"className":1842,"style":1377},[302],[15,1844,1846,1886,1889,1892,1895,1898],{"className":1845},[59],[15,1847,1849,1852],{"className":1848},[59],[15,1850,199],{"className":1851,"style":277},[59,60],[15,1853,1855],{"className":1854},[281],[15,1856,1858,1878],{"className":1857},[285,286],[15,1859,1861,1875],{"className":1860},[290],[15,1862,1864],{"className":1863,"style":295},[294],[15,1865,1866,1869],{"style":298},[15,1867],{"className":1868,"style":303},[302],[15,1870,1872],{"className":1871},[307,308,309,310],[15,1873,37],{"className":1874,"style":61},[59,60,310],[15,1876,318],{"className":1877},[317],[15,1879,1881],{"className":1880},[290],[15,1882,1884],{"className":1883,"style":325},[294],[15,1885],{},[15,1887,113],{"className":1888},[146],[15,1890,206],{"className":1891,"style":334},[59,60],[15,1893,210],{"className":1894},[59],[15,1896,213],{"className":1897},[59,60],[15,1899,120],{"className":1900},[153],[15,1902,1904,1907],{"style":1903},"top:-2.1em;",[15,1905],{"className":1906,"style":1377},[302],[15,1908],{"className":1909},[59],[15,1911,318],{"className":1912},[317],[15,1914,1916],{"className":1915},[290],[15,1917,1920],{"className":1918,"style":1919},[294],"height:2.3em;",[15,1921],{},[15,1923,1925],{"className":1924},[1451],[15,1926,1928,2240],{"className":1927},[285,286],[15,1929,1931,2237],{"className":1930},[290],[15,1932,1934,2107],{"className":1933,"style":1836},[294],[15,1935,1936,1939],{"style":1839},[15,1937],{"className":1938,"style":1377},[302],[15,1940,1942,1945,1948,1951,1954,1994,1997,2000],{"className":1941},[59],[15,1943],{"className":1944},[59],[15,1946],{"className":1947,"style":158},[157],[15,1949,123],{"className":1950},[162],[15,1952],{"className":1953,"style":158},[157],[15,1955,1957,1960],{"className":1956},[59],[15,1958,223],{"className":1959},[59,366],[15,1961,1963],{"className":1962},[281],[15,1964,1966,1986],{"className":1965},[285,286],[15,1967,1969,1983],{"className":1968},[290],[15,1970,1972],{"className":1971,"style":379},[294],[15,1973,1974,1977],{"style":382},[15,1975],{"className":1976,"style":303},[302],[15,1978,1980],{"className":1979},[307,308,309,310],[15,1981,213],{"className":1982},[59,60,310],[15,1984,318],{"className":1985},[317],[15,1987,1989],{"className":1988},[290],[15,1990,1992],{"className":1991,"style":325},[294],[15,1993],{},[15,1995],{"className":1996,"style":1512},[157],[15,1998],{"className":1999,"style":406},[157],[15,2001,2003,2009,2012,2015,2018,2101],{"className":2002},[410],[15,2004,2006],{"className":2005,"style":415},[146,414],[15,2007,230],{"className":2008},[419,309],[15,2010,37],{"className":2011,"style":61},[59,60],[15,2013],{"className":2014,"style":1512},[157],[15,2016],{"className":2017,"style":406},[157],[15,2019,2021,2027,2095],{"className":2020},[410],[15,2022,2024],{"className":2023,"style":415},[146,414],[15,2025,113],{"className":2026},[419,309],[15,2028,2030,2033,2092],{"className":2029},[59],[15,2031],{"className":2032},[146,441],[15,2034,2036],{"className":2035},[238],[15,2037,2039,2084],{"className":2038},[285,286],[15,2040,2042,2081],{"className":2041},[290],[15,2043,2045,2059,2067],{"className":2044,"style":454},[294],[15,2046,2047,2050],{"style":457},[15,2048],{"className":2049,"style":461},[302],[15,2051,2053,2056],{"className":2052},[59],[15,2054,244],{"className":2055},[59,60],[15,2057,213],{"className":2058},[59,60],[15,2060,2061,2064],{"style":473},[15,2062],{"className":2063,"style":461},[302],[15,2065],{"className":2066,"style":481},[480],[15,2068,2069,2072],{"style":484},[15,2070],{"className":2071,"style":461},[302],[15,2073,2075,2078],{"className":2074},[59],[15,2076,244],{"className":2077},[59,60],[15,2079,206],{"className":2080,"style":334},[59,60],[15,2082,318],{"className":2083},[317],[15,2085,2087],{"className":2086},[290],[15,2088,2090],{"className":2089,"style":506},[294],[15,2091],{},[15,2093],{"className":2094},[153,441],[15,2096,2098],{"className":2097,"style":415},[153,414],[15,2099,120],{"className":2100},[419,309],[15,2102,2104],{"className":2103,"style":415},[153,414],[15,2105,257],{"className":2106},[419,309],[15,2108,2109,2112],{"style":1903},[15,2110],{"className":2111,"style":1377},[302],[15,2113,2115,2118,2121,2124,2127,2130,2133,2136,2139,2142,2225,2228,2231,2234],{"className":2114},[59],[15,2116],{"className":2117},[59],[15,2119],{"className":2120,"style":158},[157],[15,2122,123],{"className":2123},[162],[15,2125],{"className":2126,"style":158},[157],[15,2128,1287],{"className":2129,"style":1487},[1484,1485,1486],[15,2131],{"className":2132,"style":406},[157],[15,2134,37],{"className":2135,"style":61},[59,60],[15,2137],{"className":2138,"style":1512},[157],[15,2140],{"className":2141,"style":406},[157],[15,2143,2145,2151,2219],{"className":2144},[410],[15,2146,2148],{"className":2147,"style":415},[146,414],[15,2149,113],{"className":2150},[419,309],[15,2152,2154,2157,2216],{"className":2153},[59],[15,2155],{"className":2156},[146,441],[15,2158,2160],{"className":2159},[238],[15,2161,2163,2208],{"className":2162},[285,286],[15,2164,2166,2205],{"className":2165},[290],[15,2167,2169,2183,2191],{"className":2168,"style":454},[294],[15,2170,2171,2174],{"style":457},[15,2172],{"className":2173,"style":461},[302],[15,2175,2177,2180],{"className":2176},[59],[15,2178,244],{"className":2179},[59,60],[15,2181,213],{"className":2182},[59,60],[15,2184,2185,2188],{"style":473},[15,2186],{"className":2187,"style":461},[302],[15,2189],{"className":2190,"style":481},[480],[15,2192,2193,2196],{"style":484},[15,2194],{"className":2195,"style":461},[302],[15,2197,2199,2202],{"className":2198},[59],[15,2200,244],{"className":2201},[59,60],[15,2203,206],{"className":2204,"style":334},[59,60],[15,2206,318],{"className":2207},[317],[15,2209,2211],{"className":2210},[290],[15,2212,2214],{"className":2213,"style":506},[294],[15,2215],{},[15,2217],{"className":2218},[153,441],[15,2220,2222],{"className":2221,"style":415},[153,414],[15,2223,120],{"className":2224},[419,309],[15,2226],{"className":2227,"style":406},[157],[15,2229,244],{"className":2230},[59,60],[15,2232,213],{"className":2233},[59,60],[15,2235,551],{"className":2236},[573],[15,2238,318],{"className":2239},[317],[15,2241,2243],{"className":2242},[290],[15,2244,2246],{"className":2245,"style":1919},[294],[15,2247],{},[11,2249,2250,2251,2280,2281,2309],{},"其中 ",[15,2252,2254,2267],{"className":2253,"translate":19},[18],[15,2255,2257],{"className":2256},[23],[25,2258,2259],{"xmlns":27},[29,2260,2261,2265],{},[32,2262,2263],{},[35,2264,944],{},[39,2266,944],{"encoding":41},[15,2268,2270],{"className":2269,"ariaHidden":46},[45],[15,2271,2273,2277],{"className":2272},[50],[15,2274],{"className":2275,"style":2276},[54],"height:0.625em;vertical-align:-0.1944em;",[15,2278,944],{"className":2279,"style":981},[59,60]," 是 ",[15,2282,2284,2297],{"className":2283,"translate":19},[18],[15,2285,2287],{"className":2286},[23],[25,2288,2289],{"xmlns":27},[29,2290,2291,2295],{},[32,2292,2293],{},[35,2294,213],{},[39,2296,213],{"encoding":41},[15,2298,2300],{"className":2299,"ariaHidden":46},[45],[15,2301,2303,2306],{"className":2302},[50],[15,2304],{"className":2305,"style":566},[54],[15,2307,213],{"className":2308},[59,60]," 的密度。",[2311,2312,2314],"h3",{"id":2313},"_11-不依赖参考测度","1.1 不依赖参考测度",[11,2316,2317,2318,2349,2350,2380,2381,2409,2410,2438,2439,2607,2608,2745,2746,2883,2884,2948,2949,3154],{},"上面的定义里出现了「密度」，这会让读者误以为它依赖 Lebesgue 测度。其实 f-散度只依赖两个分布本身。取任一 ",[15,2319,2321,2336],{"className":2320,"translate":19},[18],[15,2322,2324],{"className":2323},[23],[25,2325,2326],{"xmlns":27},[29,2327,2328,2333],{},[32,2329,2330],{},[35,2331,2332],{},"σ",[39,2334,2335],{"encoding":41},"\\sigma",[15,2337,2339],{"className":2338,"ariaHidden":46},[45],[15,2340,2342,2346],{"className":2341},[50],[15,2343],{"className":2344,"style":2345},[54],"height:0.4306em;",[15,2347,2332],{"className":2348,"style":981},[59,60],"-有限测度 ",[15,2351,2353,2368],{"className":2352,"translate":19},[18],[15,2354,2356],{"className":2355},[23],[25,2357,2358],{"xmlns":27},[29,2359,2360,2365],{},[32,2361,2362],{},[35,2363,2364],{},"μ",[39,2366,2367],{"encoding":41},"\\mu",[15,2369,2371],{"className":2370,"ariaHidden":46},[45],[15,2372,2374,2377],{"className":2373},[50],[15,2375],{"className":2376,"style":2276},[54],[15,2378,2364],{"className":2379},[59,60]," 同时控制 ",[15,2382,2384,2397],{"className":2383,"translate":19},[18],[15,2385,2387],{"className":2386},[23],[25,2388,2389],{"xmlns":27},[29,2390,2391,2395],{},[32,2392,2393],{},[35,2394,206],{},[39,2396,206],{"encoding":41},[15,2398,2400],{"className":2399,"ariaHidden":46},[45],[15,2401,2403,2406],{"className":2402},[50],[15,2404],{"className":2405,"style":664},[54],[15,2407,206],{"className":2408,"style":334},[59,60]," 与 ",[15,2411,2413,2426],{"className":2412,"translate":19},[18],[15,2414,2416],{"className":2415},[23],[25,2417,2418],{"xmlns":27},[29,2419,2420,2424],{},[32,2421,2422],{},[35,2423,213],{},[39,2425,213],{"encoding":41},[15,2427,2429],{"className":2428,"ariaHidden":46},[45],[15,2430,2432,2435],{"className":2431},[50],[15,2433],{"className":2434,"style":566},[54],[15,2436,213],{"className":2437},[59,60],"（例如 ",[15,2440,2442,2478],{"className":2441,"translate":19},[18],[15,2443,2445],{"className":2444},[23],[25,2446,2447],{"xmlns":27},[29,2448,2449,2475],{},[32,2450,2451,2453,2455,2464,2466,2468,2471,2473],{},[35,2452,2364],{},[110,2454,123],{},[1255,2456,2457],{"scriptlevel":126,"displaystyle":112},[238,2458,2459,2461],{},[115,2460,117],{},[115,2462,2463],{},"2",[110,2465,113],{"stretchy":112},[35,2467,206],{},[110,2469,2470],{},"+",[35,2472,213],{},[110,2474,120],{"stretchy":112},[39,2476,2477],{"encoding":41},"\\mu=\\tfrac12(P+Q)",[15,2479,2481,2499,2595],{"className":2480,"ariaHidden":46},[45],[15,2482,2484,2487,2490,2493,2496],{"className":2483},[50],[15,2485],{"className":2486,"style":2276},[54],[15,2488,2364],{"className":2489},[59,60],[15,2491],{"className":2492,"style":158},[157],[15,2494,123],{"className":2495},[162],[15,2497],{"className":2498,"style":158},[157],[15,2500,2502,2506,2578,2581,2584,2588,2592],{"className":2501},[50],[15,2503],{"className":2504,"style":2505},[54],"height:1.1901em;vertical-align:-0.345em;",[15,2507,2509,2512,2575],{"className":2508},[59],[15,2510],{"className":2511},[146,441],[15,2513,2515],{"className":2514},[238],[15,2516,2518,2566],{"className":2517},[285,286],[15,2519,2521,2563],{"className":2520},[290],[15,2522,2525,2540,2548],{"className":2523,"style":2524},[294],"height:0.8451em;",[15,2526,2528,2531],{"style":2527},"top:-2.655em;",[15,2529],{"className":2530,"style":461},[302],[15,2532,2534],{"className":2533},[307,308,309,310],[15,2535,2537],{"className":2536},[59,310],[15,2538,2463],{"className":2539},[59,310],[15,2541,2542,2545],{"style":473},[15,2543],{"className":2544,"style":461},[302],[15,2546],{"className":2547,"style":481},[480],[15,2549,2551,2554],{"style":2550},"top:-3.394em;",[15,2552],{"className":2553,"style":461},[302],[15,2555,2557],{"className":2556},[307,308,309,310],[15,2558,2560],{"className":2559},[59,310],[15,2561,117],{"className":2562},[59,310],[15,2564,318],{"className":2565},[317],[15,2567,2569],{"className":2568},[290],[15,2570,2573],{"className":2571,"style":2572},[294],"height:0.345em;",[15,2574],{},[15,2576],{"className":2577},[153,441],[15,2579,113],{"className":2580},[146],[15,2582,206],{"className":2583,"style":334},[59,60],[15,2585],{"className":2586,"style":2587},[157],"margin-right:0.2222em;",[15,2589,2470],{"className":2590},[2591],"mbin",[15,2593],{"className":2594,"style":2587},[157],[15,2596,2598,2601,2604],{"className":2597},[50],[15,2599],{"className":2600,"style":139},[54],[15,2602,213],{"className":2603},[59,60],[15,2605,120],{"className":2606},[153],"），令 ",[15,2609,2611,2641],{"className":2610,"translate":19},[18],[15,2612,2614],{"className":2613},[23],[25,2615,2616],{"xmlns":27},[29,2617,2618,2638],{},[32,2619,2620,2622,2624],{},[35,2621,11],{},[110,2623,123],{},[238,2625,2626,2632],{},[32,2627,2628,2630],{},[35,2629,244],{},[35,2631,206],{},[32,2633,2634,2636],{},[35,2635,244],{},[35,2637,2364],{},[39,2639,2640],{"encoding":41},"p=\\frac{dP}{d\\mu}",[15,2642,2644,2662],{"className":2643,"ariaHidden":46},[45],[15,2645,2647,2650,2653,2656,2659],{"className":2646},[50],[15,2648],{"className":2649,"style":2276},[54],[15,2651,11],{"className":2652},[59,60],[15,2654],{"className":2655,"style":158},[157],[15,2657,123],{"className":2658},[162],[15,2660],{"className":2661,"style":158},[157],[15,2663,2665,2669],{"className":2664},[50],[15,2666],{"className":2667,"style":2668},[54],"height:1.3612em;vertical-align:-0.4811em;",[15,2670,2672,2675,2742],{"className":2671},[59],[15,2673],{"className":2674},[146,441],[15,2676,2678],{"className":2677},[238],[15,2679,2681,2733],{"className":2680},[285,286],[15,2682,2684,2730],{"className":2683},[290],[15,2685,2688,2705,2713],{"className":2686,"style":2687},[294],"height:0.8801em;",[15,2689,2690,2693],{"style":2527},[15,2691],{"className":2692,"style":461},[302],[15,2694,2696],{"className":2695},[307,308,309,310],[15,2697,2699,2702],{"className":2698},[59,310],[15,2700,244],{"className":2701},[59,60,310],[15,2703,2364],{"className":2704},[59,60,310],[15,2706,2707,2710],{"style":473},[15,2708],{"className":2709,"style":461},[302],[15,2711],{"className":2712,"style":481},[480],[15,2714,2715,2718],{"style":2550},[15,2716],{"className":2717,"style":461},[302],[15,2719,2721],{"className":2720},[307,308,309,310],[15,2722,2724,2727],{"className":2723},[59,310],[15,2725,244],{"className":2726},[59,60,310],[15,2728,206],{"className":2729,"style":334},[59,60,310],[15,2731,318],{"className":2732},[317],[15,2734,2736],{"className":2735},[290],[15,2737,2740],{"className":2738,"style":2739},[294],"height:0.4811em;",[15,2741],{},[15,2743],{"className":2744},[153,441],"，",[15,2747,2749,2779],{"className":2748,"translate":19},[18],[15,2750,2752],{"className":2751},[23],[25,2753,2754],{"xmlns":27},[29,2755,2756,2776],{},[32,2757,2758,2760,2762],{},[35,2759,944],{},[110,2761,123],{},[238,2763,2764,2770],{},[32,2765,2766,2768],{},[35,2767,244],{},[35,2769,213],{},[32,2771,2772,2774],{},[35,2773,244],{},[35,2775,2364],{},[39,2777,2778],{"encoding":41},"q=\\frac{dQ}{d\\mu}",[15,2780,2782,2800],{"className":2781,"ariaHidden":46},[45],[15,2783,2785,2788,2791,2794,2797],{"className":2784},[50],[15,2786],{"className":2787,"style":2276},[54],[15,2789,944],{"className":2790,"style":981},[59,60],[15,2792],{"className":2793,"style":158},[157],[15,2795,123],{"className":2796},[162],[15,2798],{"className":2799,"style":158},[157],[15,2801,2803,2807],{"className":2802},[50],[15,2804],{"className":2805,"style":2806},[54],"height:1.4133em;vertical-align:-0.4811em;",[15,2808,2810,2813,2880],{"className":2809},[59],[15,2811],{"className":2812},[146,441],[15,2814,2816],{"className":2815},[238],[15,2817,2819,2872],{"className":2818},[285,286],[15,2820,2822,2869],{"className":2821},[290],[15,2823,2826,2843,2851],{"className":2824,"style":2825},[294],"height:0.9322em;",[15,2827,2828,2831],{"style":2527},[15,2829],{"className":2830,"style":461},[302],[15,2832,2834],{"className":2833},[307,308,309,310],[15,2835,2837,2840],{"className":2836},[59,310],[15,2838,244],{"className":2839},[59,60,310],[15,2841,2364],{"className":2842},[59,60,310],[15,2844,2845,2848],{"style":473},[15,2846],{"className":2847,"style":461},[302],[15,2849],{"className":2850,"style":481},[480],[15,2852,2854,2857],{"style":2853},"top:-3.4461em;",[15,2855],{"className":2856,"style":461},[302],[15,2858,2860],{"className":2859},[307,308,309,310],[15,2861,2863,2866],{"className":2862},[59,310],[15,2864,244],{"className":2865},[59,60,310],[15,2867,213],{"className":2868},[59,60,310],[15,2870,318],{"className":2871},[317],[15,2873,2875],{"className":2874},[290],[15,2876,2878],{"className":2877,"style":2739},[294],[15,2879],{},[15,2881],{"className":2882},[153,441],"。在集合 ",[15,2885,2887,2912],{"className":2886,"translate":19},[18],[15,2888,2890],{"className":2889},[23],[25,2891,2892],{"xmlns":27},[29,2893,2894,2909],{},[32,2895,2896,2899,2901,2904,2906],{},[110,2897,2898],{"stretchy":112},"{",[35,2900,944],{},[110,2902,2903],{},">",[115,2905,126],{},[110,2907,2908],{"stretchy":112},"}",[39,2910,2911],{"encoding":41},"\\{q>0\\}",[15,2913,2915,2936],{"className":2914,"ariaHidden":46},[45],[15,2916,2918,2921,2924,2927,2930,2933],{"className":2917},[50],[15,2919],{"className":2920,"style":139},[54],[15,2922,2898],{"className":2923},[146],[15,2925,944],{"className":2926,"style":981},[59,60],[15,2928],{"className":2929,"style":158},[157],[15,2931,2903],{"className":2932},[162],[15,2934],{"className":2935,"style":158},[157],[15,2937,2939,2942,2945],{"className":2938},[50],[15,2940],{"className":2941,"style":139},[54],[15,2943,126],{"className":2944},[59],[15,2946,2908],{"className":2947},[153]," 上有 ",[15,2950,2952,2986],{"className":2951,"translate":19},[18],[15,2953,2955],{"className":2954},[23],[25,2956,2957],{"xmlns":27},[29,2958,2959,2983],{},[32,2960,2961,2975,2977],{},[238,2962,2963,2969],{},[32,2964,2965,2967],{},[35,2966,244],{},[35,2968,206],{},[32,2970,2971,2973],{},[35,2972,244],{},[35,2974,213],{},[110,2976,123],{},[238,2978,2979,2981],{},[35,2980,11],{},[35,2982,944],{},[39,2984,2985],{"encoding":41},"\\frac{dP}{dQ}=\\frac{p}{q}",[15,2987,2989,3078],{"className":2988,"ariaHidden":46},[45],[15,2990,2992,2995,3069,3072,3075],{"className":2991},[50],[15,2993],{"className":2994,"style":2668},[54],[15,2996,2998,3001,3066],{"className":2997},[59],[15,2999],{"className":3000},[146,441],[15,3002,3004],{"className":3003},[238],[15,3005,3007,3058],{"className":3006},[285,286],[15,3008,3010,3055],{"className":3009},[290],[15,3011,3013,3030,3038],{"className":3012,"style":2687},[294],[15,3014,3015,3018],{"style":2527},[15,3016],{"className":3017,"style":461},[302],[15,3019,3021],{"className":3020},[307,308,309,310],[15,3022,3024,3027],{"className":3023},[59,310],[15,3025,244],{"className":3026},[59,60,310],[15,3028,213],{"className":3029},[59,60,310],[15,3031,3032,3035],{"style":473},[15,3033],{"className":3034,"style":461},[302],[15,3036],{"className":3037,"style":481},[480],[15,3039,3040,3043],{"style":2550},[15,3041],{"className":3042,"style":461},[302],[15,3044,3046],{"className":3045},[307,308,309,310],[15,3047,3049,3052],{"className":3048},[59,310],[15,3050,244],{"className":3051},[59,60,310],[15,3053,206],{"className":3054,"style":334},[59,60,310],[15,3056,318],{"className":3057},[317],[15,3059,3061],{"className":3060},[290],[15,3062,3064],{"className":3063,"style":2739},[294],[15,3065],{},[15,3067],{"className":3068},[153,441],[15,3070],{"className":3071,"style":158},[157],[15,3073,123],{"className":3074},[162],[15,3076],{"className":3077,"style":158},[157],[15,3079,3081,3085],{"className":3080},[50],[15,3082],{"className":3083,"style":3084},[54],"height:1.2286em;vertical-align:-0.4811em;",[15,3086,3088,3091,3151],{"className":3087},[59],[15,3089],{"className":3090},[146,441],[15,3092,3094],{"className":3093},[238],[15,3095,3097,3143],{"className":3096},[285,286],[15,3098,3100,3140],{"className":3099},[290],[15,3101,3104,3118,3126],{"className":3102,"style":3103},[294],"height:0.7475em;",[15,3105,3106,3109],{"style":2527},[15,3107],{"className":3108,"style":461},[302],[15,3110,3112],{"className":3111},[307,308,309,310],[15,3113,3115],{"className":3114},[59,310],[15,3116,944],{"className":3117,"style":981},[59,60,310],[15,3119,3120,3123],{"style":473},[15,3121],{"className":3122,"style":461},[302],[15,3124],{"className":3125,"style":481},[480],[15,3127,3128,3131],{"style":2853},[15,3129],{"className":3130,"style":461},[302],[15,3132,3134],{"className":3133},[307,308,309,310],[15,3135,3137],{"className":3136},[59,310],[15,3138,11],{"className":3139},[59,60,310],[15,3141,318],{"className":3142},[317],[15,3144,3146],{"className":3145},[290],[15,3147,3149],{"className":3148,"style":2739},[294],[15,3150],{},[15,3152],{"className":3153},[153,441],"，于是",[15,3156,3158],{"className":3157,"translate":19},[180],[15,3159,3161,3311],{"className":3160,"translate":19},[18],[15,3162,3164],{"className":3163},[23],[25,3165,3166],{"xmlns":27,"display":189},[29,3167,3168,3308],{},[1243,3169,3170,3244],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,3171,3172,3194],{},[1252,3173,3174],{},[1255,3175,3176],{"scriptlevel":126,"displaystyle":46},[32,3177,3178,3184,3186,3188,3190,3192],{},[195,3179,3180,3182],{},[35,3181,199],{},[35,3183,37],{},[110,3185,113],{"stretchy":112},[35,3187,206],{},[35,3189,210],{"mathvariant":209},[35,3191,213],{},[110,3193,120],{"stretchy":112},[1252,3195,3196],{},[1255,3197,3198],{"scriptlevel":126,"displaystyle":46},[32,3199,3200,3202,3204,3220,3222,3224,3236,3238,3240,3242],{},[32,3201],{},[110,3203,123],{},[195,3205,3206,3208],{},[110,3207,1287],{},[32,3209,3210,3212,3214,3216,3218],{},[110,3211,2898],{"stretchy":112},[35,3213,944],{},[110,3215,2903],{},[115,3217,126],{},[110,3219,2908],{"stretchy":112},[35,3221,37],{},[1297,3223,1304],{},[32,3225,3226,3228,3234],{},[110,3227,113],{"fence":46},[238,3229,3230,3232],{},[35,3231,11],{},[35,3233,944],{},[110,3235,120],{"fence":46},[35,3237,944],{},[1297,3239,1299],{},[35,3241,244],{},[35,3243,2364],{},[1249,3245,3246,3252],{},[1252,3247,3248],{},[1255,3249,3250],{"scriptlevel":126,"displaystyle":46},[32,3251],{},[1252,3253,3254],{},[1255,3255,3256],{"scriptlevel":126,"displaystyle":46},[32,3257,3258,3260,3263,3265,3281,3283,3285,3297,3300,3302,3304,3306],{},[32,3259],{},[157,3261],{"width":3262},"2em",[110,3264,2470],{},[195,3266,3267,3269],{},[110,3268,1287],{},[32,3270,3271,3273,3275,3277,3279],{},[110,3272,2898],{"stretchy":112},[35,3274,944],{},[110,3276,123],{},[115,3278,126],{},[110,3280,2908],{"stretchy":112},[35,3282,37],{},[1297,3284,1304],{},[32,3286,3287,3289,3295],{},[110,3288,113],{"fence":46},[238,3290,3291,3293],{},[35,3292,11],{},[115,3294,126],{},[110,3296,120],{"fence":46},[110,3298,3299],{},"⋅",[115,3301,126],{},[1297,3303,1299],{},[35,3305,244],{},[35,3307,2364],{},[39,3309,3310],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int_{\\{q>0\\}}\nf\\!\\left(\\frac{p}{q}\\right)q\\,d\\mu\\\\\n&\\qquad+\\int_{\\{q=0\\}}\nf\\!\\left(\\frac{p}{0}\\right)\\cdot 0\\,d\\mu\n\\end{aligned}",[15,3312,3314],{"className":3313,"ariaHidden":46},[45],[15,3315,3317,3321],{"className":3316},[50],[15,3318],{"className":3319,"style":3320},[54],"height:5.2839em;vertical-align:-2.392em;",[15,3322,3324],{"className":3323},[59],[15,3325,3327,3425],{"className":3326},[1243],[15,3328,3330],{"className":3329},[1360],[15,3331,3333,3416],{"className":3332},[285,286],[15,3334,3336,3413],{"className":3335},[290],[15,3337,3340,3404],{"className":3338,"style":3339},[294],"height:2.892em;",[15,3341,3343,3346],{"style":3342},"top:-4.892em;",[15,3344],{"className":3345,"style":1377},[302],[15,3347,3349,3389,3392,3395,3398,3401],{"className":3348},[59],[15,3350,3352,3355],{"className":3351},[59],[15,3353,199],{"className":3354,"style":277},[59,60],[15,3356,3358],{"className":3357},[281],[15,3359,3361,3381],{"className":3360},[285,286],[15,3362,3364,3378],{"className":3363},[290],[15,3365,3367],{"className":3366,"style":295},[294],[15,3368,3369,3372],{"style":298},[15,3370],{"className":3371,"style":303},[302],[15,3373,3375],{"className":3374},[307,308,309,310],[15,3376,37],{"className":3377,"style":61},[59,60,310],[15,3379,318],{"className":3380},[317],[15,3382,3384],{"className":3383},[290],[15,3385,3387],{"className":3386,"style":325},[294],[15,3388],{},[15,3390,113],{"className":3391},[146],[15,3393,206],{"className":3394,"style":334},[59,60],[15,3396,210],{"className":3397},[59],[15,3399,213],{"className":3400},[59,60],[15,3402,120],{"className":3403},[153],[15,3405,3407,3410],{"style":3406},"top:-2.145em;",[15,3408],{"className":3409,"style":1377},[302],[15,3411],{"className":3412},[59],[15,3414,318],{"className":3415},[317],[15,3417,3419],{"className":3418},[290],[15,3420,3423],{"className":3421,"style":3422},[294],"height:2.392em;",[15,3424],{},[15,3426,3428],{"className":3427},[1451],[15,3429,3431,3814],{"className":3430},[285,286],[15,3432,3434,3811],{"className":3433},[290],[15,3435,3437,3620],{"className":3436,"style":3339},[294],[15,3438,3439,3442],{"style":3342},[15,3440],{"className":3441,"style":1377},[302],[15,3443,3445,3448,3451,3454,3457,3515,3518,3521,3524,3527,3605,3608,3611,3614,3617],{"className":3444},[59],[15,3446],{"className":3447},[59],[15,3449],{"className":3450,"style":158},[157],[15,3452,123],{"className":3453},[162],[15,3455],{"className":3456,"style":158},[157],[15,3458,3460,3463],{"className":3459},[1484],[15,3461,1287],{"className":3462,"style":1487},[1484,1485,1486],[15,3464,3466],{"className":3465},[281],[15,3467,3469,3506],{"className":3468},[285,286],[15,3470,3472,3503],{"className":3471},[290],[15,3473,3476],{"className":3474,"style":3475},[294],"height:-0.3869em;",[15,3477,3479,3482],{"style":3478},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[15,3480],{"className":3481,"style":303},[302],[15,3483,3485],{"className":3484},[307,308,309,310],[15,3486,3488,3491,3494,3497,3500],{"className":3487},[59,310],[15,3489,2898],{"className":3490},[146,310],[15,3492,944],{"className":3493,"style":981},[59,60,310],[15,3495,2903],{"className":3496},[162,310],[15,3498,126],{"className":3499},[59,310],[15,3501,2908],{"className":3502},[153,310],[15,3504,318],{"className":3505},[317],[15,3507,3509],{"className":3508},[290],[15,3510,3513],{"className":3511,"style":3512},[294],"height:1.0869em;",[15,3514],{},[15,3516],{"className":3517,"style":406},[157],[15,3519,37],{"className":3520,"style":61},[59,60],[15,3522],{"className":3523,"style":1512},[157],[15,3525],{"className":3526,"style":406},[157],[15,3528,3530,3536,3599],{"className":3529},[410],[15,3531,3533],{"className":3532,"style":415},[146,414],[15,3534,113],{"className":3535},[419,309],[15,3537,3539,3542,3596],{"className":3538},[59],[15,3540],{"className":3541},[146,441],[15,3543,3545],{"className":3544},[238],[15,3546,3548,3588],{"className":3547},[285,286],[15,3549,3551,3585],{"className":3550},[290],[15,3552,3555,3566,3574],{"className":3553,"style":3554},[294],"height:1.1076em;",[15,3556,3557,3560],{"style":457},[15,3558],{"className":3559,"style":461},[302],[15,3561,3563],{"className":3562},[59],[15,3564,944],{"className":3565,"style":981},[59,60],[15,3567,3568,3571],{"style":473},[15,3569],{"className":3570,"style":461},[302],[15,3572],{"className":3573,"style":481},[480],[15,3575,3576,3579],{"style":484},[15,3577],{"className":3578,"style":461},[302],[15,3580,3582],{"className":3581},[59],[15,3583,11],{"className":3584},[59,60],[15,3586,318],{"className":3587},[317],[15,3589,3591],{"className":3590},[290],[15,3592,3594],{"className":3593,"style":506},[294],[15,3595],{},[15,3597],{"className":3598},[153,441],[15,3600,3602],{"className":3601,"style":415},[153,414],[15,3603,120],{"className":3604},[419,309],[15,3606],{"className":3607,"style":406},[157],[15,3609,944],{"className":3610,"style":981},[59,60],[15,3612],{"className":3613,"style":406},[157],[15,3615,244],{"className":3616},[59,60],[15,3618,2364],{"className":3619},[59,60],[15,3621,3622,3625],{"style":3406},[15,3623],{"className":3624,"style":1377},[302],[15,3626,3628,3631,3635,3638,3641,3644,3699,3702,3705,3708,3711,3790,3793,3796,3799,3802,3805,3808],{"className":3627},[59],[15,3629],{"className":3630},[59],[15,3632],{"className":3633,"style":3634},[157],"margin-right:2em;",[15,3636],{"className":3637,"style":2587},[157],[15,3639,2470],{"className":3640},[2591],[15,3642],{"className":3643,"style":2587},[157],[15,3645,3647,3650],{"className":3646},[1484],[15,3648,1287],{"className":3649,"style":1487},[1484,1485,1486],[15,3651,3653],{"className":3652},[281],[15,3654,3656,3691],{"className":3655},[285,286],[15,3657,3659,3688],{"className":3658},[290],[15,3660,3662],{"className":3661,"style":3475},[294],[15,3663,3664,3667],{"style":3478},[15,3665],{"className":3666,"style":303},[302],[15,3668,3670],{"className":3669},[307,308,309,310],[15,3671,3673,3676,3679,3682,3685],{"className":3672},[59,310],[15,3674,2898],{"className":3675},[146,310],[15,3677,944],{"className":3678,"style":981},[59,60,310],[15,3680,123],{"className":3681},[162,310],[15,3683,126],{"className":3684},[59,310],[15,3686,2908],{"className":3687},[153,310],[15,3689,318],{"className":3690},[317],[15,3692,3694],{"className":3693},[290],[15,3695,3697],{"className":3696,"style":3512},[294],[15,3698],{},[15,3700],{"className":3701,"style":406},[157],[15,3703,37],{"className":3704,"style":61},[59,60],[15,3706],{"className":3707,"style":1512},[157],[15,3709],{"className":3710,"style":406},[157],[15,3712,3714,3721,3784],{"className":3713},[410],[15,3715,3717],{"className":3716,"style":415},[146,414],[15,3718,113],{"className":3719},[419,3720],"size2",[15,3722,3724,3727,3781],{"className":3723},[59],[15,3725],{"className":3726},[146,441],[15,3728,3730],{"className":3729},[238],[15,3731,3733,3772],{"className":3732},[285,286],[15,3734,3736,3769],{"className":3735},[290],[15,3737,3739,3750,3758],{"className":3738,"style":3554},[294],[15,3740,3741,3744],{"style":457},[15,3742],{"className":3743,"style":461},[302],[15,3745,3747],{"className":3746},[59],[15,3748,126],{"className":3749},[59],[15,3751,3752,3755],{"style":473},[15,3753],{"className":3754,"style":461},[302],[15,3756],{"className":3757,"style":481},[480],[15,3759,3760,3763],{"style":484},[15,3761],{"className":3762,"style":461},[302],[15,3764,3766],{"className":3765},[59],[15,3767,11],{"className":3768},[59,60],[15,3770,318],{"className":3771},[317],[15,3773,3775],{"className":3774},[290],[15,3776,3779],{"className":3777,"style":3778},[294],"height:0.686em;",[15,3780],{},[15,3782],{"className":3783},[153,441],[15,3785,3787],{"className":3786,"style":415},[153,414],[15,3788,120],{"className":3789},[419,3720],[15,3791],{"className":3792,"style":2587},[157],[15,3794,3299],{"className":3795},[2591],[15,3797],{"className":3798,"style":2587},[157],[15,3800,126],{"className":3801},[59],[15,3803],{"className":3804,"style":406},[157],[15,3806,244],{"className":3807},[59,60],[15,3809,2364],{"className":3810},[59,60],[15,3812,318],{"className":3813},[317],[15,3815,3817],{"className":3816},[290],[15,3818,3820],{"className":3819,"style":3422},[294],[15,3821],{},[11,3823,3824,3825,3853,3854,3883,3884,3972,3973,4001,4002,4073,4074,4165,4166,3853,4194,4222,4223,4258],{},"第二项正是处理「支撑集不重叠」的地方。若 ",[15,3826,3828,3841],{"className":3827,"translate":19},[18],[15,3829,3831],{"className":3830},[23],[25,3832,3833],{"xmlns":27},[29,3834,3835,3839],{},[32,3836,3837],{},[35,3838,37],{},[39,3840,37],{"encoding":41},[15,3842,3844],{"className":3843,"ariaHidden":46},[45],[15,3845,3847,3850],{"className":3846},[50],[15,3848],{"className":3849,"style":55},[54],[15,3851,37],{"className":3852,"style":61},[59,60]," 在 ",[15,3855,3857,3871],{"className":3856,"translate":19},[18],[15,3858,3860],{"className":3859},[23],[25,3861,3862],{"xmlns":27},[29,3863,3864,3868],{},[32,3865,3866],{},[35,3867,1024],{"mathvariant":209},[39,3869,3870],{"encoding":41},"\\infty",[15,3872,3874],{"className":3873,"ariaHidden":46},[45],[15,3875,3877,3880],{"className":3876},[50],[15,3878],{"className":3879,"style":2345},[54],[15,3881,1024],{"className":3882},[59]," 处有界，可约定 ",[15,3885,3887,3915],{"className":3886,"translate":19},[18],[15,3888,3890],{"className":3889},[23],[25,3891,3892],{"xmlns":27},[29,3893,3894,3912],{},[32,3895,3896,3898,3900,3902,3904,3906,3908,3910],{},[115,3897,126],{},[110,3899,3299],{},[35,3901,37],{},[110,3903,113],{"stretchy":112},[35,3905,1024],{"mathvariant":209},[110,3907,120],{"stretchy":112},[110,3909,123],{},[115,3911,126],{},[39,3913,3914],{"encoding":41},"0\\cdot f(\\infty)=0",[15,3916,3918,3936,3963],{"className":3917,"ariaHidden":46},[45],[15,3919,3921,3924,3927,3930,3933],{"className":3920},[50],[15,3922],{"className":3923,"style":172},[54],[15,3925,126],{"className":3926},[59],[15,3928],{"className":3929,"style":2587},[157],[15,3931,3299],{"className":3932},[2591],[15,3934],{"className":3935,"style":2587},[157],[15,3937,3939,3942,3945,3948,3951,3954,3957,3960],{"className":3938},[50],[15,3940],{"className":3941,"style":139},[54],[15,3943,37],{"className":3944,"style":61},[59,60],[15,3946,113],{"className":3947},[146],[15,3949,1024],{"className":3950},[59],[15,3952,120],{"className":3953},[153],[15,3955],{"className":3956,"style":158},[157],[15,3958,123],{"className":3959},[162],[15,3961],{"className":3962,"style":158},[157],[15,3964,3966,3969],{"className":3965},[50],[15,3967],{"className":3968,"style":172},[54],[15,3970,126],{"className":3971},[59],"；若 ",[15,3974,3976,3989],{"className":3975,"translate":19},[18],[15,3977,3979],{"className":3978},[23],[25,3980,3981],{"xmlns":27},[29,3982,3983,3987],{},[32,3984,3985],{},[35,3986,37],{},[39,3988,37],{"encoding":41},[15,3990,3992],{"className":3991,"ariaHidden":46},[45],[15,3993,3995,3998],{"className":3994},[50],[15,3996],{"className":3997,"style":55},[54],[15,3999,37],{"className":4000,"style":61},[59,60]," 无界，则这一项是否发散决定了 ",[15,4003,4005,4023],{"className":4004,"translate":19},[18],[15,4006,4008],{"className":4007},[23],[25,4009,4010],{"xmlns":27},[29,4011,4012,4020],{},[32,4013,4014],{},[195,4015,4016,4018],{},[35,4017,199],{},[35,4019,37],{},[39,4021,4022],{"encoding":41},"D_f",[15,4024,4026],{"className":4025,"ariaHidden":46},[45],[15,4027,4029,4033],{"className":4028},[50],[15,4030],{"className":4031,"style":4032},[54],"height:0.9694em;vertical-align:-0.2861em;",[15,4034,4036,4039],{"className":4035},[59],[15,4037,199],{"className":4038,"style":277},[59,60],[15,4040,4042],{"className":4041},[281],[15,4043,4045,4065],{"className":4044},[285,286],[15,4046,4048,4062],{"className":4047},[290],[15,4049,4051],{"className":4050,"style":295},[294],[15,4052,4053,4056],{"style":298},[15,4054],{"className":4055,"style":303},[302],[15,4057,4059],{"className":4058},[307,308,309,310],[15,4060,37],{"className":4061,"style":61},[59,60,310],[15,4063,318],{"className":4064},[317],[15,4066,4068],{"className":4067},[290],[15,4069,4071],{"className":4070,"style":325},[294],[15,4072],{}," 是否有限。例如对 KL 的 ",[15,4075,4077,4109],{"className":4076,"translate":19},[18],[15,4078,4080],{"className":4079},[23],[25,4081,4082],{"xmlns":27},[29,4083,4084,4106],{},[32,4085,4086,4088,4090,4092,4094,4096,4098,4101,4104],{},[35,4087,37],{},[110,4089,113],{"stretchy":112},[35,4091,769],{},[110,4093,120],{"stretchy":112},[110,4095,123],{},[35,4097,769],{},[35,4099,4100],{},"log",[110,4102,4103],{},"⁡",[35,4105,769],{},[39,4107,4108],{"encoding":41},"f(t)=t\\log t",[15,4110,4112,4139],{"className":4111,"ariaHidden":46},[45],[15,4113,4115,4118,4121,4124,4127,4130,4133,4136],{"className":4114},[50],[15,4116],{"className":4117,"style":139},[54],[15,4119,37],{"className":4120,"style":61},[59,60],[15,4122,113],{"className":4123},[146],[15,4125,769],{"className":4126},[59,60],[15,4128,120],{"className":4129},[153],[15,4131],{"className":4132,"style":158},[157],[15,4134,123],{"className":4135},[162],[15,4137],{"className":4138,"style":158},[157],[15,4140,4142,4145,4148,4151,4159,4162],{"className":4141},[50],[15,4143],{"className":4144,"style":55},[54],[15,4146,769],{"className":4147},[59,60],[15,4149],{"className":4150,"style":406},[157],[15,4152,4154,4155],{"className":4153},[1484],"lo",[15,4156,4158],{"style":4157},"margin-right:0.0139em;","g",[15,4160],{"className":4161,"style":406},[157],[15,4163,769],{"className":4164},[59,60],"，当 ",[15,4167,4169,4182],{"className":4168,"translate":19},[18],[15,4170,4172],{"className":4171},[23],[25,4173,4174],{"xmlns":27},[29,4175,4176,4180],{},[32,4177,4178],{},[35,4179,206],{},[39,4181,206],{"encoding":41},[15,4183,4185],{"className":4184,"ariaHidden":46},[45],[15,4186,4188,4191],{"className":4187},[50],[15,4189],{"className":4190,"style":664},[54],[15,4192,206],{"className":4193,"style":334},[59,60],[15,4195,4197,4210],{"className":4196,"translate":19},[18],[15,4198,4200],{"className":4199},[23],[25,4201,4202],{"xmlns":27},[29,4203,4204,4208],{},[32,4205,4206],{},[35,4207,213],{},[39,4209,213],{"encoding":41},[15,4211,4213],{"className":4212,"ariaHidden":46},[45],[15,4214,4216,4219],{"className":4215},[50],[15,4217],{"className":4218,"style":566},[54],[15,4220,213],{"className":4221},[59,60]," 的零测集上放质量时这一项为 ",[15,4224,4226,4242],{"className":4225,"translate":19},[18],[15,4227,4229],{"className":4228},[23],[25,4230,4231],{"xmlns":27},[29,4232,4233,4239],{},[32,4234,4235,4237],{},[110,4236,2470],{},[35,4238,1024],{"mathvariant":209},[39,4240,4241],{"encoding":41},"+\\infty",[15,4243,4245],{"className":4244,"ariaHidden":46},[45],[15,4246,4248,4252,4255],{"className":4247},[50],[15,4249],{"className":4250,"style":4251},[54],"height:0.6667em;vertical-align:-0.0833em;",[15,4253,2470],{"className":4254},[59],[15,4256,1024],{"className":4257},[59],"。因此约定：",[15,4260,4262],{"className":4261,"translate":19},[180],[15,4263,4265,4379],{"className":4264,"translate":19},[18],[15,4266,4268],{"className":4267},[23],[25,4269,4270],{"xmlns":27,"display":189},[29,4271,4272,4376],{},[32,4273,4274,4276,4279,4281,4284,4287,4289,4295,4297,4299,4301,4303,4305,4307],{},[35,4275,206],{},[110,4277,4278],{},"≪̸",[35,4280,213],{},[1297,4282,4283],{}," ",[110,4285,4286],{},"⟹",[1297,4288,4283],{},[195,4290,4291,4293],{},[35,4292,199],{},[35,4294,37],{},[110,4296,113],{"stretchy":112},[35,4298,206],{},[35,4300,210],{"mathvariant":209},[35,4302,213],{},[110,4304,120],{"stretchy":112},[110,4306,123],{},[32,4308,4309,4311],{},[110,4310,2898],{"fence":46},[1243,4312,4316,4351],{"rowspacing":4313,"columnalign":4314,"columnspacing":4315},"0.36em","left left","1em",[1249,4317,4318,4330],{},[1252,4319,4320],{},[1255,4321,4322],{"scriptlevel":126,"displaystyle":112},[32,4323,4324,4326,4328],{},[110,4325,2470],{},[35,4327,1024],{"mathvariant":209},[110,4329,551],{"separator":46},[1252,4331,4332],{},[1255,4333,4334],{"scriptlevel":126,"displaystyle":112},[32,4335,4336,4339,4341,4344,4346,4349],{},[1297,4337,4338],{},"若 ",[35,4340,37],{},[1297,4342,4343],{}," 在 ",[35,4345,1024],{"mathvariant":209},[1297,4347,4348],{}," 处增长",[110,4350,551],{"separator":46},[1249,4352,4353,4364],{},[1252,4354,4355],{},[1255,4356,4357],{"scriptlevel":126,"displaystyle":112},[32,4358,4359,4362],{},[1297,4360,4361],{},"有限极限值",[110,4363,551],{"separator":46},[1252,4365,4366],{},[1255,4367,4368],{"scriptlevel":126,"displaystyle":112},[32,4369,4370,4373],{},[1297,4371,4372],{},"否则",[35,4374,4375],{"mathvariant":209},".",[39,4377,4378],{"encoding":41},"P\\not\\ll Q\\ \\Longrightarrow\\\nD_f(P\\|Q)=\n\\begin{cases}\n+\\infty, & \\text{若 } f \\text{ 在 } \\infty\n\\text{ 处增长},\\\\[2pt]\n\\text{有限极限值}, & \\text{否则}.\n\\end{cases}",[15,4380,4382,4437,4461,4531],{"className":4381,"ariaHidden":46},[45],[15,4383,4385,4388,4391,4394,4427,4431,4434],{"className":4384},[50],[15,4386],{"className":4387,"style":55},[54],[15,4389,206],{"className":4390,"style":334},[59,60],[15,4392],{"className":4393,"style":158},[157],[15,4395,4397],{"className":4396},[162],[15,4398,4401],{"className":4399},[59,4400],"vbox",[15,4402,4405],{"className":4403},[4404],"thinbox",[15,4406,4409,4412,4423],{"className":4407},[4408],"rlap",[15,4410],{"className":4411,"style":55},[54],[15,4413,4416],{"className":4414},[4415],"inner",[15,4417,4419],{"className":4418},[59],[15,4420,4422],{"className":4421},[162],"",[15,4424],{"className":4425},[4426],"fix",[15,4428],{"className":4429},[157,4430],"nobreak",[15,4432,714],{"className":4433},[162],[15,4435],{"className":4436,"style":158},[157],[15,4438,4440,4443,4446,4449,4452,4455,4458],{"className":4439},[50],[15,4441],{"className":4442,"style":566},[54],[15,4444,213],{"className":4445},[59,60],[15,4447,4283],{"className":4448},[157],[15,4450],{"className":4451,"style":158},[157],[15,4453,4286],{"className":4454},[162],[15,4456,4283],{"className":4457},[157],[15,4459],{"className":4460,"style":158},[157],[15,4462,4464,4467,4507,4510,4513,4516,4519,4522,4525,4528],{"className":4463},[50],[15,4465],{"className":4466,"style":270},[54],[15,4468,4470,4473],{"className":4469},[59],[15,4471,199],{"className":4472,"style":277},[59,60],[15,4474,4476],{"className":4475},[281],[15,4477,4479,4499],{"className":4478},[285,286],[15,4480,4482,4496],{"className":4481},[290],[15,4483,4485],{"className":4484,"style":295},[294],[15,4486,4487,4490],{"style":298},[15,4488],{"className":4489,"style":303},[302],[15,4491,4493],{"className":4492},[307,308,309,310],[15,4494,37],{"className":4495,"style":61},[59,60,310],[15,4497,318],{"className":4498},[317],[15,4500,4502],{"className":4501},[290],[15,4503,4505],{"className":4504,"style":325},[294],[15,4506],{},[15,4508,113],{"className":4509},[146],[15,4511,206],{"className":4512,"style":334},[59,60],[15,4514,210],{"className":4515},[59],[15,4517,213],{"className":4518},[59,60],[15,4520,120],{"className":4521},[153],[15,4523],{"className":4524,"style":158},[157],[15,4526,123],{"className":4527},[162],[15,4529],{"className":4530,"style":158},[157],[15,4532,4534,4538],{"className":4533},[50],[15,4535],{"className":4536,"style":4537},[54],"height:3.08em;vertical-align:-1.29em;",[15,4539,4541,4548,4713],{"className":4540},[410],[15,4542,4544],{"className":4543,"style":415},[146,414],[15,4545,2898],{"className":4546},[419,4547],"size4",[15,4549,4551],{"className":4550},[59],[15,4552,4554,4618,4623],{"className":4553},[1243],[15,4555,4557],{"className":4556},[1451],[15,4558,4560,4609],{"className":4559},[285,286],[15,4561,4563,4606],{"className":4562},[290],[15,4564,4567,4586],{"className":4565,"style":4566},[294],"height:1.79em;",[15,4568,4570,4574],{"style":4569},"top:-3.79em;",[15,4571],{"className":4572,"style":4573},[302],"height:3.008em;",[15,4575,4577,4580,4583],{"className":4576},[59],[15,4578,2470],{"className":4579},[59],[15,4581,1024],{"className":4582},[59],[15,4584,551],{"className":4585},[573],[15,4587,4589,4592],{"style":4588},"top:-2.15em;",[15,4590],{"className":4591,"style":4573},[302],[15,4593,4595,4603],{"className":4594},[59],[15,4596,4599],{"className":4597},[59,4598],"text",[15,4600,4361],{"className":4601},[59,4602],"cjk_fallback",[15,4604,551],{"className":4605},[573],[15,4607,318],{"className":4608},[317],[15,4610,4612],{"className":4611},[290],[15,4613,4616],{"className":4614,"style":4615},[294],"height:1.29em;",[15,4617],{},[15,4619],{"className":4620,"style":4622},[4621],"arraycolsep","width:1em;",[15,4624,4626],{"className":4625},[1451],[15,4627,4629,4705],{"className":4628},[285,286],[15,4630,4632,4702],{"className":4631},[290],[15,4633,4635,4685],{"className":4634,"style":4566},[294],[15,4636,4637,4640],{"style":4569},[15,4638],{"className":4639,"style":4573},[302],[15,4641,4643,4653,4656,4669,4672,4682],{"className":4642},[59],[15,4644,4646,4650],{"className":4645},[59,4598],[15,4647,4649],{"className":4648},[59,4602],"若",[15,4651,4283],{"className":4652},[59],[15,4654,37],{"className":4655,"style":61},[59,60],[15,4657,4659,4662,4666],{"className":4658},[59,4598],[15,4660,4283],{"className":4661},[59],[15,4663,4665],{"className":4664},[59,4602],"在",[15,4667,4283],{"className":4668},[59],[15,4670,1024],{"className":4671},[59],[15,4673,4675,4678],{"className":4674},[59,4598],[15,4676,4283],{"className":4677},[59],[15,4679,4681],{"className":4680},[59,4602],"处增长",[15,4683,551],{"className":4684},[573],[15,4686,4687,4690],{"style":4588},[15,4688],{"className":4689,"style":4573},[302],[15,4691,4693,4699],{"className":4692},[59],[15,4694,4696],{"className":4695},[59,4598],[15,4697,4372],{"className":4698},[59,4602],[15,4700,4375],{"className":4701},[59],[15,4703,318],{"className":4704},[317],[15,4706,4708],{"className":4707},[290],[15,4709,4711],{"className":4710,"style":4615},[294],[15,4712],{},[15,4714],{"className":4715},[153,441],[11,4717,4718,4719,3853,4747,4775,4776,4952,4953,5022,5023,5073,5074,5143,5144,5201],{},"其中「否则」指 ",[15,4720,4722,4735],{"className":4721,"translate":19},[18],[15,4723,4725],{"className":4724},[23],[25,4726,4727],{"xmlns":27},[29,4728,4729,4733],{},[32,4730,4731],{},[35,4732,37],{},[39,4734,37],{"encoding":41},[15,4736,4738],{"className":4737,"ariaHidden":46},[45],[15,4739,4741,4744],{"className":4740},[50],[15,4742],{"className":4743,"style":55},[54],[15,4745,37],{"className":4746,"style":61},[59,60],[15,4748,4750,4763],{"className":4749,"translate":19},[18],[15,4751,4753],{"className":4752},[23],[25,4754,4755],{"xmlns":27},[29,4756,4757,4761],{},[32,4758,4759],{},[35,4760,1024],{"mathvariant":209},[39,4762,3870],{"encoding":41},[15,4764,4766],{"className":4765,"ariaHidden":46},[45],[15,4767,4769,4772],{"className":4768},[50],[15,4770],{"className":4771,"style":2345},[54],[15,4773,1024],{"className":4774},[59]," 处有界（如 ",[15,4777,4779,4821],{"className":4778,"translate":19},[18],[15,4780,4782],{"className":4781},[23],[25,4783,4784],{"xmlns":27},[29,4785,4786,4818],{},[32,4787,4788,4790,4792,4794,4796,4798,4806,4809,4811,4814,4816],{},[35,4789,37],{},[110,4791,113],{"stretchy":112},[35,4793,769],{},[110,4795,120],{"stretchy":112},[110,4797,123],{},[1255,4799,4800],{"scriptlevel":126,"displaystyle":112},[238,4801,4802,4804],{},[115,4803,117],{},[115,4805,2463],{},[110,4807,4808],{"stretchy":112},"∣",[35,4810,769],{},[110,4812,4813],{},"−",[115,4815,117],{},[110,4817,4808],{"stretchy":112},[39,4819,4820],{"encoding":41},"f(t)=\\tfrac12\\lvert t-1\\rvert",[15,4822,4824,4851,4940],{"className":4823,"ariaHidden":46},[45],[15,4825,4827,4830,4833,4836,4839,4842,4845,4848],{"className":4826},[50],[15,4828],{"className":4829,"style":139},[54],[15,4831,37],{"className":4832,"style":61},[59,60],[15,4834,113],{"className":4835},[146],[15,4837,769],{"className":4838},[59,60],[15,4840,120],{"className":4841},[153],[15,4843],{"className":4844,"style":158},[157],[15,4846,123],{"className":4847},[162],[15,4849],{"className":4850,"style":158},[157],[15,4852,4854,4857,4925,4928,4931,4934,4937],{"className":4853},[50],[15,4855],{"className":4856,"style":2505},[54],[15,4858,4860,4863,4922],{"className":4859},[59],[15,4861],{"className":4862},[146,441],[15,4864,4866],{"className":4865},[238],[15,4867,4869,4914],{"className":4868},[285,286],[15,4870,4872,4911],{"className":4871},[290],[15,4873,4875,4889,4897],{"className":4874,"style":2524},[294],[15,4876,4877,4880],{"style":2527},[15,4878],{"className":4879,"style":461},[302],[15,4881,4883],{"className":4882},[307,308,309,310],[15,4884,4886],{"className":4885},[59,310],[15,4887,2463],{"className":4888},[59,310],[15,4890,4891,4894],{"style":473},[15,4892],{"className":4893,"style":461},[302],[15,4895],{"className":4896,"style":481},[480],[15,4898,4899,4902],{"style":2550},[15,4900],{"className":4901,"style":461},[302],[15,4903,4905],{"className":4904},[307,308,309,310],[15,4906,4908],{"className":4907},[59,310],[15,4909,117],{"className":4910},[59,310],[15,4912,318],{"className":4913},[317],[15,4915,4917],{"className":4916},[290],[15,4918,4920],{"className":4919,"style":2572},[294],[15,4921],{},[15,4923],{"className":4924},[153,441],[15,4926,4808],{"className":4927},[146],[15,4929,769],{"className":4930},[59,60],[15,4932],{"className":4933,"style":2587},[157],[15,4935,4813],{"className":4936},[2591],[15,4938],{"className":4939,"style":2587},[157],[15,4941,4943,4946,4949],{"className":4942},[50],[15,4944],{"className":4945,"style":139},[54],[15,4947,117],{"className":4948},[59],[15,4950,4808],{"className":4951},[153],"），此时 ",[15,4954,4956,4973],{"className":4955,"translate":19},[18],[15,4957,4959],{"className":4958},[23],[25,4960,4961],{"xmlns":27},[29,4962,4963,4971],{},[32,4964,4965],{},[195,4966,4967,4969],{},[35,4968,199],{},[35,4970,37],{},[39,4972,4022],{"encoding":41},[15,4974,4976],{"className":4975,"ariaHidden":46},[45],[15,4977,4979,4982],{"className":4978},[50],[15,4980],{"className":4981,"style":4032},[54],[15,4983,4985,4988],{"className":4984},[59],[15,4986,199],{"className":4987,"style":277},[59,60],[15,4989,4991],{"className":4990},[281],[15,4992,4994,5014],{"className":4993},[285,286],[15,4995,4997,5011],{"className":4996},[290],[15,4998,5000],{"className":4999,"style":295},[294],[15,5001,5002,5005],{"style":298},[15,5003],{"className":5004,"style":303},[302],[15,5006,5008],{"className":5007},[307,308,309,310],[15,5009,37],{"className":5010,"style":61},[59,60,310],[15,5012,318],{"className":5013},[317],[15,5015,5017],{"className":5016},[290],[15,5018,5020],{"className":5019,"style":325},[294],[15,5021],{}," 取有限极限值。下文如无特别说明，默认 ",[15,5024,5026,5043],{"className":5025,"translate":19},[18],[15,5027,5029],{"className":5028},[23],[25,5030,5031],{"xmlns":27},[29,5032,5033,5041],{},[32,5034,5035,5037,5039],{},[35,5036,206],{},[110,5038,714],{},[35,5040,213],{},[39,5042,719],{"encoding":41},[15,5044,5046,5064],{"className":5045,"ariaHidden":46},[45],[15,5047,5049,5052,5055,5058,5061],{"className":5048},[50],[15,5050],{"className":5051,"style":729},[54],[15,5053,206],{"className":5054,"style":334},[59,60],[15,5056],{"className":5057,"style":158},[157],[15,5059,714],{"className":5060},[162],[15,5062],{"className":5063,"style":158},[157],[15,5065,5067,5070],{"className":5066},[50],[15,5068],{"className":5069,"style":566},[54],[15,5071,213],{"className":5072},[59,60],"，并把 ",[15,5075,5077,5094],{"className":5076,"translate":19},[18],[15,5078,5080],{"className":5079},[23],[25,5081,5082],{"xmlns":27},[29,5083,5084,5092],{},[32,5085,5086],{},[195,5087,5088,5090],{},[35,5089,199],{},[35,5091,37],{},[39,5093,4022],{"encoding":41},[15,5095,5097],{"className":5096,"ariaHidden":46},[45],[15,5098,5100,5103],{"className":5099},[50],[15,5101],{"className":5102,"style":4032},[54],[15,5104,5106,5109],{"className":5105},[59],[15,5107,199],{"className":5108,"style":277},[59,60],[15,5110,5112],{"className":5111},[281],[15,5113,5115,5135],{"className":5114},[285,286],[15,5116,5118,5132],{"className":5117},[290],[15,5119,5121],{"className":5120,"style":295},[294],[15,5122,5123,5126],{"style":298},[15,5124],{"className":5125,"style":303},[302],[15,5127,5129],{"className":5128},[307,308,309,310],[15,5130,37],{"className":5131,"style":61},[59,60,310],[15,5133,318],{"className":5134},[317],[15,5136,5138],{"className":5137},[290],[15,5139,5141],{"className":5140,"style":325},[294],[15,5142],{}," 看成 ",[15,5145,5147,5171],{"className":5146,"translate":19},[18],[15,5148,5150],{"className":5149},[23],[25,5151,5152],{"xmlns":27},[29,5153,5154,5168],{},[32,5155,5156,5158,5160,5162,5164,5166],{},[110,5157,230],{"stretchy":112},[115,5159,126],{},[110,5161,551],{"separator":46},[110,5163,2470],{},[35,5165,1024],{"mathvariant":209},[110,5167,257],{"stretchy":112},[39,5169,5170],{"encoding":41},"[0,+\\infty]",[15,5172,5174],{"className":5173,"ariaHidden":46},[45],[15,5175,5177,5180,5183,5186,5189,5192,5195,5198],{"className":5176},[50],[15,5178],{"className":5179,"style":139},[54],[15,5181,230],{"className":5182},[146],[15,5184,126],{"className":5185},[59],[15,5187,551],{"className":5188},[573],[15,5190],{"className":5191,"style":406},[157],[15,5193,2470],{"className":5194},[59],[15,5196,1024],{"className":5197},[59],[15,5199,257],{"className":5200},[153]," 中的值。",[2311,5203,5205],{"id":5204},"_12-只依赖似然比","1.2 只依赖似然比",[11,5207,5208,5209,5304,5305,5377,5378,5455,5456,5484,5485,5527],{},"由定义立刻看出：",[15,5210,5212,5240],{"className":5211,"translate":19},[18],[15,5213,5215],{"className":5214},[23],[25,5216,5217],{"xmlns":27},[29,5218,5219,5237],{},[32,5220,5221,5227,5229,5231,5233,5235],{},[195,5222,5223,5225],{},[35,5224,199],{},[35,5226,37],{},[110,5228,113],{"stretchy":112},[35,5230,206],{},[35,5232,210],{"mathvariant":209},[35,5234,213],{},[110,5236,120],{"stretchy":112},[39,5238,5239],{"encoding":41},"D_f(P\\|Q)",[15,5241,5243],{"className":5242,"ariaHidden":46},[45],[15,5244,5246,5249,5289,5292,5295,5298,5301],{"className":5245},[50],[15,5247],{"className":5248,"style":270},[54],[15,5250,5252,5255],{"className":5251},[59],[15,5253,199],{"className":5254,"style":277},[59,60],[15,5256,5258],{"className":5257},[281],[15,5259,5261,5281],{"className":5260},[285,286],[15,5262,5264,5278],{"className":5263},[290],[15,5265,5267],{"className":5266,"style":295},[294],[15,5268,5269,5272],{"style":298},[15,5270],{"className":5271,"style":303},[302],[15,5273,5275],{"className":5274},[307,308,309,310],[15,5276,37],{"className":5277,"style":61},[59,60,310],[15,5279,318],{"className":5280},[317],[15,5282,5284],{"className":5283},[290],[15,5285,5287],{"className":5286,"style":325},[294],[15,5288],{},[15,5290,113],{"className":5291},[146],[15,5293,206],{"className":5294,"style":334},[59,60],[15,5296,210],{"className":5297},[59],[15,5299,213],{"className":5300},[59,60],[15,5302,120],{"className":5303},[153]," 只通过似然比 ",[15,5306,5308,5334],{"className":5307,"translate":19},[18],[15,5309,5311],{"className":5310},[23],[25,5312,5313],{"xmlns":27},[29,5314,5315,5331],{},[32,5316,5317,5319,5321,5323,5325,5327,5329],{},[35,5318,769],{},[110,5320,123],{},[35,5322,244],{},[35,5324,206],{},[35,5326,941],{"mathvariant":209},[35,5328,244],{},[35,5330,213],{},[39,5332,5333],{"encoding":41},"t=dP\u002FdQ",[15,5335,5337,5356],{"className":5336,"ariaHidden":46},[45],[15,5338,5340,5344,5347,5350,5353],{"className":5339},[50],[15,5341],{"className":5342,"style":5343},[54],"height:0.6151em;",[15,5345,769],{"className":5346},[59,60],[15,5348],{"className":5349,"style":158},[157],[15,5351,123],{"className":5352},[162],[15,5354],{"className":5355,"style":158},[157],[15,5357,5359,5362,5365,5368,5371,5374],{"className":5358},[50],[15,5360],{"className":5361,"style":139},[54],[15,5363,244],{"className":5364},[59,60],[15,5366,206],{"className":5367,"style":334},[59,60],[15,5369,941],{"className":5370},[59],[15,5372,244],{"className":5373},[59,60],[15,5375,213],{"className":5376},[59,60]," 起作用。也就是说，对任意可测映射 ",[15,5379,5381,5405],{"className":5380,"translate":19},[18],[15,5382,5384],{"className":5383},[23],[25,5385,5386],{"xmlns":27},[29,5387,5388,5402],{},[32,5389,5390,5393,5395,5397,5399],{},[35,5391,5392],{},"T",[110,5394,1015],{},[35,5396,598],{"mathvariant":597},[110,5398,1029],{},[35,5400,5401],{"mathvariant":597},"Y",[39,5403,5404],{"encoding":41},"T:\\mathcal X\\to\\mathcal Y",[15,5406,5408,5426,5444],{"className":5407,"ariaHidden":46},[45],[15,5409,5411,5414,5417,5420,5423],{"className":5410},[50],[15,5412],{"className":5413,"style":664},[54],[15,5415,5392],{"className":5416,"style":334},[59,60],[15,5418],{"className":5419,"style":158},[157],[15,5421,1015],{"className":5422},[162],[15,5424],{"className":5425,"style":158},[157],[15,5427,5429,5432,5435,5438,5441],{"className":5428},[50],[15,5430],{"className":5431,"style":664},[54],[15,5433,598],{"className":5434,"style":625},[59,624],[15,5436],{"className":5437,"style":158},[157],[15,5439,1029],{"className":5440},[162],[15,5442],{"className":5443,"style":158},[157],[15,5445,5447,5451],{"className":5446},[50],[15,5448],{"className":5449,"style":5450},[54],"height:0.7805em;vertical-align:-0.0972em;",[15,5452,5401],{"className":5453,"style":5454},[59,624],"margin-right:0.0822em;","，它是 ",[15,5457,5459,5472],{"className":5458,"translate":19},[18],[15,5460,5462],{"className":5461},[23],[25,5463,5464],{"xmlns":27},[29,5465,5466,5470],{},[32,5467,5468],{},[35,5469,769],{},[39,5471,769],{"encoding":41},[15,5473,5475],{"className":5474,"ariaHidden":46},[45],[15,5476,5478,5481],{"className":5477},[50],[15,5479],{"className":5480,"style":5343},[54],[15,5482,769],{"className":5483},[59,60]," 的函数，而不是 ",[15,5486,5488,5506],{"className":5487,"translate":19},[18],[15,5489,5491],{"className":5490},[23],[25,5492,5493],{"xmlns":27},[29,5494,5495,5503],{},[32,5496,5497,5499,5501],{},[35,5498,11],{},[110,5500,551],{"separator":46},[35,5502,944],{},[39,5504,5505],{"encoding":41},"p,q",[15,5507,5509],{"className":5508,"ariaHidden":46},[45],[15,5510,5512,5515,5518,5521,5524],{"className":5511},[50],[15,5513],{"className":5514,"style":2276},[54],[15,5516,11],{"className":5517},[59,60],[15,5519,551],{"className":5520},[573],[15,5522],{"className":5523,"style":406},[157],[15,5525,944],{"className":5526,"style":981},[59,60]," 各自的函数。",[11,5529,5530,5531,5570],{},"这一点是 f-散度「缺少几何」的根源，也是它与 Wasserstein 距离分道扬镳的地方（见第 6 节）：只要保持比值 ",[15,5532,5534,5552],{"className":5533,"translate":19},[18],[15,5535,5537],{"className":5536},[23],[25,5538,5539],{"xmlns":27},[29,5540,5541,5549],{},[32,5542,5543,5545,5547],{},[35,5544,11],{},[35,5546,941],{"mathvariant":209},[35,5548,944],{},[39,5550,5551],{"encoding":41},"p\u002Fq",[15,5553,5555],{"className":5554,"ariaHidden":46},[45],[15,5556,5558,5561,5564,5567],{"className":5557},[50],[15,5559],{"className":5560,"style":139},[54],[15,5562,11],{"className":5563},[59,60],[15,5565,941],{"className":5566},[59],[15,5568,944],{"className":5569,"style":981},[59,60]," 不变，把两个分布同时「搬到别处」，f-散度的值完全不动。",[2311,5572,5574],{"id":5573},"_13-非单射与仿射自由度","1.3 非单射与仿射自由度",[11,5576,5577,5578,5645,5646,5710],{},"注意 ",[15,5579,5581,5603],{"className":5580,"translate":19},[18],[15,5582,5584],{"className":5583},[23],[25,5585,5586],{"xmlns":27},[29,5587,5588,5600],{},[32,5589,5590,5592,5594,5596,5598],{},[110,5591,1287],{},[35,5593,244],{},[35,5595,213],{},[110,5597,123],{},[115,5599,117],{},[39,5601,5602],{"encoding":41},"\\int dQ=1",[15,5604,5606,5636],{"className":5605,"ariaHidden":46},[45],[15,5607,5609,5613,5618,5621,5624,5627,5630,5633],{"className":5608},[50],[15,5610],{"className":5611,"style":5612},[54],"height:1.1111em;vertical-align:-0.3061em;",[15,5614,1287],{"className":5615,"style":5617},[1484,1485,5616],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[15,5619],{"className":5620,"style":406},[157],[15,5622,244],{"className":5623},[59,60],[15,5625,213],{"className":5626},[59,60],[15,5628],{"className":5629,"style":158},[157],[15,5631,123],{"className":5632},[162],[15,5634],{"className":5635,"style":158},[157],[15,5637,5639,5642],{"className":5638},[50],[15,5640],{"className":5641,"style":172},[54],[15,5643,117],{"className":5644},[59],"、",[15,5647,5649,5671],{"className":5648,"translate":19},[18],[15,5650,5652],{"className":5651},[23],[25,5653,5654],{"xmlns":27},[29,5655,5656,5668],{},[32,5657,5658,5660,5662,5664,5666],{},[110,5659,1287],{},[35,5661,244],{},[35,5663,206],{},[110,5665,123],{},[115,5667,117],{},[39,5669,5670],{"encoding":41},"\\int dP=1",[15,5672,5674,5701],{"className":5673,"ariaHidden":46},[45],[15,5675,5677,5680,5683,5686,5689,5692,5695,5698],{"className":5676},[50],[15,5678],{"className":5679,"style":5612},[54],[15,5681,1287],{"className":5682,"style":5617},[1484,1485,5616],[15,5684],{"className":5685,"style":406},[157],[15,5687,244],{"className":5688},[59,60],[15,5690,206],{"className":5691,"style":334},[59,60],[15,5693],{"className":5694,"style":158},[157],[15,5696,123],{"className":5697},[162],[15,5699],{"className":5700,"style":158},[157],[15,5702,5704,5707],{"className":5703},[50],[15,5705],{"className":5706,"style":172},[54],[15,5708,117],{"className":5709},[59],"，因此",[15,5712,5714],{"className":5713,"translate":19},[180],[15,5715,5717,5768],{"className":5716,"translate":19},[18],[15,5718,5720],{"className":5719},[23],[25,5721,5722],{"xmlns":27,"display":189},[29,5723,5724,5765],{},[32,5725,5726,5728,5730,5732,5734,5736,5738,5740,5742,5744,5746,5748,5750,5752,5754,5756,5758,5760,5762],{},[110,5727,1287],{},[110,5729,113],{"stretchy":112},[35,5731,769],{},[110,5733,4813],{},[115,5735,117],{},[110,5737,120],{"stretchy":112},[1297,5739,1299],{},[35,5741,244],{},[35,5743,213],{},[110,5745,123],{},[110,5747,1287],{},[35,5749,244],{},[35,5751,206],{},[110,5753,4813],{},[110,5755,1287],{},[35,5757,244],{},[35,5759,213],{},[110,5761,123],{},[115,5763,5764],{},"0.",[39,5766,5767],{"encoding":41},"\\int (t-1)\\,dQ=\\int dP-\\int dQ=0 .",[15,5769,5771,5796,5826,5853,5880],{"className":5770,"ariaHidden":46},[45],[15,5772,5774,5778,5781,5784,5787,5790,5793],{"className":5773},[50],[15,5775],{"className":5776,"style":5777},[54],"height:2.2222em;vertical-align:-0.8622em;",[15,5779,1287],{"className":5780,"style":1487},[1484,1485,1486],[15,5782,113],{"className":5783},[146],[15,5785,769],{"className":5786},[59,60],[15,5788],{"className":5789,"style":2587},[157],[15,5791,4813],{"className":5792},[2591],[15,5794],{"className":5795,"style":2587},[157],[15,5797,5799,5802,5805,5808,5811,5814,5817,5820,5823],{"className":5798},[50],[15,5800],{"className":5801,"style":139},[54],[15,5803,117],{"className":5804},[59],[15,5806,120],{"className":5807},[153],[15,5809],{"className":5810,"style":406},[157],[15,5812,244],{"className":5813},[59,60],[15,5815,213],{"className":5816},[59,60],[15,5818],{"className":5819,"style":158},[157],[15,5821,123],{"className":5822},[162],[15,5824],{"className":5825,"style":158},[157],[15,5827,5829,5832,5835,5838,5841,5844,5847,5850],{"className":5828},[50],[15,5830],{"className":5831,"style":5777},[54],[15,5833,1287],{"className":5834,"style":1487},[1484,1485,1486],[15,5836],{"className":5837,"style":406},[157],[15,5839,244],{"className":5840},[59,60],[15,5842,206],{"className":5843,"style":334},[59,60],[15,5845],{"className":5846,"style":2587},[157],[15,5848,4813],{"className":5849},[2591],[15,5851],{"className":5852,"style":2587},[157],[15,5854,5856,5859,5862,5865,5868,5871,5874,5877],{"className":5855},[50],[15,5857],{"className":5858,"style":5777},[54],[15,5860,1287],{"className":5861,"style":1487},[1484,1485,1486],[15,5863],{"className":5864,"style":406},[157],[15,5866,244],{"className":5867},[59,60],[15,5869,213],{"className":5870},[59,60],[15,5872],{"className":5873,"style":158},[157],[15,5875,123],{"className":5876},[162],[15,5878],{"className":5879,"style":158},[157],[15,5881,5883,5886],{"className":5882},[50],[15,5884],{"className":5885,"style":172},[54],[15,5887,5764],{"className":5888},[59],[11,5890,5891,5892,2745],{},"于是对任意常数 ",[15,5893,5895,5915],{"className":5894,"translate":19},[18],[15,5896,5898],{"className":5897},[23],[25,5899,5900],{"xmlns":27},[29,5901,5902,5912],{},[32,5903,5904,5907,5910],{},[35,5905,5906],{},"c",[110,5908,5909],{},"∈",[35,5911,1032],{"mathvariant":222},[39,5913,5914],{"encoding":41},"c\\in\\mathbb R",[15,5916,5918,5937],{"className":5917,"ariaHidden":46},[45],[15,5919,5921,5925,5928,5931,5934],{"className":5920},[50],[15,5922],{"className":5923,"style":5924},[54],"height:0.5782em;vertical-align:-0.0391em;",[15,5926,5906],{"className":5927},[59,60],[15,5929],{"className":5930,"style":158},[157],[15,5932,5909],{"className":5933},[162],[15,5935],{"className":5936,"style":158},[157],[15,5938,5940,5943],{"className":5939},[50],[15,5941],{"className":5942,"style":1096},[54],[15,5944,1032],{"className":5945},[59,366],[15,5947,5949],{"className":5948,"translate":19},[180],[15,5950,5952,6070],{"className":5951,"translate":19},[18],[15,5953,5955],{"className":5954},[23],[25,5956,5957],{"xmlns":27,"display":189},[29,5958,5959,6067],{},[32,5960,5961,5983,5985,5987,5989,5991,5993,5995,6001,6003,6005,6007,6009,6011,6013,6015,6047,6049,6055,6057,6059,6061,6063,6065],{},[195,5962,5963,5965],{},[35,5964,199],{},[32,5966,5967,5969,5971,5973,5975,5977,5979,5981],{},[35,5968,37],{},[110,5970,2470],{},[35,5972,5906],{},[110,5974,113],{"stretchy":112},[35,5976,769],{},[110,5978,4813],{},[115,5980,117],{},[110,5982,120],{"stretchy":112},[110,5984,113],{"stretchy":112},[35,5986,206],{},[35,5988,210],{"mathvariant":209},[35,5990,213],{},[110,5992,120],{"stretchy":112},[110,5994,123],{},[195,5996,5997,5999],{},[35,5998,199],{},[35,6000,37],{},[110,6002,113],{"stretchy":112},[35,6004,206],{},[35,6006,210],{"mathvariant":209},[35,6008,213],{},[110,6010,120],{"stretchy":112},[110,6012,2470],{},[35,6014,5906],{},[6016,6017,6018,6041],"munder",{},[6016,6019,6020,6038],{},[32,6021,6022,6024,6026,6028,6030,6032,6034,6036],{},[110,6023,1287],{},[110,6025,113],{"stretchy":112},[35,6027,769],{},[110,6029,4813],{},[115,6031,117],{},[110,6033,120],{"stretchy":112},[35,6035,244],{},[35,6037,213],{},[110,6039,6040],{"stretchy":46},"⏟",[32,6042,6043,6045],{},[110,6044,123],{},[115,6046,126],{},[110,6048,123],{},[195,6050,6051,6053],{},[35,6052,199],{},[35,6054,37],{},[110,6056,113],{"stretchy":112},[35,6058,206],{},[35,6060,210],{"mathvariant":209},[35,6062,213],{},[110,6064,120],{"stretchy":112},[35,6066,4375],{"mathvariant":209},[39,6068,6069],{"encoding":41},"D_{f+c(t-1)}(P\\|Q)\n=D_f(P\\|Q)+c\\underbrace{\\int(t-1)dQ}_{=0}\n=D_f(P\\|Q).",[15,6071,6073,6171,6241,6425],{"className":6072,"ariaHidden":46},[45],[15,6074,6076,6080,6147,6150,6153,6156,6159,6162,6165,6168],{"className":6075},[50],[15,6077],{"className":6078,"style":6079},[54],"height:1.1052em;vertical-align:-0.3552em;",[15,6081,6083,6086],{"className":6082},[59],[15,6084,199],{"className":6085,"style":277},[59,60],[15,6087,6089],{"className":6088},[281],[15,6090,6092,6138],{"className":6091},[285,286],[15,6093,6095,6135],{"className":6094},[290],[15,6096,6099],{"className":6097,"style":6098},[294],"height:0.3448em;",[15,6100,6102,6105],{"style":6101},"top:-2.5198em;margin-left:-0.0278em;margin-right:0.05em;",[15,6103],{"className":6104,"style":303},[302],[15,6106,6108],{"className":6107},[307,308,309,310],[15,6109,6111,6114,6117,6120,6123,6126,6129,6132],{"className":6110},[59,310],[15,6112,37],{"className":6113,"style":61},[59,60,310],[15,6115,2470],{"className":6116},[2591,310],[15,6118,5906],{"className":6119},[59,60,310],[15,6121,113],{"className":6122},[146,310],[15,6124,769],{"className":6125},[59,60,310],[15,6127,4813],{"className":6128},[2591,310],[15,6130,117],{"className":6131},[59,310],[15,6133,120],{"className":6134},[153,310],[15,6136,318],{"className":6137},[317],[15,6139,6141],{"className":6140},[290],[15,6142,6145],{"className":6143,"style":6144},[294],"height:0.3552em;",[15,6146],{},[15,6148,113],{"className":6149},[146],[15,6151,206],{"className":6152,"style":334},[59,60],[15,6154,210],{"className":6155},[59],[15,6157,213],{"className":6158},[59,60],[15,6160,120],{"className":6161},[153],[15,6163],{"className":6164,"style":158},[157],[15,6166,123],{"className":6167},[162],[15,6169],{"className":6170,"style":158},[157],[15,6172,6174,6177,6217,6220,6223,6226,6229,6232,6235,6238],{"className":6173},[50],[15,6175],{"className":6176,"style":270},[54],[15,6178,6180,6183],{"className":6179},[59],[15,6181,199],{"className":6182,"style":277},[59,60],[15,6184,6186],{"className":6185},[281],[15,6187,6189,6209],{"className":6188},[285,286],[15,6190,6192,6206],{"className":6191},[290],[15,6193,6195],{"className":6194,"style":295},[294],[15,6196,6197,6200],{"style":298},[15,6198],{"className":6199,"style":303},[302],[15,6201,6203],{"className":6202},[307,308,309,310],[15,6204,37],{"className":6205,"style":61},[59,60,310],[15,6207,318],{"className":6208},[317],[15,6210,6212],{"className":6211},[290],[15,6213,6215],{"className":6214,"style":325},[294],[15,6216],{},[15,6218,113],{"className":6219},[146],[15,6221,206],{"className":6222,"style":334},[59,60],[15,6224,210],{"className":6225},[59],[15,6227,213],{"className":6228},[59,60],[15,6230,120],{"className":6231},[153],[15,6233],{"className":6234,"style":2587},[157],[15,6236,2470],{"className":6237},[2591],[15,6239],{"className":6240,"style":2587},[157],[15,6242,6244,6248,6251,6254,6416,6419,6422],{"className":6243},[50],[15,6245],{"className":6246,"style":6247},[54],"height:3.5214em;vertical-align:-2.1614em;",[15,6249,5906],{"className":6250},[59,60],[15,6252],{"className":6253,"style":406},[157],[15,6255,6257],{"className":6256},[410,6016],[15,6258,6260,6407],{"className":6259},[285,286],[15,6261,6263,6404],{"className":6262},[290],[15,6264,6267,6286],{"className":6265,"style":6266},[294],"height:1.36em;",[15,6268,6270,6274],{"style":6269},"top:-1.1986em;",[15,6271],{"className":6272,"style":6273},[302],"height:3.36em;",[15,6275,6277],{"className":6276},[307,308,309,310],[15,6278,6280,6283],{"className":6279},[59,310],[15,6281,123],{"className":6282},[162,310],[15,6284,126],{"className":6285},[59,310],[15,6287,6289,6292],{"style":6288},"top:-3.36em;",[15,6290],{"className":6291,"style":6273},[302],[15,6293,6295],{"className":6294},[410,6016],[15,6296,6298,6395],{"className":6297},[285,286],[15,6299,6301,6392],{"className":6300},[290],[15,6302,6304,6354],{"className":6303,"style":6266},[294],[15,6305,6309,6312],{"className":6306,"style":6308},[6307],"svg-align","top:-1.8498em;",[15,6310],{"className":6311,"style":6273},[302],[15,6313,6317,6334,6344],{"className":6314,"style":6316},[6315],"stretchy","height:0.548em;min-width:1.6em;",[15,6318,6322],{"className":6319,"style":6321},[6320],"brace-left","height:0.548em;",[6323,6324,6330],"svg",{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6329},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","0.548em","0 0 400000 548","xMinYMin slice",[6331,6332],"path",{"d":6333},"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",[15,6335,6338],{"className":6336,"style":6321},[6337],"brace-center",[6323,6339,6341],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6340},"xMidYMin slice",[6331,6342],{"d":6343},"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",[15,6345,6348],{"className":6346,"style":6321},[6347],"brace-right",[6323,6349,6351],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6350},"xMaxYMin slice",[6331,6352],{"d":6353},"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",[15,6355,6356,6359],{"style":6288},[15,6357],{"className":6358,"style":6273},[302],[15,6360,6362,6365,6368,6371,6374,6377,6380,6383,6386,6389],{"className":6361},[59],[15,6363,1287],{"className":6364,"style":1487},[1484,1485,1486],[15,6366,113],{"className":6367},[146],[15,6369,769],{"className":6370},[59,60],[15,6372],{"className":6373,"style":2587},[157],[15,6375,4813],{"className":6376},[2591],[15,6378],{"className":6379,"style":2587},[157],[15,6381,117],{"className":6382},[59],[15,6384,120],{"className":6385},[153],[15,6387,244],{"className":6388},[59,60],[15,6390,213],{"className":6391},[59,60],[15,6393,318],{"className":6394},[317],[15,6396,6398],{"className":6397},[290],[15,6399,6402],{"className":6400,"style":6401},[294],"height:1.5103em;",[15,6403],{},[15,6405,318],{"className":6406},[317],[15,6408,6410],{"className":6409},[290],[15,6411,6414],{"className":6412,"style":6413},[294],"height:2.1614em;",[15,6415],{},[15,6417],{"className":6418,"style":158},[157],[15,6420,123],{"className":6421},[162],[15,6423],{"className":6424,"style":158},[157],[15,6426,6428,6431,6471,6474,6477,6480,6483,6486],{"className":6427},[50],[15,6429],{"className":6430,"style":270},[54],[15,6432,6434,6437],{"className":6433},[59],[15,6435,199],{"className":6436,"style":277},[59,60],[15,6438,6440],{"className":6439},[281],[15,6441,6443,6463],{"className":6442},[285,286],[15,6444,6446,6460],{"className":6445},[290],[15,6447,6449],{"className":6448,"style":295},[294],[15,6450,6451,6454],{"style":298},[15,6452],{"className":6453,"style":303},[302],[15,6455,6457],{"className":6456},[307,308,309,310],[15,6458,37],{"className":6459,"style":61},[59,60,310],[15,6461,318],{"className":6462},[317],[15,6464,6466],{"className":6465},[290],[15,6467,6469],{"className":6468,"style":325},[294],[15,6470],{},[15,6472,113],{"className":6473},[146],[15,6475,206],{"className":6476,"style":334},[59,60],[15,6478,210],{"className":6479},[59],[15,6481,213],{"className":6482},[59,60],[15,6484,120],{"className":6485},[153],[15,6487,4375],{"className":6488},[59],[11,6490,6491,6494,6495,6564,6565,6593,6594,6660],{},[1225,6492,6493],{},"结论："," ",[15,6496,6498,6515],{"className":6497,"translate":19},[18],[15,6499,6501],{"className":6500},[23],[25,6502,6503],{"xmlns":27},[29,6504,6505,6513],{},[32,6506,6507],{},[195,6508,6509,6511],{},[35,6510,199],{},[35,6512,37],{},[39,6514,4022],{"encoding":41},[15,6516,6518],{"className":6517,"ariaHidden":46},[45],[15,6519,6521,6524],{"className":6520},[50],[15,6522],{"className":6523,"style":4032},[54],[15,6525,6527,6530],{"className":6526},[59],[15,6528,199],{"className":6529,"style":277},[59,60],[15,6531,6533],{"className":6532},[281],[15,6534,6536,6556],{"className":6535},[285,286],[15,6537,6539,6553],{"className":6538},[290],[15,6540,6542],{"className":6541,"style":295},[294],[15,6543,6544,6547],{"style":298},[15,6545],{"className":6546,"style":303},[302],[15,6548,6550],{"className":6549},[307,308,309,310],[15,6551,37],{"className":6552,"style":61},[59,60,310],[15,6554,318],{"className":6555},[317],[15,6557,6559],{"className":6558},[290],[15,6560,6562],{"className":6561,"style":325},[294],[15,6563],{}," 只依赖 ",[15,6566,6568,6581],{"className":6567,"translate":19},[18],[15,6569,6571],{"className":6570},[23],[25,6572,6573],{"xmlns":27},[29,6574,6575,6579],{},[32,6576,6577],{},[35,6578,37],{},[39,6580,37],{"encoding":41},[15,6582,6584],{"className":6583,"ariaHidden":46},[45],[15,6585,6587,6590],{"className":6586},[50],[15,6588],{"className":6589,"style":55},[54],[15,6591,37],{"className":6592,"style":61},[59,60]," 在「模去 ",[15,6595,6597,6621],{"className":6596,"translate":19},[18],[15,6598,6600],{"className":6599},[23],[25,6601,6602],{"xmlns":27},[29,6603,6604,6618],{},[32,6605,6606,6608,6610,6612,6614,6616],{},[35,6607,5906],{},[110,6609,113],{"stretchy":112},[35,6611,769],{},[110,6613,4813],{},[115,6615,117],{},[110,6617,120],{"stretchy":112},[39,6619,6620],{"encoding":41},"c(t-1)",[15,6622,6624,6648],{"className":6623,"ariaHidden":46},[45],[15,6625,6627,6630,6633,6636,6639,6642,6645],{"className":6626},[50],[15,6628],{"className":6629,"style":139},[54],[15,6631,5906],{"className":6632},[59,60],[15,6634,113],{"className":6635},[146],[15,6637,769],{"className":6638},[59,60],[15,6640],{"className":6641,"style":2587},[157],[15,6643,4813],{"className":6644},[2591],[15,6646],{"className":6647,"style":2587},[157],[15,6649,6651,6654,6657],{"className":6650},[50],[15,6652],{"className":6653,"style":139},[54],[15,6655,117],{"className":6656},[59],[15,6658,120],{"className":6659},[153],"」之后的等价类。两个常用规范化是：",[6662,6663,6664,6733],"ol",{},[6665,6666,6667,6732],"li",{},[15,6668,6670,6693],{"className":6669,"translate":19},[18],[15,6671,6673],{"className":6672},[23],[25,6674,6675],{"xmlns":27},[29,6676,6677,6691],{},[32,6678,6679,6681,6683,6685,6687,6689],{},[35,6680,37],{},[110,6682,113],{"stretchy":112},[115,6684,117],{},[110,6686,120],{"stretchy":112},[110,6688,123],{},[115,6690,126],{},[39,6692,129],{"encoding":41},[15,6694,6696,6723],{"className":6695,"ariaHidden":46},[45],[15,6697,6699,6702,6705,6708,6711,6714,6717,6720],{"className":6698},[50],[15,6700],{"className":6701,"style":139},[54],[15,6703,37],{"className":6704,"style":61},[59,60],[15,6706,113],{"className":6707},[146],[15,6709,117],{"className":6710},[59],[15,6712,120],{"className":6713},[153],[15,6715],{"className":6716,"style":158},[157],[15,6718,123],{"className":6719},[162],[15,6721],{"className":6722,"style":158},[157],[15,6724,6726,6729],{"className":6725},[50],[15,6727],{"className":6728,"style":172},[54],[15,6730,126],{"className":6731},[59],"（本文采用）；",[6665,6734,6735,6800,6801,6905,6906,2745,7117,7145],{},[15,6736,6738,6761],{"className":6737,"translate":19},[18],[15,6739,6741],{"className":6740},[23],[25,6742,6743],{"xmlns":27},[29,6744,6745,6759],{},[32,6746,6747,6749,6751,6753,6755,6757],{},[35,6748,37],{},[110,6750,113],{"stretchy":112},[115,6752,117],{},[110,6754,120],{"stretchy":112},[110,6756,123],{},[115,6758,126],{},[39,6760,129],{"encoding":41},[15,6762,6764,6791],{"className":6763,"ariaHidden":46},[45],[15,6765,6767,6770,6773,6776,6779,6782,6785,6788],{"className":6766},[50],[15,6768],{"className":6769,"style":139},[54],[15,6771,37],{"className":6772,"style":61},[59,60],[15,6774,113],{"className":6775},[146],[15,6777,117],{"className":6778},[59],[15,6780,120],{"className":6781},[153],[15,6783],{"className":6784,"style":158},[157],[15,6786,123],{"className":6787},[162],[15,6789],{"className":6790,"style":158},[157],[15,6792,6794,6797],{"className":6793},[50],[15,6795],{"className":6796,"style":172},[54],[15,6798,126],{"className":6799},[59]," 且 ",[15,6802,6804,6834],{"className":6803,"translate":19},[18],[15,6805,6807],{"className":6806},[23],[25,6808,6809],{"xmlns":27},[29,6810,6811,6831],{},[32,6812,6813,6821,6823,6825,6827,6829],{},[6814,6815,6816,6818],"msup",{},[35,6817,37],{},[110,6819,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},"′",[110,6822,113],{"stretchy":112},[115,6824,117],{},[110,6826,120],{"stretchy":112},[110,6828,123],{},[115,6830,126],{},[39,6832,6833],{"encoding":41},"f'(1)=0",[15,6835,6837,6896],{"className":6836,"ariaHidden":46},[45],[15,6838,6840,6844,6878,6881,6884,6887,6890,6893],{"className":6839},[50],[15,6841],{"className":6842,"style":6843},[54],"height:1.0019em;vertical-align:-0.25em;",[15,6845,6847,6850],{"className":6846},[59],[15,6848,37],{"className":6849,"style":61},[59,60],[15,6851,6853],{"className":6852},[281],[15,6854,6856],{"className":6855},[285],[15,6857,6859],{"className":6858},[290],[15,6860,6863],{"className":6861,"style":6862},[294],"height:0.7519em;",[15,6864,6866,6869],{"style":6865},"top:-3.063em;margin-right:0.05em;",[15,6867],{"className":6868,"style":303},[302],[15,6870,6872],{"className":6871},[307,308,309,310],[15,6873,6875],{"className":6874},[59,310],[15,6876,6820],{"className":6877},[59,310],[15,6879,113],{"className":6880},[146],[15,6882,117],{"className":6883},[59],[15,6885,120],{"className":6886},[153],[15,6888],{"className":6889,"style":158},[157],[15,6891,123],{"className":6892},[162],[15,6894],{"className":6895,"style":158},[157],[15,6897,6899,6902],{"className":6898},[50],[15,6900],{"className":6901,"style":172},[54],[15,6903,126],{"className":6904},[59],"——此时由凸性 ",[15,6907,6909,6968],{"className":6908,"translate":19},[18],[15,6910,6912],{"className":6911},[23],[25,6913,6914],{"xmlns":27},[29,6915,6916,6965],{},[32,6917,6918,6920,6922,6924,6926,6929,6931,6933,6935,6937,6939,6945,6947,6949,6951,6953,6955,6957,6959,6961,6963],{},[35,6919,37],{},[110,6921,113],{"stretchy":112},[35,6923,769],{},[110,6925,120],{"stretchy":112},[110,6927,6928],{},"≥",[35,6930,37],{},[110,6932,113],{"stretchy":112},[115,6934,117],{},[110,6936,120],{"stretchy":112},[110,6938,2470],{},[6814,6940,6941,6943],{},[35,6942,37],{},[110,6944,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,6946,113],{"stretchy":112},[115,6948,117],{},[110,6950,120],{"stretchy":112},[110,6952,113],{"stretchy":112},[35,6954,769],{},[110,6956,4813],{},[115,6958,117],{},[110,6960,120],{"stretchy":112},[110,6962,123],{},[115,6964,126],{},[39,6966,6967],{"encoding":41},"f(t)\\ge f(1)+f'(1)(t-1)=0",[15,6969,6971,6998,7025,7087,7108],{"className":6970,"ariaHidden":46},[45],[15,6972,6974,6977,6980,6983,6986,6989,6992,6995],{"className":6973},[50],[15,6975],{"className":6976,"style":139},[54],[15,6978,37],{"className":6979,"style":61},[59,60],[15,6981,113],{"className":6982},[146],[15,6984,769],{"className":6985},[59,60],[15,6987,120],{"className":6988},[153],[15,6990],{"className":6991,"style":158},[157],[15,6993,6928],{"className":6994},[162],[15,6996],{"className":6997,"style":158},[157],[15,6999,7001,7004,7007,7010,7013,7016,7019,7022],{"className":7000},[50],[15,7002],{"className":7003,"style":139},[54],[15,7005,37],{"className":7006,"style":61},[59,60],[15,7008,113],{"className":7009},[146],[15,7011,117],{"className":7012},[59],[15,7014,120],{"className":7015},[153],[15,7017],{"className":7018,"style":2587},[157],[15,7020,2470],{"className":7021},[2591],[15,7023],{"className":7024,"style":2587},[157],[15,7026,7028,7031,7063,7066,7069,7072,7075,7078,7081,7084],{"className":7027},[50],[15,7029],{"className":7030,"style":6843},[54],[15,7032,7034,7037],{"className":7033},[59],[15,7035,37],{"className":7036,"style":61},[59,60],[15,7038,7040],{"className":7039},[281],[15,7041,7043],{"className":7042},[285],[15,7044,7046],{"className":7045},[290],[15,7047,7049],{"className":7048,"style":6862},[294],[15,7050,7051,7054],{"style":6865},[15,7052],{"className":7053,"style":303},[302],[15,7055,7057],{"className":7056},[307,308,309,310],[15,7058,7060],{"className":7059},[59,310],[15,7061,6820],{"className":7062},[59,310],[15,7064,113],{"className":7065},[146],[15,7067,117],{"className":7068},[59],[15,7070,120],{"className":7071},[153],[15,7073,113],{"className":7074},[146],[15,7076,769],{"className":7077},[59,60],[15,7079],{"className":7080,"style":2587},[157],[15,7082,4813],{"className":7083},[2591],[15,7085],{"className":7086,"style":2587},[157],[15,7088,7090,7093,7096,7099,7102,7105],{"className":7089},[50],[15,7091],{"className":7092,"style":139},[54],[15,7094,117],{"className":7095},[59],[15,7097,120],{"className":7098},[153],[15,7100],{"className":7101,"style":158},[157],[15,7103,123],{"className":7104},[162],[15,7106],{"className":7107,"style":158},[157],[15,7109,7111,7114],{"className":7110},[50],[15,7112],{"className":7113,"style":172},[54],[15,7115,126],{"className":7116},[59],[15,7118,7120,7133],{"className":7119,"translate":19},[18],[15,7121,7123],{"className":7122},[23],[25,7124,7125],{"xmlns":27},[29,7126,7127,7131],{},[32,7128,7129],{},[35,7130,37],{},[39,7132,37],{"encoding":41},[15,7134,7136],{"className":7135,"ariaHidden":46},[45],[15,7137,7139,7142],{"className":7138},[50],[15,7140],{"className":7141,"style":55},[54],[15,7143,37],{"className":7144,"style":61},[59,60]," 在整个定义域上非负。",[11,7147,7148,7149,7234,7235,7288,7289,7358],{},"第 3 节里的 KL 的 ",[15,7150,7152,7181],{"className":7151,"translate":19},[18],[15,7153,7155],{"className":7154},[23],[25,7156,7157],{"xmlns":27},[29,7158,7159,7179],{},[32,7160,7161,7163,7165,7167,7169,7171,7173,7175,7177],{},[35,7162,37],{},[110,7164,113],{"stretchy":112},[35,7166,769],{},[110,7168,120],{"stretchy":112},[110,7170,123],{},[35,7172,769],{},[35,7174,4100],{},[110,7176,4103],{},[35,7178,769],{},[39,7180,4108],{"encoding":41},[15,7182,7184,7211],{"className":7183,"ariaHidden":46},[45],[15,7185,7187,7190,7193,7196,7199,7202,7205,7208],{"className":7186},[50],[15,7188],{"className":7189,"style":139},[54],[15,7191,37],{"className":7192,"style":61},[59,60],[15,7194,113],{"className":7195},[146],[15,7197,769],{"className":7198},[59,60],[15,7200,120],{"className":7201},[153],[15,7203],{"className":7204,"style":158},[157],[15,7206,123],{"className":7207},[162],[15,7209],{"className":7210,"style":158},[157],[15,7212,7214,7217,7220,7223,7228,7231],{"className":7213},[50],[15,7215],{"className":7216,"style":55},[54],[15,7218,769],{"className":7219},[59,60],[15,7221],{"className":7222,"style":406},[157],[15,7224,4154,7226],{"className":7225},[1484],[15,7227,4158],{"style":4157},[15,7229],{"className":7230,"style":406},[157],[15,7232,769],{"className":7233},[59,60]," 不满足第 2 条（它在 ",[15,7236,7238,7257],{"className":7237,"translate":19},[18],[15,7239,7241],{"className":7240},[23],[25,7242,7243],{"xmlns":27},[29,7244,7245,7254],{},[32,7246,7247,7249,7252],{},[35,7248,769],{},[110,7250,7251],{},"\u003C",[115,7253,117],{},[39,7255,7256],{"encoding":41},"t\u003C1",[15,7258,7260,7279],{"className":7259,"ariaHidden":46},[45],[15,7261,7263,7267,7270,7273,7276],{"className":7262},[50],[15,7264],{"className":7265,"style":7266},[54],"height:0.6542em;vertical-align:-0.0391em;",[15,7268,769],{"className":7269},[59,60],[15,7271],{"className":7272,"style":158},[157],[15,7274,7251],{"className":7275},[162],[15,7277],{"className":7278,"style":158},[157],[15,7280,7282,7285],{"className":7281},[50],[15,7283],{"className":7284,"style":172},[54],[15,7286,117],{"className":7287},[59]," 时取负值），但这无妨：",[15,7290,7292,7309],{"className":7291,"translate":19},[18],[15,7293,7295],{"className":7294},[23],[25,7296,7297],{"xmlns":27},[29,7298,7299,7307],{},[32,7300,7301],{},[195,7302,7303,7305],{},[35,7304,199],{},[35,7306,37],{},[39,7308,4022],{"encoding":41},[15,7310,7312],{"className":7311,"ariaHidden":46},[45],[15,7313,7315,7318],{"className":7314},[50],[15,7316],{"className":7317,"style":4032},[54],[15,7319,7321,7324],{"className":7320},[59],[15,7322,199],{"className":7323,"style":277},[59,60],[15,7325,7327],{"className":7326},[281],[15,7328,7330,7350],{"className":7329},[285,286],[15,7331,7333,7347],{"className":7332},[290],[15,7334,7336],{"className":7335,"style":295},[294],[15,7337,7338,7341],{"style":298},[15,7339],{"className":7340,"style":303},[302],[15,7342,7344],{"className":7343},[307,308,309,310],[15,7345,37],{"className":7346,"style":61},[59,60,310],[15,7348,318],{"className":7349},[317],[15,7351,7353],{"className":7352},[290],[15,7354,7356],{"className":7355,"style":325},[294],[15,7357],{}," 仍然非负（见 4.1），因为「逐点非负」从来不是 f-散度非负性的必要条件。",[2311,7360,7362],{"id":7361},"_14-等价书写形式","1.4 等价书写形式",[15,7364,7366],{"className":7365,"translate":19},[180],[15,7367,7369,7603],{"className":7368,"translate":19},[18],[15,7370,7372],{"className":7371},[23],[25,7373,7374],{"xmlns":27,"display":189},[29,7375,7376,7600],{},[1243,7377,7378,7450,7522],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,7379,7380,7402],{},[1252,7381,7382],{},[1255,7383,7384],{"scriptlevel":126,"displaystyle":46},[32,7385,7386,7392,7394,7396,7398,7400],{},[195,7387,7388,7390],{},[35,7389,199],{},[35,7391,37],{},[110,7393,113],{"stretchy":112},[35,7395,206],{},[35,7397,210],{"mathvariant":209},[35,7399,213],{},[110,7401,120],{"stretchy":112},[1252,7403,7404],{},[1255,7405,7406],{"scriptlevel":126,"displaystyle":46},[32,7407,7408,7410,7412,7418,7420],{},[32,7409],{},[110,7411,123],{},[195,7413,7414,7416],{},[35,7415,223],{"mathvariant":222},[35,7417,213],{},[1297,7419,1304],{},[32,7421,7422,7424,7426,7428,7448],{},[110,7423,230],{"fence":46},[35,7425,37],{},[1297,7427,1304],{},[32,7429,7430,7432,7446],{},[110,7431,113],{"fence":46},[238,7433,7434,7440],{},[32,7435,7436,7438],{},[35,7437,244],{},[35,7439,206],{},[32,7441,7442,7444],{},[35,7443,244],{},[35,7445,213],{},[110,7447,120],{"fence":46},[110,7449,257],{"fence":46},[1249,7451,7452,7458],{},[1252,7453,7454],{},[1255,7455,7456],{"scriptlevel":126,"displaystyle":46},[32,7457],{},[1252,7459,7460],{},[1255,7461,7462],{"scriptlevel":126,"displaystyle":46},[32,7463,7464,7466,7468,7474,7476],{},[32,7465],{},[110,7467,123],{},[195,7469,7470,7472],{},[35,7471,223],{"mathvariant":222},[35,7473,206],{},[1297,7475,1304],{},[32,7477,7478,7480,7494,7496,7498,7500,7520],{},[110,7479,230],{"fence":46},[238,7481,7482,7488],{},[32,7483,7484,7486],{},[35,7485,244],{},[35,7487,213],{},[32,7489,7490,7492],{},[35,7491,244],{},[35,7493,206],{},[1297,7495,1299],{},[35,7497,37],{},[1297,7499,1304],{},[32,7501,7502,7504,7518],{},[110,7503,113],{"fence":46},[238,7505,7506,7512],{},[32,7507,7508,7510],{},[35,7509,244],{},[35,7511,206],{},[32,7513,7514,7516],{},[35,7515,244],{},[35,7517,213],{},[110,7519,120],{"fence":46},[110,7521,257],{"fence":46},[1249,7523,7524,7530],{},[1252,7525,7526],{},[1255,7527,7528],{"scriptlevel":126,"displaystyle":46},[32,7529],{},[1252,7531,7532],{},[1255,7533,7534],{"scriptlevel":126,"displaystyle":46},[32,7535,7536,7538,7540,7546,7548,7598],{},[32,7537],{},[110,7539,123],{},[195,7541,7542,7544],{},[35,7543,223],{"mathvariant":222},[35,7545,206],{},[1297,7547,1304],{},[32,7549,7550,7552,7574,7576,7596],{},[110,7551,230],{"fence":46},[7553,7554,7555,7557,7571],"msubsup",{},[35,7556,37],{},[32,7558,7559,7562,7565,7568],{},[35,7560,7561],{},"s",[35,7563,7564],{},"k",[35,7566,7567],{},"e",[35,7569,7570],{},"w",[110,7572,7573],{"lspace":1247,"rspace":1247},"∗",[1297,7575,1304],{},[32,7577,7578,7580,7594],{},[110,7579,113],{"fence":46},[238,7581,7582,7588],{},[32,7583,7584,7586],{},[35,7585,244],{},[35,7587,213],{},[32,7589,7590,7592],{},[35,7591,244],{},[35,7593,206],{},[110,7595,120],{"fence":46},[110,7597,257],{"fence":46},[110,7599,551],{"separator":46},[39,7601,7602],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\[2pt]\n&=\\mathbb E_P\\!\\left[\\frac{dQ}{dP}\\,\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\mathbb E_P\\!\\left[\nf^{*}_{skew}\\!\\left(\\frac{dQ}{dP}\\right)\\right],\n\\end{aligned}",[15,7604,7606],{"className":7605,"ariaHidden":46},[45],[15,7607,7609,7613],{"className":7608},[50],[15,7610],{"className":7611,"style":7612},[54],"height:7.8001em;vertical-align:-3.65em;",[15,7614,7616],{"className":7615},[59],[15,7617,7619,7725],{"className":7618},[1243],[15,7620,7622],{"className":7621},[1360],[15,7623,7625,7716],{"className":7624},[285,286],[15,7626,7628,7713],{"className":7627},[290],[15,7629,7632,7696,7704],{"className":7630,"style":7631},[294],"height:4.15em;",[15,7633,7635,7638],{"style":7634},"top:-6.15em;",[15,7636],{"className":7637,"style":1377},[302],[15,7639,7641,7681,7684,7687,7690,7693],{"className":7640},[59],[15,7642,7644,7647],{"className":7643},[59],[15,7645,199],{"className":7646,"style":277},[59,60],[15,7648,7650],{"className":7649},[281],[15,7651,7653,7673],{"className":7652},[285,286],[15,7654,7656,7670],{"className":7655},[290],[15,7657,7659],{"className":7658,"style":295},[294],[15,7660,7661,7664],{"style":298},[15,7662],{"className":7663,"style":303},[302],[15,7665,7667],{"className":7666},[307,308,309,310],[15,7668,37],{"className":7669,"style":61},[59,60,310],[15,7671,318],{"className":7672},[317],[15,7674,7676],{"className":7675},[290],[15,7677,7679],{"className":7678,"style":325},[294],[15,7680],{},[15,7682,113],{"className":7683},[146],[15,7685,206],{"className":7686,"style":334},[59,60],[15,7688,210],{"className":7689},[59],[15,7691,213],{"className":7692},[59,60],[15,7694,120],{"className":7695},[153],[15,7697,7698,7701],{"style":1373},[15,7699],{"className":7700,"style":1377},[302],[15,7702],{"className":7703},[59],[15,7705,7707,7710],{"style":7706},"top:-0.75em;",[15,7708],{"className":7709,"style":1377},[302],[15,7711],{"className":7712},[59],[15,7714,318],{"className":7715},[317],[15,7717,7719],{"className":7718},[290],[15,7720,7723],{"className":7721,"style":7722},[294],"height:3.65em;",[15,7724],{},[15,7726,7728],{"className":7727},[1451],[15,7729,7731,8406],{"className":7730},[285,286],[15,7732,7734,8403],{"className":7733},[290],[15,7735,7737,7910,8155],{"className":7736,"style":7631},[294],[15,7738,7739,7742],{"style":7634},[15,7740],{"className":7741,"style":1377},[302],[15,7743,7745,7748,7751,7754,7757,7797,7800,7803],{"className":7744},[59],[15,7746],{"className":7747},[59],[15,7749],{"className":7750,"style":158},[157],[15,7752,123],{"className":7753},[162],[15,7755],{"className":7756,"style":158},[157],[15,7758,7760,7763],{"className":7759},[59],[15,7761,223],{"className":7762},[59,366],[15,7764,7766],{"className":7765},[281],[15,7767,7769,7789],{"className":7768},[285,286],[15,7770,7772,7786],{"className":7771},[290],[15,7773,7775],{"className":7774,"style":379},[294],[15,7776,7777,7780],{"style":382},[15,7778],{"className":7779,"style":303},[302],[15,7781,7783],{"className":7782},[307,308,309,310],[15,7784,213],{"className":7785},[59,60,310],[15,7787,318],{"className":7788},[317],[15,7790,7792],{"className":7791},[290],[15,7793,7795],{"className":7794,"style":325},[294],[15,7796],{},[15,7798],{"className":7799,"style":1512},[157],[15,7801],{"className":7802,"style":406},[157],[15,7804,7806,7812,7815,7818,7821,7904],{"className":7805},[410],[15,7807,7809],{"className":7808,"style":415},[146,414],[15,7810,230],{"className":7811},[419,309],[15,7813,37],{"className":7814,"style":61},[59,60],[15,7816],{"className":7817,"style":1512},[157],[15,7819],{"className":7820,"style":406},[157],[15,7822,7824,7830,7898],{"className":7823},[410],[15,7825,7827],{"className":7826,"style":415},[146,414],[15,7828,113],{"className":7829},[419,309],[15,7831,7833,7836,7895],{"className":7832},[59],[15,7834],{"className":7835},[146,441],[15,7837,7839],{"className":7838},[238],[15,7840,7842,7887],{"className":7841},[285,286],[15,7843,7845,7884],{"className":7844},[290],[15,7846,7848,7862,7870],{"className":7847,"style":454},[294],[15,7849,7850,7853],{"style":457},[15,7851],{"className":7852,"style":461},[302],[15,7854,7856,7859],{"className":7855},[59],[15,7857,244],{"className":7858},[59,60],[15,7860,213],{"className":7861},[59,60],[15,7863,7864,7867],{"style":473},[15,7865],{"className":7866,"style":461},[302],[15,7868],{"className":7869,"style":481},[480],[15,7871,7872,7875],{"style":484},[15,7873],{"className":7874,"style":461},[302],[15,7876,7878,7881],{"className":7877},[59],[15,7879,244],{"className":7880},[59,60],[15,7882,206],{"className":7883,"style":334},[59,60],[15,7885,318],{"className":7886},[317],[15,7888,7890],{"className":7889},[290],[15,7891,7893],{"className":7892,"style":506},[294],[15,7894],{},[15,7896],{"className":7897},[153,441],[15,7899,7901],{"className":7900,"style":415},[153,414],[15,7902,120],{"className":7903},[419,309],[15,7905,7907],{"className":7906,"style":415},[153,414],[15,7908,257],{"className":7909},[419,309],[15,7911,7912,7915],{"style":1373},[15,7913],{"className":7914,"style":1377},[302],[15,7916,7918,7921,7924,7927,7930,7971,7974,7977],{"className":7917},[59],[15,7919],{"className":7920},[59],[15,7922],{"className":7923,"style":158},[157],[15,7925,123],{"className":7926},[162],[15,7928],{"className":7929,"style":158},[157],[15,7931,7933,7936],{"className":7932},[59],[15,7934,223],{"className":7935},[59,366],[15,7937,7939],{"className":7938},[281],[15,7940,7942,7962],{"className":7941},[285,286],[15,7943,7945,7959],{"className":7944},[290],[15,7946,7948],{"className":7947,"style":379},[294],[15,7949,7950,7953],{"style":382},[15,7951],{"className":7952,"style":303},[302],[15,7954,7956],{"className":7955},[307,308,309,310],[15,7957,206],{"className":7958,"style":334},[59,60,310],[15,7960,318],{"className":7961},[317],[15,7963,7965],{"className":7964},[290],[15,7966,7969],{"className":7967,"style":7968},[294],"height:0.15em;",[15,7970],{},[15,7972],{"className":7973,"style":1512},[157],[15,7975],{"className":7976,"style":406},[157],[15,7978,7980,7986,8054,8057,8060,8063,8066,8149],{"className":7979},[410],[15,7981,7983],{"className":7982,"style":415},[146,414],[15,7984,230],{"className":7985},[419,309],[15,7987,7989,7992,8051],{"className":7988},[59],[15,7990],{"className":7991},[146,441],[15,7993,7995],{"className":7994},[238],[15,7996,7998,8043],{"className":7997},[285,286],[15,7999,8001,8040],{"className":8000},[290],[15,8002,8004,8018,8026],{"className":8003,"style":454},[294],[15,8005,8006,8009],{"style":457},[15,8007],{"className":8008,"style":461},[302],[15,8010,8012,8015],{"className":8011},[59],[15,8013,244],{"className":8014},[59,60],[15,8016,206],{"className":8017,"style":334},[59,60],[15,8019,8020,8023],{"style":473},[15,8021],{"className":8022,"style":461},[302],[15,8024],{"className":8025,"style":481},[480],[15,8027,8028,8031],{"style":484},[15,8029],{"className":8030,"style":461},[302],[15,8032,8034,8037],{"className":8033},[59],[15,8035,244],{"className":8036},[59,60],[15,8038,213],{"className":8039},[59,60],[15,8041,318],{"className":8042},[317],[15,8044,8046],{"className":8045},[290],[15,8047,8049],{"className":8048,"style":3778},[294],[15,8050],{},[15,8052],{"className":8053},[153,441],[15,8055],{"className":8056,"style":406},[157],[15,8058,37],{"className":8059,"style":61},[59,60],[15,8061],{"className":8062,"style":1512},[157],[15,8064],{"className":8065,"style":406},[157],[15,8067,8069,8075,8143],{"className":8068},[410],[15,8070,8072],{"className":8071,"style":415},[146,414],[15,8073,113],{"className":8074},[419,309],[15,8076,8078,8081,8140],{"className":8077},[59],[15,8079],{"className":8080},[146,441],[15,8082,8084],{"className":8083},[238],[15,8085,8087,8132],{"className":8086},[285,286],[15,8088,8090,8129],{"className":8089},[290],[15,8091,8093,8107,8115],{"className":8092,"style":454},[294],[15,8094,8095,8098],{"style":457},[15,8096],{"className":8097,"style":461},[302],[15,8099,8101,8104],{"className":8100},[59],[15,8102,244],{"className":8103},[59,60],[15,8105,213],{"className":8106},[59,60],[15,8108,8109,8112],{"style":473},[15,8110],{"className":8111,"style":461},[302],[15,8113],{"className":8114,"style":481},[480],[15,8116,8117,8120],{"style":484},[15,8118],{"className":8119,"style":461},[302],[15,8121,8123,8126],{"className":8122},[59],[15,8124,244],{"className":8125},[59,60],[15,8127,206],{"className":8128,"style":334},[59,60],[15,8130,318],{"className":8131},[317],[15,8133,8135],{"className":8134},[290],[15,8136,8138],{"className":8137,"style":506},[294],[15,8139],{},[15,8141],{"className":8142},[153,441],[15,8144,8146],{"className":8145,"style":415},[153,414],[15,8147,120],{"className":8148},[419,309],[15,8150,8152],{"className":8151,"style":415},[153,414],[15,8153,257],{"className":8154},[419,309],[15,8156,8157,8160],{"style":7706},[15,8158],{"className":8159,"style":1377},[302],[15,8161,8163,8166,8169,8172,8175,8215,8218,8221,8397,8400],{"className":8162},[59],[15,8164],{"className":8165},[59],[15,8167],{"className":8168,"style":158},[157],[15,8170,123],{"className":8171},[162],[15,8173],{"className":8174,"style":158},[157],[15,8176,8178,8181],{"className":8177},[59],[15,8179,223],{"className":8180},[59,366],[15,8182,8184],{"className":8183},[281],[15,8185,8187,8207],{"className":8186},[285,286],[15,8188,8190,8204],{"className":8189},[290],[15,8191,8193],{"className":8192,"style":379},[294],[15,8194,8195,8198],{"style":382},[15,8196],{"className":8197,"style":303},[302],[15,8199,8201],{"className":8200},[307,308,309,310],[15,8202,206],{"className":8203,"style":334},[59,60,310],[15,8205,318],{"className":8206},[317],[15,8208,8210],{"className":8209},[290],[15,8211,8213],{"className":8212,"style":7968},[294],[15,8214],{},[15,8216],{"className":8217,"style":1512},[157],[15,8219],{"className":8220,"style":406},[157],[15,8222,8224,8230,8302,8305,8308,8391],{"className":8223},[410],[15,8225,8227],{"className":8226,"style":415},[146,414],[15,8228,230],{"className":8229},[419,309],[15,8231,8233,8236],{"className":8232},[59],[15,8234,37],{"className":8235,"style":61},[59,60],[15,8237,8239],{"className":8238},[281],[15,8240,8242,8293],{"className":8241},[285,286],[15,8243,8245,8290],{"className":8244},[290],[15,8246,8249,8275],{"className":8247,"style":8248},[294],"height:0.7387em;",[15,8250,8252,8255],{"style":8251},"top:-2.453em;margin-left:-0.1076em;margin-right:0.05em;",[15,8253],{"className":8254,"style":303},[302],[15,8256,8258],{"className":8257},[307,308,309,310],[15,8259,8261,8264,8268,8271],{"className":8260},[59,310],[15,8262,7561],{"className":8263},[59,60,310],[15,8265,7564],{"className":8266,"style":8267},[59,60,310],"margin-right:0.0315em;",[15,8269,7567],{"className":8270},[59,60,310],[15,8272,7570],{"className":8273,"style":8274},[59,60,310],"margin-right:0.0269em;",[15,8276,8278,8281],{"style":8277},"top:-3.113em;margin-right:0.05em;",[15,8279],{"className":8280,"style":303},[302],[15,8282,8284],{"className":8283},[307,308,309,310],[15,8285,8287],{"className":8286},[59,310],[15,8288,7573],{"className":8289},[59,310],[15,8291,318],{"className":8292},[317],[15,8294,8296],{"className":8295},[290],[15,8297,8300],{"className":8298,"style":8299},[294],"height:0.247em;",[15,8301],{},[15,8303],{"className":8304,"style":1512},[157],[15,8306],{"className":8307,"style":406},[157],[15,8309,8311,8317,8385],{"className":8310},[410],[15,8312,8314],{"className":8313,"style":415},[146,414],[15,8315,113],{"className":8316},[419,309],[15,8318,8320,8323,8382],{"className":8319},[59],[15,8321],{"className":8322},[146,441],[15,8324,8326],{"className":8325},[238],[15,8327,8329,8374],{"className":8328},[285,286],[15,8330,8332,8371],{"className":8331},[290],[15,8333,8335,8349,8357],{"className":8334,"style":454},[294],[15,8336,8337,8340],{"style":457},[15,8338],{"className":8339,"style":461},[302],[15,8341,8343,8346],{"className":8342},[59],[15,8344,244],{"className":8345},[59,60],[15,8347,206],{"className":8348,"style":334},[59,60],[15,8350,8351,8354],{"style":473},[15,8352],{"className":8353,"style":461},[302],[15,8355],{"className":8356,"style":481},[480],[15,8358,8359,8362],{"style":484},[15,8360],{"className":8361,"style":461},[302],[15,8363,8365,8368],{"className":8364},[59],[15,8366,244],{"className":8367},[59,60],[15,8369,213],{"className":8370},[59,60],[15,8372,318],{"className":8373},[317],[15,8375,8377],{"className":8376},[290],[15,8378,8380],{"className":8379,"style":3778},[294],[15,8381],{},[15,8383],{"className":8384},[153,441],[15,8386,8388],{"className":8387,"style":415},[153,414],[15,8389,120],{"className":8390},[419,309],[15,8392,8394],{"className":8393,"style":415},[153,414],[15,8395,257],{"className":8396},[419,309],[15,8398],{"className":8399,"style":406},[157],[15,8401,551],{"className":8402},[573],[15,8404,318],{"className":8405},[317],[15,8407,8409],{"className":8408},[290],[15,8410,8412],{"className":8411,"style":7722},[294],[15,8413],{},[11,8415,2250,8416,8596,8597,8638,8639,8667,8668,8748],{},[15,8417,8419,8471],{"className":8418,"translate":19},[18],[15,8420,8422],{"className":8421},[23],[25,8423,8424],{"xmlns":27},[29,8425,8426,8468],{},[32,8427,8428,8444,8446,8448,8450,8452,8454,8456,8458,8460,8462,8464,8466],{},[7553,8429,8430,8432,8442],{},[35,8431,37],{},[32,8433,8434,8436,8438,8440],{},[35,8435,7561],{},[35,8437,7564],{},[35,8439,7567],{},[35,8441,7570],{},[110,8443,7573],{"lspace":1247,"rspace":1247},[110,8445,113],{"stretchy":112},[35,8447,769],{},[110,8449,120],{"stretchy":112},[110,8451,123],{},[35,8453,769],{},[1297,8455,1299],{},[35,8457,37],{},[110,8459,113],{"stretchy":112},[115,8461,117],{},[35,8463,941],{"mathvariant":209},[35,8465,769],{},[110,8467,120],{"stretchy":112},[39,8469,8470],{"encoding":41},"f^{*}_{skew}(t)=t\\,f(1\u002Ft)",[15,8472,8474,8568],{"className":8473,"ariaHidden":46},[45],[15,8475,8477,8481,8550,8553,8556,8559,8562,8565],{"className":8476},[50],[15,8478],{"className":8479,"style":8480},[54],"height:1.0331em;vertical-align:-0.2831em;",[15,8482,8484,8487],{"className":8483},[59],[15,8485,37],{"className":8486,"style":61},[59,60],[15,8488,8490],{"className":8489},[281],[15,8491,8493,8541],{"className":8492},[285,286],[15,8494,8496,8538],{"className":8495},[290],[15,8497,8500,8524],{"className":8498,"style":8499},[294],"height:0.6887em;",[15,8501,8503,8506],{"style":8502},"top:-2.4169em;margin-left:-0.1076em;margin-right:0.05em;",[15,8504],{"className":8505,"style":303},[302],[15,8507,8509],{"className":8508},[307,308,309,310],[15,8510,8512,8515,8518,8521],{"className":8511},[59,310],[15,8513,7561],{"className":8514},[59,60,310],[15,8516,7564],{"className":8517,"style":8267},[59,60,310],[15,8519,7567],{"className":8520},[59,60,310],[15,8522,7570],{"className":8523,"style":8274},[59,60,310],[15,8525,8526,8529],{"style":6865},[15,8527],{"className":8528,"style":303},[302],[15,8530,8532],{"className":8531},[307,308,309,310],[15,8533,8535],{"className":8534},[59,310],[15,8536,7573],{"className":8537},[59,310],[15,8539,318],{"className":8540},[317],[15,8542,8544],{"className":8543},[290],[15,8545,8548],{"className":8546,"style":8547},[294],"height:0.2831em;",[15,8549],{},[15,8551,113],{"className":8552},[146],[15,8554,769],{"className":8555},[59,60],[15,8557,120],{"className":8558},[153],[15,8560],{"className":8561,"style":158},[157],[15,8563,123],{"className":8564},[162],[15,8566],{"className":8567,"style":158},[157],[15,8569,8571,8574,8577,8580,8583,8586,8590,8593],{"className":8570},[50],[15,8572],{"className":8573,"style":139},[54],[15,8575,769],{"className":8576},[59,60],[15,8578],{"className":8579,"style":406},[157],[15,8581,37],{"className":8582,"style":61},[59,60],[15,8584,113],{"className":8585},[146],[15,8587,8589],{"className":8588},[59],"1\u002F",[15,8591,769],{"className":8592},[59,60],[15,8594,120],{"className":8595},[153]," 是后面 4.3 节的「斜共轭」。最后一个等式说明：交换 ",[15,8598,8600,8617],{"className":8599,"translate":19},[18],[15,8601,8603],{"className":8602},[23],[25,8604,8605],{"xmlns":27},[29,8606,8607,8615],{},[32,8608,8609,8611,8613],{},[35,8610,206],{},[110,8612,551],{"separator":46},[35,8614,213],{},[39,8616,556],{"encoding":41},[15,8618,8620],{"className":8619,"ariaHidden":46},[45],[15,8621,8623,8626,8629,8632,8635],{"className":8622},[50],[15,8624],{"className":8625,"style":566},[54],[15,8627,206],{"className":8628,"style":334},[59,60],[15,8630,551],{"className":8631},[573],[15,8633],{"className":8634,"style":406},[157],[15,8636,213],{"className":8637},[59,60]," 只是把 ",[15,8640,8642,8655],{"className":8641,"translate":19},[18],[15,8643,8645],{"className":8644},[23],[25,8646,8647],{"xmlns":27},[29,8648,8649,8653],{},[32,8650,8651],{},[35,8652,37],{},[39,8654,37],{"encoding":41},[15,8656,8658],{"className":8657,"ariaHidden":46},[45],[15,8659,8661,8664],{"className":8660},[50],[15,8662],{"className":8663,"style":55},[54],[15,8665,37],{"className":8666,"style":61},[59,60]," 换成 ",[15,8669,8671,8702],{"className":8670,"translate":19},[18],[15,8672,8674],{"className":8673},[23],[25,8675,8676],{"xmlns":27},[29,8677,8678,8699],{},[32,8679,8680,8682,8685,8687,8689,8691,8693,8695,8697],{},[35,8681,769],{},[110,8683,8684],{},"↦",[35,8686,769],{},[35,8688,37],{},[110,8690,113],{"stretchy":112},[115,8692,117],{},[35,8694,941],{"mathvariant":209},[35,8696,769],{},[110,8698,120],{"stretchy":112},[39,8700,8701],{"encoding":41},"t\\mapsto t f(1\u002Ft)",[15,8703,8705,8724],{"className":8704,"ariaHidden":46},[45],[15,8706,8708,8712,8715,8718,8721],{"className":8707},[50],[15,8709],{"className":8710,"style":8711},[54],"height:0.6261em;vertical-align:-0.011em;",[15,8713,769],{"className":8714},[59,60],[15,8716],{"className":8717,"style":158},[157],[15,8719,8684],{"className":8720},[162],[15,8722],{"className":8723,"style":158},[157],[15,8725,8727,8730,8733,8736,8739,8742,8745],{"className":8726},[50],[15,8728],{"className":8729,"style":139},[54],[15,8731,769],{"className":8732},[59,60],[15,8734,37],{"className":8735,"style":61},[59,60],[15,8737,113],{"className":8738},[146],[15,8740,8589],{"className":8741},[59],[15,8743,769],{"className":8744},[59,60],[15,8746,120],{"className":8747},[153],"，这对推导「反向 KL」之类的对称性非常方便。",[528,8750,8752,8753,8781,8782],{"id":8751},"_2-为何-fff-凸且-f10f10f10","2. 为何 ",[15,8754,8756,8769],{"className":8755,"translate":19},[18],[15,8757,8759],{"className":8758},[23],[25,8760,8761],{"xmlns":27},[29,8762,8763,8767],{},[32,8764,8765],{},[35,8766,37],{},[39,8768,37],{"encoding":41},[15,8770,8772],{"className":8771,"ariaHidden":46},[45],[15,8773,8775,8778],{"className":8774},[50],[15,8776],{"className":8777,"style":55},[54],[15,8779,37],{"className":8780,"style":61},[59,60]," 凸且 ",[15,8783,8785,8808],{"className":8784,"translate":19},[18],[15,8786,8788],{"className":8787},[23],[25,8789,8790],{"xmlns":27},[29,8791,8792,8806],{},[32,8793,8794,8796,8798,8800,8802,8804],{},[35,8795,37],{},[110,8797,113],{"stretchy":112},[115,8799,117],{},[110,8801,120],{"stretchy":112},[110,8803,123],{},[115,8805,126],{},[39,8807,129],{"encoding":41},[15,8809,8811,8838],{"className":8810,"ariaHidden":46},[45],[15,8812,8814,8817,8820,8823,8826,8829,8832,8835],{"className":8813},[50],[15,8815],{"className":8816,"style":139},[54],[15,8818,37],{"className":8819,"style":61},[59,60],[15,8821,113],{"className":8822},[146],[15,8824,117],{"className":8825},[59],[15,8827,120],{"className":8828},[153],[15,8830],{"className":8831,"style":158},[157],[15,8833,123],{"className":8834},[162],[15,8836],{"className":8837,"style":158},[157],[15,8839,8841,8844],{"className":8840},[50],[15,8842],{"className":8843,"style":172},[54],[15,8845,126],{"className":8846},[59],[2311,8848,8850],{"id":8849},"_21-非负性与-jensen","2.1 非负性与 Jensen",[11,8852,534,8853,1166,8906,8950,8951,9020,9021,9091],{},[15,8854,8856,8875],{"className":8855,"translate":19},[18],[15,8857,8859],{"className":8858},[23],[25,8860,8861],{"xmlns":27},[29,8862,8863,8872],{},[32,8864,8865,8867,8870],{},[35,8866,598],{},[110,8868,8869],{},"∼",[35,8871,213],{},[39,8873,8874],{"encoding":41},"X\\sim Q",[15,8876,8878,8897],{"className":8877,"ariaHidden":46},[45],[15,8879,8881,8884,8888,8891,8894],{"className":8880},[50],[15,8882],{"className":8883,"style":664},[54],[15,8885,598],{"className":8886,"style":8887},[59,60],"margin-right:0.0785em;",[15,8889],{"className":8890,"style":158},[157],[15,8892,8869],{"className":8893},[162],[15,8895],{"className":8896,"style":158},[157],[15,8898,8900,8903],{"className":8899},[50],[15,8901],{"className":8902,"style":566},[54],[15,8904,213],{"className":8905},[59,60],[15,8907,8909,8929],{"className":8908,"translate":19},[18],[15,8910,8912],{"className":8911},[23],[25,8913,8914],{"xmlns":27},[29,8915,8916,8926],{},[32,8917,8918,8920,8922,8924],{},[35,8919,37],{},[110,8921,113],{"stretchy":112},[35,8923,598],{},[110,8925,120],{"stretchy":112},[39,8927,8928],{"encoding":41},"f(X)",[15,8930,8932],{"className":8931,"ariaHidden":46},[45],[15,8933,8935,8938,8941,8944,8947],{"className":8934},[50],[15,8936],{"className":8937,"style":139},[54],[15,8939,37],{"className":8940,"style":61},[59,60],[15,8942,113],{"className":8943},[146],[15,8945,598],{"className":8946,"style":8887},[59,60],[15,8948,120],{"className":8949},[153]," 的期望就是 ",[15,8952,8954,8971],{"className":8953,"translate":19},[18],[15,8955,8957],{"className":8956},[23],[25,8958,8959],{"xmlns":27},[29,8960,8961,8969],{},[32,8962,8963],{},[195,8964,8965,8967],{},[35,8966,199],{},[35,8968,37],{},[39,8970,4022],{"encoding":41},[15,8972,8974],{"className":8973,"ariaHidden":46},[45],[15,8975,8977,8980],{"className":8976},[50],[15,8978],{"className":8979,"style":4032},[54],[15,8981,8983,8986],{"className":8982},[59],[15,8984,199],{"className":8985,"style":277},[59,60],[15,8987,8989],{"className":8988},[281],[15,8990,8992,9012],{"className":8991},[285,286],[15,8993,8995,9009],{"className":8994},[290],[15,8996,8998],{"className":8997,"style":295},[294],[15,8999,9000,9003],{"style":298},[15,9001],{"className":9002,"style":303},[302],[15,9004,9006],{"className":9005},[307,308,309,310],[15,9007,37],{"className":9008,"style":61},[59,60,310],[15,9010,318],{"className":9011},[317],[15,9013,9015],{"className":9014},[290],[15,9016,9018],{"className":9017,"style":325},[294],[15,9019],{},"。因为 ",[15,9022,9024,9049],{"className":9023,"translate":19},[18],[15,9025,9027],{"className":9026},[23],[25,9028,9029],{"xmlns":27},[29,9030,9031,9047],{},[32,9032,9033,9035,9037,9039,9041,9043,9045],{},[35,9034,769],{},[110,9036,123],{},[35,9038,244],{},[35,9040,206],{},[35,9042,941],{"mathvariant":209},[35,9044,244],{},[35,9046,213],{},[39,9048,5333],{"encoding":41},[15,9050,9052,9070],{"className":9051,"ariaHidden":46},[45],[15,9053,9055,9058,9061,9064,9067],{"className":9054},[50],[15,9056],{"className":9057,"style":5343},[54],[15,9059,769],{"className":9060},[59,60],[15,9062],{"className":9063,"style":158},[157],[15,9065,123],{"className":9066},[162],[15,9068],{"className":9069,"style":158},[157],[15,9071,9073,9076,9079,9082,9085,9088],{"className":9072},[50],[15,9074],{"className":9075,"style":139},[54],[15,9077,244],{"className":9078},[59,60],[15,9080,206],{"className":9081,"style":334},[59,60],[15,9083,941],{"className":9084},[59],[15,9086,244],{"className":9087},[59,60],[15,9089,213],{"className":9090},[59,60]," 满足",[15,9093,9095],{"className":9094,"translate":19},[180],[15,9096,9098,9160],{"className":9097,"translate":19},[18],[15,9099,9101],{"className":9100},[23],[25,9102,9103],{"xmlns":27,"display":189},[29,9104,9105,9157],{},[32,9106,9107,9113,9115,9117,9119,9121,9123,9137,9139,9141,9143,9145,9147,9149,9151,9153,9155],{},[195,9108,9109,9111],{},[35,9110,223],{"mathvariant":222},[35,9112,213],{},[110,9114,230],{"stretchy":112},[35,9116,769],{},[110,9118,257],{"stretchy":112},[110,9120,123],{},[110,9122,1287],{},[238,9124,9125,9131],{},[32,9126,9127,9129],{},[35,9128,244],{},[35,9130,206],{},[32,9132,9133,9135],{},[35,9134,244],{},[35,9136,213],{},[1297,9138,1299],{},[35,9140,244],{},[35,9142,213],{},[110,9144,123],{},[110,9146,1287],{},[35,9148,244],{},[35,9150,206],{},[110,9152,123],{},[115,9154,117],{},[110,9156,551],{"separator":46},[39,9158,9159],{"encoding":41},"\\mathbb E_Q[t]=\\int \\frac{dP}{dQ}\\,dQ=\\int dP=1,",[15,9161,9163,9227,9325,9352],{"className":9162,"ariaHidden":46},[45],[15,9164,9166,9169,9209,9212,9215,9218,9221,9224],{"className":9165},[50],[15,9167],{"className":9168,"style":270},[54],[15,9170,9172,9175],{"className":9171},[59],[15,9173,223],{"className":9174},[59,366],[15,9176,9178],{"className":9177},[281],[15,9179,9181,9201],{"className":9180},[285,286],[15,9182,9184,9198],{"className":9183},[290],[15,9185,9187],{"className":9186,"style":379},[294],[15,9188,9189,9192],{"style":382},[15,9190],{"className":9191,"style":303},[302],[15,9193,9195],{"className":9194},[307,308,309,310],[15,9196,213],{"className":9197},[59,60,310],[15,9199,318],{"className":9200},[317],[15,9202,9204],{"className":9203},[290],[15,9205,9207],{"className":9206,"style":325},[294],[15,9208],{},[15,9210,230],{"className":9211},[146],[15,9213,769],{"className":9214},[59,60],[15,9216,257],{"className":9217},[153],[15,9219],{"className":9220,"style":158},[157],[15,9222,123],{"className":9223},[162],[15,9225],{"className":9226,"style":158},[157],[15,9228,9230,9233,9236,9239,9307,9310,9313,9316,9319,9322],{"className":9229},[50],[15,9231],{"className":9232,"style":838},[54],[15,9234,1287],{"className":9235,"style":1487},[1484,1485,1486],[15,9237],{"className":9238,"style":406},[157],[15,9240,9242,9245,9304],{"className":9241},[59],[15,9243],{"className":9244},[146,441],[15,9246,9248],{"className":9247},[238],[15,9249,9251,9296],{"className":9250},[285,286],[15,9252,9254,9293],{"className":9253},[290],[15,9255,9257,9271,9279],{"className":9256,"style":454},[294],[15,9258,9259,9262],{"style":457},[15,9260],{"className":9261,"style":461},[302],[15,9263,9265,9268],{"className":9264},[59],[15,9266,244],{"className":9267},[59,60],[15,9269,213],{"className":9270},[59,60],[15,9272,9273,9276],{"style":473},[15,9274],{"className":9275,"style":461},[302],[15,9277],{"className":9278,"style":481},[480],[15,9280,9281,9284],{"style":484},[15,9282],{"className":9283,"style":461},[302],[15,9285,9287,9290],{"className":9286},[59],[15,9288,244],{"className":9289},[59,60],[15,9291,206],{"className":9292,"style":334},[59,60],[15,9294,318],{"className":9295},[317],[15,9297,9299],{"className":9298},[290],[15,9300,9302],{"className":9301,"style":506},[294],[15,9303],{},[15,9305],{"className":9306},[153,441],[15,9308],{"className":9309,"style":406},[157],[15,9311,244],{"className":9312},[59,60],[15,9314,213],{"className":9315},[59,60],[15,9317],{"className":9318,"style":158},[157],[15,9320,123],{"className":9321},[162],[15,9323],{"className":9324,"style":158},[157],[15,9326,9328,9331,9334,9337,9340,9343,9346,9349],{"className":9327},[50],[15,9329],{"className":9330,"style":5777},[54],[15,9332,1287],{"className":9333,"style":1487},[1484,1485,1486],[15,9335],{"className":9336,"style":406},[157],[15,9338,244],{"className":9339},[59,60],[15,9341,206],{"className":9342,"style":334},[59,60],[15,9344],{"className":9345,"style":158},[157],[15,9347,123],{"className":9348},[162],[15,9350],{"className":9351,"style":158},[157],[15,9353,9355,9359,9362],{"className":9354},[50],[15,9356],{"className":9357,"style":9358},[54],"height:0.8389em;vertical-align:-0.1944em;",[15,9360,117],{"className":9361},[59],[15,9363,551],{"className":9364},[573],[11,9366,9367,9368,9396,9397,9400],{},"对凸函数 ",[15,9369,9371,9384],{"className":9370,"translate":19},[18],[15,9372,9374],{"className":9373},[23],[25,9375,9376],{"xmlns":27},[29,9377,9378,9382],{},[32,9379,9380],{},[35,9381,37],{},[39,9383,37],{"encoding":41},[15,9385,9387],{"className":9386,"ariaHidden":46},[45],[15,9388,9390,9393],{"className":9389},[50],[15,9391],{"className":9392,"style":55},[54],[15,9394,37],{"className":9395,"style":61},[59,60]," 用 ",[1225,9398,9399],{},"Jensen 不等式","：",[15,9402,9404],{"className":9403,"translate":19},[180],[15,9405,9407,9526],{"className":9406,"translate":19},[18],[15,9408,9410],{"className":9409},[23],[25,9411,9412],{"xmlns":27,"display":189},[29,9413,9414,9523],{},[1243,9415,9416,9493],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,9417,9418,9461],{},[1252,9419,9420],{},[1255,9421,9422],{"scriptlevel":126,"displaystyle":46},[32,9423,9424,9430,9432,9434,9436,9438,9440,9442,9448,9451,9453,9455,9457,9459],{},[195,9425,9426,9428],{},[35,9427,199],{},[35,9429,37],{},[110,9431,113],{"stretchy":112},[35,9433,206],{},[35,9435,210],{"mathvariant":209},[35,9437,213],{},[110,9439,120],{"stretchy":112},[110,9441,123],{},[195,9443,9444,9446],{},[35,9445,223],{"mathvariant":222},[35,9447,213],{},[110,9449,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},"1.2em",[35,9452,37],{},[110,9454,113],{"stretchy":112},[35,9456,769],{},[110,9458,120],{"stretchy":112},[110,9460,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1252,9462,9463],{},[1255,9464,9465],{"scriptlevel":126,"displaystyle":46},[32,9466,9467,9469,9471,9473,9475,9477,9479,9485,9487,9489,9491],{},[32,9468],{},[1297,9470,4283],{},[110,9472,6928],{},[1297,9474,4283],{},[35,9476,37],{},[110,9478,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,9480,9481,9483],{},[35,9482,223],{"mathvariant":222},[35,9484,213],{},[110,9486,230],{"stretchy":112},[35,9488,769],{},[110,9490,257],{"stretchy":112},[110,9492,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,9494,9495,9501],{},[1252,9496,9497],{},[1255,9498,9499],{"scriptlevel":126,"displaystyle":46},[32,9500],{},[1252,9502,9503],{},[1255,9504,9505],{"scriptlevel":126,"displaystyle":46},[32,9506,9507,9509,9511,9513,9515,9517,9519,9521],{},[32,9508],{},[110,9510,123],{},[35,9512,37],{},[110,9514,113],{"stretchy":112},[115,9516,117],{},[110,9518,120],{"stretchy":112},[110,9520,123],{},[115,9522,5764],{},[39,9524,9525],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)=\\mathbb E_Q\\big[f(t)\\big]\n&\\ \\ge\\ f\\big(\\mathbb E_Q[t]\\big)\\\\[2pt]\n&=f(1)=0 .\n\\end{aligned}",[15,9527,9529],{"className":9528,"ariaHidden":46},[45],[15,9530,9532,9536],{"className":9531},[50],[15,9533],{"className":9534,"style":9535},[54],"height:2.91em;vertical-align:-1.205em;",[15,9537,9539],{"className":9538},[59],[15,9540,9542,9714],{"className":9541},[1243],[15,9543,9545],{"className":9544},[1360],[15,9546,9548,9705],{"className":9547},[285,286],[15,9549,9551,9702],{"className":9550},[290],[15,9552,9555,9693],{"className":9553,"style":9554},[294],"height:1.705em;",[15,9556,9558,9561],{"style":9557},"top:-3.855em;",[15,9559],{"className":9560,"style":461},[302],[15,9562,9564,9604,9607,9610,9613,9616,9619,9622,9625,9628,9668,9675,9678,9681,9684,9687],{"className":9563},[59],[15,9565,9567,9570],{"className":9566},[59],[15,9568,199],{"className":9569,"style":277},[59,60],[15,9571,9573],{"className":9572},[281],[15,9574,9576,9596],{"className":9575},[285,286],[15,9577,9579,9593],{"className":9578},[290],[15,9580,9582],{"className":9581,"style":295},[294],[15,9583,9584,9587],{"style":298},[15,9585],{"className":9586,"style":303},[302],[15,9588,9590],{"className":9589},[307,308,309,310],[15,9591,37],{"className":9592,"style":61},[59,60,310],[15,9594,318],{"className":9595},[317],[15,9597,9599],{"className":9598},[290],[15,9600,9602],{"className":9601,"style":325},[294],[15,9603],{},[15,9605,113],{"className":9606},[146],[15,9608,206],{"className":9609,"style":334},[59,60],[15,9611,210],{"className":9612},[59],[15,9614,213],{"className":9615},[59,60],[15,9617,120],{"className":9618},[153],[15,9620],{"className":9621,"style":158},[157],[15,9623,123],{"className":9624},[162],[15,9626],{"className":9627,"style":158},[157],[15,9629,9631,9634],{"className":9630},[59],[15,9632,223],{"className":9633},[59,366],[15,9635,9637],{"className":9636},[281],[15,9638,9640,9660],{"className":9639},[285,286],[15,9641,9643,9657],{"className":9642},[290],[15,9644,9646],{"className":9645,"style":379},[294],[15,9647,9648,9651],{"style":382},[15,9649],{"className":9650,"style":303},[302],[15,9652,9654],{"className":9653},[307,308,309,310],[15,9655,213],{"className":9656},[59,60,310],[15,9658,318],{"className":9659},[317],[15,9661,9663],{"className":9662},[290],[15,9664,9666],{"className":9665,"style":325},[294],[15,9667],{},[15,9669,9671],{"className":9670},[59],[15,9672,230],{"className":9673},[419,9674],"size1",[15,9676,37],{"className":9677,"style":61},[59,60],[15,9679,113],{"className":9680},[146],[15,9682,769],{"className":9683},[59,60],[15,9685,120],{"className":9686},[153],[15,9688,9690],{"className":9689},[59],[15,9691,257],{"className":9692},[419,9674],[15,9694,9696,9699],{"style":9695},"top:-2.155em;",[15,9697],{"className":9698,"style":461},[302],[15,9700],{"className":9701},[59],[15,9703,318],{"className":9704},[317],[15,9706,9708],{"className":9707},[290],[15,9709,9712],{"className":9710,"style":9711},[294],"height:1.205em;",[15,9713],{},[15,9715,9717],{"className":9716},[1451],[15,9718,9720,9863],{"className":9719},[285,286],[15,9721,9723,9860],{"className":9722},[290],[15,9724,9726,9816],{"className":9725,"style":9554},[294],[15,9727,9728,9731],{"style":9557},[15,9729],{"className":9730,"style":461},[302],[15,9732,9734,9737,9740,9743,9746,9749,9752,9755,9761,9801,9804,9807,9810],{"className":9733},[59],[15,9735],{"className":9736},[59],[15,9738,4283],{"className":9739},[157],[15,9741],{"className":9742,"style":158},[157],[15,9744,6928],{"className":9745},[162],[15,9747,4283],{"className":9748},[157],[15,9750],{"className":9751,"style":158},[157],[15,9753,37],{"className":9754,"style":61},[59,60],[15,9756,9758],{"className":9757},[59],[15,9759,113],{"className":9760},[419,9674],[15,9762,9764,9767],{"className":9763},[59],[15,9765,223],{"className":9766},[59,366],[15,9768,9770],{"className":9769},[281],[15,9771,9773,9793],{"className":9772},[285,286],[15,9774,9776,9790],{"className":9775},[290],[15,9777,9779],{"className":9778,"style":379},[294],[15,9780,9781,9784],{"style":382},[15,9782],{"className":9783,"style":303},[302],[15,9785,9787],{"className":9786},[307,308,309,310],[15,9788,213],{"className":9789},[59,60,310],[15,9791,318],{"className":9792},[317],[15,9794,9796],{"className":9795},[290],[15,9797,9799],{"className":9798,"style":325},[294],[15,9800],{},[15,9802,230],{"className":9803},[146],[15,9805,769],{"className":9806},[59,60],[15,9808,257],{"className":9809},[153],[15,9811,9813],{"className":9812},[59],[15,9814,120],{"className":9815},[419,9674],[15,9817,9818,9821],{"style":9695},[15,9819],{"className":9820,"style":461},[302],[15,9822,9824,9827,9830,9833,9836,9839,9842,9845,9848,9851,9854,9857],{"className":9823},[59],[15,9825],{"className":9826},[59],[15,9828],{"className":9829,"style":158},[157],[15,9831,123],{"className":9832},[162],[15,9834],{"className":9835,"style":158},[157],[15,9837,37],{"className":9838,"style":61},[59,60],[15,9840,113],{"className":9841},[146],[15,9843,117],{"className":9844},[59],[15,9846,120],{"className":9847},[153],[15,9849],{"className":9850,"style":158},[157],[15,9852,123],{"className":9853},[162],[15,9855],{"className":9856,"style":158},[157],[15,9858,5764],{"className":9859},[59],[15,9861,318],{"className":9862},[317],[15,9864,9866],{"className":9865},[290],[15,9867,9869],{"className":9868,"style":9711},[294],[15,9870],{},[11,9872,9873,9874,9902,9903,9931,9932,10025],{},"这就是非负性。",[15,9875,9877,9890],{"className":9876,"translate":19},[18],[15,9878,9880],{"className":9879},[23],[25,9881,9882],{"xmlns":27},[29,9883,9884,9888],{},[32,9885,9886],{},[35,9887,37],{},[39,9889,37],{"encoding":41},[15,9891,9893],{"className":9892,"ariaHidden":46},[45],[15,9894,9896,9899],{"className":9895},[50],[15,9897],{"className":9898,"style":55},[54],[15,9900,37],{"className":9901,"style":61},[59,60]," 的凸性是关键：若 ",[15,9904,9906,9919],{"className":9905,"translate":19},[18],[15,9907,9909],{"className":9908},[23],[25,9910,9911],{"xmlns":27},[29,9912,9913,9917],{},[32,9914,9915],{},[35,9916,37],{},[39,9918,37],{"encoding":41},[15,9920,9922],{"className":9921,"ariaHidden":46},[45],[15,9923,9925,9928],{"className":9924},[50],[15,9926],{"className":9927,"style":55},[54],[15,9929,37],{"className":9930,"style":61},[59,60]," 是凹函数，Jensen 方向反转，",[15,9933,9935,9958],{"className":9934,"translate":19},[18],[15,9936,9938],{"className":9937},[23],[25,9939,9940],{"xmlns":27},[29,9941,9942,9955],{},[32,9943,9944,9950,9953],{},[195,9945,9946,9948],{},[35,9947,199],{},[35,9949,37],{},[110,9951,9952],{},"≤",[115,9954,126],{},[39,9956,9957],{"encoding":41},"D_f\\le 0",[15,9959,9961,10016],{"className":9960,"ariaHidden":46},[45],[15,9962,9964,9967,10007,10010,10013],{"className":9963},[50],[15,9965],{"className":9966,"style":4032},[54],[15,9968,9970,9973],{"className":9969},[59],[15,9971,199],{"className":9972,"style":277},[59,60],[15,9974,9976],{"className":9975},[281],[15,9977,9979,9999],{"className":9978},[285,286],[15,9980,9982,9996],{"className":9981},[290],[15,9983,9985],{"className":9984,"style":295},[294],[15,9986,9987,9990],{"style":298},[15,9988],{"className":9989,"style":303},[302],[15,9991,9993],{"className":9992},[307,308,309,310],[15,9994,37],{"className":9995,"style":61},[59,60,310],[15,9997,318],{"className":9998},[317],[15,10000,10002],{"className":10001},[290],[15,10003,10005],{"className":10004,"style":325},[294],[15,10006],{},[15,10008],{"className":10009,"style":158},[157],[15,10011,9952],{"className":10012},[162],[15,10014],{"className":10015,"style":158},[157],[15,10017,10019,10022],{"className":10018},[50],[15,10020],{"className":10021,"style":172},[54],[15,10023,126],{"className":10024},[59],"，那就不是「散度」了。",[10027,10028,10029,10181],"ul",{},[6665,10030,10031,10062,10063,10180],{},[1225,10032,10033,10061],{},[15,10034,10036,10049],{"className":10035,"translate":19},[18],[15,10037,10039],{"className":10038},[23],[25,10040,10041],{"xmlns":27},[29,10042,10043,10047],{},[32,10044,10045],{},[35,10046,37],{},[39,10048,37],{"encoding":41},[15,10050,10052],{"className":10051,"ariaHidden":46},[45],[15,10053,10055,10058],{"className":10054},[50],[15,10056],{"className":10057,"style":55},[54],[15,10059,37],{"className":10060,"style":61},[59,60]," 凸","：保证 ",[15,10064,10066,10098],{"className":10065,"translate":19},[18],[15,10067,10069],{"className":10068},[23],[25,10070,10071],{"xmlns":27},[29,10072,10073,10095],{},[32,10074,10075,10081,10083,10085,10087,10089,10091,10093],{},[195,10076,10077,10079],{},[35,10078,199],{},[35,10080,37],{},[110,10082,113],{"stretchy":112},[35,10084,206],{},[35,10086,210],{"mathvariant":209},[35,10088,213],{},[110,10090,120],{"stretchy":112},[110,10092,6928],{},[115,10094,126],{},[39,10096,10097],{"encoding":41},"D_f(P\\|Q)\\ge 0",[15,10099,10101,10171],{"className":10100,"ariaHidden":46},[45],[15,10102,10104,10107,10147,10150,10153,10156,10159,10162,10165,10168],{"className":10103},[50],[15,10105],{"className":10106,"style":270},[54],[15,10108,10110,10113],{"className":10109},[59],[15,10111,199],{"className":10112,"style":277},[59,60],[15,10114,10116],{"className":10115},[281],[15,10117,10119,10139],{"className":10118},[285,286],[15,10120,10122,10136],{"className":10121},[290],[15,10123,10125],{"className":10124,"style":295},[294],[15,10126,10127,10130],{"style":298},[15,10128],{"className":10129,"style":303},[302],[15,10131,10133],{"className":10132},[307,308,309,310],[15,10134,37],{"className":10135,"style":61},[59,60,310],[15,10137,318],{"className":10138},[317],[15,10140,10142],{"className":10141},[290],[15,10143,10145],{"className":10144,"style":325},[294],[15,10146],{},[15,10148,113],{"className":10149},[146],[15,10151,206],{"className":10152,"style":334},[59,60],[15,10154,210],{"className":10155},[59],[15,10157,213],{"className":10158},[59,60],[15,10160,120],{"className":10161},[153],[15,10163],{"className":10164,"style":158},[157],[15,10166,6928],{"className":10167},[162],[15,10169],{"className":10170,"style":158},[157],[15,10172,10174,10177],{"className":10173},[50],[15,10175],{"className":10176,"style":172},[54],[15,10178,126],{"className":10179},[59],"。",[6665,10182,10183,10250,10251,10302,10303,10437,10438,10180],{},[1225,10184,10185],{},[15,10186,10188,10211],{"className":10187,"translate":19},[18],[15,10189,10191],{"className":10190},[23],[25,10192,10193],{"xmlns":27},[29,10194,10195,10209],{},[32,10196,10197,10199,10201,10203,10205,10207],{},[35,10198,37],{},[110,10200,113],{"stretchy":112},[115,10202,117],{},[110,10204,120],{"stretchy":112},[110,10206,123],{},[115,10208,126],{},[39,10210,129],{"encoding":41},[15,10212,10214,10241],{"className":10213,"ariaHidden":46},[45],[15,10215,10217,10220,10223,10226,10229,10232,10235,10238],{"className":10216},[50],[15,10218],{"className":10219,"style":139},[54],[15,10221,37],{"className":10222,"style":61},[59,60],[15,10224,113],{"className":10225},[146],[15,10227,117],{"className":10228},[59],[15,10230,120],{"className":10231},[153],[15,10233],{"className":10234,"style":158},[157],[15,10236,123],{"className":10237},[162],[15,10239],{"className":10240,"style":158},[157],[15,10242,10244,10247],{"className":10243},[50],[15,10245],{"className":10246,"style":172},[54],[15,10248,126],{"className":10249},[59],"：保证当 ",[15,10252,10254,10272],{"className":10253,"translate":19},[18],[15,10255,10257],{"className":10256},[23],[25,10258,10259],{"xmlns":27},[29,10260,10261,10269],{},[32,10262,10263,10265,10267],{},[35,10264,206],{},[110,10266,123],{},[35,10268,213],{},[39,10270,10271],{"encoding":41},"P=Q",[15,10273,10275,10293],{"className":10274,"ariaHidden":46},[45],[15,10276,10278,10281,10284,10287,10290],{"className":10277},[50],[15,10279],{"className":10280,"style":664},[54],[15,10282,206],{"className":10283,"style":334},[59,60],[15,10285],{"className":10286,"style":158},[157],[15,10288,123],{"className":10289},[162],[15,10291],{"className":10292,"style":158},[157],[15,10294,10296,10299],{"className":10295},[50],[15,10297],{"className":10298,"style":566},[54],[15,10300,213],{"className":10301},[59,60]," 时，",[15,10304,10306,10336],{"className":10305,"translate":19},[18],[15,10307,10309],{"className":10308},[23],[25,10310,10311],{"xmlns":27},[29,10312,10313,10333],{},[32,10314,10315,10329,10331],{},[238,10316,10317,10323],{},[32,10318,10319,10321],{},[35,10320,244],{},[35,10322,206],{},[32,10324,10325,10327],{},[35,10326,244],{},[35,10328,213],{},[110,10330,123],{},[115,10332,117],{},[39,10334,10335],{"encoding":41},"\\frac{dP}{dQ}=1",[15,10337,10339,10428],{"className":10338,"ariaHidden":46},[45],[15,10340,10342,10345,10419,10422,10425],{"className":10341},[50],[15,10343],{"className":10344,"style":2668},[54],[15,10346,10348,10351,10416],{"className":10347},[59],[15,10349],{"className":10350},[146,441],[15,10352,10354],{"className":10353},[238],[15,10355,10357,10408],{"className":10356},[285,286],[15,10358,10360,10405],{"className":10359},[290],[15,10361,10363,10380,10388],{"className":10362,"style":2687},[294],[15,10364,10365,10368],{"style":2527},[15,10366],{"className":10367,"style":461},[302],[15,10369,10371],{"className":10370},[307,308,309,310],[15,10372,10374,10377],{"className":10373},[59,310],[15,10375,244],{"className":10376},[59,60,310],[15,10378,213],{"className":10379},[59,60,310],[15,10381,10382,10385],{"style":473},[15,10383],{"className":10384,"style":461},[302],[15,10386],{"className":10387,"style":481},[480],[15,10389,10390,10393],{"style":2550},[15,10391],{"className":10392,"style":461},[302],[15,10394,10396],{"className":10395},[307,308,309,310],[15,10397,10399,10402],{"className":10398},[59,310],[15,10400,244],{"className":10401},[59,60,310],[15,10403,206],{"className":10404,"style":334},[59,60,310],[15,10406,318],{"className":10407},[317],[15,10409,10411],{"className":10410},[290],[15,10412,10414],{"className":10413,"style":2739},[294],[15,10415],{},[15,10417],{"className":10418},[153,441],[15,10420],{"className":10421,"style":158},[157],[15,10423,123],{"className":10424},[162],[15,10426],{"className":10427,"style":158},[157],[15,10429,10431,10434],{"className":10430},[50],[15,10432],{"className":10433,"style":172},[54],[15,10435,117],{"className":10436},[59],"，从而 ",[15,10439,10441,10473],{"className":10440,"translate":19},[18],[15,10442,10444],{"className":10443},[23],[25,10445,10446],{"xmlns":27},[29,10447,10448,10470],{},[32,10449,10450,10456,10458,10460,10462,10464,10466,10468],{},[195,10451,10452,10454],{},[35,10453,199],{},[35,10455,37],{},[110,10457,113],{"stretchy":112},[35,10459,206],{},[35,10461,210],{"mathvariant":209},[35,10463,206],{},[110,10465,120],{"stretchy":112},[110,10467,123],{},[115,10469,126],{},[39,10471,10472],{"encoding":41},"D_f(P\\|P)=0",[15,10474,10476,10546],{"className":10475,"ariaHidden":46},[45],[15,10477,10479,10482,10522,10525,10528,10531,10534,10537,10540,10543],{"className":10478},[50],[15,10480],{"className":10481,"style":270},[54],[15,10483,10485,10488],{"className":10484},[59],[15,10486,199],{"className":10487,"style":277},[59,60],[15,10489,10491],{"className":10490},[281],[15,10492,10494,10514],{"className":10493},[285,286],[15,10495,10497,10511],{"className":10496},[290],[15,10498,10500],{"className":10499,"style":295},[294],[15,10501,10502,10505],{"style":298},[15,10503],{"className":10504,"style":303},[302],[15,10506,10508],{"className":10507},[307,308,309,310],[15,10509,37],{"className":10510,"style":61},[59,60,310],[15,10512,318],{"className":10513},[317],[15,10515,10517],{"className":10516},[290],[15,10518,10520],{"className":10519,"style":325},[294],[15,10521],{},[15,10523,113],{"className":10524},[146],[15,10526,206],{"className":10527,"style":334},[59,60],[15,10529,210],{"className":10530},[59],[15,10532,206],{"className":10533,"style":334},[59,60],[15,10535,120],{"className":10536},[153],[15,10538],{"className":10539,"style":158},[157],[15,10541,123],{"className":10542},[162],[15,10544],{"className":10545,"style":158},[157],[15,10547,10549,10552],{"className":10548},[50],[15,10550],{"className":10551,"style":172},[54],[15,10553,126],{"className":10554},[59],[11,10556,10557],{},"因此 f-散度天然具有非负性和「相同分布散度为零」的性质。",[2311,10559,10561],{"id":10560},"_22-凸性为何必需","2.2 凸性为何必需",[11,10563,10564,10565,10634,10635,10663],{},"有人会问：凸性是不是一个过强的技术条件？答案是否定的。若要求 ",[15,10566,10568,10585],{"className":10567,"translate":19},[18],[15,10569,10571],{"className":10570},[23],[25,10572,10573],{"xmlns":27},[29,10574,10575,10583],{},[32,10576,10577],{},[195,10578,10579,10581],{},[35,10580,199],{},[35,10582,37],{},[39,10584,4022],{"encoding":41},[15,10586,10588],{"className":10587,"ariaHidden":46},[45],[15,10589,10591,10594],{"className":10590},[50],[15,10592],{"className":10593,"style":4032},[54],[15,10595,10597,10600],{"className":10596},[59],[15,10598,199],{"className":10599,"style":277},[59,60],[15,10601,10603],{"className":10602},[281],[15,10604,10606,10626],{"className":10605},[285,286],[15,10607,10609,10623],{"className":10608},[290],[15,10610,10612],{"className":10611,"style":295},[294],[15,10613,10614,10617],{"style":298},[15,10615],{"className":10616,"style":303},[302],[15,10618,10620],{"className":10619},[307,308,309,310],[15,10621,37],{"className":10622,"style":61},[59,60,310],[15,10624,318],{"className":10625},[317],[15,10627,10629],{"className":10628},[290],[15,10630,10632],{"className":10631,"style":325},[294],[15,10633],{}," 对一切「随机变换」（马尔可夫核）单调不增（即第 4.5 节的数据处理不等式），那么 ",[15,10636,10638,10651],{"className":10637,"translate":19},[18],[15,10639,10641],{"className":10640},[23],[25,10642,10643],{"xmlns":27},[29,10644,10645,10649],{},[32,10646,10647],{},[35,10648,37],{},[39,10650,37],{"encoding":41},[15,10652,10654],{"className":10653,"ariaHidden":46},[45],[15,10655,10657,10660],{"className":10656},[50],[15,10658],{"className":10659,"style":55},[54],[15,10661,37],{"className":10662,"style":61},[59,60]," 必须凸。二元分布上就能看到这一点。",[993,10665,10667],{"title":10666},"命题 2.1（Csiszár 刻画）",[11,10668,10669,10670,10865,10866,10907,10908,10936,10937,10965],{},"若数据处理不等式 ",[15,10671,10673,10724],{"className":10672,"translate":19},[18],[15,10674,10676],{"className":10675},[23],[25,10677,10678],{"xmlns":27},[29,10679,10680,10721],{},[32,10681,10682,10688,10690,10692,10695,10697,10699,10701,10703,10705,10711,10713,10715,10717,10719],{},[195,10683,10684,10686],{},[35,10685,199],{},[35,10687,37],{},[110,10689,113],{"stretchy":112},[35,10691,206],{},[35,10693,10694],{},"K",[35,10696,210],{"mathvariant":209},[35,10698,213],{},[35,10700,10694],{},[110,10702,120],{"stretchy":112},[110,10704,9952],{},[195,10706,10707,10709],{},[35,10708,199],{},[35,10710,37],{},[110,10712,113],{"stretchy":112},[35,10714,206],{},[35,10716,210],{"mathvariant":209},[35,10718,213],{},[110,10720,120],{"stretchy":112},[39,10722,10723],{"encoding":41},"D_f(PK\\|QK)\\le D_f(P\\|Q)",[15,10725,10727,10804],{"className":10726,"ariaHidden":46},[45],[15,10728,10730,10733,10773,10776,10779,10783,10786,10789,10792,10795,10798,10801],{"className":10729},[50],[15,10731],{"className":10732,"style":270},[54],[15,10734,10736,10739],{"className":10735},[59],[15,10737,199],{"className":10738,"style":277},[59,60],[15,10740,10742],{"className":10741},[281],[15,10743,10745,10765],{"className":10744},[285,286],[15,10746,10748,10762],{"className":10747},[290],[15,10749,10751],{"className":10750,"style":295},[294],[15,10752,10753,10756],{"style":298},[15,10754],{"className":10755,"style":303},[302],[15,10757,10759],{"className":10758},[307,308,309,310],[15,10760,37],{"className":10761,"style":61},[59,60,310],[15,10763,318],{"className":10764},[317],[15,10766,10768],{"className":10767},[290],[15,10769,10771],{"className":10770,"style":325},[294],[15,10772],{},[15,10774,113],{"className":10775},[146],[15,10777,206],{"className":10778,"style":334},[59,60],[15,10780,10694],{"className":10781,"style":10782},[59,60],"margin-right:0.0715em;",[15,10784,210],{"className":10785},[59],[15,10787,213],{"className":10788},[59,60],[15,10790,10694],{"className":10791,"style":10782},[59,60],[15,10793,120],{"className":10794},[153],[15,10796],{"className":10797,"style":158},[157],[15,10799,9952],{"className":10800},[162],[15,10802],{"className":10803,"style":158},[157],[15,10805,10807,10810,10850,10853,10856,10859,10862],{"className":10806},[50],[15,10808],{"className":10809,"style":270},[54],[15,10811,10813,10816],{"className":10812},[59],[15,10814,199],{"className":10815,"style":277},[59,60],[15,10817,10819],{"className":10818},[281],[15,10820,10822,10842],{"className":10821},[285,286],[15,10823,10825,10839],{"className":10824},[290],[15,10826,10828],{"className":10827,"style":295},[294],[15,10829,10830,10833],{"style":298},[15,10831],{"className":10832,"style":303},[302],[15,10834,10836],{"className":10835},[307,308,309,310],[15,10837,37],{"className":10838,"style":61},[59,60,310],[15,10840,318],{"className":10841},[317],[15,10843,10845],{"className":10844},[290],[15,10846,10848],{"className":10847,"style":325},[294],[15,10849],{},[15,10851,113],{"className":10852},[146],[15,10854,206],{"className":10855,"style":334},[59,60],[15,10857,210],{"className":10858},[59],[15,10860,213],{"className":10861},[59,60],[15,10863,120],{"className":10864},[153]," 对一切概率对 ",[15,10867,10869,10886],{"className":10868,"translate":19},[18],[15,10870,10872],{"className":10871},[23],[25,10873,10874],{"xmlns":27},[29,10875,10876,10884],{},[32,10877,10878,10880,10882],{},[35,10879,206],{},[110,10881,551],{"separator":46},[35,10883,213],{},[39,10885,556],{"encoding":41},[15,10887,10889],{"className":10888,"ariaHidden":46},[45],[15,10890,10892,10895,10898,10901,10904],{"className":10891},[50],[15,10893],{"className":10894,"style":566},[54],[15,10896,206],{"className":10897,"style":334},[59,60],[15,10899,551],{"className":10900},[573],[15,10902],{"className":10903,"style":406},[157],[15,10905,213],{"className":10906},[59,60]," 与一切马尔可夫核 ",[15,10909,10911,10924],{"className":10910,"translate":19},[18],[15,10912,10914],{"className":10913},[23],[25,10915,10916],{"xmlns":27},[29,10917,10918,10922],{},[32,10919,10920],{},[35,10921,10694],{},[39,10923,10694],{"encoding":41},[15,10925,10927],{"className":10926,"ariaHidden":46},[45],[15,10928,10930,10933],{"className":10929},[50],[15,10931],{"className":10932,"style":664},[54],[15,10934,10694],{"className":10935,"style":10782},[59,60]," 成立，则 ",[15,10938,10940,10953],{"className":10939,"translate":19},[18],[15,10941,10943],{"className":10942},[23],[25,10944,10945],{"xmlns":27},[29,10946,10947,10951],{},[32,10948,10949],{},[35,10950,37],{},[39,10952,37],{"encoding":41},[15,10954,10956],{"className":10955,"ariaHidden":46},[45],[15,10957,10959,10962],{"className":10958},[50],[15,10960],{"className":10961,"style":55},[54],[15,10963,37],{"className":10964,"style":61},[59,60]," 凸。",[11,10967,10968],{},[1225,10969,10970],{},"证明（两步）。",[11,10972,10973,11060,11061,2280,11295,11324,11325,11401,11402,5645,11600,11797,11798,11935],{},[1225,10974,10975,10976,6494,11007,11059],{},"第一步：DPI ",[15,10977,10979,10994],{"className":10978,"translate":19},[18],[15,10980,10982],{"className":10981},[23],[25,10983,10984],{"xmlns":27},[29,10985,10986,10991],{},[32,10987,10988],{},[110,10989,10990],{},"⇒",[39,10992,10993],{"encoding":41},"\\Rightarrow",[15,10995,10997],{"className":10996,"ariaHidden":46},[45],[15,10998,11000,11004],{"className":10999},[50],[15,11001],{"className":11002,"style":11003},[54],"height:0.3669em;",[15,11005,10990],{"className":11006},[162],[15,11008,11010,11032],{"className":11009,"translate":19},[18],[15,11011,11013],{"className":11012},[23],[25,11014,11015],{"xmlns":27},[29,11016,11017,11029],{},[32,11018,11019,11021,11023,11025,11027],{},[110,11020,113],{"stretchy":112},[35,11022,206],{},[110,11024,551],{"separator":46},[35,11026,213],{},[110,11028,120],{"stretchy":112},[39,11030,11031],{"encoding":41},"(P,Q)",[15,11033,11035],{"className":11034,"ariaHidden":46},[45],[15,11036,11038,11041,11044,11047,11050,11053,11056],{"className":11037},[50],[15,11039],{"className":11040,"style":139},[54],[15,11042,113],{"className":11043},[146],[15,11045,206],{"className":11046,"style":334},[59,60],[15,11048,551],{"className":11049},[573],[15,11051],{"className":11052,"style":406},[157],[15,11054,213],{"className":11055},[59,60],[15,11057,120],{"className":11058},[153]," 联合凸。"," 设 ",[15,11062,11064,11106],{"className":11063,"translate":19},[18],[15,11065,11067],{"className":11066},[23],[25,11068,11069],{"xmlns":27},[29,11070,11071,11103],{},[32,11072,11073,11079,11081,11087,11089,11095,11097],{},[195,11074,11075,11077],{},[35,11076,206],{},[115,11078,117],{},[110,11080,551],{"separator":46},[195,11082,11083,11085],{},[35,11084,206],{},[115,11086,2463],{},[110,11088,551],{"separator":46},[195,11090,11091,11093],{},[35,11092,213],{},[115,11094,117],{},[110,11096,551],{"separator":46},[195,11098,11099,11101],{},[35,11100,213],{},[115,11102,2463],{},[39,11104,11105],{"encoding":41},"P_1,P_2,Q_1,Q_2",[15,11107,11109],{"className":11108,"ariaHidden":46},[45],[15,11110,11112,11115,11157,11160,11163,11203,11206,11209,11249,11252,11255],{"className":11111},[50],[15,11113],{"className":11114,"style":566},[54],[15,11116,11118,11121],{"className":11117},[59],[15,11119,206],{"className":11120,"style":334},[59,60],[15,11122,11124],{"className":11123},[281],[15,11125,11127,11149],{"className":11126},[285,286],[15,11128,11130,11146],{"className":11129},[290],[15,11131,11134],{"className":11132,"style":11133},[294],"height:0.3011em;",[15,11135,11137,11140],{"style":11136},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[15,11138],{"className":11139,"style":303},[302],[15,11141,11143],{"className":11142},[307,308,309,310],[15,11144,117],{"className":11145},[59,310],[15,11147,318],{"className":11148},[317],[15,11150,11152],{"className":11151},[290],[15,11153,11155],{"className":11154,"style":7968},[294],[15,11156],{},[15,11158,551],{"className":11159},[573],[15,11161],{"className":11162,"style":406},[157],[15,11164,11166,11169],{"className":11165},[59],[15,11167,206],{"className":11168,"style":334},[59,60],[15,11170,11172],{"className":11171},[281],[15,11173,11175,11195],{"className":11174},[285,286],[15,11176,11178,11192],{"className":11177},[290],[15,11179,11181],{"className":11180,"style":11133},[294],[15,11182,11183,11186],{"style":11136},[15,11184],{"className":11185,"style":303},[302],[15,11187,11189],{"className":11188},[307,308,309,310],[15,11190,2463],{"className":11191},[59,310],[15,11193,318],{"className":11194},[317],[15,11196,11198],{"className":11197},[290],[15,11199,11201],{"className":11200,"style":7968},[294],[15,11202],{},[15,11204,551],{"className":11205},[573],[15,11207],{"className":11208,"style":406},[157],[15,11210,11212,11215],{"className":11211},[59],[15,11213,213],{"className":11214},[59,60],[15,11216,11218],{"className":11217},[281],[15,11219,11221,11241],{"className":11220},[285,286],[15,11222,11224,11238],{"className":11223},[290],[15,11225,11227],{"className":11226,"style":11133},[294],[15,11228,11229,11232],{"style":382},[15,11230],{"className":11231,"style":303},[302],[15,11233,11235],{"className":11234},[307,308,309,310],[15,11236,117],{"className":11237},[59,310],[15,11239,318],{"className":11240},[317],[15,11242,11244],{"className":11243},[290],[15,11245,11247],{"className":11246,"style":7968},[294],[15,11248],{},[15,11250,551],{"className":11251},[573],[15,11253],{"className":11254,"style":406},[157],[15,11256,11258,11261],{"className":11257},[59],[15,11259,213],{"className":11260},[59,60],[15,11262,11264],{"className":11263},[281],[15,11265,11267,11287],{"className":11266},[285,286],[15,11268,11270,11284],{"className":11269},[290],[15,11271,11273],{"className":11272,"style":11133},[294],[15,11274,11275,11278],{"style":382},[15,11276],{"className":11277,"style":303},[302],[15,11279,11281],{"className":11280},[307,308,309,310],[15,11282,2463],{"className":11283},[59,310],[15,11285,318],{"className":11286},[317],[15,11288,11290],{"className":11289},[290],[15,11291,11293],{"className":11292,"style":7968},[294],[15,11294],{},[15,11296,11298,11312],{"className":11297,"translate":19},[18],[15,11299,11301],{"className":11300},[23],[25,11302,11303],{"xmlns":27},[29,11304,11305,11309],{},[32,11306,11307],{},[35,11308,598],{"mathvariant":597},[39,11310,11311],{"encoding":41},"\\mathcal X",[15,11313,11315],{"className":11314,"ariaHidden":46},[45],[15,11316,11318,11321],{"className":11317},[50],[15,11319],{"className":11320,"style":664},[54],[15,11322,598],{"className":11323,"style":625},[59,624]," 上任给的四对分布，",[15,11326,11328,11355],{"className":11327,"translate":19},[18],[15,11329,11331],{"className":11330},[23],[25,11332,11333],{"xmlns":27},[29,11334,11335,11352],{},[32,11336,11337,11340,11342,11344,11346,11348,11350],{},[35,11338,11339],{},"λ",[110,11341,5909],{},[110,11343,113],{"stretchy":112},[115,11345,126],{},[110,11347,551],{"separator":46},[115,11349,117],{},[110,11351,120],{"stretchy":112},[39,11353,11354],{"encoding":41},"\\lambda\\in(0,1)",[15,11356,11358,11377],{"className":11357,"ariaHidden":46},[45],[15,11359,11361,11365,11368,11371,11374],{"className":11360},[50],[15,11362],{"className":11363,"style":11364},[54],"height:0.7335em;vertical-align:-0.0391em;",[15,11366,11339],{"className":11367},[59,60],[15,11369],{"className":11370,"style":158},[157],[15,11372,5909],{"className":11373},[162],[15,11375],{"className":11376,"style":158},[157],[15,11378,11380,11383,11386,11389,11392,11395,11398],{"className":11379},[50],[15,11381],{"className":11382,"style":139},[54],[15,11384,113],{"className":11385},[146],[15,11387,126],{"className":11388},[59],[15,11390,551],{"className":11391},[573],[15,11393],{"className":11394,"style":406},[157],[15,11396,117],{"className":11397},[59],[15,11399,120],{"className":11400},[153],"，记 ",[15,11403,11405,11447],{"className":11404,"translate":19},[18],[15,11406,11408],{"className":11407},[23],[25,11409,11410],{"xmlns":27},[29,11411,11412,11444],{},[32,11413,11414,11416,11418,11420,11426,11428,11430,11432,11434,11436,11438],{},[35,11415,206],{},[110,11417,123],{},[35,11419,11339],{},[195,11421,11422,11424],{},[35,11423,206],{},[115,11425,117],{},[110,11427,2470],{},[110,11429,113],{"stretchy":112},[115,11431,117],{},[110,11433,4813],{},[35,11435,11339],{},[110,11437,120],{"stretchy":112},[195,11439,11440,11442],{},[35,11441,206],{},[115,11443,2463],{},[39,11445,11446],{"encoding":41},"P=\\lambda P_1+(1-\\lambda)P_2",[15,11448,11450,11468,11527,11548],{"className":11449,"ariaHidden":46},[45],[15,11451,11453,11456,11459,11462,11465],{"className":11452},[50],[15,11454],{"className":11455,"style":664},[54],[15,11457,206],{"className":11458,"style":334},[59,60],[15,11460],{"className":11461,"style":158},[157],[15,11463,123],{"className":11464},[162],[15,11466],{"className":11467,"style":158},[157],[15,11469,11471,11475,11478,11518,11521,11524],{"className":11470},[50],[15,11472],{"className":11473,"style":11474},[54],"height:0.8444em;vertical-align:-0.15em;",[15,11476,11339],{"className":11477},[59,60],[15,11479,11481,11484],{"className":11480},[59],[15,11482,206],{"className":11483,"style":334},[59,60],[15,11485,11487],{"className":11486},[281],[15,11488,11490,11510],{"className":11489},[285,286],[15,11491,11493,11507],{"className":11492},[290],[15,11494,11496],{"className":11495,"style":11133},[294],[15,11497,11498,11501],{"style":11136},[15,11499],{"className":11500,"style":303},[302],[15,11502,11504],{"className":11503},[307,308,309,310],[15,11505,117],{"className":11506},[59,310],[15,11508,318],{"className":11509},[317],[15,11511,11513],{"className":11512},[290],[15,11514,11516],{"className":11515,"style":7968},[294],[15,11517],{},[15,11519],{"className":11520,"style":2587},[157],[15,11522,2470],{"className":11523},[2591],[15,11525],{"className":11526,"style":2587},[157],[15,11528,11530,11533,11536,11539,11542,11545],{"className":11529},[50],[15,11531],{"className":11532,"style":139},[54],[15,11534,113],{"className":11535},[146],[15,11537,117],{"className":11538},[59],[15,11540],{"className":11541,"style":2587},[157],[15,11543,4813],{"className":11544},[2591],[15,11546],{"className":11547,"style":2587},[157],[15,11549,11551,11554,11557,11560],{"className":11550},[50],[15,11552],{"className":11553,"style":139},[54],[15,11555,11339],{"className":11556},[59,60],[15,11558,120],{"className":11559},[153],[15,11561,11563,11566],{"className":11562},[59],[15,11564,206],{"className":11565,"style":334},[59,60],[15,11567,11569],{"className":11568},[281],[15,11570,11572,11592],{"className":11571},[285,286],[15,11573,11575,11589],{"className":11574},[290],[15,11576,11578],{"className":11577,"style":11133},[294],[15,11579,11580,11583],{"style":11136},[15,11581],{"className":11582,"style":303},[302],[15,11584,11586],{"className":11585},[307,308,309,310],[15,11587,2463],{"className":11588},[59,310],[15,11590,318],{"className":11591},[317],[15,11593,11595],{"className":11594},[290],[15,11596,11598],{"className":11597,"style":7968},[294],[15,11599],{},[15,11601,11603,11645],{"className":11602,"translate":19},[18],[15,11604,11606],{"className":11605},[23],[25,11607,11608],{"xmlns":27},[29,11609,11610,11642],{},[32,11611,11612,11614,11616,11618,11624,11626,11628,11630,11632,11634,11636],{},[35,11613,213],{},[110,11615,123],{},[35,11617,11339],{},[195,11619,11620,11622],{},[35,11621,213],{},[115,11623,117],{},[110,11625,2470],{},[110,11627,113],{"stretchy":112},[115,11629,117],{},[110,11631,4813],{},[35,11633,11339],{},[110,11635,120],{"stretchy":112},[195,11637,11638,11640],{},[35,11639,213],{},[115,11641,2463],{},[39,11643,11644],{"encoding":41},"Q=\\lambda Q_1+(1-\\lambda)Q_2",[15,11646,11648,11666,11724,11745],{"className":11647,"ariaHidden":46},[45],[15,11649,11651,11654,11657,11660,11663],{"className":11650},[50],[15,11652],{"className":11653,"style":566},[54],[15,11655,213],{"className":11656},[59,60],[15,11658],{"className":11659,"style":158},[157],[15,11661,123],{"className":11662},[162],[15,11664],{"className":11665,"style":158},[157],[15,11667,11669,11672,11675,11715,11718,11721],{"className":11668},[50],[15,11670],{"className":11671,"style":55},[54],[15,11673,11339],{"className":11674},[59,60],[15,11676,11678,11681],{"className":11677},[59],[15,11679,213],{"className":11680},[59,60],[15,11682,11684],{"className":11683},[281],[15,11685,11687,11707],{"className":11686},[285,286],[15,11688,11690,11704],{"className":11689},[290],[15,11691,11693],{"className":11692,"style":11133},[294],[15,11694,11695,11698],{"style":382},[15,11696],{"className":11697,"style":303},[302],[15,11699,11701],{"className":11700},[307,308,309,310],[15,11702,117],{"className":11703},[59,310],[15,11705,318],{"className":11706},[317],[15,11708,11710],{"className":11709},[290],[15,11711,11713],{"className":11712,"style":7968},[294],[15,11714],{},[15,11716],{"className":11717,"style":2587},[157],[15,11719,2470],{"className":11720},[2591],[15,11722],{"className":11723,"style":2587},[157],[15,11725,11727,11730,11733,11736,11739,11742],{"className":11726},[50],[15,11728],{"className":11729,"style":139},[54],[15,11731,113],{"className":11732},[146],[15,11734,117],{"className":11735},[59],[15,11737],{"className":11738,"style":2587},[157],[15,11740,4813],{"className":11741},[2591],[15,11743],{"className":11744,"style":2587},[157],[15,11746,11748,11751,11754,11757],{"className":11747},[50],[15,11749],{"className":11750,"style":139},[54],[15,11752,11339],{"className":11753},[59,60],[15,11755,120],{"className":11756},[153],[15,11758,11760,11763],{"className":11759},[59],[15,11761,213],{"className":11762},[59,60],[15,11764,11766],{"className":11765},[281],[15,11767,11769,11789],{"className":11768},[285,286],[15,11770,11772,11786],{"className":11771},[290],[15,11773,11775],{"className":11774,"style":11133},[294],[15,11776,11777,11780],{"style":382},[15,11778],{"className":11779,"style":303},[302],[15,11781,11783],{"className":11782},[307,308,309,310],[15,11784,2463],{"className":11785},[59,310],[15,11787,318],{"className":11788},[317],[15,11790,11792],{"className":11791},[290],[15,11793,11795],{"className":11794,"style":7968},[294],[15,11796],{},"。构造扩大一倍的样本空间 ",[15,11799,11801,11838],{"className":11800,"translate":19},[18],[15,11802,11804],{"className":11803},[23],[25,11805,11806],{"xmlns":27},[29,11807,11808,11835],{},[32,11809,11810,11818,11820,11822,11824,11826,11828,11830,11833],{},[11811,11812,11813,11815],"mover",{"accent":46},[35,11814,598],{"mathvariant":597},[110,11816,11817],{},"~",[110,11819,123],{},[110,11821,2898],{"stretchy":112},[115,11823,117],{},[110,11825,551],{"separator":46},[115,11827,2463],{},[110,11829,2908],{"stretchy":112},[110,11831,11832],{},"×",[35,11834,598],{"mathvariant":597},[39,11836,11837],{"encoding":41},"\\tilde{\\mathcal X}=\\{1,2\\}\\times\\mathcal X",[15,11839,11841,11893,11926],{"className":11840,"ariaHidden":46},[45],[15,11842,11844,11848,11884,11887,11890],{"className":11843},[50],[15,11845],{"className":11846,"style":11847},[54],"height:0.9202em;",[15,11849,11852],{"className":11850},[59,11851],"accent",[15,11853,11855],{"className":11854},[285],[15,11856,11858],{"className":11857},[290],[15,11859,11861,11870],{"className":11860,"style":11847},[294],[15,11862,11864,11867],{"style":11863},"top:-3em;",[15,11865],{"className":11866,"style":461},[302],[15,11868,598],{"className":11869,"style":625},[59,624],[15,11871,11873,11876],{"style":11872},"top:-3.6023em;",[15,11874],{"className":11875,"style":461},[302],[15,11877,11881],{"className":11878,"style":11880},[11879],"accent-body","left:-0.1111em;",[15,11882,11817],{"className":11883},[59],[15,11885],{"className":11886,"style":158},[157],[15,11888,123],{"className":11889},[162],[15,11891],{"className":11892,"style":158},[157],[15,11894,11896,11899,11902,11905,11908,11911,11914,11917,11920,11923],{"className":11895},[50],[15,11897],{"className":11898,"style":139},[54],[15,11900,2898],{"className":11901},[146],[15,11903,117],{"className":11904},[59],[15,11906,551],{"className":11907},[573],[15,11909],{"className":11910,"style":406},[157],[15,11912,2463],{"className":11913},[59],[15,11915,2908],{"className":11916},[153],[15,11918],{"className":11919,"style":2587},[157],[15,11921,11832],{"className":11922},[2591],[15,11924],{"className":11925,"style":2587},[157],[15,11927,11929,11932],{"className":11928},[50],[15,11930],{"className":11931,"style":664},[54],[15,11933,598],{"className":11934,"style":625},[59,624]," 及其上的两个分块分布：",[15,11937,11939],{"className":11938,"translate":19},[180],[15,11940,11942,12077],{"className":11941,"translate":19},[18],[15,11943,11945],{"className":11944},[23],[25,11946,11947],{"xmlns":27,"display":189},[29,11948,11949,12074],{},[32,11950,11951,11957,11959,11961,11964,11966,11968,11970,11972,11974,11980,11982,11988,11990,11992,11994,11996,11998,12004,12006,12008,12010,12012,12014,12016,12018,12020,12026,12028,12034,12036,12038,12040,12042,12044,12050,12052,12054,12056,12058,12064,12066,12068,12070,12072],{},[11811,11952,11953,11955],{"accent":46},[35,11954,206],{},[110,11956,11817],{},[110,11958,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,11960,113],{"stretchy":112},[35,11962,11963],{},"i",[110,11965,551],{"separator":46},[35,11967,774],{},[110,11969,120],{"stretchy":112},[110,11971,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,11973,123],{},[195,11975,11976,11978],{},[35,11977,7570],{},[35,11979,11963],{},[1297,11981,1299],{},[195,11983,11984,11986],{},[35,11985,206],{},[35,11987,11963],{},[110,11989,113],{"stretchy":112},[35,11991,774],{},[110,11993,120],{"stretchy":112},[110,11995,551],{"separator":46},[157,11997],{"width":3262},[11811,11999,12000,12002],{"accent":46},[35,12001,213],{},[110,12003,11817],{},[110,12005,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,12007,113],{"stretchy":112},[35,12009,11963],{},[110,12011,551],{"separator":46},[35,12013,774],{},[110,12015,120],{"stretchy":112},[110,12017,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,12019,123],{},[195,12021,12022,12024],{},[35,12023,7570],{},[35,12025,11963],{},[1297,12027,1299],{},[195,12029,12030,12032],{},[35,12031,213],{},[35,12033,11963],{},[110,12035,113],{"stretchy":112},[35,12037,774],{},[110,12039,120],{"stretchy":112},[110,12041,551],{"separator":46},[157,12043],{"width":3262},[195,12045,12046,12048],{},[35,12047,7570],{},[115,12049,117],{},[110,12051,123],{},[35,12053,11339],{},[110,12055,551],{"separator":46},[1297,12057,4283],{},[195,12059,12060,12062],{},[35,12061,7570],{},[115,12063,2463],{},[110,12065,123],{},[115,12067,117],{},[110,12069,4813],{},[35,12071,11339],{},[35,12073,4375],{"mathvariant":209},[39,12075,12076],{"encoding":41},"\\tilde P\\big((i,x)\\big)=w_i\\,P_i(x),\\qquad\n\\tilde Q\\big((i,x)\\big)=w_i\\,Q_i(x),\\qquad\nw_1=\\lambda,\\ w_2=1-\\lambda .",[15,12078,12080,12158,12349,12505,12572,12591],{"className":12079,"ariaHidden":46},[45],[15,12081,12083,12087,12119,12125,12128,12131,12134,12137,12140,12143,12149,12152,12155],{"className":12082},[50],[15,12084],{"className":12085,"style":12086},[54],"height:1.2702em;vertical-align:-0.35em;",[15,12088,12090],{"className":12089},[59,11851],[15,12091,12093],{"className":12092},[285],[15,12094,12096],{"className":12095},[290],[15,12097,12099,12107],{"className":12098,"style":11847},[294],[15,12100,12101,12104],{"style":11863},[15,12102],{"className":12103,"style":461},[302],[15,12105,206],{"className":12106,"style":334},[59,60],[15,12108,12109,12112],{"style":11872},[15,12110],{"className":12111,"style":461},[302],[15,12113,12116],{"className":12114,"style":12115},[11879],"left:-0.1667em;",[15,12117,11817],{"className":12118},[59],[15,12120,12122],{"className":12121},[59],[15,12123,113],{"className":12124},[419,9674],[15,12126,113],{"className":12127},[146],[15,12129,11963],{"className":12130},[59,60],[15,12132,551],{"className":12133},[573],[15,12135],{"className":12136,"style":406},[157],[15,12138,774],{"className":12139},[59,60],[15,12141,120],{"className":12142},[153],[15,12144,12146],{"className":12145},[59],[15,12147,120],{"className":12148},[419,9674],[15,12150],{"className":12151,"style":158},[157],[15,12153,123],{"className":12154},[162],[15,12156],{"className":12157,"style":158},[157],[15,12159,12161,12164,12206,12209,12249,12252,12255,12258,12261,12264,12267,12310,12316,12319,12322,12325,12328,12331,12334,12340,12343,12346],{"className":12160},[50],[15,12162],{"className":12163,"style":12086},[54],[15,12165,12167,12170],{"className":12166},[59],[15,12168,7570],{"className":12169,"style":8274},[59,60],[15,12171,12173],{"className":12172},[281],[15,12174,12176,12198],{"className":12175},[285,286],[15,12177,12179,12195],{"className":12178},[290],[15,12180,12183],{"className":12181,"style":12182},[294],"height:0.3117em;",[15,12184,12186,12189],{"style":12185},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[15,12187],{"className":12188,"style":303},[302],[15,12190,12192],{"className":12191},[307,308,309,310],[15,12193,11963],{"className":12194},[59,60,310],[15,12196,318],{"className":12197},[317],[15,12199,12201],{"className":12200},[290],[15,12202,12204],{"className":12203,"style":7968},[294],[15,12205],{},[15,12207],{"className":12208,"style":406},[157],[15,12210,12212,12215],{"className":12211},[59],[15,12213,206],{"className":12214,"style":334},[59,60],[15,12216,12218],{"className":12217},[281],[15,12219,12221,12241],{"className":12220},[285,286],[15,12222,12224,12238],{"className":12223},[290],[15,12225,12227],{"className":12226,"style":12182},[294],[15,12228,12229,12232],{"style":11136},[15,12230],{"className":12231,"style":303},[302],[15,12233,12235],{"className":12234},[307,308,309,310],[15,12236,11963],{"className":12237},[59,60,310],[15,12239,318],{"className":12240},[317],[15,12242,12244],{"className":12243},[290],[15,12245,12247],{"className":12246,"style":7968},[294],[15,12248],{},[15,12250,113],{"className":12251},[146],[15,12253,774],{"className":12254},[59,60],[15,12256,120],{"className":12257},[153],[15,12259,551],{"className":12260},[573],[15,12262],{"className":12263,"style":3634},[157],[15,12265],{"className":12266,"style":406},[157],[15,12268,12270],{"className":12269},[59,11851],[15,12271,12273,12301],{"className":12272},[285,286],[15,12274,12276,12298],{"className":12275},[290],[15,12277,12279,12287],{"className":12278,"style":11847},[294],[15,12280,12281,12284],{"style":11863},[15,12282],{"className":12283,"style":461},[302],[15,12285,213],{"className":12286},[59,60],[15,12288,12289,12292],{"style":11872},[15,12290],{"className":12291,"style":461},[302],[15,12293,12295],{"className":12294,"style":12115},[11879],[15,12296,11817],{"className":12297},[59],[15,12299,318],{"className":12300},[317],[15,12302,12304],{"className":12303},[290],[15,12305,12308],{"className":12306,"style":12307},[294],"height:0.1944em;",[15,12309],{},[15,12311,12313],{"className":12312},[59],[15,12314,113],{"className":12315},[419,9674],[15,12317,113],{"className":12318},[146],[15,12320,11963],{"className":12321},[59,60],[15,12323,551],{"className":12324},[573],[15,12326],{"className":12327,"style":406},[157],[15,12329,774],{"className":12330},[59,60],[15,12332,120],{"className":12333},[153],[15,12335,12337],{"className":12336},[59],[15,12338,120],{"className":12339},[419,9674],[15,12341],{"className":12342,"style":158},[157],[15,12344,123],{"className":12345},[162],[15,12347],{"className":12348,"style":158},[157],[15,12350,12352,12355,12395,12398,12438,12441,12444,12447,12450,12453,12456,12496,12499,12502],{"className":12351},[50],[15,12353],{"className":12354,"style":139},[54],[15,12356,12358,12361],{"className":12357},[59],[15,12359,7570],{"className":12360,"style":8274},[59,60],[15,12362,12364],{"className":12363},[281],[15,12365,12367,12387],{"className":12366},[285,286],[15,12368,12370,12384],{"className":12369},[290],[15,12371,12373],{"className":12372,"style":12182},[294],[15,12374,12375,12378],{"style":12185},[15,12376],{"className":12377,"style":303},[302],[15,12379,12381],{"className":12380},[307,308,309,310],[15,12382,11963],{"className":12383},[59,60,310],[15,12385,318],{"className":12386},[317],[15,12388,12390],{"className":12389},[290],[15,12391,12393],{"className":12392,"style":7968},[294],[15,12394],{},[15,12396],{"className":12397,"style":406},[157],[15,12399,12401,12404],{"className":12400},[59],[15,12402,213],{"className":12403},[59,60],[15,12405,12407],{"className":12406},[281],[15,12408,12410,12430],{"className":12409},[285,286],[15,12411,12413,12427],{"className":12412},[290],[15,12414,12416],{"className":12415,"style":12182},[294],[15,12417,12418,12421],{"style":382},[15,12419],{"className":12420,"style":303},[302],[15,12422,12424],{"className":12423},[307,308,309,310],[15,12425,11963],{"className":12426},[59,60,310],[15,12428,318],{"className":12429},[317],[15,12431,12433],{"className":12432},[290],[15,12434,12436],{"className":12435,"style":7968},[294],[15,12437],{},[15,12439,113],{"className":12440},[146],[15,12442,774],{"className":12443},[59,60],[15,12445,120],{"className":12446},[153],[15,12448,551],{"className":12449},[573],[15,12451],{"className":12452,"style":3634},[157],[15,12454],{"className":12455,"style":406},[157],[15,12457,12459,12462],{"className":12458},[59],[15,12460,7570],{"className":12461,"style":8274},[59,60],[15,12463,12465],{"className":12464},[281],[15,12466,12468,12488],{"className":12467},[285,286],[15,12469,12471,12485],{"className":12470},[290],[15,12472,12474],{"className":12473,"style":11133},[294],[15,12475,12476,12479],{"style":12185},[15,12477],{"className":12478,"style":303},[302],[15,12480,12482],{"className":12481},[307,308,309,310],[15,12483,117],{"className":12484},[59,310],[15,12486,318],{"className":12487},[317],[15,12489,12491],{"className":12490},[290],[15,12492,12494],{"className":12493,"style":7968},[294],[15,12495],{},[15,12497],{"className":12498,"style":158},[157],[15,12500,123],{"className":12501},[162],[15,12503],{"className":12504,"style":158},[157],[15,12506,12508,12511,12514,12517,12520,12523,12563,12566,12569],{"className":12507},[50],[15,12509],{"className":12510,"style":55},[54],[15,12512,11339],{"className":12513},[59,60],[15,12515,551],{"className":12516},[573],[15,12518,4283],{"className":12519},[157],[15,12521],{"className":12522,"style":406},[157],[15,12524,12526,12529],{"className":12525},[59],[15,12527,7570],{"className":12528,"style":8274},[59,60],[15,12530,12532],{"className":12531},[281],[15,12533,12535,12555],{"className":12534},[285,286],[15,12536,12538,12552],{"className":12537},[290],[15,12539,12541],{"className":12540,"style":11133},[294],[15,12542,12543,12546],{"style":12185},[15,12544],{"className":12545,"style":303},[302],[15,12547,12549],{"className":12548},[307,308,309,310],[15,12550,2463],{"className":12551},[59,310],[15,12553,318],{"className":12554},[317],[15,12556,12558],{"className":12557},[290],[15,12559,12561],{"className":12560,"style":7968},[294],[15,12562],{},[15,12564],{"className":12565,"style":158},[157],[15,12567,123],{"className":12568},[162],[15,12570],{"className":12571,"style":158},[157],[15,12573,12575,12579,12582,12585,12588],{"className":12574},[50],[15,12576],{"className":12577,"style":12578},[54],"height:0.7278em;vertical-align:-0.0833em;",[15,12580,117],{"className":12581},[59],[15,12583],{"className":12584,"style":2587},[157],[15,12586,4813],{"className":12587},[2591],[15,12589],{"className":12590,"style":2587},[157],[15,12592,12594,12598,12601],{"className":12593},[50],[15,12595],{"className":12596,"style":12597},[54],"height:0.6944em;",[15,12599,11339],{"className":12600},[59,60],[15,12602,4375],{"className":12603},[59],[11,12605,12606,12607,6494,12610,12711,12712,12740,12741,5645,12829,12929,12930,13343,13344,13415],{},"取",[1225,12608,12609],{},"确定性核",[15,12611,12613,12645],{"className":12612,"translate":19},[18],[15,12614,12616],{"className":12615},[23],[25,12617,12618],{"xmlns":27},[29,12619,12620,12642],{},[32,12621,12622,12624,12626,12628,12630,12632,12634,12636,12638,12640],{},[35,12623,10694],{},[110,12625,1015],{},[1297,12627,1299],{},[110,12629,113],{"stretchy":112},[35,12631,11963],{},[110,12633,551],{"separator":46},[35,12635,774],{},[110,12637,120],{"stretchy":112},[110,12639,8684],{},[35,12641,774],{},[39,12643,12644],{"encoding":41},"K:\\,(i,x)\\mapsto x",[15,12646,12648,12669,12702],{"className":12647,"ariaHidden":46},[45],[15,12649,12651,12654,12657,12660,12663,12666],{"className":12650},[50],[15,12652],{"className":12653,"style":664},[54],[15,12655,10694],{"className":12656,"style":10782},[59,60],[15,12658],{"className":12659,"style":158},[157],[15,12661,1015],{"className":12662},[162],[15,12664],{"className":12665,"style":406},[157],[15,12667],{"className":12668,"style":158},[157],[15,12670,12672,12675,12678,12681,12684,12687,12690,12693,12696,12699],{"className":12671},[50],[15,12673],{"className":12674,"style":139},[54],[15,12676,113],{"className":12677},[146],[15,12679,11963],{"className":12680},[59,60],[15,12682,551],{"className":12683},[573],[15,12685],{"className":12686,"style":406},[157],[15,12688,774],{"className":12689},[59,60],[15,12691,120],{"className":12692},[153],[15,12694],{"className":12695,"style":158},[157],[15,12697,8684],{"className":12698},[162],[15,12700],{"className":12701,"style":158},[157],[15,12703,12705,12708],{"className":12704},[50],[15,12706],{"className":12707,"style":2345},[54],[15,12709,774],{"className":12710},[59,60],"（\"擦掉\"分量下标，只保留 ",[15,12713,12715,12728],{"className":12714,"translate":19},[18],[15,12716,12718],{"className":12717},[23],[25,12719,12720],{"xmlns":27},[29,12721,12722,12726],{},[32,12723,12724],{},[35,12725,774],{},[39,12727,774],{"encoding":41},[15,12729,12731],{"className":12730,"ariaHidden":46},[45],[15,12732,12734,12737],{"className":12733},[50],[15,12735],{"className":12736,"style":2345},[54],[15,12738,774],{"className":12739},[59,60],"）。由分块结构立刻算出 ",[15,12742,12744,12768],{"className":12743,"translate":19},[18],[15,12745,12747],{"className":12746},[23],[25,12748,12749],{"xmlns":27},[29,12750,12751,12765],{},[32,12752,12753,12759,12761,12763],{},[11811,12754,12755,12757],{"accent":46},[35,12756,206],{},[110,12758,11817],{},[35,12760,10694],{},[110,12762,123],{},[35,12764,206],{},[39,12766,12767],{"encoding":41},"\\tilde PK=P",[15,12769,12771,12820],{"className":12770,"ariaHidden":46},[45],[15,12772,12774,12777,12808,12811,12814,12817],{"className":12773},[50],[15,12775],{"className":12776,"style":11847},[54],[15,12778,12780],{"className":12779},[59,11851],[15,12781,12783],{"className":12782},[285],[15,12784,12786],{"className":12785},[290],[15,12787,12789,12797],{"className":12788,"style":11847},[294],[15,12790,12791,12794],{"style":11863},[15,12792],{"className":12793,"style":461},[302],[15,12795,206],{"className":12796,"style":334},[59,60],[15,12798,12799,12802],{"style":11872},[15,12800],{"className":12801,"style":461},[302],[15,12803,12805],{"className":12804,"style":12115},[11879],[15,12806,11817],{"className":12807},[59],[15,12809,10694],{"className":12810,"style":10782},[59,60],[15,12812],{"className":12813,"style":158},[157],[15,12815,123],{"className":12816},[162],[15,12818],{"className":12819,"style":158},[157],[15,12821,12823,12826],{"className":12822},[50],[15,12824],{"className":12825,"style":664},[54],[15,12827,206],{"className":12828,"style":334},[59,60],[15,12830,12832,12856],{"className":12831,"translate":19},[18],[15,12833,12835],{"className":12834},[23],[25,12836,12837],{"xmlns":27},[29,12838,12839,12853],{},[32,12840,12841,12847,12849,12851],{},[11811,12842,12843,12845],{"accent":46},[35,12844,213],{},[110,12846,11817],{},[35,12848,10694],{},[110,12850,123],{},[35,12852,213],{},[39,12854,12855],{"encoding":41},"\\tilde QK=Q",[15,12857,12859,12920],{"className":12858,"ariaHidden":46},[45],[15,12860,12862,12866,12908,12911,12914,12917],{"className":12861},[50],[15,12863],{"className":12864,"style":12865},[54],"height:1.1146em;vertical-align:-0.1944em;",[15,12867,12869],{"className":12868},[59,11851],[15,12870,12872,12900],{"className":12871},[285,286],[15,12873,12875,12897],{"className":12874},[290],[15,12876,12878,12886],{"className":12877,"style":11847},[294],[15,12879,12880,12883],{"style":11863},[15,12881],{"className":12882,"style":461},[302],[15,12884,213],{"className":12885},[59,60],[15,12887,12888,12891],{"style":11872},[15,12889],{"className":12890,"style":461},[302],[15,12892,12894],{"className":12893,"style":12115},[11879],[15,12895,11817],{"className":12896},[59],[15,12898,318],{"className":12899},[317],[15,12901,12903],{"className":12902},[290],[15,12904,12906],{"className":12905,"style":12307},[294],[15,12907],{},[15,12909,10694],{"className":12910,"style":10782},[59,60],[15,12912],{"className":12913,"style":158},[157],[15,12915,123],{"className":12916},[162],[15,12918],{"className":12919,"style":158},[157],[15,12921,12923,12926],{"className":12922},[50],[15,12924],{"className":12925,"style":566},[54],[15,12927,213],{"className":12928},[59,60],"，且似然比是分块恒定的：",[15,12931,12933,13011],{"className":12932,"translate":19},[18],[15,12934,12936],{"className":12935},[23],[25,12937,12938],{"xmlns":27},[29,12939,12940,13008],{},[32,12941,12942,12966,12968,12970,12972,12974,12976,12978,13002,13004,13006],{},[1255,12943,12944],{"scriptlevel":126,"displaystyle":46},[238,12945,12946,12956],{},[32,12947,12948,12950],{},[35,12949,244],{},[11811,12951,12952,12954],{"accent":46},[35,12953,206],{},[110,12955,11817],{},[32,12957,12958,12960],{},[35,12959,244],{},[11811,12961,12962,12964],{"accent":46},[35,12963,213],{},[110,12965,11817],{},[110,12967,113],{"stretchy":112},[35,12969,11963],{},[110,12971,551],{"separator":46},[35,12973,774],{},[110,12975,120],{"stretchy":112},[110,12977,123],{},[1255,12979,12980],{"scriptlevel":126,"displaystyle":46},[238,12981,12982,12992],{},[32,12983,12984,12986],{},[35,12985,244],{},[195,12987,12988,12990],{},[35,12989,206],{},[35,12991,11963],{},[32,12993,12994,12996],{},[35,12995,244],{},[195,12997,12998,13000],{},[35,12999,213],{},[35,13001,11963],{},[110,13003,113],{"stretchy":112},[35,13005,774],{},[110,13007,120],{"stretchy":112},[39,13009,13010],{"encoding":41},"\\dfrac{d\\tilde P}{d\\tilde Q}(i,x)=\\dfrac{dP_i}{dQ_i}(x)",[15,13012,13014,13186],{"className":13013,"ariaHidden":46},[45],[15,13015,13017,13021,13159,13162,13165,13168,13171,13174,13177,13180,13183],{"className":13016},[50],[15,13018],{"className":13019,"style":13020},[54],"height:2.6018em;vertical-align:-1.0046em;",[15,13022,13024,13027,13156],{"className":13023},[59],[15,13025],{"className":13026},[146,441],[15,13028,13030],{"className":13029},[238],[15,13031,13033,13147],{"className":13032},[285,286],[15,13034,13036,13144],{"className":13035},[290],[15,13037,13040,13094,13102],{"className":13038,"style":13039},[294],"height:1.5972em;",[15,13041,13043,13046],{"style":13042},"top:-2.1898em;",[15,13044],{"className":13045,"style":461},[302],[15,13047,13049,13052],{"className":13048},[59],[15,13050,244],{"className":13051},[59,60],[15,13053,13055],{"className":13054},[59,11851],[15,13056,13058,13086],{"className":13057},[285,286],[15,13059,13061,13083],{"className":13060},[290],[15,13062,13064,13072],{"className":13063,"style":11847},[294],[15,13065,13066,13069],{"style":11863},[15,13067],{"className":13068,"style":461},[302],[15,13070,213],{"className":13071},[59,60],[15,13073,13074,13077],{"style":11872},[15,13075],{"className":13076,"style":461},[302],[15,13078,13080],{"className":13079,"style":12115},[11879],[15,13081,11817],{"className":13082},[59],[15,13084,318],{"className":13085},[317],[15,13087,13089],{"className":13088},[290],[15,13090,13092],{"className":13091,"style":12307},[294],[15,13093],{},[15,13095,13096,13099],{"style":473},[15,13097],{"className":13098,"style":461},[302],[15,13100],{"className":13101,"style":481},[480],[15,13103,13104,13107],{"style":484},[15,13105],{"className":13106,"style":461},[302],[15,13108,13110,13113],{"className":13109},[59],[15,13111,244],{"className":13112},[59,60],[15,13114,13116],{"className":13115},[59,11851],[15,13117,13119],{"className":13118},[285],[15,13120,13122],{"className":13121},[290],[15,13123,13125,13133],{"className":13124,"style":11847},[294],[15,13126,13127,13130],{"style":11863},[15,13128],{"className":13129,"style":461},[302],[15,13131,206],{"className":13132,"style":334},[59,60],[15,13134,13135,13138],{"style":11872},[15,13136],{"className":13137,"style":461},[302],[15,13139,13141],{"className":13140,"style":12115},[11879],[15,13142,11817],{"className":13143},[59],[15,13145,318],{"className":13146},[317],[15,13148,13150],{"className":13149},[290],[15,13151,13154],{"className":13152,"style":13153},[294],"height:1.0046em;",[15,13155],{},[15,13157],{"className":13158},[153,441],[15,13160,113],{"className":13161},[146],[15,13163,11963],{"className":13164},[59,60],[15,13166,551],{"className":13167},[573],[15,13169],{"className":13170,"style":406},[157],[15,13172,774],{"className":13173},[59,60],[15,13175,120],{"className":13176},[153],[15,13178],{"className":13179,"style":158},[157],[15,13181,123],{"className":13182},[162],[15,13184],{"className":13185,"style":158},[157],[15,13187,13189,13192,13334,13337,13340],{"className":13188},[50],[15,13190],{"className":13191,"style":838},[54],[15,13193,13195,13198,13331],{"className":13194},[59],[15,13196],{"className":13197},[146,441],[15,13199,13201],{"className":13200},[238],[15,13202,13204,13323],{"className":13203},[285,286],[15,13205,13207,13320],{"className":13206},[290],[15,13208,13210,13261,13269],{"className":13209,"style":454},[294],[15,13211,13212,13215],{"style":457},[15,13213],{"className":13214,"style":461},[302],[15,13216,13218,13221],{"className":13217},[59],[15,13219,244],{"className":13220},[59,60],[15,13222,13224,13227],{"className":13223},[59],[15,13225,213],{"className":13226},[59,60],[15,13228,13230],{"className":13229},[281],[15,13231,13233,13253],{"className":13232},[285,286],[15,13234,13236,13250],{"className":13235},[290],[15,13237,13239],{"className":13238,"style":12182},[294],[15,13240,13241,13244],{"style":382},[15,13242],{"className":13243,"style":303},[302],[15,13245,13247],{"className":13246},[307,308,309,310],[15,13248,11963],{"className":13249},[59,60,310],[15,13251,318],{"className":13252},[317],[15,13254,13256],{"className":13255},[290],[15,13257,13259],{"className":13258,"style":7968},[294],[15,13260],{},[15,13262,13263,13266],{"style":473},[15,13264],{"className":13265,"style":461},[302],[15,13267],{"className":13268,"style":481},[480],[15,13270,13271,13274],{"style":484},[15,13272],{"className":13273,"style":461},[302],[15,13275,13277,13280],{"className":13276},[59],[15,13278,244],{"className":13279},[59,60],[15,13281,13283,13286],{"className":13282},[59],[15,13284,206],{"className":13285,"style":334},[59,60],[15,13287,13289],{"className":13288},[281],[15,13290,13292,13312],{"className":13291},[285,286],[15,13293,13295,13309],{"className":13294},[290],[15,13296,13298],{"className":13297,"style":12182},[294],[15,13299,13300,13303],{"style":11136},[15,13301],{"className":13302,"style":303},[302],[15,13304,13306],{"className":13305},[307,308,309,310],[15,13307,11963],{"className":13308},[59,60,310],[15,13310,318],{"className":13311},[317],[15,13313,13315],{"className":13314},[290],[15,13316,13318],{"className":13317,"style":7968},[294],[15,13319],{},[15,13321,318],{"className":13322},[317],[15,13324,13326],{"className":13325},[290],[15,13327,13329],{"className":13328,"style":506},[294],[15,13330],{},[15,13332],{"className":13333},[153,441],[15,13335,113],{"className":13336},[146],[15,13338,774],{"className":13339},[59,60],[15,13341,120],{"className":13342},[153],"（权重 ",[15,13345,13347,13365],{"className":13346,"translate":19},[18],[15,13348,13350],{"className":13349},[23],[25,13351,13352],{"xmlns":27},[29,13353,13354,13362],{},[32,13355,13356],{},[195,13357,13358,13360],{},[35,13359,7570],{},[35,13361,11963],{},[39,13363,13364],{"encoding":41},"w_i",[15,13366,13368],{"className":13367,"ariaHidden":46},[45],[15,13369,13371,13375],{"className":13370},[50],[15,13372],{"className":13373,"style":13374},[54],"height:0.5806em;vertical-align:-0.15em;",[15,13376,13378,13381],{"className":13377},[59],[15,13379,7570],{"className":13380,"style":8274},[59,60],[15,13382,13384],{"className":13383},[281],[15,13385,13387,13407],{"className":13386},[285,286],[15,13388,13390,13404],{"className":13389},[290],[15,13391,13393],{"className":13392,"style":12182},[294],[15,13394,13395,13398],{"style":12185},[15,13396],{"className":13397,"style":303},[302],[15,13399,13401],{"className":13400},[307,308,309,310],[15,13402,11963],{"className":13403},[59,60,310],[15,13405,318],{"className":13406},[317],[15,13408,13410],{"className":13409},[290],[15,13411,13413],{"className":13412,"style":7968},[294],[15,13414],{}," 在分子分母中约去）。代入定义：",[15,13417,13419],{"className":13418,"translate":19},[180],[15,13420,13422,13565],{"className":13421,"translate":19},[18],[15,13423,13425],{"className":13424},[23],[25,13426,13427],{"xmlns":27,"display":189},[29,13428,13429,13562],{},[32,13430,13431,13437,13439,13445,13447,13453,13455,13457,13464,13470,13472,13478,13480,13486,13488,13494,13496,13498,13500,13506,13508,13514,13516,13522,13524,13526,13528,13530,13532,13534,13536,13542,13544,13550,13552,13558,13560],{},[195,13432,13433,13435],{},[35,13434,199],{},[35,13436,37],{},[110,13438,113],{"stretchy":112},[11811,13440,13441,13443],{"accent":46},[35,13442,206],{},[110,13444,11817],{},[35,13446,210],{"mathvariant":209},[11811,13448,13449,13451],{"accent":46},[35,13450,213],{},[110,13452,11817],{},[110,13454,120],{"stretchy":112},[110,13456,123],{},[6016,13458,13459,13462],{},[110,13460,13461],{},"∑",[35,13463,11963],{},[195,13465,13466,13468],{},[35,13467,7570],{},[35,13469,11963],{},[1297,13471,1299],{},[195,13473,13474,13476],{},[35,13475,199],{},[35,13477,37],{},[110,13479,113],{"stretchy":112},[195,13481,13482,13484],{},[35,13483,206],{},[35,13485,11963],{},[35,13487,210],{"mathvariant":209},[195,13489,13490,13492],{},[35,13491,213],{},[35,13493,11963],{},[110,13495,120],{"stretchy":112},[110,13497,123],{},[35,13499,11339],{},[195,13501,13502,13504],{},[35,13503,199],{},[35,13505,37],{},[110,13507,113],{"stretchy":112},[195,13509,13510,13512],{},[35,13511,206],{},[115,13513,117],{},[35,13515,210],{"mathvariant":209},[195,13517,13518,13520],{},[35,13519,213],{},[115,13521,117],{},[110,13523,120],{"stretchy":112},[110,13525,2470],{},[110,13527,113],{"stretchy":112},[115,13529,117],{},[110,13531,4813],{},[35,13533,11339],{},[110,13535,120],{"stretchy":112},[195,13537,13538,13540],{},[35,13539,199],{},[35,13541,37],{},[110,13543,113],{"stretchy":112},[195,13545,13546,13548],{},[35,13547,206],{},[115,13549,2463],{},[35,13551,210],{"mathvariant":209},[195,13553,13554,13556],{},[35,13555,213],{},[115,13557,2463],{},[110,13559,120],{"stretchy":112},[35,13561,4375],{"mathvariant":209},[39,13563,13564],{"encoding":41},"D_f(\\tilde P\\|\\tilde Q)\n=\\sum_i w_i\\,D_f(P_i\\|Q_i)\n=\\lambda D_f(P_1\\|Q_1)+(1-\\lambda)D_f(P_2\\|Q_2).",[15,13566,13568,13706,13947,14094,14115],{"className":13567,"ariaHidden":46},[45],[15,13569,13571,13575,13615,13618,13649,13652,13694,13697,13700,13703],{"className":13570},[50],[15,13572],{"className":13573,"style":13574},[54],"height:1.2063em;vertical-align:-0.2861em;",[15,13576,13578,13581],{"className":13577},[59],[15,13579,199],{"className":13580,"style":277},[59,60],[15,13582,13584],{"className":13583},[281],[15,13585,13587,13607],{"className":13586},[285,286],[15,13588,13590,13604],{"className":13589},[290],[15,13591,13593],{"className":13592,"style":295},[294],[15,13594,13595,13598],{"style":298},[15,13596],{"className":13597,"style":303},[302],[15,13599,13601],{"className":13600},[307,308,309,310],[15,13602,37],{"className":13603,"style":61},[59,60,310],[15,13605,318],{"className":13606},[317],[15,13608,13610],{"className":13609},[290],[15,13611,13613],{"className":13612,"style":325},[294],[15,13614],{},[15,13616,113],{"className":13617},[146],[15,13619,13621],{"className":13620},[59,11851],[15,13622,13624],{"className":13623},[285],[15,13625,13627],{"className":13626},[290],[15,13628,13630,13638],{"className":13629,"style":11847},[294],[15,13631,13632,13635],{"style":11863},[15,13633],{"className":13634,"style":461},[302],[15,13636,206],{"className":13637,"style":334},[59,60],[15,13639,13640,13643],{"style":11872},[15,13641],{"className":13642,"style":461},[302],[15,13644,13646],{"className":13645,"style":12115},[11879],[15,13647,11817],{"className":13648},[59],[15,13650,210],{"className":13651},[59],[15,13653,13655],{"className":13654},[59,11851],[15,13656,13658,13686],{"className":13657},[285,286],[15,13659,13661,13683],{"className":13660},[290],[15,13662,13664,13672],{"className":13663,"style":11847},[294],[15,13665,13666,13669],{"style":11863},[15,13667],{"className":13668,"style":461},[302],[15,13670,213],{"className":13671},[59,60],[15,13673,13674,13677],{"style":11872},[15,13675],{"className":13676,"style":461},[302],[15,13678,13680],{"className":13679,"style":12115},[11879],[15,13681,11817],{"className":13682},[59],[15,13684,318],{"className":13685},[317],[15,13687,13689],{"className":13688},[290],[15,13690,13692],{"className":13691,"style":12307},[294],[15,13693],{},[15,13695,120],{"className":13696},[153],[15,13698],{"className":13699,"style":158},[157],[15,13701,123],{"className":13702},[162],[15,13704],{"className":13705,"style":158},[157],[15,13707,13709,13713,13763,13766,13806,13809,13849,13852,13892,13895,13935,13938,13941,13944],{"className":13708},[50],[15,13710],{"className":13711,"style":13712},[54],"height:2.3277em;vertical-align:-1.2777em;",[15,13714,13717],{"className":13715},[1484,13716],"op-limits",[15,13718,13720,13754],{"className":13719},[285,286],[15,13721,13723,13751],{"className":13722},[290],[15,13724,13727,13740],{"className":13725,"style":13726},[294],"height:1.05em;",[15,13728,13730,13734],{"style":13729},"top:-1.8723em;margin-left:0em;",[15,13731],{"className":13732,"style":13733},[302],"height:3.05em;",[15,13735,13737],{"className":13736},[307,308,309,310],[15,13738,11963],{"className":13739},[59,60,310],[15,13741,13743,13746],{"style":13742},"top:-3.05em;",[15,13744],{"className":13745,"style":13733},[302],[15,13747,13748],{},[15,13749,13461],{"className":13750},[1484,1485,1486],[15,13752,318],{"className":13753},[317],[15,13755,13757],{"className":13756},[290],[15,13758,13761],{"className":13759,"style":13760},[294],"height:1.2777em;",[15,13762],{},[15,13764],{"className":13765,"style":406},[157],[15,13767,13769,13772],{"className":13768},[59],[15,13770,7570],{"className":13771,"style":8274},[59,60],[15,13773,13775],{"className":13774},[281],[15,13776,13778,13798],{"className":13777},[285,286],[15,13779,13781,13795],{"className":13780},[290],[15,13782,13784],{"className":13783,"style":12182},[294],[15,13785,13786,13789],{"style":12185},[15,13787],{"className":13788,"style":303},[302],[15,13790,13792],{"className":13791},[307,308,309,310],[15,13793,11963],{"className":13794},[59,60,310],[15,13796,318],{"className":13797},[317],[15,13799,13801],{"className":13800},[290],[15,13802,13804],{"className":13803,"style":7968},[294],[15,13805],{},[15,13807],{"className":13808,"style":406},[157],[15,13810,13812,13815],{"className":13811},[59],[15,13813,199],{"className":13814,"style":277},[59,60],[15,13816,13818],{"className":13817},[281],[15,13819,13821,13841],{"className":13820},[285,286],[15,13822,13824,13838],{"className":13823},[290],[15,13825,13827],{"className":13826,"style":295},[294],[15,13828,13829,13832],{"style":298},[15,13830],{"className":13831,"style":303},[302],[15,13833,13835],{"className":13834},[307,308,309,310],[15,13836,37],{"className":13837,"style":61},[59,60,310],[15,13839,318],{"className":13840},[317],[15,13842,13844],{"className":13843},[290],[15,13845,13847],{"className":13846,"style":325},[294],[15,13848],{},[15,13850,113],{"className":13851},[146],[15,13853,13855,13858],{"className":13854},[59],[15,13856,206],{"className":13857,"style":334},[59,60],[15,13859,13861],{"className":13860},[281],[15,13862,13864,13884],{"className":13863},[285,286],[15,13865,13867,13881],{"className":13866},[290],[15,13868,13870],{"className":13869,"style":12182},[294],[15,13871,13872,13875],{"style":11136},[15,13873],{"className":13874,"style":303},[302],[15,13876,13878],{"className":13877},[307,308,309,310],[15,13879,11963],{"className":13880},[59,60,310],[15,13882,318],{"className":13883},[317],[15,13885,13887],{"className":13886},[290],[15,13888,13890],{"className":13889,"style":7968},[294],[15,13891],{},[15,13893,210],{"className":13894},[59],[15,13896,13898,13901],{"className":13897},[59],[15,13899,213],{"className":13900},[59,60],[15,13902,13904],{"className":13903},[281],[15,13905,13907,13927],{"className":13906},[285,286],[15,13908,13910,13924],{"className":13909},[290],[15,13911,13913],{"className":13912,"style":12182},[294],[15,13914,13915,13918],{"style":382},[15,13916],{"className":13917,"style":303},[302],[15,13919,13921],{"className":13920},[307,308,309,310],[15,13922,11963],{"className":13923},[59,60,310],[15,13925,318],{"className":13926},[317],[15,13928,13930],{"className":13929},[290],[15,13931,13933],{"className":13932,"style":7968},[294],[15,13934],{},[15,13936,120],{"className":13937},[153],[15,13939],{"className":13940,"style":158},[157],[15,13942,123],{"className":13943},[162],[15,13945],{"className":13946,"style":158},[157],[15,13948,13950,13953,13956,13996,13999,14039,14042,14082,14085,14088,14091],{"className":13949},[50],[15,13951],{"className":13952,"style":270},[54],[15,13954,11339],{"className":13955},[59,60],[15,13957,13959,13962],{"className":13958},[59],[15,13960,199],{"className":13961,"style":277},[59,60],[15,13963,13965],{"className":13964},[281],[15,13966,13968,13988],{"className":13967},[285,286],[15,13969,13971,13985],{"className":13970},[290],[15,13972,13974],{"className":13973,"style":295},[294],[15,13975,13976,13979],{"style":298},[15,13977],{"className":13978,"style":303},[302],[15,13980,13982],{"className":13981},[307,308,309,310],[15,13983,37],{"className":13984,"style":61},[59,60,310],[15,13986,318],{"className":13987},[317],[15,13989,13991],{"className":13990},[290],[15,13992,13994],{"className":13993,"style":325},[294],[15,13995],{},[15,13997,113],{"className":13998},[146],[15,14000,14002,14005],{"className":14001},[59],[15,14003,206],{"className":14004,"style":334},[59,60],[15,14006,14008],{"className":14007},[281],[15,14009,14011,14031],{"className":14010},[285,286],[15,14012,14014,14028],{"className":14013},[290],[15,14015,14017],{"className":14016,"style":11133},[294],[15,14018,14019,14022],{"style":11136},[15,14020],{"className":14021,"style":303},[302],[15,14023,14025],{"className":14024},[307,308,309,310],[15,14026,117],{"className":14027},[59,310],[15,14029,318],{"className":14030},[317],[15,14032,14034],{"className":14033},[290],[15,14035,14037],{"className":14036,"style":7968},[294],[15,14038],{},[15,14040,210],{"className":14041},[59],[15,14043,14045,14048],{"className":14044},[59],[15,14046,213],{"className":14047},[59,60],[15,14049,14051],{"className":14050},[281],[15,14052,14054,14074],{"className":14053},[285,286],[15,14055,14057,14071],{"className":14056},[290],[15,14058,14060],{"className":14059,"style":11133},[294],[15,14061,14062,14065],{"style":382},[15,14063],{"className":14064,"style":303},[302],[15,14066,14068],{"className":14067},[307,308,309,310],[15,14069,117],{"className":14070},[59,310],[15,14072,318],{"className":14073},[317],[15,14075,14077],{"className":14076},[290],[15,14078,14080],{"className":14079,"style":7968},[294],[15,14081],{},[15,14083,120],{"className":14084},[153],[15,14086],{"className":14087,"style":2587},[157],[15,14089,2470],{"className":14090},[2591],[15,14092],{"className":14093,"style":2587},[157],[15,14095,14097,14100,14103,14106,14109,14112],{"className":14096},[50],[15,14098],{"className":14099,"style":139},[54],[15,14101,113],{"className":14102},[146],[15,14104,117],{"className":14105},[59],[15,14107],{"className":14108,"style":2587},[157],[15,14110,4813],{"className":14111},[2591],[15,14113],{"className":14114,"style":2587},[157],[15,14116,14118,14121,14124,14127,14167,14170,14210,14213,14253,14256],{"className":14117},[50],[15,14119],{"className":14120,"style":270},[54],[15,14122,11339],{"className":14123},[59,60],[15,14125,120],{"className":14126},[153],[15,14128,14130,14133],{"className":14129},[59],[15,14131,199],{"className":14132,"style":277},[59,60],[15,14134,14136],{"className":14135},[281],[15,14137,14139,14159],{"className":14138},[285,286],[15,14140,14142,14156],{"className":14141},[290],[15,14143,14145],{"className":14144,"style":295},[294],[15,14146,14147,14150],{"style":298},[15,14148],{"className":14149,"style":303},[302],[15,14151,14153],{"className":14152},[307,308,309,310],[15,14154,37],{"className":14155,"style":61},[59,60,310],[15,14157,318],{"className":14158},[317],[15,14160,14162],{"className":14161},[290],[15,14163,14165],{"className":14164,"style":325},[294],[15,14166],{},[15,14168,113],{"className":14169},[146],[15,14171,14173,14176],{"className":14172},[59],[15,14174,206],{"className":14175,"style":334},[59,60],[15,14177,14179],{"className":14178},[281],[15,14180,14182,14202],{"className":14181},[285,286],[15,14183,14185,14199],{"className":14184},[290],[15,14186,14188],{"className":14187,"style":11133},[294],[15,14189,14190,14193],{"style":11136},[15,14191],{"className":14192,"style":303},[302],[15,14194,14196],{"className":14195},[307,308,309,310],[15,14197,2463],{"className":14198},[59,310],[15,14200,318],{"className":14201},[317],[15,14203,14205],{"className":14204},[290],[15,14206,14208],{"className":14207,"style":7968},[294],[15,14209],{},[15,14211,210],{"className":14212},[59],[15,14214,14216,14219],{"className":14215},[59],[15,14217,213],{"className":14218},[59,60],[15,14220,14222],{"className":14221},[281],[15,14223,14225,14245],{"className":14224},[285,286],[15,14226,14228,14242],{"className":14227},[290],[15,14229,14231],{"className":14230,"style":11133},[294],[15,14232,14233,14236],{"style":382},[15,14234],{"className":14235,"style":303},[302],[15,14237,14239],{"className":14238},[307,308,309,310],[15,14240,2463],{"className":14241},[59,310],[15,14243,318],{"className":14244},[317],[15,14246,14248],{"className":14247},[290],[15,14249,14251],{"className":14250,"style":7968},[294],[15,14252],{},[15,14254,120],{"className":14255},[153],[15,14257,4375],{"className":14258},[59],[11,14260,14261,14262,14390],{},"对 ",[15,14263,14265,14295],{"className":14264,"translate":19},[18],[15,14266,14268],{"className":14267},[23],[25,14269,14270],{"xmlns":27},[29,14271,14272,14292],{},[32,14273,14274,14276,14282,14284,14290],{},[110,14275,113],{"stretchy":112},[11811,14277,14278,14280],{"accent":46},[35,14279,206],{},[110,14281,11817],{},[110,14283,551],{"separator":46},[11811,14285,14286,14288],{"accent":46},[35,14287,213],{},[110,14289,11817],{},[110,14291,120],{"stretchy":112},[39,14293,14294],{"encoding":41},"(\\tilde P,\\tilde Q)",[15,14296,14298],{"className":14297,"ariaHidden":46},[45],[15,14299,14301,14305,14308,14339,14342,14345,14387],{"className":14300},[50],[15,14302],{"className":14303,"style":14304},[54],"height:1.1702em;vertical-align:-0.25em;",[15,14306,113],{"className":14307},[146],[15,14309,14311],{"className":14310},[59,11851],[15,14312,14314],{"className":14313},[285],[15,14315,14317],{"className":14316},[290],[15,14318,14320,14328],{"className":14319,"style":11847},[294],[15,14321,14322,14325],{"style":11863},[15,14323],{"className":14324,"style":461},[302],[15,14326,206],{"className":14327,"style":334},[59,60],[15,14329,14330,14333],{"style":11872},[15,14331],{"className":14332,"style":461},[302],[15,14334,14336],{"className":14335,"style":12115},[11879],[15,14337,11817],{"className":14338},[59],[15,14340,551],{"className":14341},[573],[15,14343],{"className":14344,"style":406},[157],[15,14346,14348],{"className":14347},[59,11851],[15,14349,14351,14379],{"className":14350},[285,286],[15,14352,14354,14376],{"className":14353},[290],[15,14355,14357,14365],{"className":14356,"style":11847},[294],[15,14358,14359,14362],{"style":11863},[15,14360],{"className":14361,"style":461},[302],[15,14363,213],{"className":14364},[59,60],[15,14366,14367,14370],{"style":11872},[15,14368],{"className":14369,"style":461},[302],[15,14371,14373],{"className":14372,"style":12115},[11879],[15,14374,11817],{"className":14375},[59],[15,14377,318],{"className":14378},[317],[15,14380,14382],{"className":14381},[290],[15,14383,14385],{"className":14384,"style":12307},[294],[15,14386],{},[15,14388,120],{"className":14389},[153]," 使用 DPI，即得到联合凸性：",[15,14392,14394],{"className":14393,"translate":19},[180],[15,14395,14397,14577],{"className":14396,"translate":19},[18],[15,14398,14400],{"className":14399},[23],[25,14401,14402],{"xmlns":27,"display":189},[29,14403,14404,14574],{},[1243,14405,14406,14490],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,14407,14408,14414],{},[1252,14409,14410],{},[1255,14411,14412],{"scriptlevel":126,"displaystyle":46},[32,14413],{},[1252,14415,14416],{},[1255,14417,14418],{"scriptlevel":126,"displaystyle":46},[32,14419,14420,14422,14428,14430,14432,14438,14440,14442,14444,14446,14448,14450,14456,14458,14460,14462,14464,14470,14472,14474,14476,14478,14480,14482,14488],{},[32,14421],{},[195,14423,14424,14426],{},[35,14425,199],{},[35,14427,37],{},[110,14429,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,14431,11339],{},[195,14433,14434,14436],{},[35,14435,206],{},[115,14437,117],{},[110,14439,2470],{},[110,14441,113],{"stretchy":112},[115,14443,117],{},[110,14445,4813],{},[35,14447,11339],{},[110,14449,120],{"stretchy":112},[195,14451,14452,14454],{},[35,14453,206],{},[115,14455,2463],{},[1297,14457,1299],{},[110,14459,210],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,14461,1299],{},[35,14463,11339],{},[195,14465,14466,14468],{},[35,14467,213],{},[115,14469,117],{},[110,14471,2470],{},[110,14473,113],{"stretchy":112},[115,14475,117],{},[110,14477,4813],{},[35,14479,11339],{},[110,14481,120],{"stretchy":112},[195,14483,14484,14486],{},[35,14485,213],{},[115,14487,2463],{},[110,14489,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,14491,14492,14498],{},[1252,14493,14494],{},[1255,14495,14496],{"scriptlevel":126,"displaystyle":46},[32,14497],{},[1252,14499,14500],{},[1255,14501,14502],{"scriptlevel":126,"displaystyle":46},[32,14503,14504,14506,14508,14510,14512,14518,14520,14526,14528,14534,14536,14538,14540,14542,14544,14546,14548,14554,14556,14562,14564,14570,14572],{},[32,14505],{},[157,14507],{"width":3262},[110,14509,9952],{},[35,14511,11339],{},[195,14513,14514,14516],{},[35,14515,199],{},[35,14517,37],{},[110,14519,113],{"stretchy":112},[195,14521,14522,14524],{},[35,14523,206],{},[115,14525,117],{},[35,14527,210],{"mathvariant":209},[195,14529,14530,14532],{},[35,14531,213],{},[115,14533,117],{},[110,14535,120],{"stretchy":112},[110,14537,2470],{},[110,14539,113],{"stretchy":112},[115,14541,117],{},[110,14543,4813],{},[35,14545,11339],{},[110,14547,120],{"stretchy":112},[195,14549,14550,14552],{},[35,14551,199],{},[35,14553,37],{},[110,14555,113],{"stretchy":112},[195,14557,14558,14560],{},[35,14559,206],{},[115,14561,2463],{},[35,14563,210],{"mathvariant":209},[195,14565,14566,14568],{},[35,14567,213],{},[115,14569,2463],{},[110,14571,120],{"stretchy":112},[35,14573,4375],{"mathvariant":209},[39,14575,14576],{"encoding":41},"\\begin{aligned}\n&D_f\\big(\\lambda P_1+(1-\\lambda)P_2\n\\,\\big\\|\\,\\lambda Q_1+(1-\\lambda)Q_2\\big)\\\\\n&\\qquad\\le \\lambda D_f(P_1\\|Q_1)\n+(1-\\lambda)D_f(P_2\\|Q_2).\n\\end{aligned}",[15,14578,14580],{"className":14579,"ariaHidden":46},[45],[15,14581,14583,14587],{"className":14582},[50],[15,14584],{"className":14585,"style":14586},[54],"height:2.71em;vertical-align:-1.105em;",[15,14588,14590],{"className":14589},[59],[15,14591,14593,14637],{"className":14592},[1243],[15,14594,14596],{"className":14595},[1360],[15,14597,14599,14628],{"className":14598},[285,286],[15,14600,14602,14625],{"className":14601},[290],[15,14603,14606,14616],{"className":14604,"style":14605},[294],"height:1.605em;",[15,14607,14609,14613],{"style":14608},"top:-3.605em;",[15,14610],{"className":14611,"style":14612},[302],"height:2.85em;",[15,14614],{"className":14615},[59],[15,14617,14619,14622],{"style":14618},"top:-2.105em;",[15,14620],{"className":14621,"style":14612},[302],[15,14623],{"className":14624},[59],[15,14626,318],{"className":14627},[317],[15,14629,14631],{"className":14630},[290],[15,14632,14635],{"className":14633,"style":14634},[294],"height:1.105em;",[15,14636],{},[15,14638,14640],{"className":14639},[1451],[15,14641,14643,15312],{"className":14642},[285,286],[15,14644,14646,15309],{"className":14645},[290],[15,14647,14649,14991],{"className":14648,"style":14605},[294],[15,14650,14652,14655],{"style":14651},"top:-3.755em;",[15,14653],{"className":14654,"style":461},[302],[15,14656,14658,14661,14701,14707,14710,14750,14753,14756,14759,14762,14765,14768,14771,14774,14777,14780,14820,14823,14869,14872,14875,14915,14918,14921,14924,14927,14930,14933,14936,14939,14942,14945,14985],{"className":14657},[59],[15,14659],{"className":14660},[59],[15,14662,14664,14667],{"className":14663},[59],[15,14665,199],{"className":14666,"style":277},[59,60],[15,14668,14670],{"className":14669},[281],[15,14671,14673,14693],{"className":14672},[285,286],[15,14674,14676,14690],{"className":14675},[290],[15,14677,14679],{"className":14678,"style":295},[294],[15,14680,14681,14684],{"style":298},[15,14682],{"className":14683,"style":303},[302],[15,14685,14687],{"className":14686},[307,308,309,310],[15,14688,37],{"className":14689,"style":61},[59,60,310],[15,14691,318],{"className":14692},[317],[15,14694,14696],{"className":14695},[290],[15,14697,14699],{"className":14698,"style":325},[294],[15,14700],{},[15,14702,14704],{"className":14703},[59],[15,14705,113],{"className":14706},[419,9674],[15,14708,11339],{"className":14709},[59,60],[15,14711,14713,14716],{"className":14712},[59],[15,14714,206],{"className":14715,"style":334},[59,60],[15,14717,14719],{"className":14718},[281],[15,14720,14722,14742],{"className":14721},[285,286],[15,14723,14725,14739],{"className":14724},[290],[15,14726,14728],{"className":14727,"style":11133},[294],[15,14729,14730,14733],{"style":11136},[15,14731],{"className":14732,"style":303},[302],[15,14734,14736],{"className":14735},[307,308,309,310],[15,14737,117],{"className":14738},[59,310],[15,14740,318],{"className":14741},[317],[15,14743,14745],{"className":14744},[290],[15,14746,14748],{"className":14747,"style":7968},[294],[15,14749],{},[15,14751],{"className":14752,"style":2587},[157],[15,14754,2470],{"className":14755},[2591],[15,14757],{"className":14758,"style":2587},[157],[15,14760,113],{"className":14761},[146],[15,14763,117],{"className":14764},[59],[15,14766],{"className":14767,"style":2587},[157],[15,14769,4813],{"className":14770},[2591],[15,14772],{"className":14773,"style":2587},[157],[15,14775,11339],{"className":14776},[59,60],[15,14778,120],{"className":14779},[153],[15,14781,14783,14786],{"className":14782},[59],[15,14784,206],{"className":14785,"style":334},[59,60],[15,14787,14789],{"className":14788},[281],[15,14790,14792,14812],{"className":14791},[285,286],[15,14793,14795,14809],{"className":14794},[290],[15,14796,14798],{"className":14797,"style":11133},[294],[15,14799,14800,14803],{"style":11136},[15,14801],{"className":14802,"style":303},[302],[15,14804,14806],{"className":14805},[307,308,309,310],[15,14807,2463],{"className":14808},[59,310],[15,14810,318],{"className":14811},[317],[15,14813,14815],{"className":14814},[290],[15,14816,14818],{"className":14817,"style":7968},[294],[15,14819],{},[15,14821],{"className":14822,"style":406},[157],[15,14824,14826],{"className":14825},[59],[15,14827,14830],{"className":14828},[419,14829],"mult",[15,14831,14833,14860],{"className":14832},[285,286],[15,14834,14836,14857],{"className":14835},[290],[15,14837,14840],{"className":14838,"style":14839},[294],"height:0.85em;",[15,14841,14843,14847],{"style":14842},"top:-2.85em;",[15,14844],{"className":14845,"style":14846},[302],"height:3.2em;",[15,14848,14850],{"style":14849},"width:0.556em;height:1.2em;",[6323,14851,14854],{"xmlns":6325,"width":14852,"height":9450,"viewBox":14853},"0.556em","0 0 556 1200",[6331,14855],{"d":14856},"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",[15,14858,318],{"className":14859},[317],[15,14861,14863],{"className":14862},[290],[15,14864,14867],{"className":14865,"style":14866},[294],"height:0.35em;",[15,14868],{},[15,14870],{"className":14871,"style":406},[157],[15,14873,11339],{"className":14874},[59,60],[15,14876,14878,14881],{"className":14877},[59],[15,14879,213],{"className":14880},[59,60],[15,14882,14884],{"className":14883},[281],[15,14885,14887,14907],{"className":14886},[285,286],[15,14888,14890,14904],{"className":14889},[290],[15,14891,14893],{"className":14892,"style":11133},[294],[15,14894,14895,14898],{"style":382},[15,14896],{"className":14897,"style":303},[302],[15,14899,14901],{"className":14900},[307,308,309,310],[15,14902,117],{"className":14903},[59,310],[15,14905,318],{"className":14906},[317],[15,14908,14910],{"className":14909},[290],[15,14911,14913],{"className":14912,"style":7968},[294],[15,14914],{},[15,14916],{"className":14917,"style":2587},[157],[15,14919,2470],{"className":14920},[2591],[15,14922],{"className":14923,"style":2587},[157],[15,14925,113],{"className":14926},[146],[15,14928,117],{"className":14929},[59],[15,14931],{"className":14932,"style":2587},[157],[15,14934,4813],{"className":14935},[2591],[15,14937],{"className":14938,"style":2587},[157],[15,14940,11339],{"className":14941},[59,60],[15,14943,120],{"className":14944},[153],[15,14946,14948,14951],{"className":14947},[59],[15,14949,213],{"className":14950},[59,60],[15,14952,14954],{"className":14953},[281],[15,14955,14957,14977],{"className":14956},[285,286],[15,14958,14960,14974],{"className":14959},[290],[15,14961,14963],{"className":14962,"style":11133},[294],[15,14964,14965,14968],{"style":382},[15,14966],{"className":14967,"style":303},[302],[15,14969,14971],{"className":14970},[307,308,309,310],[15,14972,2463],{"className":14973},[59,310],[15,14975,318],{"className":14976},[317],[15,14978,14980],{"className":14979},[290],[15,14981,14983],{"className":14982,"style":7968},[294],[15,14984],{},[15,14986,14988],{"className":14987},[59],[15,14989,120],{"className":14990},[419,9674],[15,14992,14994,14997],{"style":14993},"top:-2.255em;",[15,14995],{"className":14996,"style":461},[302],[15,14998,15000,15003,15006,15009,15012,15015,15018,15058,15061,15101,15104,15144,15147,15150,15153,15156,15159,15162,15165,15168,15171,15174,15177,15217,15220,15260,15263,15303,15306],{"className":14999},[59],[15,15001],{"className":15002},[59],[15,15004],{"className":15005,"style":3634},[157],[15,15007],{"className":15008,"style":158},[157],[15,15010,9952],{"className":15011},[162],[15,15013],{"className":15014,"style":158},[157],[15,15016,11339],{"className":15017},[59,60],[15,15019,15021,15024],{"className":15020},[59],[15,15022,199],{"className":15023,"style":277},[59,60],[15,15025,15027],{"className":15026},[281],[15,15028,15030,15050],{"className":15029},[285,286],[15,15031,15033,15047],{"className":15032},[290],[15,15034,15036],{"className":15035,"style":295},[294],[15,15037,15038,15041],{"style":298},[15,15039],{"className":15040,"style":303},[302],[15,15042,15044],{"className":15043},[307,308,309,310],[15,15045,37],{"className":15046,"style":61},[59,60,310],[15,15048,318],{"className":15049},[317],[15,15051,15053],{"className":15052},[290],[15,15054,15056],{"className":15055,"style":325},[294],[15,15057],{},[15,15059,113],{"className":15060},[146],[15,15062,15064,15067],{"className":15063},[59],[15,15065,206],{"className":15066,"style":334},[59,60],[15,15068,15070],{"className":15069},[281],[15,15071,15073,15093],{"className":15072},[285,286],[15,15074,15076,15090],{"className":15075},[290],[15,15077,15079],{"className":15078,"style":11133},[294],[15,15080,15081,15084],{"style":11136},[15,15082],{"className":15083,"style":303},[302],[15,15085,15087],{"className":15086},[307,308,309,310],[15,15088,117],{"className":15089},[59,310],[15,15091,318],{"className":15092},[317],[15,15094,15096],{"className":15095},[290],[15,15097,15099],{"className":15098,"style":7968},[294],[15,15100],{},[15,15102,210],{"className":15103},[59],[15,15105,15107,15110],{"className":15106},[59],[15,15108,213],{"className":15109},[59,60],[15,15111,15113],{"className":15112},[281],[15,15114,15116,15136],{"className":15115},[285,286],[15,15117,15119,15133],{"className":15118},[290],[15,15120,15122],{"className":15121,"style":11133},[294],[15,15123,15124,15127],{"style":382},[15,15125],{"className":15126,"style":303},[302],[15,15128,15130],{"className":15129},[307,308,309,310],[15,15131,117],{"className":15132},[59,310],[15,15134,318],{"className":15135},[317],[15,15137,15139],{"className":15138},[290],[15,15140,15142],{"className":15141,"style":7968},[294],[15,15143],{},[15,15145,120],{"className":15146},[153],[15,15148],{"className":15149,"style":2587},[157],[15,15151,2470],{"className":15152},[2591],[15,15154],{"className":15155,"style":2587},[157],[15,15157,113],{"className":15158},[146],[15,15160,117],{"className":15161},[59],[15,15163],{"className":15164,"style":2587},[157],[15,15166,4813],{"className":15167},[2591],[15,15169],{"className":15170,"style":2587},[157],[15,15172,11339],{"className":15173},[59,60],[15,15175,120],{"className":15176},[153],[15,15178,15180,15183],{"className":15179},[59],[15,15181,199],{"className":15182,"style":277},[59,60],[15,15184,15186],{"className":15185},[281],[15,15187,15189,15209],{"className":15188},[285,286],[15,15190,15192,15206],{"className":15191},[290],[15,15193,15195],{"className":15194,"style":295},[294],[15,15196,15197,15200],{"style":298},[15,15198],{"className":15199,"style":303},[302],[15,15201,15203],{"className":15202},[307,308,309,310],[15,15204,37],{"className":15205,"style":61},[59,60,310],[15,15207,318],{"className":15208},[317],[15,15210,15212],{"className":15211},[290],[15,15213,15215],{"className":15214,"style":325},[294],[15,15216],{},[15,15218,113],{"className":15219},[146],[15,15221,15223,15226],{"className":15222},[59],[15,15224,206],{"className":15225,"style":334},[59,60],[15,15227,15229],{"className":15228},[281],[15,15230,15232,15252],{"className":15231},[285,286],[15,15233,15235,15249],{"className":15234},[290],[15,15236,15238],{"className":15237,"style":11133},[294],[15,15239,15240,15243],{"style":11136},[15,15241],{"className":15242,"style":303},[302],[15,15244,15246],{"className":15245},[307,308,309,310],[15,15247,2463],{"className":15248},[59,310],[15,15250,318],{"className":15251},[317],[15,15253,15255],{"className":15254},[290],[15,15256,15258],{"className":15257,"style":7968},[294],[15,15259],{},[15,15261,210],{"className":15262},[59],[15,15264,15266,15269],{"className":15265},[59],[15,15267,213],{"className":15268},[59,60],[15,15270,15272],{"className":15271},[281],[15,15273,15275,15295],{"className":15274},[285,286],[15,15276,15278,15292],{"className":15277},[290],[15,15279,15281],{"className":15280,"style":11133},[294],[15,15282,15283,15286],{"style":382},[15,15284],{"className":15285,"style":303},[302],[15,15287,15289],{"className":15288},[307,308,309,310],[15,15290,2463],{"className":15291},[59,310],[15,15293,318],{"className":15294},[317],[15,15296,15298],{"className":15297},[290],[15,15299,15301],{"className":15300,"style":7968},[294],[15,15302],{},[15,15304,120],{"className":15305},[153],[15,15307,4375],{"className":15308},[59],[15,15310,318],{"className":15311},[317],[15,15313,15315],{"className":15314},[290],[15,15316,15318],{"className":15317,"style":14634},[294],[15,15319],{},[11,15321,15322,15381,15382,2409,15448,15521,15522,15638,15639,15691,15692,15795,15796,15870],{},[1225,15323,15324,15325,6494,15353,10965],{},"第二步：联合凸 ",[15,15326,15328,15341],{"className":15327,"translate":19},[18],[15,15329,15331],{"className":15330},[23],[25,15332,15333],{"xmlns":27},[29,15334,15335,15339],{},[32,15336,15337],{},[110,15338,10990],{},[39,15340,10993],{"encoding":41},[15,15342,15344],{"className":15343,"ariaHidden":46},[45],[15,15345,15347,15350],{"className":15346},[50],[15,15348],{"className":15349,"style":11003},[54],[15,15351,10990],{"className":15352},[162],[15,15354,15356,15369],{"className":15355,"translate":19},[18],[15,15357,15359],{"className":15358},[23],[25,15360,15361],{"xmlns":27},[29,15362,15363,15367],{},[32,15364,15365],{},[35,15366,37],{},[39,15368,37],{"encoding":41},[15,15370,15372],{"className":15371,"ariaHidden":46},[45],[15,15373,15375,15378],{"className":15374},[50],[15,15376],{"className":15377,"style":55},[54],[15,15379,37],{"className":15380,"style":61},[59,60]," 固定 ",[15,15383,15385,15408],{"className":15384,"translate":19},[18],[15,15386,15388],{"className":15387},[23],[25,15389,15390],{"xmlns":27},[29,15391,15392,15405],{},[32,15393,15394,15396,15398,15401,15403],{},[35,15395,7561],{},[110,15397,551],{"separator":46},[35,15399,15400],{},"u",[110,15402,6928],{},[115,15404,126],{},[39,15406,15407],{"encoding":41},"s,u\\ge0",[15,15409,15411,15439],{"className":15410,"ariaHidden":46},[45],[15,15412,15414,15418,15421,15424,15427,15430,15433,15436],{"className":15413},[50],[15,15415],{"className":15416,"style":15417},[54],"height:0.8304em;vertical-align:-0.1944em;",[15,15419,7561],{"className":15420},[59,60],[15,15422,551],{"className":15423},[573],[15,15425],{"className":15426,"style":406},[157],[15,15428,15400],{"className":15429},[59,60],[15,15431],{"className":15432,"style":158},[157],[15,15434,6928],{"className":15435},[162],[15,15437],{"className":15438,"style":158},[157],[15,15440,15442,15445],{"className":15441},[50],[15,15443],{"className":15444,"style":172},[54],[15,15446,126],{"className":15447},[59],[15,15449,15451,15476],{"className":15450,"translate":19},[18],[15,15452,15454],{"className":15453},[23],[25,15455,15456],{"xmlns":27},[29,15457,15458,15474],{},[32,15459,15460,15462,15464,15466,15468,15470,15472],{},[35,15461,11339],{},[110,15463,5909],{},[110,15465,113],{"stretchy":112},[115,15467,126],{},[110,15469,551],{"separator":46},[115,15471,117],{},[110,15473,120],{"stretchy":112},[39,15475,11354],{"encoding":41},[15,15477,15479,15497],{"className":15478,"ariaHidden":46},[45],[15,15480,15482,15485,15488,15491,15494],{"className":15481},[50],[15,15483],{"className":15484,"style":11364},[54],[15,15486,11339],{"className":15487},[59,60],[15,15489],{"className":15490,"style":158},[157],[15,15492,5909],{"className":15493},[162],[15,15495],{"className":15496,"style":158},[157],[15,15498,15500,15503,15506,15509,15512,15515,15518],{"className":15499},[50],[15,15501],{"className":15502,"style":139},[54],[15,15504,113],{"className":15505},[146],[15,15507,126],{"className":15508},[59],[15,15510,551],{"className":15511},[573],[15,15513],{"className":15514,"style":406},[157],[15,15516,117],{"className":15517},[59],[15,15519,120],{"className":15520},[153],"，记目标值 ",[15,15523,15525,15559],{"className":15524,"translate":19},[18],[15,15526,15528],{"className":15527},[23],[25,15529,15530],{"xmlns":27},[29,15531,15532,15556],{},[32,15533,15534,15536,15538,15540,15542,15544,15546,15548,15550,15552,15554],{},[35,15535,7570],{},[110,15537,123],{},[35,15539,11339],{},[35,15541,7561],{},[110,15543,2470],{},[110,15545,113],{"stretchy":112},[115,15547,117],{},[110,15549,4813],{},[35,15551,11339],{},[110,15553,120],{"stretchy":112},[35,15555,15400],{},[39,15557,15558],{"encoding":41},"w=\\lambda s+(1-\\lambda)u",[15,15560,15562,15580,15602,15623],{"className":15561,"ariaHidden":46},[45],[15,15563,15565,15568,15571,15574,15577],{"className":15564},[50],[15,15566],{"className":15567,"style":2345},[54],[15,15569,7570],{"className":15570,"style":8274},[59,60],[15,15572],{"className":15573,"style":158},[157],[15,15575,123],{"className":15576},[162],[15,15578],{"className":15579,"style":158},[157],[15,15581,15583,15587,15590,15593,15596,15599],{"className":15582},[50],[15,15584],{"className":15585,"style":15586},[54],"height:0.7778em;vertical-align:-0.0833em;",[15,15588,11339],{"className":15589},[59,60],[15,15591,7561],{"className":15592},[59,60],[15,15594],{"className":15595,"style":2587},[157],[15,15597,2470],{"className":15598},[2591],[15,15600],{"className":15601,"style":2587},[157],[15,15603,15605,15608,15611,15614,15617,15620],{"className":15604},[50],[15,15606],{"className":15607,"style":139},[54],[15,15609,113],{"className":15610},[146],[15,15612,117],{"className":15613},[59],[15,15615],{"className":15616,"style":2587},[157],[15,15618,4813],{"className":15619},[2591],[15,15621],{"className":15622,"style":2587},[157],[15,15624,15626,15629,15632,15635],{"className":15625},[50],[15,15627],{"className":15628,"style":139},[54],[15,15630,11339],{"className":15631},[59,60],[15,15633,120],{"className":15634},[153],[15,15636,15400],{"className":15637},[59,60],"。在两点空间 ",[15,15640,15642,15664],{"className":15641,"translate":19},[18],[15,15643,15645],{"className":15644},[23],[25,15646,15647],{"xmlns":27},[29,15648,15649,15661],{},[32,15650,15651,15653,15655,15657,15659],{},[110,15652,2898],{"stretchy":112},[115,15654,117],{},[110,15656,551],{"separator":46},[115,15658,2463],{},[110,15660,2908],{"stretchy":112},[39,15662,15663],{"encoding":41},"\\{1,2\\}",[15,15665,15667],{"className":15666,"ariaHidden":46},[45],[15,15668,15670,15673,15676,15679,15682,15685,15688],{"className":15669},[50],[15,15671],{"className":15672,"style":139},[54],[15,15674,2898],{"className":15675},[146],[15,15677,117],{"className":15678},[59],[15,15680,551],{"className":15681},[573],[15,15683],{"className":15684,"style":406},[157],[15,15686,2463],{"className":15687},[59],[15,15689,2908],{"className":15690},[153]," 上取同一个底分布 ",[15,15693,15695,15728],{"className":15694,"translate":19},[18],[15,15696,15698],{"className":15697},[23],[25,15699,15700],{"xmlns":27},[29,15701,15702,15725],{},[32,15703,15704,15706,15708,15710,15713,15715,15717,15719,15721,15723],{},[35,15705,213],{},[110,15707,123],{},[110,15709,113],{"stretchy":112},[35,15711,15712],{},"δ",[110,15714,551],{"separator":46},[1297,15716,1299],{},[115,15718,117],{},[110,15720,4813],{},[35,15722,15712],{},[110,15724,120],{"stretchy":112},[39,15726,15727],{"encoding":41},"Q=(\\delta,\\,1-\\delta)",[15,15729,15731,15749,15783],{"className":15730,"ariaHidden":46},[45],[15,15732,15734,15737,15740,15743,15746],{"className":15733},[50],[15,15735],{"className":15736,"style":566},[54],[15,15738,213],{"className":15739},[59,60],[15,15741],{"className":15742,"style":158},[157],[15,15744,123],{"className":15745},[162],[15,15747],{"className":15748,"style":158},[157],[15,15750,15752,15755,15758,15762,15765,15768,15771,15774,15777,15780],{"className":15751},[50],[15,15753],{"className":15754,"style":139},[54],[15,15756,113],{"className":15757},[146],[15,15759,15712],{"className":15760,"style":15761},[59,60],"margin-right:0.0379em;",[15,15763,551],{"className":15764},[573],[15,15766],{"className":15767,"style":406},[157],[15,15769],{"className":15770,"style":406},[157],[15,15772,117],{"className":15773},[59],[15,15775],{"className":15776,"style":2587},[157],[15,15778,4813],{"className":15779},[2591],[15,15781],{"className":15782,"style":2587},[157],[15,15784,15786,15789,15792],{"className":15785},[50],[15,15787],{"className":15788,"style":139},[54],[15,15790,15712],{"className":15791,"style":15761},[59,60],[15,15793,120],{"className":15794},[153],"（",[15,15797,15799,15825],{"className":15798,"translate":19},[18],[15,15800,15802],{"className":15801},[23],[25,15803,15804],{"xmlns":27},[29,15805,15806,15822],{},[32,15807,15808,15810,15812,15814,15816,15818,15820],{},[35,15809,15712],{},[110,15811,5909],{},[110,15813,113],{"stretchy":112},[115,15815,126],{},[110,15817,551],{"separator":46},[115,15819,117],{},[110,15821,120],{"stretchy":112},[39,15823,15824],{"encoding":41},"\\delta\\in(0,1)",[15,15826,15828,15846],{"className":15827,"ariaHidden":46},[45],[15,15829,15831,15834,15837,15840,15843],{"className":15830},[50],[15,15832],{"className":15833,"style":11364},[54],[15,15835,15712],{"className":15836,"style":15761},[59,60],[15,15838],{"className":15839,"style":158},[157],[15,15841,5909],{"className":15842},[162],[15,15844],{"className":15845,"style":158},[157],[15,15847,15849,15852,15855,15858,15861,15864,15867],{"className":15848},[50],[15,15850],{"className":15851,"style":139},[54],[15,15853,113],{"className":15854},[146],[15,15856,126],{"className":15857},[59],[15,15859,551],{"className":15860},[573],[15,15862],{"className":15863,"style":406},[157],[15,15865,117],{"className":15866},[59],[15,15868,120],{"className":15869},[153]," 充分小），并取似然比在第一坐标上为常数的分布：",[15,15872,15874],{"className":15873,"translate":19},[180],[15,15875,15877,15952],{"className":15876,"translate":19},[18],[15,15878,15880],{"className":15879},[23],[25,15881,15882],{"xmlns":27,"display":189},[29,15883,15884,15949],{},[32,15885,15886,15892,15894,15896,15898,15900,15902,15905,15907,15909,15911,15913,15915,15917,15919,15925,15927,15929,15931,15933,15935,15937,15939,15941,15943,15945,15947],{},[195,15887,15888,15890],{},[35,15889,206],{},[115,15891,117],{},[110,15893,123],{},[110,15895,113],{"stretchy":112},[35,15897,7561],{},[35,15899,15712],{},[110,15901,551],{"separator":46},[1297,15903,15904],{},"  ",[115,15906,117],{},[110,15908,4813],{},[35,15910,7561],{},[35,15912,15712],{},[110,15914,120],{"stretchy":112},[110,15916,551],{"separator":46},[157,15918],{"width":3262},[195,15920,15921,15923],{},[35,15922,206],{},[115,15924,2463],{},[110,15926,123],{},[110,15928,113],{"stretchy":112},[35,15930,15400],{},[35,15932,15712],{},[110,15934,551],{"separator":46},[1297,15936,15904],{},[115,15938,117],{},[110,15940,4813],{},[35,15942,15400],{},[35,15944,15712],{},[110,15946,120],{"stretchy":112},[110,15948,551],{"separator":46},[39,15950,15951],{"encoding":41},"P_1=(s\\delta,\\;1-s\\delta),\\qquad\nP_2=(u\\delta,\\;1-u\\delta),",[15,15953,15955,16011,16045,16115,16151],{"className":15954,"ariaHidden":46},[45],[15,15956,15958,15962,16002,16005,16008],{"className":15957},[50],[15,15959],{"className":15960,"style":15961},[54],"height:0.8333em;vertical-align:-0.15em;",[15,15963,15965,15968],{"className":15964},[59],[15,15966,206],{"className":15967,"style":334},[59,60],[15,15969,15971],{"className":15970},[281],[15,15972,15974,15994],{"className":15973},[285,286],[15,15975,15977,15991],{"className":15976},[290],[15,15978,15980],{"className":15979,"style":11133},[294],[15,15981,15982,15985],{"style":11136},[15,15983],{"className":15984,"style":303},[302],[15,15986,15988],{"className":15987},[307,308,309,310],[15,15989,117],{"className":15990},[59,310],[15,15992,318],{"className":15993},[317],[15,15995,15997],{"className":15996},[290],[15,15998,16000],{"className":15999,"style":7968},[294],[15,16001],{},[15,16003],{"className":16004,"style":158},[157],[15,16006,123],{"className":16007},[162],[15,16009],{"className":16010,"style":158},[157],[15,16012,16014,16017,16020,16024,16027,16030,16033,16036,16039,16042],{"className":16013},[50],[15,16015],{"className":16016,"style":139},[54],[15,16018,113],{"className":16019},[146],[15,16021,16023],{"className":16022,"style":15761},[59,60],"sδ",[15,16025,551],{"className":16026},[573],[15,16028],{"className":16029,"style":158},[157],[15,16031],{"className":16032,"style":406},[157],[15,16034,117],{"className":16035},[59],[15,16037],{"className":16038,"style":2587},[157],[15,16040,4813],{"className":16041},[2591],[15,16043],{"className":16044,"style":2587},[157],[15,16046,16048,16051,16054,16057,16060,16063,16066,16106,16109,16112],{"className":16047},[50],[15,16049],{"className":16050,"style":139},[54],[15,16052,16023],{"className":16053,"style":15761},[59,60],[15,16055,120],{"className":16056},[153],[15,16058,551],{"className":16059},[573],[15,16061],{"className":16062,"style":3634},[157],[15,16064],{"className":16065,"style":406},[157],[15,16067,16069,16072],{"className":16068},[59],[15,16070,206],{"className":16071,"style":334},[59,60],[15,16073,16075],{"className":16074},[281],[15,16076,16078,16098],{"className":16077},[285,286],[15,16079,16081,16095],{"className":16080},[290],[15,16082,16084],{"className":16083,"style":11133},[294],[15,16085,16086,16089],{"style":11136},[15,16087],{"className":16088,"style":303},[302],[15,16090,16092],{"className":16091},[307,308,309,310],[15,16093,2463],{"className":16094},[59,310],[15,16096,318],{"className":16097},[317],[15,16099,16101],{"className":16100},[290],[15,16102,16104],{"className":16103,"style":7968},[294],[15,16105],{},[15,16107],{"className":16108,"style":158},[157],[15,16110,123],{"className":16111},[162],[15,16113],{"className":16114,"style":158},[157],[15,16116,16118,16121,16124,16127,16130,16133,16136,16139,16142,16145,16148],{"className":16117},[50],[15,16119],{"className":16120,"style":139},[54],[15,16122,113],{"className":16123},[146],[15,16125,15400],{"className":16126},[59,60],[15,16128,15712],{"className":16129,"style":15761},[59,60],[15,16131,551],{"className":16132},[573],[15,16134],{"className":16135,"style":158},[157],[15,16137],{"className":16138,"style":406},[157],[15,16140,117],{"className":16141},[59],[15,16143],{"className":16144,"style":2587},[157],[15,16146,4813],{"className":16147},[2591],[15,16149],{"className":16150,"style":2587},[157],[15,16152,16154,16157,16160,16163,16166],{"className":16153},[50],[15,16155],{"className":16156,"style":139},[54],[15,16158,15400],{"className":16159},[59,60],[15,16161,15712],{"className":16162,"style":15761},[59,60],[15,16164,120],{"className":16165},[153],[15,16167,551],{"className":16168},[573],[11,16170,15795,16171,16200,16201,16243,16244,2409,16272,16435,16436,16465,16466,2745],{},[15,16172,16174,16188],{"className":16173,"translate":19},[18],[15,16175,16177],{"className":16176},[23],[25,16178,16179],{"xmlns":27},[29,16180,16181,16185],{},[32,16182,16183],{},[35,16184,15712],{},[39,16186,16187],{"encoding":41},"\\delta",[15,16189,16191],{"className":16190,"ariaHidden":46},[45],[15,16192,16194,16197],{"className":16193},[50],[15,16195],{"className":16196,"style":12597},[54],[15,16198,15712],{"className":16199,"style":15761},[59,60]," 足够小时这都是合法概率分布；",[15,16202,16204,16222],{"className":16203,"translate":19},[18],[15,16205,16207],{"className":16206},[23],[25,16208,16209],{"xmlns":27},[29,16210,16211,16219],{},[32,16212,16213,16215,16217],{},[115,16214,126],{},[110,16216,551],{"separator":46},[115,16218,117],{},[39,16220,16221],{"encoding":41},"0,1",[15,16223,16225],{"className":16224,"ariaHidden":46},[45],[15,16226,16228,16231,16234,16237,16240],{"className":16227},[50],[15,16229],{"className":16230,"style":9358},[54],[15,16232,126],{"className":16233},[59],[15,16235,551],{"className":16236},[573],[15,16238],{"className":16239,"style":406},[157],[15,16241,117],{"className":16242},[59]," 两点上的似然比分别为 ",[15,16245,16247,16260],{"className":16246,"translate":19},[18],[15,16248,16250],{"className":16249},[23],[25,16251,16252],{"xmlns":27},[29,16253,16254,16258],{},[32,16255,16256],{},[35,16257,7561],{},[39,16259,7561],{"encoding":41},[15,16261,16263],{"className":16262,"ariaHidden":46},[45],[15,16264,16266,16269],{"className":16265},[50],[15,16267],{"className":16268,"style":2345},[54],[15,16270,7561],{"className":16271},[59,60],[15,16273,16275,16317],{"className":16274,"translate":19},[18],[15,16276,16278],{"className":16277},[23],[25,16279,16280],{"xmlns":27},[29,16281,16282,16314],{},[32,16283,16284,16286,16288,16290,16292,16294],{},[35,16285,4158],{},[110,16287,113],{"stretchy":112},[35,16289,7561],{},[110,16291,120],{"stretchy":112},[110,16293,123],{},[238,16295,16296,16306],{},[32,16297,16298,16300,16302,16304],{},[115,16299,117],{},[110,16301,4813],{},[35,16303,7561],{},[35,16305,15712],{},[32,16307,16308,16310,16312],{},[115,16309,117],{},[110,16311,4813],{},[35,16313,15712],{},[39,16315,16316],{"encoding":41},"g(s)=\\frac{1-s\\delta}{1-\\delta}",[15,16318,16320,16347],{"className":16319,"ariaHidden":46},[45],[15,16321,16323,16326,16329,16332,16335,16338,16341,16344],{"className":16322},[50],[15,16324],{"className":16325,"style":139},[54],[15,16327,4158],{"className":16328,"style":981},[59,60],[15,16330,113],{"className":16331},[146],[15,16333,7561],{"className":16334},[59,60],[15,16336,120],{"className":16337},[153],[15,16339],{"className":16340,"style":158},[157],[15,16342,123],{"className":16343},[162],[15,16345],{"className":16346,"style":158},[157],[15,16348,16350,16354],{"className":16349},[50],[15,16351],{"className":16352,"style":16353},[54],"height:1.2834em;vertical-align:-0.4033em;",[15,16355,16357,16360,16432],{"className":16356},[59],[15,16358],{"className":16359},[146,441],[15,16361,16363],{"className":16362},[238],[15,16364,16366,16423],{"className":16365},[285,286],[15,16367,16369,16420],{"className":16368},[290],[15,16370,16372,16392,16400],{"className":16371,"style":2687},[294],[15,16373,16374,16377],{"style":2527},[15,16375],{"className":16376,"style":461},[302],[15,16378,16380],{"className":16379},[307,308,309,310],[15,16381,16383,16386,16389],{"className":16382},[59,310],[15,16384,117],{"className":16385},[59,310],[15,16387,4813],{"className":16388},[2591,310],[15,16390,15712],{"className":16391,"style":15761},[59,60,310],[15,16393,16394,16397],{"style":473},[15,16395],{"className":16396,"style":461},[302],[15,16398],{"className":16399,"style":481},[480],[15,16401,16402,16405],{"style":2550},[15,16403],{"className":16404,"style":461},[302],[15,16406,16408],{"className":16407},[307,308,309,310],[15,16409,16411,16414,16417],{"className":16410},[59,310],[15,16412,117],{"className":16413},[59,310],[15,16415,4813],{"className":16416},[2591,310],[15,16418,16023],{"className":16419,"style":15761},[59,60,310],[15,16421,318],{"className":16422},[317],[15,16424,16426],{"className":16425},[290],[15,16427,16430],{"className":16428,"style":16429},[294],"height:0.4033em;",[15,16431],{},[15,16433],{"className":16434},[153,441],"）。于是一般公式给出：对任何第一坐标似然比为常值 ",[15,16437,16439,16453],{"className":16438,"translate":19},[18],[15,16440,16442],{"className":16441},[23],[25,16443,16444],{"xmlns":27},[29,16445,16446,16451],{},[32,16447,16448],{},[35,16449,16450],{},"r",[39,16452,16450],{"encoding":41},[15,16454,16456],{"className":16455,"ariaHidden":46},[45],[15,16457,16459,16462],{"className":16458},[50],[15,16460],{"className":16461,"style":2345},[54],[15,16463,16450],{"className":16464,"style":277},[59,60]," 的分布 ",[15,16467,16469,16489],{"className":16468,"translate":19},[18],[15,16470,16472],{"className":16471},[23],[25,16473,16474],{"xmlns":27},[29,16475,16476,16486],{},[32,16477,16478,16480,16482,16484],{},[35,16479,206],{},[110,16481,113],{"stretchy":112},[35,16483,16450],{},[110,16485,120],{"stretchy":112},[39,16487,16488],{"encoding":41},"P(r)",[15,16490,16492],{"className":16491,"ariaHidden":46},[45],[15,16493,16495,16498,16501,16504,16507],{"className":16494},[50],[15,16496],{"className":16497,"style":139},[54],[15,16499,206],{"className":16500,"style":334},[59,60],[15,16502,113],{"className":16503},[146],[15,16505,16450],{"className":16506,"style":277},[59,60],[15,16508,120],{"className":16509},[153],[15,16511,16513],{"className":16512,"translate":19},[180],[15,16514,16516,16648],{"className":16515,"translate":19},[18],[15,16517,16519],{"className":16518},[23],[25,16520,16521],{"xmlns":27,"display":189},[29,16522,16523,16645],{},[1243,16524,16525,16581],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,16526,16527,16559],{},[1252,16528,16529],{},[1255,16530,16531],{"scriptlevel":126,"displaystyle":46},[32,16532,16533,16539,16541,16543,16545,16547,16549,16551,16553,16555,16557],{},[195,16534,16535,16537],{},[35,16536,199],{},[35,16538,37],{},[110,16540,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,16542,206],{},[110,16544,113],{"stretchy":112},[35,16546,16450],{},[110,16548,120],{"stretchy":112},[1297,16550,1299],{},[110,16552,210],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,16554,1299],{},[35,16556,213],{},[110,16558,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1252,16560,16561],{},[1255,16562,16563],{"scriptlevel":126,"displaystyle":46},[32,16564,16565,16567,16569,16571,16573,16575,16577,16579],{},[32,16566],{},[110,16568,123],{},[35,16570,15712],{},[1297,16572,1299],{},[35,16574,37],{},[110,16576,113],{"stretchy":112},[35,16578,16450],{},[110,16580,120],{"stretchy":112},[1249,16582,16583,16589],{},[1252,16584,16585],{},[1255,16586,16587],{"scriptlevel":126,"displaystyle":46},[32,16588],{},[1252,16590,16591],{},[1255,16592,16593],{"scriptlevel":126,"displaystyle":46},[32,16594,16595,16597,16599,16601,16603,16605,16607,16609,16611,16613,16615,16617,16643],{},[32,16596],{},[157,16598],{"width":3262},[110,16600,2470],{},[110,16602,113],{"stretchy":112},[115,16604,117],{},[110,16606,4813],{},[35,16608,15712],{},[110,16610,120],{"stretchy":112},[1297,16612,1299],{},[35,16614,37],{},[1297,16616,1304],{},[32,16618,16619,16621,16641],{},[110,16620,113],{"fence":46},[238,16622,16623,16633],{},[32,16624,16625,16627,16629,16631],{},[115,16626,117],{},[110,16628,4813],{},[35,16630,16450],{},[35,16632,15712],{},[32,16634,16635,16637,16639],{},[115,16636,117],{},[110,16638,4813],{},[35,16640,15712],{},[110,16642,120],{"fence":46},[35,16644,4375],{"mathvariant":209},[39,16646,16647],{"encoding":41},"\\begin{aligned}\nD_f\\big(P(r)\\,\\big\\|\\,Q\\big)\n&=\\delta\\,f(r)\\\\\n&\\qquad +(1-\\delta)\\,\nf\\!\\left(\\frac{1-r\\delta}{1-\\delta}\\right).\n\\end{aligned}",[15,16649,16651],{"className":16650,"ariaHidden":46},[45],[15,16652,16654,16658],{"className":16653},[50],[15,16655],{"className":16656,"style":16657},[54],"height:3.91em;vertical-align:-1.705em;",[15,16659,16661],{"className":16660},[59],[15,16662,16664,16816],{"className":16663},[1243],[15,16665,16667],{"className":16666},[1360],[15,16668,16670,16808],{"className":16669},[285,286],[15,16671,16673,16805],{"className":16672},[290],[15,16674,16677,16796],{"className":16675,"style":16676},[294],"height:2.205em;",[15,16678,16680,16683],{"style":16679},"top:-4.805em;",[15,16681],{"className":16682,"style":1377},[302],[15,16684,16686,16726,16732,16735,16738,16741,16744,16747,16784,16787,16790],{"className":16685},[59],[15,16687,16689,16692],{"className":16688},[59],[15,16690,199],{"className":16691,"style":277},[59,60],[15,16693,16695],{"className":16694},[281],[15,16696,16698,16718],{"className":16697},[285,286],[15,16699,16701,16715],{"className":16700},[290],[15,16702,16704],{"className":16703,"style":295},[294],[15,16705,16706,16709],{"style":298},[15,16707],{"className":16708,"style":303},[302],[15,16710,16712],{"className":16711},[307,308,309,310],[15,16713,37],{"className":16714,"style":61},[59,60,310],[15,16716,318],{"className":16717},[317],[15,16719,16721],{"className":16720},[290],[15,16722,16724],{"className":16723,"style":325},[294],[15,16725],{},[15,16727,16729],{"className":16728},[59],[15,16730,113],{"className":16731},[419,9674],[15,16733,206],{"className":16734,"style":334},[59,60],[15,16736,113],{"className":16737},[146],[15,16739,16450],{"className":16740,"style":277},[59,60],[15,16742,120],{"className":16743},[153],[15,16745],{"className":16746,"style":406},[157],[15,16748,16750],{"className":16749},[59],[15,16751,16753],{"className":16752},[419,14829],[15,16754,16756,16776],{"className":16755},[285,286],[15,16757,16759,16773],{"className":16758},[290],[15,16760,16762],{"className":16761,"style":14839},[294],[15,16763,16764,16767],{"style":14842},[15,16765],{"className":16766,"style":14846},[302],[15,16768,16769],{"style":14849},[6323,16770,16771],{"xmlns":6325,"width":14852,"height":9450,"viewBox":14853},[6331,16772],{"d":14856},[15,16774,318],{"className":16775},[317],[15,16777,16779],{"className":16778},[290],[15,16780,16782],{"className":16781,"style":14866},[294],[15,16783],{},[15,16785],{"className":16786,"style":406},[157],[15,16788,213],{"className":16789},[59,60],[15,16791,16793],{"className":16792},[59],[15,16794,120],{"className":16795},[419,9674],[15,16797,16799,16802],{"style":16798},"top:-2.695em;",[15,16800],{"className":16801,"style":1377},[302],[15,16803],{"className":16804},[59],[15,16806,318],{"className":16807},[317],[15,16809,16811],{"className":16810},[290],[15,16812,16814],{"className":16813,"style":9554},[294],[15,16815],{},[15,16817,16819],{"className":16818},[1451],[15,16820,16822,17036],{"className":16821},[285,286],[15,16823,16825,17033],{"className":16824},[290],[15,16826,16828,16866],{"className":16827,"style":16676},[294],[15,16829,16830,16833],{"style":16679},[15,16831],{"className":16832,"style":1377},[302],[15,16834,16836,16839,16842,16845,16848,16851,16854,16857,16860,16863],{"className":16835},[59],[15,16837],{"className":16838},[59],[15,16840],{"className":16841,"style":158},[157],[15,16843,123],{"className":16844},[162],[15,16846],{"className":16847,"style":158},[157],[15,16849,15712],{"className":16850,"style":15761},[59,60],[15,16852],{"className":16853,"style":406},[157],[15,16855,37],{"className":16856,"style":61},[59,60],[15,16858,113],{"className":16859},[146],[15,16861,16450],{"className":16862,"style":277},[59,60],[15,16864,120],{"className":16865},[153],[15,16867,16868,16871],{"style":16798},[15,16869],{"className":16870,"style":1377},[302],[15,16872,16874,16877,16880,16883,16886,16889,16892,16895,16898,16901,16904,16907,16910,16913,16916,16919,16922,17027,17030],{"className":16873},[59],[15,16875],{"className":16876},[59],[15,16878],{"className":16879,"style":3634},[157],[15,16881],{"className":16882,"style":2587},[157],[15,16884,2470],{"className":16885},[2591],[15,16887],{"className":16888,"style":2587},[157],[15,16890,113],{"className":16891},[146],[15,16893,117],{"className":16894},[59],[15,16896],{"className":16897,"style":2587},[157],[15,16899,4813],{"className":16900},[2591],[15,16902],{"className":16903,"style":2587},[157],[15,16905,15712],{"className":16906,"style":15761},[59,60],[15,16908,120],{"className":16909},[153],[15,16911],{"className":16912,"style":406},[157],[15,16914,37],{"className":16915,"style":61},[59,60],[15,16917],{"className":16918,"style":1512},[157],[15,16920],{"className":16921,"style":406},[157],[15,16923,16925,16931,17021],{"className":16924},[410],[15,16926,16928],{"className":16927,"style":415},[146,414],[15,16929,113],{"className":16930},[419,309],[15,16932,16934,16937,17018],{"className":16933},[59],[15,16935],{"className":16936},[146,441],[15,16938,16940],{"className":16939},[238],[15,16941,16943,17009],{"className":16942},[285,286],[15,16944,16946,17006],{"className":16945},[290],[15,16947,16949,16972,16980],{"className":16948,"style":454},[294],[15,16950,16951,16954],{"style":457},[15,16952],{"className":16953,"style":461},[302],[15,16955,16957,16960,16963,16966,16969],{"className":16956},[59],[15,16958,117],{"className":16959},[59],[15,16961],{"className":16962,"style":2587},[157],[15,16964,4813],{"className":16965},[2591],[15,16967],{"className":16968,"style":2587},[157],[15,16970,15712],{"className":16971,"style":15761},[59,60],[15,16973,16974,16977],{"style":473},[15,16975],{"className":16976,"style":461},[302],[15,16978],{"className":16979,"style":481},[480],[15,16981,16982,16985],{"style":484},[15,16983],{"className":16984,"style":461},[302],[15,16986,16988,16991,16994,16997,17000,17003],{"className":16987},[59],[15,16989,117],{"className":16990},[59],[15,16992],{"className":16993,"style":2587},[157],[15,16995,4813],{"className":16996},[2591],[15,16998],{"className":16999,"style":2587},[157],[15,17001,16450],{"className":17002,"style":277},[59,60],[15,17004,15712],{"className":17005,"style":15761},[59,60],[15,17007,318],{"className":17008},[317],[15,17010,17012],{"className":17011},[290],[15,17013,17016],{"className":17014,"style":17015},[294],"height:0.7693em;",[15,17017],{},[15,17019],{"className":17020},[153,441],[15,17022,17024],{"className":17023,"style":415},[153,414],[15,17025,120],{"className":17026},[419,309],[15,17028],{"className":17029,"style":406},[157],[15,17031,4375],{"className":17032},[59],[15,17034,318],{"className":17035},[317],[15,17037,17039],{"className":17038},[290],[15,17040,17042],{"className":17041,"style":9554},[294],[15,17043],{},[11,17045,17046,17047,5645,17098,17149,17150,17201,17202,17317,17318,6494,17321,17349],{},"把 ",[15,17048,17050,17068],{"className":17049,"translate":19},[18],[15,17051,17053],{"className":17052},[23],[25,17054,17055],{"xmlns":27},[29,17056,17057,17065],{},[32,17058,17059,17061,17063],{},[35,17060,16450],{},[110,17062,123],{},[35,17064,7561],{},[39,17066,17067],{"encoding":41},"r=s",[15,17069,17071,17089],{"className":17070,"ariaHidden":46},[45],[15,17072,17074,17077,17080,17083,17086],{"className":17073},[50],[15,17075],{"className":17076,"style":2345},[54],[15,17078,16450],{"className":17079,"style":277},[59,60],[15,17081],{"className":17082,"style":158},[157],[15,17084,123],{"className":17085},[162],[15,17087],{"className":17088,"style":158},[157],[15,17090,17092,17095],{"className":17091},[50],[15,17093],{"className":17094,"style":2345},[54],[15,17096,7561],{"className":17097},[59,60],[15,17099,17101,17119],{"className":17100,"translate":19},[18],[15,17102,17104],{"className":17103},[23],[25,17105,17106],{"xmlns":27},[29,17107,17108,17116],{},[32,17109,17110,17112,17114],{},[35,17111,16450],{},[110,17113,123],{},[35,17115,15400],{},[39,17117,17118],{"encoding":41},"r=u",[15,17120,17122,17140],{"className":17121,"ariaHidden":46},[45],[15,17123,17125,17128,17131,17134,17137],{"className":17124},[50],[15,17126],{"className":17127,"style":2345},[54],[15,17129,16450],{"className":17130,"style":277},[59,60],[15,17132],{"className":17133,"style":158},[157],[15,17135,123],{"className":17136},[162],[15,17138],{"className":17139,"style":158},[157],[15,17141,17143,17146],{"className":17142},[50],[15,17144],{"className":17145,"style":2345},[54],[15,17147,15400],{"className":17148},[59,60],"、以及混合后的 ",[15,17151,17153,17171],{"className":17152,"translate":19},[18],[15,17154,17156],{"className":17155},[23],[25,17157,17158],{"xmlns":27},[29,17159,17160,17168],{},[32,17161,17162,17164,17166],{},[35,17163,16450],{},[110,17165,123],{},[35,17167,7570],{},[39,17169,17170],{"encoding":41},"r=w",[15,17172,17174,17192],{"className":17173,"ariaHidden":46},[45],[15,17175,17177,17180,17183,17186,17189],{"className":17176},[50],[15,17178],{"className":17179,"style":2345},[54],[15,17181,16450],{"className":17182,"style":277},[59,60],[15,17184],{"className":17185,"style":158},[157],[15,17187,123],{"className":17188},[162],[15,17190],{"className":17191,"style":158},[157],[15,17193,17195,17198],{"className":17194},[50],[15,17196],{"className":17197,"style":2345},[54],[15,17199,7570],{"className":17200,"style":8274},[59,60],"（混合后第一坐标似然比恰为 ",[15,17203,17205,17239],{"className":17204,"translate":19},[18],[15,17206,17208],{"className":17207},[23],[25,17209,17210],{"xmlns":27},[29,17211,17212,17236],{},[32,17213,17214,17216,17218,17220,17222,17224,17226,17228,17230,17232,17234],{},[35,17215,11339],{},[35,17217,7561],{},[110,17219,2470],{},[110,17221,113],{"stretchy":112},[115,17223,117],{},[110,17225,4813],{},[35,17227,11339],{},[110,17229,120],{"stretchy":112},[35,17231,15400],{},[110,17233,123],{},[35,17235,7570],{},[39,17237,17238],{"encoding":41},"\\lambda s+(1-\\lambda)u=w",[15,17240,17242,17263,17284,17308],{"className":17241,"ariaHidden":46},[45],[15,17243,17245,17248,17251,17254,17257,17260],{"className":17244},[50],[15,17246],{"className":17247,"style":15586},[54],[15,17249,11339],{"className":17250},[59,60],[15,17252,7561],{"className":17253},[59,60],[15,17255],{"className":17256,"style":2587},[157],[15,17258,2470],{"className":17259},[2591],[15,17261],{"className":17262,"style":2587},[157],[15,17264,17266,17269,17272,17275,17278,17281],{"className":17265},[50],[15,17267],{"className":17268,"style":139},[54],[15,17270,113],{"className":17271},[146],[15,17273,117],{"className":17274},[59],[15,17276],{"className":17277,"style":2587},[157],[15,17279,4813],{"className":17280},[2591],[15,17282],{"className":17283,"style":2587},[157],[15,17285,17287,17290,17293,17296,17299,17302,17305],{"className":17286},[50],[15,17288],{"className":17289,"style":139},[54],[15,17291,11339],{"className":17292},[59,60],[15,17294,120],{"className":17295},[153],[15,17297,15400],{"className":17298},[59,60],[15,17300],{"className":17301,"style":158},[157],[15,17303,123],{"className":17304},[162],[15,17306],{"className":17307,"style":158},[157],[15,17309,17311,17314],{"className":17310},[50],[15,17312],{"className":17313,"style":2345},[54],[15,17315,7570],{"className":17316,"style":8274},[59,60],"，因为两个分布在",[1225,17319,17320],{},"同一个",[15,17322,17324,17337],{"className":17323,"translate":19},[18],[15,17325,17327],{"className":17326},[23],[25,17328,17329],{"xmlns":27},[29,17330,17331,17335],{},[32,17332,17333],{},[35,17334,213],{},[39,17336,213],{"encoding":41},[15,17338,17340],{"className":17339,"ariaHidden":46},[45],[15,17341,17343,17346],{"className":17342},[50],[15,17344],{"className":17345,"style":566},[54],[15,17347,213],{"className":17348},[59,60]," 下混合，比值线性）代入第一步的联合凸性：",[15,17351,17353],{"className":17352,"translate":19},[180],[15,17354,17356,17553],{"className":17355,"translate":19},[18],[15,17357,17359],{"className":17358},[23],[25,17360,17361],{"xmlns":27,"display":189},[29,17362,17363,17550],{},[1243,17364,17365,17417,17478],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,17366,17367,17373],{},[1252,17368,17369],{},[1255,17370,17371],{"scriptlevel":126,"displaystyle":46},[32,17372],{},[1252,17374,17375],{},[1255,17376,17377],{"scriptlevel":126,"displaystyle":46},[32,17378,17379,17381,17383,17385,17387,17389,17391,17393,17395,17397,17399,17401,17403,17405,17407,17409,17411,17413,17415],{},[32,17380],{},[35,17382,15712],{},[35,17384,37],{},[110,17386,113],{"stretchy":112},[35,17388,7570],{},[110,17390,120],{"stretchy":112},[110,17392,2470],{},[110,17394,113],{"stretchy":112},[115,17396,117],{},[110,17398,4813],{},[35,17400,15712],{},[110,17402,120],{"stretchy":112},[35,17404,37],{},[110,17406,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,17408,4158],{},[110,17410,113],{"stretchy":112},[35,17412,7570],{},[110,17414,120],{"stretchy":112},[110,17416,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,17418,17419,17425],{},[1252,17420,17421],{},[1255,17422,17423],{"scriptlevel":126,"displaystyle":46},[32,17424],{},[1252,17426,17427],{},[1255,17428,17429],{"scriptlevel":126,"displaystyle":46},[32,17430,17431,17433,17435,17437,17440,17442,17444,17446,17448,17450,17452,17454,17456,17458,17460,17462,17464,17466,17468,17470,17472,17474,17476],{},[32,17432],{},[110,17434,9952],{},[35,17436,11339],{},[110,17438,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},"1.8em",[35,17441,15712],{},[35,17443,37],{},[110,17445,113],{"stretchy":112},[35,17447,7561],{},[110,17449,120],{"stretchy":112},[110,17451,2470],{},[110,17453,113],{"stretchy":112},[115,17455,117],{},[110,17457,4813],{},[35,17459,15712],{},[110,17461,120],{"stretchy":112},[35,17463,37],{},[110,17465,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,17467,4158],{},[110,17469,113],{"stretchy":112},[35,17471,7561],{},[110,17473,120],{"stretchy":112},[110,17475,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,17477,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,17479,17480,17486],{},[1252,17481,17482],{},[1255,17483,17484],{"scriptlevel":126,"displaystyle":46},[32,17485],{},[1252,17487,17488],{},[1255,17489,17490],{"scriptlevel":126,"displaystyle":46},[32,17491,17492,17494,17496,17498,17500,17502,17504,17506,17508,17510,17512,17514,17516,17518,17520,17522,17524,17526,17528,17530,17532,17534,17536,17538,17540,17542,17544,17546,17548],{},[32,17493],{},[157,17495],{"width":3262},[110,17497,2470],{},[110,17499,113],{"stretchy":112},[115,17501,117],{},[110,17503,4813],{},[35,17505,11339],{},[110,17507,120],{"stretchy":112},[110,17509,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,17511,15712],{},[35,17513,37],{},[110,17515,113],{"stretchy":112},[35,17517,15400],{},[110,17519,120],{"stretchy":112},[110,17521,2470],{},[110,17523,113],{"stretchy":112},[115,17525,117],{},[110,17527,4813],{},[35,17529,15712],{},[110,17531,120],{"stretchy":112},[35,17533,37],{},[110,17535,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,17537,4158],{},[110,17539,113],{"stretchy":112},[35,17541,15400],{},[110,17543,120],{"stretchy":112},[110,17545,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,17547,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,17549,551],{"separator":46},[39,17551,17552],{"encoding":41},"\\begin{aligned}\n&\\delta f(w)+(1-\\delta)f\\big(g(w)\\big)\\\\\n&\\le \\lambda\\Big[\\delta f(s)\n+(1-\\delta)f\\big(g(s)\\big)\\Big]\\\\\n&\\qquad+(1-\\lambda)\\Big[\\delta f(u)\n+(1-\\delta)f\\big(g(u)\\big)\\Big],\n\\end{aligned}",[15,17554,17556],{"className":17555,"ariaHidden":46},[45],[15,17557,17559,17563],{"className":17558},[50],[15,17560],{"className":17561,"style":17562},[54],"height:5.41em;vertical-align:-2.455em;",[15,17564,17566],{"className":17565},[59],[15,17567,17569,17622],{"className":17568},[1243],[15,17570,17572],{"className":17571},[1360],[15,17573,17575,17613],{"className":17574},[285,286],[15,17576,17578,17610],{"className":17577},[290],[15,17579,17582,17592,17601],{"className":17580,"style":17581},[294],"height:2.955em;",[15,17583,17585,17589],{"style":17584},"top:-5.255em;",[15,17586],{"className":17587,"style":17588},[302],"height:3.15em;",[15,17590],{"className":17591},[59],[15,17593,17595,17598],{"style":17594},"top:-3.445em;",[15,17596],{"className":17597,"style":17588},[302],[15,17599],{"className":17600},[59],[15,17602,17604,17607],{"style":17603},"top:-1.345em;",[15,17605],{"className":17606,"style":17588},[302],[15,17608],{"className":17609},[59],[15,17611,318],{"className":17612},[317],[15,17614,17616],{"className":17615},[290],[15,17617,17620],{"className":17618,"style":17619},[294],"height:2.455em;",[15,17621],{},[15,17623,17625],{"className":17624},[1451],[15,17626,17628,17958],{"className":17627},[285,286],[15,17629,17631,17955],{"className":17630},[290],[15,17632,17634,17717,17824],{"className":17633,"style":17581},[294],[15,17635,17636,17639],{"style":17584},[15,17637],{"className":17638,"style":17588},[302],[15,17640,17642,17645,17648,17651,17654,17657,17660,17663,17666,17669,17672,17675,17678,17681,17684,17687,17690,17693,17699,17702,17705,17708,17711],{"className":17641},[59],[15,17643],{"className":17644},[59],[15,17646,15712],{"className":17647,"style":15761},[59,60],[15,17649,37],{"className":17650,"style":61},[59,60],[15,17652,113],{"className":17653},[146],[15,17655,7570],{"className":17656,"style":8274},[59,60],[15,17658,120],{"className":17659},[153],[15,17661],{"className":17662,"style":2587},[157],[15,17664,2470],{"className":17665},[2591],[15,17667],{"className":17668,"style":2587},[157],[15,17670,113],{"className":17671},[146],[15,17673,117],{"className":17674},[59],[15,17676],{"className":17677,"style":2587},[157],[15,17679,4813],{"className":17680},[2591],[15,17682],{"className":17683,"style":2587},[157],[15,17685,15712],{"className":17686,"style":15761},[59,60],[15,17688,120],{"className":17689},[153],[15,17691,37],{"className":17692,"style":61},[59,60],[15,17694,17696],{"className":17695},[59],[15,17697,113],{"className":17698},[419,9674],[15,17700,4158],{"className":17701,"style":981},[59,60],[15,17703,113],{"className":17704},[146],[15,17706,7570],{"className":17707,"style":8274},[59,60],[15,17709,120],{"className":17710},[153],[15,17712,17714],{"className":17713},[59],[15,17715,120],{"className":17716},[419,9674],[15,17718,17719,17722],{"style":17594},[15,17720],{"className":17721,"style":17588},[302],[15,17723,17725,17728,17731,17734,17737,17740,17746,17749,17752,17755,17758,17761,17764,17767,17770,17773,17776,17779,17782,17785,17788,17791,17794,17800,17803,17806,17809,17812,17818],{"className":17724},[59],[15,17726],{"className":17727},[59],[15,17729],{"className":17730,"style":158},[157],[15,17732,9952],{"className":17733},[162],[15,17735],{"className":17736,"style":158},[157],[15,17738,11339],{"className":17739},[59,60],[15,17741,17743],{"className":17742},[59],[15,17744,230],{"className":17745},[419,3720],[15,17747,15712],{"className":17748,"style":15761},[59,60],[15,17750,37],{"className":17751,"style":61},[59,60],[15,17753,113],{"className":17754},[146],[15,17756,7561],{"className":17757},[59,60],[15,17759,120],{"className":17760},[153],[15,17762],{"className":17763,"style":2587},[157],[15,17765,2470],{"className":17766},[2591],[15,17768],{"className":17769,"style":2587},[157],[15,17771,113],{"className":17772},[146],[15,17774,117],{"className":17775},[59],[15,17777],{"className":17778,"style":2587},[157],[15,17780,4813],{"className":17781},[2591],[15,17783],{"className":17784,"style":2587},[157],[15,17786,15712],{"className":17787,"style":15761},[59,60],[15,17789,120],{"className":17790},[153],[15,17792,37],{"className":17793,"style":61},[59,60],[15,17795,17797],{"className":17796},[59],[15,17798,113],{"className":17799},[419,9674],[15,17801,4158],{"className":17802,"style":981},[59,60],[15,17804,113],{"className":17805},[146],[15,17807,7561],{"className":17808},[59,60],[15,17810,120],{"className":17811},[153],[15,17813,17815],{"className":17814},[59],[15,17816,120],{"className":17817},[419,9674],[15,17819,17821],{"className":17820},[59],[15,17822,257],{"className":17823},[419,3720],[15,17825,17826,17829],{"style":17603},[15,17827],{"className":17828,"style":17588},[302],[15,17830,17832,17835,17838,17841,17844,17847,17850,17853,17856,17859,17862,17865,17868,17874,17877,17880,17883,17886,17889,17892,17895,17898,17901,17904,17907,17910,17913,17916,17919,17922,17928,17931,17934,17937,17940,17946,17952],{"className":17831},[59],[15,17833],{"className":17834},[59],[15,17836],{"className":17837,"style":3634},[157],[15,17839],{"className":17840,"style":2587},[157],[15,17842,2470],{"className":17843},[2591],[15,17845],{"className":17846,"style":2587},[157],[15,17848,113],{"className":17849},[146],[15,17851,117],{"className":17852},[59],[15,17854],{"className":17855,"style":2587},[157],[15,17857,4813],{"className":17858},[2591],[15,17860],{"className":17861,"style":2587},[157],[15,17863,11339],{"className":17864},[59,60],[15,17866,120],{"className":17867},[153],[15,17869,17871],{"className":17870},[59],[15,17872,230],{"className":17873},[419,3720],[15,17875,15712],{"className":17876,"style":15761},[59,60],[15,17878,37],{"className":17879,"style":61},[59,60],[15,17881,113],{"className":17882},[146],[15,17884,15400],{"className":17885},[59,60],[15,17887,120],{"className":17888},[153],[15,17890],{"className":17891,"style":2587},[157],[15,17893,2470],{"className":17894},[2591],[15,17896],{"className":17897,"style":2587},[157],[15,17899,113],{"className":17900},[146],[15,17902,117],{"className":17903},[59],[15,17905],{"className":17906,"style":2587},[157],[15,17908,4813],{"className":17909},[2591],[15,17911],{"className":17912,"style":2587},[157],[15,17914,15712],{"className":17915,"style":15761},[59,60],[15,17917,120],{"className":17918},[153],[15,17920,37],{"className":17921,"style":61},[59,60],[15,17923,17925],{"className":17924},[59],[15,17926,113],{"className":17927},[419,9674],[15,17929,4158],{"className":17930,"style":981},[59,60],[15,17932,113],{"className":17933},[146],[15,17935,15400],{"className":17936},[59,60],[15,17938,120],{"className":17939},[153],[15,17941,17943],{"className":17942},[59],[15,17944,120],{"className":17945},[419,9674],[15,17947,17949],{"className":17948},[59],[15,17950,257],{"className":17951},[419,3720],[15,17953,551],{"className":17954},[573],[15,17956,318],{"className":17957},[317],[15,17959,17961],{"className":17960},[290],[15,17962,17964],{"className":17963,"style":17619},[294],[15,17965],{},[11,17967,2250,17968,18141,18142,18170,18171,18331,18332,3853,18360,18388,18389,18630,18631,18708,18709,18891,18892,18962,18963,2745,18991,19048,19049,19077],{},[15,17969,17971,18015],{"className":17970,"translate":19},[18],[15,17972,17974],{"className":17973},[23],[25,17975,17976],{"xmlns":27},[29,17977,17978,18012],{},[32,17979,17980,17982,17984,17986,17988,17990],{},[35,17981,4158],{},[110,17983,113],{"stretchy":112},[35,17985,16450],{},[110,17987,120],{"stretchy":112},[110,17989,123],{},[1255,17991,17992],{"scriptlevel":126,"displaystyle":46},[238,17993,17994,18004],{},[32,17995,17996,17998,18000,18002],{},[115,17997,117],{},[110,17999,4813],{},[35,18001,16450],{},[35,18003,15712],{},[32,18005,18006,18008,18010],{},[115,18007,117],{},[110,18009,4813],{},[35,18011,15712],{},[39,18013,18014],{"encoding":41},"g(r)=\\dfrac{1-r\\delta}{1-\\delta}",[15,18016,18018,18045],{"className":18017,"ariaHidden":46},[45],[15,18019,18021,18024,18027,18030,18033,18036,18039,18042],{"className":18020},[50],[15,18022],{"className":18023,"style":139},[54],[15,18025,4158],{"className":18026,"style":981},[59,60],[15,18028,113],{"className":18029},[146],[15,18031,16450],{"className":18032,"style":277},[59,60],[15,18034,120],{"className":18035},[153],[15,18037],{"className":18038,"style":158},[157],[15,18040,123],{"className":18041},[162],[15,18043],{"className":18044,"style":158},[157],[15,18046,18048,18052],{"className":18047},[50],[15,18049],{"className":18050,"style":18051},[54],"height:2.1408em;vertical-align:-0.7693em;",[15,18053,18055,18058,18138],{"className":18054},[59],[15,18056],{"className":18057},[146,441],[15,18059,18061],{"className":18060},[238],[15,18062,18064,18130],{"className":18063},[285,286],[15,18065,18067,18127],{"className":18066},[290],[15,18068,18070,18093,18101],{"className":18069,"style":454},[294],[15,18071,18072,18075],{"style":457},[15,18073],{"className":18074,"style":461},[302],[15,18076,18078,18081,18084,18087,18090],{"className":18077},[59],[15,18079,117],{"className":18080},[59],[15,18082],{"className":18083,"style":2587},[157],[15,18085,4813],{"className":18086},[2591],[15,18088],{"className":18089,"style":2587},[157],[15,18091,15712],{"className":18092,"style":15761},[59,60],[15,18094,18095,18098],{"style":473},[15,18096],{"className":18097,"style":461},[302],[15,18099],{"className":18100,"style":481},[480],[15,18102,18103,18106],{"style":484},[15,18104],{"className":18105,"style":461},[302],[15,18107,18109,18112,18115,18118,18121,18124],{"className":18108},[59],[15,18110,117],{"className":18111},[59],[15,18113],{"className":18114,"style":2587},[157],[15,18116,4813],{"className":18117},[2591],[15,18119],{"className":18120,"style":2587},[157],[15,18122,16450],{"className":18123,"style":277},[59,60],[15,18125,15712],{"className":18126,"style":15761},[59,60],[15,18128,318],{"className":18129},[317],[15,18131,18133],{"className":18132},[290],[15,18134,18136],{"className":18135,"style":17015},[294],[15,18137],{},[15,18139],{"className":18140},[153,441],"。注意 ",[15,18143,18145,18158],{"className":18144,"translate":19},[18],[15,18146,18148],{"className":18147},[23],[25,18149,18150],{"xmlns":27},[29,18151,18152,18156],{},[32,18153,18154],{},[35,18155,4158],{},[39,18157,4158],{"encoding":41},[15,18159,18161],{"className":18160,"ariaHidden":46},[45],[15,18162,18164,18167],{"className":18163},[50],[15,18165],{"className":18166,"style":2276},[54],[15,18168,4158],{"className":18169,"style":981},[59,60]," 是仿射函数且 ",[15,18172,18174,18226],{"className":18173,"translate":19},[18],[15,18175,18177],{"className":18176},[23],[25,18178,18179],{"xmlns":27},[29,18180,18181,18223],{},[32,18182,18183,18185,18187,18189,18191,18193,18195,18197,18199,18201,18203,18205,18207,18209,18211,18213,18215,18217,18219,18221],{},[35,18184,4158],{},[110,18186,113],{"stretchy":112},[35,18188,7570],{},[110,18190,120],{"stretchy":112},[110,18192,123],{},[35,18194,11339],{},[35,18196,4158],{},[110,18198,113],{"stretchy":112},[35,18200,7561],{},[110,18202,120],{"stretchy":112},[110,18204,2470],{},[110,18206,113],{"stretchy":112},[115,18208,117],{},[110,18210,4813],{},[35,18212,11339],{},[110,18214,120],{"stretchy":112},[35,18216,4158],{},[110,18218,113],{"stretchy":112},[35,18220,15400],{},[110,18222,120],{"stretchy":112},[39,18224,18225],{"encoding":41},"g(w)=\\lambda g(s)+(1-\\lambda)g(u)",[15,18227,18229,18256,18286,18307],{"className":18228,"ariaHidden":46},[45],[15,18230,18232,18235,18238,18241,18244,18247,18250,18253],{"className":18231},[50],[15,18233],{"className":18234,"style":139},[54],[15,18236,4158],{"className":18237,"style":981},[59,60],[15,18239,113],{"className":18240},[146],[15,18242,7570],{"className":18243,"style":8274},[59,60],[15,18245,120],{"className":18246},[153],[15,18248],{"className":18249,"style":158},[157],[15,18251,123],{"className":18252},[162],[15,18254],{"className":18255,"style":158},[157],[15,18257,18259,18262,18265,18268,18271,18274,18277,18280,18283],{"className":18258},[50],[15,18260],{"className":18261,"style":139},[54],[15,18263,11339],{"className":18264},[59,60],[15,18266,4158],{"className":18267,"style":981},[59,60],[15,18269,113],{"className":18270},[146],[15,18272,7561],{"className":18273},[59,60],[15,18275,120],{"className":18276},[153],[15,18278],{"className":18279,"style":2587},[157],[15,18281,2470],{"className":18282},[2591],[15,18284],{"className":18285,"style":2587},[157],[15,18287,18289,18292,18295,18298,18301,18304],{"className":18288},[50],[15,18290],{"className":18291,"style":139},[54],[15,18293,113],{"className":18294},[146],[15,18296,117],{"className":18297},[59],[15,18299],{"className":18300,"style":2587},[157],[15,18302,4813],{"className":18303},[2591],[15,18305],{"className":18306,"style":2587},[157],[15,18308,18310,18313,18316,18319,18322,18325,18328],{"className":18309},[50],[15,18311],{"className":18312,"style":139},[54],[15,18314,11339],{"className":18315},[59,60],[15,18317,120],{"className":18318},[153],[15,18320,4158],{"className":18321,"style":981},[59,60],[15,18323,113],{"className":18324},[146],[15,18326,15400],{"className":18327},[59,60],[15,18329,120],{"className":18330},[153],"，用 ",[15,18333,18335,18348],{"className":18334,"translate":19},[18],[15,18336,18338],{"className":18337},[23],[25,18339,18340],{"xmlns":27},[29,18341,18342,18346],{},[32,18343,18344],{},[35,18345,37],{},[39,18347,37],{"encoding":41},[15,18349,18351],{"className":18350,"ariaHidden":46},[45],[15,18352,18354,18357],{"className":18353},[50],[15,18355],{"className":18356,"style":55},[54],[15,18358,37],{"className":18359,"style":61},[59,60],[15,18361,18363,18376],{"className":18362,"translate":19},[18],[15,18364,18366],{"className":18365},[23],[25,18367,18368],{"xmlns":27},[29,18369,18370,18374],{},[32,18371,18372],{},[115,18373,117],{},[39,18375,117],{"encoding":41},[15,18377,18379],{"className":18378,"ariaHidden":46},[45],[15,18380,18382,18385],{"className":18381},[50],[15,18383],{"className":18384,"style":172},[54],[15,18386,117],{"className":18387},[59]," 处的支撑线（凸函数在可微点处 ",[15,18390,18392,18458],{"className":18391,"translate":19},[18],[15,18393,18395],{"className":18394},[23],[25,18396,18397],{"xmlns":27},[29,18398,18399,18455],{},[32,18400,18401,18403,18405,18407,18409,18411,18413,18415,18417,18419,18421,18427,18429,18431,18433,18435,18437,18439,18441,18443,18449,18451,18453],{},[35,18402,37],{},[110,18404,113],{"stretchy":112},[35,18406,769],{},[110,18408,120],{"stretchy":112},[110,18410,6928],{},[35,18412,37],{},[110,18414,113],{"stretchy":112},[115,18416,117],{},[110,18418,120],{"stretchy":112},[110,18420,2470],{},[6814,18422,18423,18425],{},[35,18424,37],{},[110,18426,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,18428,113],{"stretchy":112},[115,18430,117],{},[110,18432,120],{"stretchy":112},[110,18434,113],{"stretchy":112},[35,18436,769],{},[110,18438,4813],{},[115,18440,117],{},[110,18442,120],{"stretchy":112},[6814,18444,18445,18447],{},[35,18446,37],{},[110,18448,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,18450,113],{"stretchy":112},[115,18452,117],{},[110,18454,120],{"stretchy":112},[39,18456,18457],{"encoding":41},"f(t)\\ge f(1)+f'(1)(t-1)f'(1)",[15,18459,18461,18488,18515,18577],{"className":18460,"ariaHidden":46},[45],[15,18462,18464,18467,18470,18473,18476,18479,18482,18485],{"className":18463},[50],[15,18465],{"className":18466,"style":139},[54],[15,18468,37],{"className":18469,"style":61},[59,60],[15,18471,113],{"className":18472},[146],[15,18474,769],{"className":18475},[59,60],[15,18477,120],{"className":18478},[153],[15,18480],{"className":18481,"style":158},[157],[15,18483,6928],{"className":18484},[162],[15,18486],{"className":18487,"style":158},[157],[15,18489,18491,18494,18497,18500,18503,18506,18509,18512],{"className":18490},[50],[15,18492],{"className":18493,"style":139},[54],[15,18495,37],{"className":18496,"style":61},[59,60],[15,18498,113],{"className":18499},[146],[15,18501,117],{"className":18502},[59],[15,18504,120],{"className":18505},[153],[15,18507],{"className":18508,"style":2587},[157],[15,18510,2470],{"className":18511},[2591],[15,18513],{"className":18514,"style":2587},[157],[15,18516,18518,18521,18553,18556,18559,18562,18565,18568,18571,18574],{"className":18517},[50],[15,18519],{"className":18520,"style":6843},[54],[15,18522,18524,18527],{"className":18523},[59],[15,18525,37],{"className":18526,"style":61},[59,60],[15,18528,18530],{"className":18529},[281],[15,18531,18533],{"className":18532},[285],[15,18534,18536],{"className":18535},[290],[15,18537,18539],{"className":18538,"style":6862},[294],[15,18540,18541,18544],{"style":6865},[15,18542],{"className":18543,"style":303},[302],[15,18545,18547],{"className":18546},[307,308,309,310],[15,18548,18550],{"className":18549},[59,310],[15,18551,6820],{"className":18552},[59,310],[15,18554,113],{"className":18555},[146],[15,18557,117],{"className":18558},[59],[15,18560,120],{"className":18561},[153],[15,18563,113],{"className":18564},[146],[15,18566,769],{"className":18567},[59,60],[15,18569],{"className":18570,"style":2587},[157],[15,18572,4813],{"className":18573},[2591],[15,18575],{"className":18576,"style":2587},[157],[15,18578,18580,18583,18586,18589,18621,18624,18627],{"className":18579},[50],[15,18581],{"className":18582,"style":6843},[54],[15,18584,117],{"className":18585},[59],[15,18587,120],{"className":18588},[153],[15,18590,18592,18595],{"className":18591},[59],[15,18593,37],{"className":18594,"style":61},[59,60],[15,18596,18598],{"className":18597},[281],[15,18599,18601],{"className":18600},[285],[15,18602,18604],{"className":18603},[290],[15,18605,18607],{"className":18606,"style":6862},[294],[15,18608,18609,18612],{"style":6865},[15,18610],{"className":18611,"style":303},[302],[15,18613,18615],{"className":18614},[307,308,309,310],[15,18616,18618],{"className":18617},[59,310],[15,18619,6820],{"className":18620},[59,310],[15,18622,113],{"className":18623},[146],[15,18625,117],{"className":18626},[59],[15,18628,120],{"className":18629},[153],"，此处只需次梯度 ",[15,18632,18634,18658],{"className":18633,"translate":19},[18],[15,18635,18637],{"className":18636},[23],[25,18638,18639],{"xmlns":27},[29,18640,18641,18655],{},[32,18642,18643,18649,18651,18653],{},[6814,18644,18645,18647],{},[35,18646,37],{},[110,18648,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,18650,113],{"stretchy":112},[115,18652,117],{},[110,18654,120],{"stretchy":112},[39,18656,18657],{"encoding":41},"f'(1)",[15,18659,18661],{"className":18660,"ariaHidden":46},[45],[15,18662,18664,18667,18699,18702,18705],{"className":18663},[50],[15,18665],{"className":18666,"style":6843},[54],[15,18668,18670,18673],{"className":18669},[59],[15,18671,37],{"className":18672,"style":61},[59,60],[15,18674,18676],{"className":18675},[281],[15,18677,18679],{"className":18678},[285],[15,18680,18682],{"className":18681},[290],[15,18683,18685],{"className":18684,"style":6862},[294],[15,18686,18687,18690],{"style":6865},[15,18688],{"className":18689,"style":303},[302],[15,18691,18693],{"className":18692},[307,308,309,310],[15,18694,18696],{"className":18695},[59,310],[15,18697,6820],{"className":18698},[59,310],[15,18700,113],{"className":18701},[146],[15,18703,117],{"className":18704},[59],[15,18706,120],{"className":18707},[153],"，即 ",[15,18710,18712,18760],{"className":18711,"translate":19},[18],[15,18713,18715],{"className":18714},[23],[25,18716,18717],{"xmlns":27},[29,18718,18719,18757],{},[32,18720,18721,18723,18725,18727,18729,18731,18733,18735,18737,18739,18741,18747,18749,18751,18753,18755],{},[35,18722,37],{},[110,18724,113],{"stretchy":112},[35,18726,769],{},[110,18728,120],{"stretchy":112},[110,18730,6928],{},[35,18732,37],{},[110,18734,113],{"stretchy":112},[115,18736,117],{},[110,18738,120],{"stretchy":112},[110,18740,2470],{},[195,18742,18743,18745],{},[35,18744,4158],{},[115,18746,117],{},[110,18748,113],{"stretchy":112},[35,18750,769],{},[110,18752,4813],{},[115,18754,117],{},[110,18756,120],{"stretchy":112},[39,18758,18759],{"encoding":41},"f(t)\\ge f(1)+g_1(t-1)",[15,18761,18763,18790,18817,18879],{"className":18762,"ariaHidden":46},[45],[15,18764,18766,18769,18772,18775,18778,18781,18784,18787],{"className":18765},[50],[15,18767],{"className":18768,"style":139},[54],[15,18770,37],{"className":18771,"style":61},[59,60],[15,18773,113],{"className":18774},[146],[15,18776,769],{"className":18777},[59,60],[15,18779,120],{"className":18780},[153],[15,18782],{"className":18783,"style":158},[157],[15,18785,6928],{"className":18786},[162],[15,18788],{"className":18789,"style":158},[157],[15,18791,18793,18796,18799,18802,18805,18808,18811,18814],{"className":18792},[50],[15,18794],{"className":18795,"style":139},[54],[15,18797,37],{"className":18798,"style":61},[59,60],[15,18800,113],{"className":18801},[146],[15,18803,117],{"className":18804},[59],[15,18806,120],{"className":18807},[153],[15,18809],{"className":18810,"style":2587},[157],[15,18812,2470],{"className":18813},[2591],[15,18815],{"className":18816,"style":2587},[157],[15,18818,18820,18823,18864,18867,18870,18873,18876],{"className":18819},[50],[15,18821],{"className":18822,"style":139},[54],[15,18824,18826,18829],{"className":18825},[59],[15,18827,4158],{"className":18828,"style":981},[59,60],[15,18830,18832],{"className":18831},[281],[15,18833,18835,18856],{"className":18834},[285,286],[15,18836,18838,18853],{"className":18837},[290],[15,18839,18841],{"className":18840,"style":11133},[294],[15,18842,18844,18847],{"style":18843},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[15,18845],{"className":18846,"style":303},[302],[15,18848,18850],{"className":18849},[307,308,309,310],[15,18851,117],{"className":18852},[59,310],[15,18854,318],{"className":18855},[317],[15,18857,18859],{"className":18858},[290],[15,18860,18862],{"className":18861,"style":7968},[294],[15,18863],{},[15,18865,113],{"className":18866},[146],[15,18868,769],{"className":18869},[59,60],[15,18871],{"className":18872,"style":2587},[157],[15,18874,4813],{"className":18875},[2591],[15,18877],{"className":18878,"style":2587},[157],[15,18880,18882,18885,18888],{"className":18881},[50],[15,18883],{"className":18884,"style":139},[54],[15,18886,117],{"className":18887},[59],[15,18889,120],{"className":18890},[153]," 对任一次梯度 ",[15,18893,18895,18913],{"className":18894,"translate":19},[18],[15,18896,18898],{"className":18897},[23],[25,18899,18900],{"xmlns":27},[29,18901,18902,18910],{},[32,18903,18904],{},[195,18905,18906,18908],{},[35,18907,4158],{},[115,18909,117],{},[39,18911,18912],{"encoding":41},"g_1",[15,18914,18916],{"className":18915,"ariaHidden":46},[45],[15,18917,18919,18922],{"className":18918},[50],[15,18920],{"className":18921,"style":2276},[54],[15,18923,18925,18928],{"className":18924},[59],[15,18926,4158],{"className":18927,"style":981},[59,60],[15,18929,18931],{"className":18930},[281],[15,18932,18934,18954],{"className":18933},[285,286],[15,18935,18937,18951],{"className":18936},[290],[15,18938,18940],{"className":18939,"style":11133},[294],[15,18941,18942,18945],{"style":18843},[15,18943],{"className":18944,"style":303},[302],[15,18946,18948],{"className":18947},[307,308,309,310],[15,18949,117],{"className":18950},[59,310],[15,18952,318],{"className":18953},[317],[15,18955,18957],{"className":18956},[290],[15,18958,18960],{"className":18959,"style":7968},[294],[15,18961],{},"）处理非主项：对凸的 ",[15,18964,18966,18979],{"className":18965,"translate":19},[18],[15,18967,18969],{"className":18968},[23],[25,18970,18971],{"xmlns":27},[29,18972,18973,18977],{},[32,18974,18975],{},[35,18976,37],{},[39,18978,37],{"encoding":41},[15,18980,18982],{"className":18981,"ariaHidden":46},[45],[15,18983,18985,18988],{"className":18984},[50],[15,18986],{"className":18987,"style":55},[54],[15,18989,37],{"className":18990,"style":61},[59,60],[15,18992,18994,19020],{"className":18993,"translate":19},[18],[15,18995,18997],{"className":18996},[23],[25,18998,18999],{"xmlns":27},[29,19000,19001,19017],{},[32,19002,19003,19005,19007,19009,19011,19013,19015],{},[35,19004,37],{},[110,19006,113],{"stretchy":112},[35,19008,4158],{},[110,19010,113],{"stretchy":112},[35,19012,16450],{},[110,19014,120],{"stretchy":112},[110,19016,120],{"stretchy":112},[39,19018,19019],{"encoding":41},"f(g(r))",[15,19021,19023],{"className":19022,"ariaHidden":46},[45],[15,19024,19026,19029,19032,19035,19038,19041,19044],{"className":19025},[50],[15,19027],{"className":19028,"style":139},[54],[15,19030,37],{"className":19031,"style":61},[59,60],[15,19033,113],{"className":19034},[146],[15,19036,4158],{"className":19037,"style":981},[59,60],[15,19039,113],{"className":19040},[146],[15,19042,16450],{"className":19043,"style":277},[59,60],[15,19045,19047],{"className":19046},[153],"))"," 中关于 ",[15,19050,19052,19065],{"className":19051,"translate":19},[18],[15,19053,19055],{"className":19054},[23],[25,19056,19057],{"xmlns":27},[29,19058,19059,19063],{},[32,19060,19061],{},[35,19062,16450],{},[39,19064,16450],{"encoding":41},[15,19066,19068],{"className":19067,"ariaHidden":46},[45],[15,19069,19071,19074],{"className":19070},[50],[15,19072],{"className":19073,"style":2345},[54],[15,19075,16450],{"className":19076,"style":277},[59,60]," 的\"非主项\"部分为",[15,19079,19081],{"className":19080,"translate":19},[180],[15,19082,19084,19289],{"className":19083,"translate":19},[18],[15,19085,19087],{"className":19086},[23],[25,19088,19089],{"xmlns":27,"display":189},[29,19090,19091,19286],{},[1243,19092,19093,19157,19232],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,19094,19095,19115],{},[1252,19096,19097],{},[1255,19098,19099],{"scriptlevel":126,"displaystyle":46},[32,19100,19101,19103,19105,19107,19109,19111,19113],{},[35,19102,37],{},[110,19104,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,19106,4158],{},[110,19108,113],{"stretchy":112},[35,19110,16450],{},[110,19112,120],{"stretchy":112},[110,19114,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1252,19116,19117],{},[1255,19118,19119],{"scriptlevel":126,"displaystyle":46},[32,19120,19121,19123,19125,19127,19129,19131,19133,19135,19155],{},[32,19122],{},[110,19124,123],{},[35,19126,37],{},[110,19128,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,19130,117],{},[110,19132,2470],{},[35,19134,15712],{},[1255,19136,19137],{"scriptlevel":126,"displaystyle":112},[238,19138,19139,19147],{},[32,19140,19141,19143,19145],{},[115,19142,117],{},[110,19144,4813],{},[35,19146,16450],{},[32,19148,19149,19151,19153],{},[115,19150,117],{},[110,19152,4813],{},[35,19154,15712],{},[110,19156,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,19158,19159,19165],{},[1252,19160,19161],{},[1255,19162,19163],{"scriptlevel":126,"displaystyle":46},[32,19164],{},[1252,19166,19167],{},[1255,19168,19169],{"scriptlevel":126,"displaystyle":46},[32,19170,19171,19173,19175,19177,19179,19181,19183,19185,19191,19193,19195,19197,19217,19219,19222,19224,19230],{},[32,19172],{},[110,19174,123],{},[35,19176,37],{},[110,19178,113],{"stretchy":112},[115,19180,117],{},[110,19182,120],{"stretchy":112},[110,19184,2470],{},[195,19186,19187,19189],{},[35,19188,4158],{},[115,19190,117],{},[110,19192,3299],{},[35,19194,15712],{},[1297,19196,1299],{},[1255,19198,19199],{"scriptlevel":126,"displaystyle":112},[238,19200,19201,19209],{},[32,19202,19203,19205,19207],{},[115,19204,117],{},[110,19206,4813],{},[35,19208,16450],{},[32,19210,19211,19213,19215],{},[115,19212,117],{},[110,19214,4813],{},[35,19216,15712],{},[110,19218,2470],{},[35,19220,19221],{},"O",[110,19223,113],{"stretchy":112},[6814,19225,19226,19228],{},[35,19227,15712],{},[115,19229,2463],{},[110,19231,120],{"stretchy":112},[1249,19233,19234,19240],{},[1252,19235,19236],{},[1255,19237,19238],{"scriptlevel":126,"displaystyle":46},[32,19239],{},[1252,19241,19242],{},[1255,19243,19244],{"scriptlevel":126,"displaystyle":46},[32,19245,19246,19248,19250,19256,19258,19260,19262,19264,19266,19268,19270,19272,19274,19276,19282,19284],{},[32,19247],{},[110,19249,123],{},[195,19251,19252,19254],{},[35,19253,4158],{},[115,19255,117],{},[1297,19257,1299],{},[35,19259,15712],{},[110,19261,113],{"stretchy":112},[115,19263,117],{},[110,19265,4813],{},[35,19267,16450],{},[110,19269,120],{"stretchy":112},[110,19271,2470],{},[35,19273,19221],{},[110,19275,113],{"stretchy":112},[6814,19277,19278,19280],{},[35,19279,15712],{},[115,19281,2463],{},[110,19283,120],{"stretchy":112},[110,19285,551],{"separator":46},[39,19287,19288],{"encoding":41},"\\begin{aligned}\nf\\big(g(r)\\big)\n&=f\\big(1+\\delta\\tfrac{1-r}{1-\\delta}\\big)\\\\\n&= f(1)+g_1\\cdot\\delta\\,\\tfrac{1-r}{1-\\delta}\n+O(\\delta^2)\\\\\n&= g_1\\,\\delta(1-r)+O(\\delta^2),\n\\end{aligned}",[15,19290,19292],{"className":19291,"ariaHidden":46},[45],[15,19293,19295,19299],{"className":19294},[50],[15,19296],{"className":19297,"style":19298},[54],"height:4.3449em;vertical-align:-1.9224em;",[15,19300,19302],{"className":19301},[59],[15,19303,19305,19384],{"className":19304},[1243],[15,19306,19308],{"className":19307},[1360],[15,19309,19311,19375],{"className":19310},[285,286],[15,19312,19314,19372],{"className":19313},[290],[15,19315,19318,19354,19363],{"className":19316,"style":19317},[294],"height:2.4224em;",[15,19319,19321,19324],{"style":19320},"top:-4.5724em;",[15,19322],{"className":19323,"style":461},[302],[15,19325,19327,19330,19336,19339,19342,19345,19348],{"className":19326},[59],[15,19328,37],{"className":19329,"style":61},[59,60],[15,19331,19333],{"className":19332},[59],[15,19334,113],{"className":19335},[419,9674],[15,19337,4158],{"className":19338,"style":981},[59,60],[15,19340,113],{"className":19341},[146],[15,19343,16450],{"className":19344,"style":277},[59,60],[15,19346,120],{"className":19347},[153],[15,19349,19351],{"className":19350},[59],[15,19352,120],{"className":19353},[419,9674],[15,19355,19357,19360],{"style":19356},"top:-3.005em;",[15,19358],{"className":19359,"style":461},[302],[15,19361],{"className":19362},[59],[15,19364,19366,19369],{"style":19365},"top:-1.4376em;",[15,19367],{"className":19368,"style":461},[302],[15,19370],{"className":19371},[59],[15,19373,318],{"className":19374},[317],[15,19376,19378],{"className":19377},[290],[15,19379,19382],{"className":19380,"style":19381},[294],"height:1.9224em;",[15,19383],{},[15,19385,19387],{"className":19386},[1451],[15,19388,19390,19890],{"className":19389},[285,286],[15,19391,19393,19887],{"className":19392},[290],[15,19394,19396,19526,19750],{"className":19395,"style":19317},[294],[15,19397,19398,19401],{"style":19320},[15,19399],{"className":19400,"style":461},[302],[15,19402,19404,19407,19410,19413,19416,19419,19425,19428,19431,19434,19437,19440,19520],{"className":19403},[59],[15,19405],{"className":19406},[59],[15,19408],{"className":19409,"style":158},[157],[15,19411,123],{"className":19412},[162],[15,19414],{"className":19415,"style":158},[157],[15,19417,37],{"className":19418,"style":61},[59,60],[15,19420,19422],{"className":19421},[59],[15,19423,113],{"className":19424},[419,9674],[15,19426,117],{"className":19427},[59],[15,19429],{"className":19430,"style":2587},[157],[15,19432,2470],{"className":19433},[2591],[15,19435],{"className":19436,"style":2587},[157],[15,19438,15712],{"className":19439,"style":15761},[59,60],[15,19441,19443,19446,19517],{"className":19442},[59],[15,19444],{"className":19445},[146,441],[15,19447,19449],{"className":19448},[238],[15,19450,19452,19509],{"className":19451},[285,286],[15,19453,19455,19506],{"className":19454},[290],[15,19456,19458,19478,19486],{"className":19457,"style":2524},[294],[15,19459,19460,19463],{"style":2527},[15,19461],{"className":19462,"style":461},[302],[15,19464,19466],{"className":19465},[307,308,309,310],[15,19467,19469,19472,19475],{"className":19468},[59,310],[15,19470,117],{"className":19471},[59,310],[15,19473,4813],{"className":19474},[2591,310],[15,19476,15712],{"className":19477,"style":15761},[59,60,310],[15,19479,19480,19483],{"style":473},[15,19481],{"className":19482,"style":461},[302],[15,19484],{"className":19485,"style":481},[480],[15,19487,19488,19491],{"style":2550},[15,19489],{"className":19490,"style":461},[302],[15,19492,19494],{"className":19493},[307,308,309,310],[15,19495,19497,19500,19503],{"className":19496},[59,310],[15,19498,117],{"className":19499},[59,310],[15,19501,4813],{"className":19502},[2591,310],[15,19504,16450],{"className":19505,"style":277},[59,60,310],[15,19507,318],{"className":19508},[317],[15,19510,19512],{"className":19511},[290],[15,19513,19515],{"className":19514,"style":16429},[294],[15,19516],{},[15,19518],{"className":19519},[153,441],[15,19521,19523],{"className":19522},[59],[15,19524,120],{"className":19525},[419,9674],[15,19527,19528,19531],{"style":19356},[15,19529],{"className":19530,"style":461},[302],[15,19532,19534,19537,19540,19543,19546,19549,19552,19555,19558,19561,19564,19567,19607,19610,19613,19616,19619,19622,19702,19705,19708,19711,19714,19717,19747],{"className":19533},[59],[15,19535],{"className":19536},[59],[15,19538],{"className":19539,"style":158},[157],[15,19541,123],{"className":19542},[162],[15,19544],{"className":19545,"style":158},[157],[15,19547,37],{"className":19548,"style":61},[59,60],[15,19550,113],{"className":19551},[146],[15,19553,117],{"className":19554},[59],[15,19556,120],{"className":19557},[153],[15,19559],{"className":19560,"style":2587},[157],[15,19562,2470],{"className":19563},[2591],[15,19565],{"className":19566,"style":2587},[157],[15,19568,19570,19573],{"className":19569},[59],[15,19571,4158],{"className":19572,"style":981},[59,60],[15,19574,19576],{"className":19575},[281],[15,19577,19579,19599],{"className":19578},[285,286],[15,19580,19582,19596],{"className":19581},[290],[15,19583,19585],{"className":19584,"style":11133},[294],[15,19586,19587,19590],{"style":18843},[15,19588],{"className":19589,"style":303},[302],[15,19591,19593],{"className":19592},[307,308,309,310],[15,19594,117],{"className":19595},[59,310],[15,19597,318],{"className":19598},[317],[15,19600,19602],{"className":19601},[290],[15,19603,19605],{"className":19604,"style":7968},[294],[15,19606],{},[15,19608],{"className":19609,"style":2587},[157],[15,19611,3299],{"className":19612},[2591],[15,19614],{"className":19615,"style":2587},[157],[15,19617,15712],{"className":19618,"style":15761},[59,60],[15,19620],{"className":19621,"style":406},[157],[15,19623,19625,19628,19699],{"className":19624},[59],[15,19626],{"className":19627},[146,441],[15,19629,19631],{"className":19630},[238],[15,19632,19634,19691],{"className":19633},[285,286],[15,19635,19637,19688],{"className":19636},[290],[15,19638,19640,19660,19668],{"className":19639,"style":2524},[294],[15,19641,19642,19645],{"style":2527},[15,19643],{"className":19644,"style":461},[302],[15,19646,19648],{"className":19647},[307,308,309,310],[15,19649,19651,19654,19657],{"className":19650},[59,310],[15,19652,117],{"className":19653},[59,310],[15,19655,4813],{"className":19656},[2591,310],[15,19658,15712],{"className":19659,"style":15761},[59,60,310],[15,19661,19662,19665],{"style":473},[15,19663],{"className":19664,"style":461},[302],[15,19666],{"className":19667,"style":481},[480],[15,19669,19670,19673],{"style":2550},[15,19671],{"className":19672,"style":461},[302],[15,19674,19676],{"className":19675},[307,308,309,310],[15,19677,19679,19682,19685],{"className":19678},[59,310],[15,19680,117],{"className":19681},[59,310],[15,19683,4813],{"className":19684},[2591,310],[15,19686,16450],{"className":19687,"style":277},[59,60,310],[15,19689,318],{"className":19690},[317],[15,19692,19694],{"className":19693},[290],[15,19695,19697],{"className":19696,"style":16429},[294],[15,19698],{},[15,19700],{"className":19701},[153,441],[15,19703],{"className":19704,"style":2587},[157],[15,19706,2470],{"className":19707},[2591],[15,19709],{"className":19710,"style":2587},[157],[15,19712,19221],{"className":19713,"style":277},[59,60],[15,19715,113],{"className":19716},[146],[15,19718,19720,19723],{"className":19719},[59],[15,19721,15712],{"className":19722,"style":15761},[59,60],[15,19724,19726],{"className":19725},[281],[15,19727,19729],{"className":19728},[285],[15,19730,19732],{"className":19731},[290],[15,19733,19736],{"className":19734,"style":19735},[294],"height:0.8641em;",[15,19737,19738,19741],{"style":8277},[15,19739],{"className":19740,"style":303},[302],[15,19742,19744],{"className":19743},[307,308,309,310],[15,19745,2463],{"className":19746},[59,310],[15,19748,120],{"className":19749},[153],[15,19751,19752,19755],{"style":19365},[15,19753],{"className":19754,"style":461},[302],[15,19756,19758,19761,19764,19767,19770,19810,19813,19816,19819,19822,19825,19828,19831,19834,19837,19840,19843,19846,19849,19852,19881,19884],{"className":19757},[59],[15,19759],{"className":19760},[59],[15,19762],{"className":19763,"style":158},[157],[15,19765,123],{"className":19766},[162],[15,19768],{"className":19769,"style":158},[157],[15,19771,19773,19776],{"className":19772},[59],[15,19774,4158],{"className":19775,"style":981},[59,60],[15,19777,19779],{"className":19778},[281],[15,19780,19782,19802],{"className":19781},[285,286],[15,19783,19785,19799],{"className":19784},[290],[15,19786,19788],{"className":19787,"style":11133},[294],[15,19789,19790,19793],{"style":18843},[15,19791],{"className":19792,"style":303},[302],[15,19794,19796],{"className":19795},[307,308,309,310],[15,19797,117],{"className":19798},[59,310],[15,19800,318],{"className":19801},[317],[15,19803,19805],{"className":19804},[290],[15,19806,19808],{"className":19807,"style":7968},[294],[15,19809],{},[15,19811],{"className":19812,"style":406},[157],[15,19814,15712],{"className":19815,"style":15761},[59,60],[15,19817,113],{"className":19818},[146],[15,19820,117],{"className":19821},[59],[15,19823],{"className":19824,"style":2587},[157],[15,19826,4813],{"className":19827},[2591],[15,19829],{"className":19830,"style":2587},[157],[15,19832,16450],{"className":19833,"style":277},[59,60],[15,19835,120],{"className":19836},[153],[15,19838],{"className":19839,"style":2587},[157],[15,19841,2470],{"className":19842},[2591],[15,19844],{"className":19845,"style":2587},[157],[15,19847,19221],{"className":19848,"style":277},[59,60],[15,19850,113],{"className":19851},[146],[15,19853,19855,19858],{"className":19854},[59],[15,19856,15712],{"className":19857,"style":15761},[59,60],[15,19859,19861],{"className":19860},[281],[15,19862,19864],{"className":19863},[285],[15,19865,19867],{"className":19866},[290],[15,19868,19870],{"className":19869,"style":19735},[294],[15,19871,19872,19875],{"style":8277},[15,19873],{"className":19874,"style":303},[302],[15,19876,19878],{"className":19877},[307,308,309,310],[15,19879,2463],{"className":19880},[59,310],[15,19882,120],{"className":19883},[153],[15,19885,551],{"className":19886},[573],[15,19888,318],{"className":19889},[317],[15,19891,19893],{"className":19892},[290],[15,19894,19896],{"className":19895,"style":19381},[294],[15,19897],{},[11,19899,19900,19901,19966,19967,20043,20044,20072,20073,6800,20176,20204,20205,20254,20255,2409,20391,20440],{},"（用了 ",[15,19902,19904,19927],{"className":19903,"translate":19},[18],[15,19905,19907],{"className":19906},[23],[25,19908,19909],{"xmlns":27},[29,19910,19911,19925],{},[32,19912,19913,19915,19917,19919,19921,19923],{},[35,19914,37],{},[110,19916,113],{"stretchy":112},[115,19918,117],{},[110,19920,120],{"stretchy":112},[110,19922,123],{},[115,19924,126],{},[39,19926,129],{"encoding":41},[15,19928,19930,19957],{"className":19929,"ariaHidden":46},[45],[15,19931,19933,19936,19939,19942,19945,19948,19951,19954],{"className":19932},[50],[15,19934],{"className":19935,"style":139},[54],[15,19937,37],{"className":19938,"style":61},[59,60],[15,19940,113],{"className":19941},[146],[15,19943,117],{"className":19944},[59],[15,19946,120],{"className":19947},[153],[15,19949],{"className":19950,"style":158},[157],[15,19952,123],{"className":19953},[162],[15,19955],{"className":19956,"style":158},[157],[15,19958,19960,19963],{"className":19959},[50],[15,19961],{"className":19962,"style":172},[54],[15,19964,126],{"className":19965},[59],"；",[15,19968,19970,19994],{"className":19969,"translate":19},[18],[15,19971,19973],{"className":19972},[23],[25,19974,19975],{"xmlns":27},[29,19976,19977,19991],{},[32,19978,19979,19981,19983,19989],{},[35,19980,19221],{},[110,19982,113],{"stretchy":112},[6814,19984,19985,19987],{},[35,19986,15712],{},[115,19988,2463],{},[110,19990,120],{"stretchy":112},[39,19992,19993],{"encoding":41},"O(\\delta^2)",[15,19995,19997],{"className":19996,"ariaHidden":46},[45],[15,19998,20000,20004,20007,20010,20040],{"className":19999},[50],[15,20001],{"className":20002,"style":20003},[54],"height:1.0641em;vertical-align:-0.25em;",[15,20005,19221],{"className":20006,"style":277},[59,60],[15,20008,113],{"className":20009},[146],[15,20011,20013,20016],{"className":20012},[59],[15,20014,15712],{"className":20015,"style":15761},[59,60],[15,20017,20019],{"className":20018},[281],[15,20020,20022],{"className":20021},[285],[15,20023,20025],{"className":20024},[290],[15,20026,20029],{"className":20027,"style":20028},[294],"height:0.8141em;",[15,20030,20031,20034],{"style":6865},[15,20032],{"className":20033,"style":303},[302],[15,20035,20037],{"className":20036},[307,308,309,310],[15,20038,2463],{"className":20039},[59,310],[15,20041,120],{"className":20042},[153]," 项在 ",[15,20045,20047,20060],{"className":20046,"translate":19},[18],[15,20048,20050],{"className":20049},[23],[25,20051,20052],{"xmlns":27},[29,20053,20054,20058],{},[32,20055,20056],{},[35,20057,16450],{},[39,20059,16450],{"encoding":41},[15,20061,20063],{"className":20062,"ariaHidden":46},[45],[15,20064,20066,20069],{"className":20065},[50],[15,20067],{"className":20068,"style":2345},[54],[15,20070,16450],{"className":20071,"style":277},[59,60]," 变化时一致有界，因为 ",[15,20074,20076,20110],{"className":20075,"translate":19},[18],[15,20077,20079],{"className":20078},[23],[25,20080,20081],{"xmlns":27},[29,20082,20083,20107],{},[32,20084,20085,20087,20089,20091,20093,20095,20097,20099,20101,20103,20105],{},[35,20086,4158],{},[110,20088,113],{"stretchy":112},[35,20090,16450],{},[110,20092,120],{"stretchy":112},[110,20094,123],{},[115,20096,117],{},[110,20098,2470],{},[35,20100,19221],{},[110,20102,113],{"stretchy":112},[35,20104,15712],{},[110,20106,120],{"stretchy":112},[39,20108,20109],{"encoding":41},"g(r)=1+O(\\delta)",[15,20111,20113,20140,20158],{"className":20112,"ariaHidden":46},[45],[15,20114,20116,20119,20122,20125,20128,20131,20134,20137],{"className":20115},[50],[15,20117],{"className":20118,"style":139},[54],[15,20120,4158],{"className":20121,"style":981},[59,60],[15,20123,113],{"className":20124},[146],[15,20126,16450],{"className":20127,"style":277},[59,60],[15,20129,120],{"className":20130},[153],[15,20132],{"className":20133,"style":158},[157],[15,20135,123],{"className":20136},[162],[15,20138],{"className":20139,"style":158},[157],[15,20141,20143,20146,20149,20152,20155],{"className":20142},[50],[15,20144],{"className":20145,"style":12578},[54],[15,20147,117],{"className":20148},[59],[15,20150],{"className":20151,"style":2587},[157],[15,20153,2470],{"className":20154},[2591],[15,20156],{"className":20157,"style":2587},[157],[15,20159,20161,20164,20167,20170,20173],{"className":20160},[50],[15,20162],{"className":20163,"style":139},[54],[15,20165,19221],{"className":20166,"style":277},[59,60],[15,20168,113],{"className":20169},[146],[15,20171,15712],{"className":20172,"style":15761},[59,60],[15,20174,120],{"className":20175},[153],[15,20177,20179,20192],{"className":20178,"translate":19},[18],[15,20180,20182],{"className":20181},[23],[25,20183,20184],{"xmlns":27},[29,20185,20186,20190],{},[32,20187,20188],{},[35,20189,37],{},[39,20191,37],{"encoding":41},[15,20193,20195],{"className":20194,"ariaHidden":46},[45],[15,20196,20198,20201],{"className":20197},[50],[15,20199],{"className":20200,"style":55},[54],[15,20202,37],{"className":20203,"style":61},[59,60]," 连续）。代回不等式：两边的主项（",[15,20206,20208,20230],{"className":20207,"translate":19},[18],[15,20209,20211],{"className":20210},[23],[25,20212,20213],{"xmlns":27},[29,20214,20215,20227],{},[32,20216,20217,20219,20221,20223,20225],{},[35,20218,15712],{},[35,20220,37],{},[110,20222,113],{"stretchy":112},[110,20224,3299],{},[110,20226,120],{"stretchy":112},[39,20228,20229],{"encoding":41},"\\delta f(\\cdot)",[15,20231,20233],{"className":20232,"ariaHidden":46},[45],[15,20234,20236,20239,20242,20245,20248,20251],{"className":20235},[50],[15,20237],{"className":20238,"style":139},[54],[15,20240,15712],{"className":20241,"style":15761},[59,60],[15,20243,37],{"className":20244,"style":61},[59,60],[15,20246,113],{"className":20247},[146],[15,20249,3299],{"className":20250},[59],[15,20252,120],{"className":20253},[153]," 部分）正是 ",[15,20256,20258,20306],{"className":20257,"translate":19},[18],[15,20259,20261],{"className":20260},[23],[25,20262,20263],{"xmlns":27},[29,20264,20265,20303],{},[32,20266,20267,20269,20271,20273,20275,20277,20279,20281,20283,20285,20287,20289,20291,20293,20295,20297,20299,20301],{},[35,20268,15712],{},[110,20270,230],{"stretchy":112},[35,20272,11339],{},[35,20274,37],{},[110,20276,113],{"stretchy":112},[35,20278,7561],{},[110,20280,120],{"stretchy":112},[110,20282,2470],{},[110,20284,113],{"stretchy":112},[115,20286,117],{},[110,20288,4813],{},[35,20290,11339],{},[110,20292,120],{"stretchy":112},[35,20294,37],{},[110,20296,113],{"stretchy":112},[35,20298,15400],{},[110,20300,120],{"stretchy":112},[110,20302,257],{"stretchy":112},[39,20304,20305],{"encoding":41},"\\delta[\\lambda f(s)+(1-\\lambda)f(u)]",[15,20307,20309,20345,20366],{"className":20308,"ariaHidden":46},[45],[15,20310,20312,20315,20318,20321,20324,20327,20330,20333,20336,20339,20342],{"className":20311},[50],[15,20313],{"className":20314,"style":139},[54],[15,20316,15712],{"className":20317,"style":15761},[59,60],[15,20319,230],{"className":20320},[146],[15,20322,11339],{"className":20323},[59,60],[15,20325,37],{"className":20326,"style":61},[59,60],[15,20328,113],{"className":20329},[146],[15,20331,7561],{"className":20332},[59,60],[15,20334,120],{"className":20335},[153],[15,20337],{"className":20338,"style":2587},[157],[15,20340,2470],{"className":20341},[2591],[15,20343],{"className":20344,"style":2587},[157],[15,20346,20348,20351,20354,20357,20360,20363],{"className":20347},[50],[15,20349],{"className":20350,"style":139},[54],[15,20352,113],{"className":20353},[146],[15,20355,117],{"className":20356},[59],[15,20358],{"className":20359,"style":2587},[157],[15,20361,4813],{"className":20362},[2591],[15,20364],{"className":20365,"style":2587},[157],[15,20367,20369,20372,20375,20378,20381,20384,20387],{"className":20368},[50],[15,20370],{"className":20371,"style":139},[54],[15,20373,11339],{"className":20374},[59,60],[15,20376,120],{"className":20377},[153],[15,20379,37],{"className":20380,"style":61},[59,60],[15,20382,113],{"className":20383},[146],[15,20385,15400],{"className":20386},[59,60],[15,20388,20390],{"className":20389},[153],")]",[15,20392,20394,20416],{"className":20393,"translate":19},[18],[15,20395,20397],{"className":20396},[23],[25,20398,20399],{"xmlns":27},[29,20400,20401,20413],{},[32,20402,20403,20405,20407,20409,20411],{},[35,20404,15712],{},[35,20406,37],{},[110,20408,113],{"stretchy":112},[35,20410,7570],{},[110,20412,120],{"stretchy":112},[39,20414,20415],{"encoding":41},"\\delta f(w)",[15,20417,20419],{"className":20418,"ariaHidden":46},[45],[15,20420,20422,20425,20428,20431,20434,20437],{"className":20421},[50],[15,20423],{"className":20424,"style":139},[54],[15,20426,15712],{"className":20427,"style":15761},[59,60],[15,20429,37],{"className":20430,"style":61},[59,60],[15,20432,113],{"className":20433},[146],[15,20435,7570],{"className":20436,"style":8274},[59,60],[15,20438,120],{"className":20439},[153],"；非主项部分",[15,20442,20444],{"className":20443,"translate":19},[180],[15,20445,20447,20533],{"className":20446,"translate":19},[18],[15,20448,20450],{"className":20449},[23],[25,20451,20452],{"xmlns":27,"display":189},[29,20453,20454,20530],{},[32,20455,20456,20458,20460,20462,20464,20466,20468,20474,20476,20478,20480,20482,20484,20486,20488,20490,20492,20494,20496,20498,20500,20502,20504,20506,20508,20510,20512,20514,20516,20518,20520,20522,20524,20526,20528],{},[110,20457,113],{"stretchy":112},[115,20459,117],{},[110,20461,4813],{},[35,20463,15712],{},[110,20465,120],{"stretchy":112},[1297,20467,1299],{},[195,20469,20470,20472],{},[35,20471,4158],{},[115,20473,117],{},[35,20475,15712],{},[110,20477,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,20479,11339],{},[110,20481,113],{"stretchy":112},[115,20483,117],{},[110,20485,4813],{},[35,20487,7561],{},[110,20489,120],{"stretchy":112},[110,20491,2470],{},[110,20493,113],{"stretchy":112},[115,20495,117],{},[110,20497,4813],{},[35,20499,11339],{},[110,20501,120],{"stretchy":112},[110,20503,113],{"stretchy":112},[115,20505,117],{},[110,20507,4813],{},[35,20509,15400],{},[110,20511,120],{"stretchy":112},[110,20513,4813],{},[110,20515,113],{"stretchy":112},[115,20517,117],{},[110,20519,4813],{},[35,20521,7570],{},[110,20523,120],{"stretchy":112},[110,20525,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,20527,123],{},[115,20529,126],{},[39,20531,20532],{"encoding":41},"(1-\\delta)\\,g_1\\delta\\big[\\lambda(1-s)\n+(1-\\lambda)(1-u)-(1-w)\\big]=0",[15,20534,20536,20557,20640,20661,20682,20709,20730,20751,20778],{"className":20535,"ariaHidden":46},[45],[15,20537,20539,20542,20545,20548,20551,20554],{"className":20538},[50],[15,20540],{"className":20541,"style":139},[54],[15,20543,113],{"className":20544},[146],[15,20546,117],{"className":20547},[59],[15,20549],{"className":20550,"style":2587},[157],[15,20552,4813],{"className":20553},[2591],[15,20555],{"className":20556,"style":2587},[157],[15,20558,20560,20564,20567,20570,20573,20613,20616,20622,20625,20628,20631,20634,20637],{"className":20559},[50],[15,20561],{"className":20562,"style":20563},[54],"height:1.2em;vertical-align:-0.35em;",[15,20565,15712],{"className":20566,"style":15761},[59,60],[15,20568,120],{"className":20569},[153],[15,20571],{"className":20572,"style":406},[157],[15,20574,20576,20579],{"className":20575},[59],[15,20577,4158],{"className":20578,"style":981},[59,60],[15,20580,20582],{"className":20581},[281],[15,20583,20585,20605],{"className":20584},[285,286],[15,20586,20588,20602],{"className":20587},[290],[15,20589,20591],{"className":20590,"style":11133},[294],[15,20592,20593,20596],{"style":18843},[15,20594],{"className":20595,"style":303},[302],[15,20597,20599],{"className":20598},[307,308,309,310],[15,20600,117],{"className":20601},[59,310],[15,20603,318],{"className":20604},[317],[15,20606,20608],{"className":20607},[290],[15,20609,20611],{"className":20610,"style":7968},[294],[15,20612],{},[15,20614,15712],{"className":20615,"style":15761},[59,60],[15,20617,20619],{"className":20618},[59],[15,20620,230],{"className":20621},[419,9674],[15,20623,11339],{"className":20624},[59,60],[15,20626,113],{"className":20627},[146],[15,20629,117],{"className":20630},[59],[15,20632],{"className":20633,"style":2587},[157],[15,20635,4813],{"className":20636},[2591],[15,20638],{"className":20639,"style":2587},[157],[15,20641,20643,20646,20649,20652,20655,20658],{"className":20642},[50],[15,20644],{"className":20645,"style":139},[54],[15,20647,7561],{"className":20648},[59,60],[15,20650,120],{"className":20651},[153],[15,20653],{"className":20654,"style":2587},[157],[15,20656,2470],{"className":20657},[2591],[15,20659],{"className":20660,"style":2587},[157],[15,20662,20664,20667,20670,20673,20676,20679],{"className":20663},[50],[15,20665],{"className":20666,"style":139},[54],[15,20668,113],{"className":20669},[146],[15,20671,117],{"className":20672},[59],[15,20674],{"className":20675,"style":2587},[157],[15,20677,4813],{"className":20678},[2591],[15,20680],{"className":20681,"style":2587},[157],[15,20683,20685,20688,20691,20694,20697,20700,20703,20706],{"className":20684},[50],[15,20686],{"className":20687,"style":139},[54],[15,20689,11339],{"className":20690},[59,60],[15,20692,120],{"className":20693},[153],[15,20695,113],{"className":20696},[146],[15,20698,117],{"className":20699},[59],[15,20701],{"className":20702,"style":2587},[157],[15,20704,4813],{"className":20705},[2591],[15,20707],{"className":20708,"style":2587},[157],[15,20710,20712,20715,20718,20721,20724,20727],{"className":20711},[50],[15,20713],{"className":20714,"style":139},[54],[15,20716,15400],{"className":20717},[59,60],[15,20719,120],{"className":20720},[153],[15,20722],{"className":20723,"style":2587},[157],[15,20725,4813],{"className":20726},[2591],[15,20728],{"className":20729,"style":2587},[157],[15,20731,20733,20736,20739,20742,20745,20748],{"className":20732},[50],[15,20734],{"className":20735,"style":139},[54],[15,20737,113],{"className":20738},[146],[15,20740,117],{"className":20741},[59],[15,20743],{"className":20744,"style":2587},[157],[15,20746,4813],{"className":20747},[2591],[15,20749],{"className":20750,"style":2587},[157],[15,20752,20754,20757,20760,20763,20769,20772,20775],{"className":20753},[50],[15,20755],{"className":20756,"style":20563},[54],[15,20758,7570],{"className":20759,"style":8274},[59,60],[15,20761,120],{"className":20762},[153],[15,20764,20766],{"className":20765},[59],[15,20767,257],{"className":20768},[419,9674],[15,20770],{"className":20771,"style":158},[157],[15,20773,123],{"className":20774},[162],[15,20776],{"className":20777,"style":158},[157],[15,20779,20781,20784],{"className":20780},[50],[15,20782],{"className":20783,"style":172},[54],[15,20785,126],{"className":20786},[59],[11,20788,20789,20790,20904,20905,20956,20957,21039],{},"（方括号内恰为 0，因为 ",[15,20791,20793,20826],{"className":20792,"translate":19},[18],[15,20794,20796],{"className":20795},[23],[25,20797,20798],{"xmlns":27},[29,20799,20800,20824],{},[32,20801,20802,20804,20806,20808,20810,20812,20814,20816,20818,20820,20822],{},[35,20803,7570],{},[110,20805,123],{},[35,20807,11339],{},[35,20809,7561],{},[110,20811,2470],{},[110,20813,113],{"stretchy":112},[115,20815,117],{},[110,20817,4813],{},[35,20819,11339],{},[110,20821,120],{"stretchy":112},[35,20823,15400],{},[39,20825,15558],{"encoding":41},[15,20827,20829,20847,20868,20889],{"className":20828,"ariaHidden":46},[45],[15,20830,20832,20835,20838,20841,20844],{"className":20831},[50],[15,20833],{"className":20834,"style":2345},[54],[15,20836,7570],{"className":20837,"style":8274},[59,60],[15,20839],{"className":20840,"style":158},[157],[15,20842,123],{"className":20843},[162],[15,20845],{"className":20846,"style":158},[157],[15,20848,20850,20853,20856,20859,20862,20865],{"className":20849},[50],[15,20851],{"className":20852,"style":15586},[54],[15,20854,11339],{"className":20855},[59,60],[15,20857,7561],{"className":20858},[59,60],[15,20860],{"className":20861,"style":2587},[157],[15,20863,2470],{"className":20864},[2591],[15,20866],{"className":20867,"style":2587},[157],[15,20869,20871,20874,20877,20880,20883,20886],{"className":20870},[50],[15,20872],{"className":20873,"style":139},[54],[15,20875,113],{"className":20876},[146],[15,20878,117],{"className":20879},[59],[15,20881],{"className":20882,"style":2587},[157],[15,20884,4813],{"className":20885},[2591],[15,20887],{"className":20888,"style":2587},[157],[15,20890,20892,20895,20898,20901],{"className":20891},[50],[15,20893],{"className":20894,"style":139},[54],[15,20896,11339],{"className":20897},[59,60],[15,20899,120],{"className":20900},[153],[15,20902,15400],{"className":20903},[59,60],"）。于是不等式两边同除以 ",[15,20906,20908,20926],{"className":20907,"translate":19},[18],[15,20909,20911],{"className":20910},[23],[25,20912,20913],{"xmlns":27},[29,20914,20915,20923],{},[32,20916,20917,20919,20921],{},[35,20918,15712],{},[110,20920,2903],{},[115,20922,126],{},[39,20924,20925],{"encoding":41},"\\delta>0",[15,20927,20929,20947],{"className":20928,"ariaHidden":46},[45],[15,20930,20932,20935,20938,20941,20944],{"className":20931},[50],[15,20933],{"className":20934,"style":11364},[54],[15,20936,15712],{"className":20937,"style":15761},[59,60],[15,20939],{"className":20940,"style":158},[157],[15,20942,2903],{"className":20943},[162],[15,20945],{"className":20946,"style":158},[157],[15,20948,20950,20953],{"className":20949},[50],[15,20951],{"className":20952,"style":172},[54],[15,20954,126],{"className":20955},[59],"，令 ",[15,20958,20960,20982],{"className":20959,"translate":19},[18],[15,20961,20963],{"className":20962},[23],[25,20964,20965],{"xmlns":27},[29,20966,20967,20979],{},[32,20968,20969,20971,20973],{},[35,20970,15712],{},[110,20972,1029],{},[6814,20974,20975,20977],{},[115,20976,126],{},[110,20978,2470],{},[39,20980,20981],{"encoding":41},"\\delta\\to0^+",[15,20983,20985,21003],{"className":20984,"ariaHidden":46},[45],[15,20986,20988,20991,20994,20997,21000],{"className":20987},[50],[15,20989],{"className":20990,"style":12597},[54],[15,20992,15712],{"className":20993,"style":15761},[59,60],[15,20995],{"className":20996,"style":158},[157],[15,20998,1029],{"className":20999},[162],[15,21001],{"className":21002,"style":158},[157],[15,21004,21006,21010],{"className":21005},[50],[15,21007],{"className":21008,"style":21009},[54],"height:0.7713em;",[15,21011,21013,21016],{"className":21012},[59],[15,21014,126],{"className":21015},[59],[15,21017,21019],{"className":21018},[281],[15,21020,21022],{"className":21021},[285],[15,21023,21025],{"className":21024},[290],[15,21026,21028],{"className":21027,"style":21009},[294],[15,21029,21030,21033],{"style":6865},[15,21031],{"className":21032,"style":303},[302],[15,21034,21036],{"className":21035},[307,308,309,310],[15,21037,2470],{"className":21038},[2591,310],"，得",[15,21041,21043],{"className":21042,"translate":19},[180],[15,21044,21046,21116],{"className":21045,"translate":19},[18],[15,21047,21049],{"className":21048},[23],[25,21050,21051],{"xmlns":27,"display":189},[29,21052,21053,21113],{},[32,21054,21055,21057,21059,21061,21063,21065,21067,21069,21071,21073,21075,21077,21079,21081,21083,21085,21087,21089,21091,21093,21095,21097,21099,21101,21103,21105,21107,21109,21111],{},[35,21056,37],{},[110,21058,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,21060,11339],{},[35,21062,7561],{},[110,21064,2470],{},[110,21066,113],{"stretchy":112},[115,21068,117],{},[110,21070,4813],{},[35,21072,11339],{},[110,21074,120],{"stretchy":112},[35,21076,15400],{},[110,21078,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,21080,9952],{},[35,21082,11339],{},[35,21084,37],{},[110,21086,113],{"stretchy":112},[35,21088,7561],{},[110,21090,120],{"stretchy":112},[110,21092,2470],{},[110,21094,113],{"stretchy":112},[115,21096,117],{},[110,21098,4813],{},[35,21100,11339],{},[110,21102,120],{"stretchy":112},[35,21104,37],{},[110,21106,113],{"stretchy":112},[35,21108,15400],{},[110,21110,120],{"stretchy":112},[110,21112,551],{"separator":46},[39,21114,21115],{"encoding":41},"f\\big(\\lambda s+(1-\\lambda)u\\big)\n\\le\\lambda f(s)+(1-\\lambda)f(u),",[15,21117,21119,21149,21170,21200,21230,21251],{"className":21118,"ariaHidden":46},[45],[15,21120,21122,21125,21128,21134,21137,21140,21143,21146],{"className":21121},[50],[15,21123],{"className":21124,"style":20563},[54],[15,21126,37],{"className":21127,"style":61},[59,60],[15,21129,21131],{"className":21130},[59],[15,21132,113],{"className":21133},[419,9674],[15,21135,11339],{"className":21136},[59,60],[15,21138,7561],{"className":21139},[59,60],[15,21141],{"className":21142,"style":2587},[157],[15,21144,2470],{"className":21145},[2591],[15,21147],{"className":21148,"style":2587},[157],[15,21150,21152,21155,21158,21161,21164,21167],{"className":21151},[50],[15,21153],{"className":21154,"style":139},[54],[15,21156,113],{"className":21157},[146],[15,21159,117],{"className":21160},[59],[15,21162],{"className":21163,"style":2587},[157],[15,21165,4813],{"className":21166},[2591],[15,21168],{"className":21169,"style":2587},[157],[15,21171,21173,21176,21179,21182,21185,21191,21194,21197],{"className":21172},[50],[15,21174],{"className":21175,"style":20563},[54],[15,21177,11339],{"className":21178},[59,60],[15,21180,120],{"className":21181},[153],[15,21183,15400],{"className":21184},[59,60],[15,21186,21188],{"className":21187},[59],[15,21189,120],{"className":21190},[419,9674],[15,21192],{"className":21193,"style":158},[157],[15,21195,9952],{"className":21196},[162],[15,21198],{"className":21199,"style":158},[157],[15,21201,21203,21206,21209,21212,21215,21218,21221,21224,21227],{"className":21202},[50],[15,21204],{"className":21205,"style":139},[54],[15,21207,11339],{"className":21208},[59,60],[15,21210,37],{"className":21211,"style":61},[59,60],[15,21213,113],{"className":21214},[146],[15,21216,7561],{"className":21217},[59,60],[15,21219,120],{"className":21220},[153],[15,21222],{"className":21223,"style":2587},[157],[15,21225,2470],{"className":21226},[2591],[15,21228],{"className":21229,"style":2587},[157],[15,21231,21233,21236,21239,21242,21245,21248],{"className":21232},[50],[15,21234],{"className":21235,"style":139},[54],[15,21237,113],{"className":21238},[146],[15,21240,117],{"className":21241},[59],[15,21243],{"className":21244,"style":2587},[157],[15,21246,4813],{"className":21247},[2591],[15,21249],{"className":21250,"style":2587},[157],[15,21252,21254,21257,21260,21263,21266,21269,21272,21275],{"className":21253},[50],[15,21255],{"className":21256,"style":139},[54],[15,21258,11339],{"className":21259},[59,60],[15,21261,120],{"className":21262},[153],[15,21264,37],{"className":21265,"style":61},[59,60],[15,21267,113],{"className":21268},[146],[15,21270,15400],{"className":21271},[59,60],[15,21273,120],{"className":21274},[153],[15,21276,551],{"className":21277},[573],[11,21279,21280,21281,10965],{},"即 ",[15,21282,21284,21297],{"className":21283,"translate":19},[18],[15,21285,21287],{"className":21286},[23],[25,21288,21289],{"xmlns":27},[29,21290,21291,21295],{},[32,21292,21293],{},[35,21294,37],{},[39,21296,37],{"encoding":41},[15,21298,21300],{"className":21299,"ariaHidden":46},[45],[15,21301,21303,21306],{"className":21302},[50],[15,21304],{"className":21305,"style":55},[54],[15,21307,37],{"className":21308,"style":61},[59,60],[11,21310,21311,21312,21315,21316,21344,21345,21375,21376,21404],{},"所以\"凸\"与\"数据处理\"是同一件事的两面。这也是 f-散度族成为\"一切满足数据处理不等式的最一般散度\"的原因：它不是一堆例子的偶然汇总，而是一个有刻画定理支撑的完整族。换句话说，Csiszár–Ali–Silvey 定理给出一个完整的",[1225,21313,21314],{},"刻画","：凸函数 ",[15,21317,21319,21332],{"className":21318,"translate":19},[18],[15,21320,21322],{"className":21321},[23],[25,21323,21324],{"xmlns":27},[29,21325,21326,21330],{},[32,21327,21328],{},[35,21329,37],{},[39,21331,37],{"encoding":41},[15,21333,21335],{"className":21334,"ariaHidden":46},[45],[15,21336,21338,21341],{"className":21337},[50],[15,21339],{"className":21340,"style":55},[54],[15,21342,37],{"className":21343,"style":61},[59,60],"（模去仿射项）",[15,21346,21348,21363],{"className":21347,"translate":19},[18],[15,21349,21351],{"className":21350},[23],[25,21352,21353],{"xmlns":27},[29,21354,21355,21360],{},[32,21356,21357],{},[110,21358,21359],{},"↔",[39,21361,21362],{"encoding":41},"\\leftrightarrow",[15,21364,21366],{"className":21365,"ariaHidden":46},[45],[15,21367,21369,21372],{"className":21368},[50],[15,21370],{"className":21371,"style":11003},[54],[15,21373,21359],{"className":21374},[162]," 联合凸泛函 ",[15,21377,21379,21392],{"className":21378,"translate":19},[18],[15,21380,21382],{"className":21381},[23],[25,21383,21384],{"xmlns":27},[29,21385,21386,21390],{},[32,21387,21388],{},[110,21389,21359],{},[39,21391,21362],{"encoding":41},[15,21393,21395],{"className":21394,"ariaHidden":46},[45],[15,21396,21398,21401],{"className":21397},[50],[15,21399],{"className":21400,"style":11003},[54],[15,21402,21359],{"className":21403},[162]," 满足数据处理不等式的分布差异度量，三者一一对应。",[528,21406,21408],{"id":21407},"_3-常见散度","3. 常见散度",[11,21410,21411,21412,21440],{},"不同的 ",[15,21413,21415,21428],{"className":21414,"translate":19},[18],[15,21416,21418],{"className":21417},[23],[25,21419,21420],{"xmlns":27},[29,21421,21422,21426],{},[32,21423,21424],{},[35,21425,37],{},[39,21427,37],{"encoding":41},[15,21429,21431],{"className":21430,"ariaHidden":46},[45],[15,21432,21434,21437],{"className":21433},[50],[15,21435],{"className":21436,"style":55},[54],[15,21438,37],{"className":21439,"style":61},[59,60]," 对应不同的散度。KL、JS、全变差、卡方、Hellinger、Wasserstein、MMD 等散度，表面上都是「衡量两个分布差多少」，但它们的根本区别可以归结为几个维度：",[11,21442,21443],{},"它们对「差异」的定义方式不同，对「支撑集不重叠」的处理不同，对「几何\u002F度量结构」的利用不同，因而导出的拓扑、梯度行为和优化性质也不同。",[11,21445,21446],{},"可以把不同散度的区别归纳为五个核心问题：",[6662,21448,21449,21452,21455,21458,21461],{},[6665,21450,21451],{},"差异定义在什么量上？是密度比值、密度差、累积分布差，还是搬运质量？",[6665,21453,21454],{},"是否对称？",[6665,21456,21457],{},"是否有界？",[6665,21459,21460],{},"是否利用样本空间的几何结构？",[6665,21462,21463],{},"诱导的拓扑强弱如何？",[11,21465,21466],{},"这五点决定了散度在理论性质和实际优化中的行为差异。下面逐个把常用散度「代入模板」并验算。",[2311,21468,21470],{"id":21469},"_31-kl-散度","3.1 KL 散度",[11,21472,21473],{},"取：",[15,21475,21477],{"className":21476,"translate":19},[180],[15,21478,21480,21509],{"className":21479,"translate":19},[18],[15,21481,21483],{"className":21482},[23],[25,21484,21485],{"xmlns":27,"display":189},[29,21486,21487,21507],{},[32,21488,21489,21491,21493,21495,21497,21499,21501,21503,21505],{},[35,21490,37],{},[110,21492,113],{"stretchy":112},[35,21494,769],{},[110,21496,120],{"stretchy":112},[110,21498,123],{},[35,21500,769],{},[35,21502,4100],{},[110,21504,4103],{},[35,21506,769],{},[39,21508,4108],{"encoding":41},[15,21510,21512,21539],{"className":21511,"ariaHidden":46},[45],[15,21513,21515,21518,21521,21524,21527,21530,21533,21536],{"className":21514},[50],[15,21516],{"className":21517,"style":139},[54],[15,21519,37],{"className":21520,"style":61},[59,60],[15,21522,113],{"className":21523},[146],[15,21525,769],{"className":21526},[59,60],[15,21528,120],{"className":21529},[153],[15,21531],{"className":21532,"style":158},[157],[15,21534,123],{"className":21535},[162],[15,21537],{"className":21538,"style":158},[157],[15,21540,21542,21545,21548,21551,21556,21559],{"className":21541},[50],[15,21543],{"className":21544,"style":55},[54],[15,21546,769],{"className":21547},[59,60],[15,21549],{"className":21550,"style":406},[157],[15,21552,4154,21554],{"className":21553},[1484],[15,21555,4158],{"style":4157},[15,21557],{"className":21558,"style":406},[157],[15,21560,769],{"className":21561},[59,60],[11,21563,21564,21565,21598,21599,2745,21664,21797],{},"（下面 ",[15,21566,21568,21584],{"className":21567,"translate":19},[18],[15,21569,21571],{"className":21570},[23],[25,21572,21573],{"xmlns":27},[29,21574,21575,21581],{},[32,21576,21577,21579],{},[35,21578,4100],{},[110,21580,4103],{},[39,21582,21583],{"encoding":41},"\\log",[15,21585,21587],{"className":21586,"ariaHidden":46},[45],[15,21588,21590,21593],{"className":21589},[50],[15,21591],{"className":21592,"style":55},[54],[15,21594,4154,21596],{"className":21595},[1484],[15,21597,4158],{"style":4157}," 均为自然对数。）则 ",[15,21600,21602,21625],{"className":21601,"translate":19},[18],[15,21603,21605],{"className":21604},[23],[25,21606,21607],{"xmlns":27},[29,21608,21609,21623],{},[32,21610,21611,21613,21615,21617,21619,21621],{},[35,21612,37],{},[110,21614,113],{"stretchy":112},[115,21616,117],{},[110,21618,120],{"stretchy":112},[110,21620,123],{},[115,21622,126],{},[39,21624,129],{"encoding":41},[15,21626,21628,21655],{"className":21627,"ariaHidden":46},[45],[15,21629,21631,21634,21637,21640,21643,21646,21649,21652],{"className":21630},[50],[15,21632],{"className":21633,"style":139},[54],[15,21635,37],{"className":21636,"style":61},[59,60],[15,21638,113],{"className":21639},[146],[15,21641,117],{"className":21642},[59],[15,21644,120],{"className":21645},[153],[15,21647],{"className":21648,"style":158},[157],[15,21650,123],{"className":21651},[162],[15,21653],{"className":21654,"style":158},[157],[15,21656,21658,21661],{"className":21657},[50],[15,21659],{"className":21660,"style":172},[54],[15,21662,126],{"className":21663},[59],[15,21665,21667,21707],{"className":21666,"translate":19},[18],[15,21668,21670],{"className":21669},[23],[25,21671,21672],{"xmlns":27},[29,21673,21674,21704],{},[32,21675,21676,21686,21688,21690,21692,21694,21696,21698,21700,21702],{},[6814,21677,21678,21680],{},[35,21679,37],{},[32,21681,21682,21684],{},[110,21683,6820],{"mathvariant":209},[110,21685,6820],{"mathvariant":209},[110,21687,113],{"stretchy":112},[35,21689,769],{},[110,21691,120],{"stretchy":112},[110,21693,123],{},[115,21695,117],{},[35,21697,941],{"mathvariant":209},[35,21699,769],{},[110,21701,2903],{},[115,21703,126],{},[39,21705,21706],{"encoding":41},"f''(t)=1\u002Ft>0",[15,21708,21710,21767,21788],{"className":21709,"ariaHidden":46},[45],[15,21711,21713,21716,21749,21752,21755,21758,21761,21764],{"className":21712},[50],[15,21714],{"className":21715,"style":6843},[54],[15,21717,21719,21722],{"className":21718},[59],[15,21720,37],{"className":21721,"style":61},[59,60],[15,21723,21725],{"className":21724},[281],[15,21726,21728],{"className":21727},[285],[15,21729,21731],{"className":21730},[290],[15,21732,21734],{"className":21733,"style":6862},[294],[15,21735,21736,21739],{"style":6865},[15,21737],{"className":21738,"style":303},[302],[15,21740,21742],{"className":21741},[307,308,309,310],[15,21743,21745],{"className":21744},[59,310],[15,21746,21748],{"className":21747},[59,310],"′′",[15,21750,113],{"className":21751},[146],[15,21753,769],{"className":21754},[59,60],[15,21756,120],{"className":21757},[153],[15,21759],{"className":21760,"style":158},[157],[15,21762,123],{"className":21763},[162],[15,21765],{"className":21766,"style":158},[157],[15,21768,21770,21773,21776,21779,21782,21785],{"className":21769},[50],[15,21771],{"className":21772,"style":139},[54],[15,21774,8589],{"className":21775},[59],[15,21777,769],{"className":21778},[59,60],[15,21780],{"className":21781,"style":158},[157],[15,21783,2903],{"className":21784},[162],[15,21786],{"className":21787,"style":158},[157],[15,21789,21791,21794],{"className":21790},[50],[15,21792],{"className":21793,"style":172},[54],[15,21795,126],{"className":21796},[59]," 凸。代入模板：",[15,21799,21801],{"className":21800,"translate":19},[180],[15,21802,21804,21907],{"className":21803,"translate":19},[18],[15,21805,21807],{"className":21806},[23],[25,21808,21809],{"xmlns":27,"display":189},[29,21810,21811,21904],{},[32,21812,21813,21819,21821,21823,21825,21827,21829,21831,21833,21835,21837,21843,21845,21847,21853,21855,21857,21859,21861,21863,21865,21867,21869,21875,21877,21879,21881,21883,21894,21896,21898,21900,21902],{},[195,21814,21815,21817],{},[35,21816,199],{},[35,21818,37],{},[110,21820,113],{"stretchy":112},[35,21822,206],{},[35,21824,210],{"mathvariant":209},[35,21826,213],{},[110,21828,120],{"stretchy":112},[110,21830,123],{},[110,21832,1287],{},[35,21834,944],{},[110,21836,3299],{},[238,21838,21839,21841],{},[35,21840,11],{},[35,21842,944],{},[35,21844,4100],{},[110,21846,4103],{},[238,21848,21849,21851],{},[35,21850,11],{},[35,21852,944],{},[1297,21854,1299],{},[35,21856,244],{},[35,21858,774],{},[110,21860,123],{},[110,21862,1287],{},[35,21864,11],{},[35,21866,4100],{},[110,21868,4103],{},[238,21870,21871,21873],{},[35,21872,11],{},[35,21874,944],{},[1297,21876,1299],{},[35,21878,244],{},[35,21880,774],{},[110,21882,123],{},[195,21884,21885,21887],{},[35,21886,199],{},[32,21888,21889,21891],{},[35,21890,10694],{},[35,21892,21893],{},"L",[110,21895,113],{"stretchy":112},[35,21897,206],{},[35,21899,210],{"mathvariant":209},[35,21901,213],{},[110,21903,120],{"stretchy":112},[39,21905,21906],{"encoding":41},"D_f(P\\|Q)\n=\\int q\\cdot \\frac{p}{q}\\log\\frac{p}{q}\\,dx\n=\\int p\\log\\frac{p}{q}\\,dx\n=D_{KL}(P\\|Q)",[15,21908,21910,21980,22004,22164,22271],{"className":21909,"ariaHidden":46},[45],[15,21911,21913,21916,21956,21959,21962,21965,21968,21971,21974,21977],{"className":21912},[50],[15,21914],{"className":21915,"style":270},[54],[15,21917,21919,21922],{"className":21918},[59],[15,21920,199],{"className":21921,"style":277},[59,60],[15,21923,21925],{"className":21924},[281],[15,21926,21928,21948],{"className":21927},[285,286],[15,21929,21931,21945],{"className":21930},[290],[15,21932,21934],{"className":21933,"style":295},[294],[15,21935,21936,21939],{"style":298},[15,21937],{"className":21938,"style":303},[302],[15,21940,21942],{"className":21941},[307,308,309,310],[15,21943,37],{"className":21944,"style":61},[59,60,310],[15,21946,318],{"className":21947},[317],[15,21949,21951],{"className":21950},[290],[15,21952,21954],{"className":21953,"style":325},[294],[15,21955],{},[15,21957,113],{"className":21958},[146],[15,21960,206],{"className":21961,"style":334},[59,60],[15,21963,210],{"className":21964},[59],[15,21966,213],{"className":21967},[59,60],[15,21969,120],{"className":21970},[153],[15,21972],{"className":21973,"style":158},[157],[15,21975,123],{"className":21976},[162],[15,21978],{"className":21979,"style":158},[157],[15,21981,21983,21986,21989,21992,21995,21998,22001],{"className":21982},[50],[15,21984],{"className":21985,"style":5777},[54],[15,21987,1287],{"className":21988,"style":1487},[1484,1485,1486],[15,21990],{"className":21991,"style":406},[157],[15,21993,944],{"className":21994,"style":981},[59,60],[15,21996],{"className":21997,"style":2587},[157],[15,21999,3299],{"className":22000},[2591],[15,22002],{"className":22003,"style":2587},[157],[15,22005,22007,22011,22073,22076,22081,22084,22146,22149,22152,22155,22158,22161],{"className":22006},[50],[15,22008],{"className":22009,"style":22010},[54],"height:1.988em;vertical-align:-0.8804em;",[15,22012,22014,22017,22070],{"className":22013},[59],[15,22015],{"className":22016},[146,441],[15,22018,22020],{"className":22019},[238],[15,22021,22023,22062],{"className":22022},[285,286],[15,22024,22026,22059],{"className":22025},[290],[15,22027,22029,22040,22048],{"className":22028,"style":3554},[294],[15,22030,22031,22034],{"style":457},[15,22032],{"className":22033,"style":461},[302],[15,22035,22037],{"className":22036},[59],[15,22038,944],{"className":22039,"style":981},[59,60],[15,22041,22042,22045],{"style":473},[15,22043],{"className":22044,"style":461},[302],[15,22046],{"className":22047,"style":481},[480],[15,22049,22050,22053],{"style":484},[15,22051],{"className":22052,"style":461},[302],[15,22054,22056],{"className":22055},[59],[15,22057,11],{"className":22058},[59,60],[15,22060,318],{"className":22061},[317],[15,22063,22065],{"className":22064},[290],[15,22066,22068],{"className":22067,"style":506},[294],[15,22069],{},[15,22071],{"className":22072},[153,441],[15,22074],{"className":22075,"style":406},[157],[15,22077,4154,22079],{"className":22078},[1484],[15,22080,4158],{"style":4157},[15,22082],{"className":22083,"style":406},[157],[15,22085,22087,22090,22143],{"className":22086},[59],[15,22088],{"className":22089},[146,441],[15,22091,22093],{"className":22092},[238],[15,22094,22096,22135],{"className":22095},[285,286],[15,22097,22099,22132],{"className":22098},[290],[15,22100,22102,22113,22121],{"className":22101,"style":3554},[294],[15,22103,22104,22107],{"style":457},[15,22105],{"className":22106,"style":461},[302],[15,22108,22110],{"className":22109},[59],[15,22111,944],{"className":22112,"style":981},[59,60],[15,22114,22115,22118],{"style":473},[15,22116],{"className":22117,"style":461},[302],[15,22119],{"className":22120,"style":481},[480],[15,22122,22123,22126],{"style":484},[15,22124],{"className":22125,"style":461},[302],[15,22127,22129],{"className":22128},[59],[15,22130,11],{"className":22131},[59,60],[15,22133,318],{"className":22134},[317],[15,22136,22138],{"className":22137},[290],[15,22139,22141],{"className":22140,"style":506},[294],[15,22142],{},[15,22144],{"className":22145},[153,441],[15,22147],{"className":22148,"style":406},[157],[15,22150,244],{"className":22151},[59,60],[15,22153,774],{"className":22154},[59,60],[15,22156],{"className":22157,"style":158},[157],[15,22159,123],{"className":22160},[162],[15,22162],{"className":22163,"style":158},[157],[15,22165,22167,22171,22174,22177,22180,22183,22188,22191,22253,22256,22259,22262,22265,22268],{"className":22166},[50],[15,22168],{"className":22169,"style":22170},[54],"height:2.2404em;vertical-align:-0.8804em;",[15,22172,1287],{"className":22173,"style":1487},[1484,1485,1486],[15,22175],{"className":22176,"style":406},[157],[15,22178,11],{"className":22179},[59,60],[15,22181],{"className":22182,"style":406},[157],[15,22184,4154,22186],{"className":22185},[1484],[15,22187,4158],{"style":4157},[15,22189],{"className":22190,"style":406},[157],[15,22192,22194,22197,22250],{"className":22193},[59],[15,22195],{"className":22196},[146,441],[15,22198,22200],{"className":22199},[238],[15,22201,22203,22242],{"className":22202},[285,286],[15,22204,22206,22239],{"className":22205},[290],[15,22207,22209,22220,22228],{"className":22208,"style":3554},[294],[15,22210,22211,22214],{"style":457},[15,22212],{"className":22213,"style":461},[302],[15,22215,22217],{"className":22216},[59],[15,22218,944],{"className":22219,"style":981},[59,60],[15,22221,22222,22225],{"style":473},[15,22223],{"className":22224,"style":461},[302],[15,22226],{"className":22227,"style":481},[480],[15,22229,22230,22233],{"style":484},[15,22231],{"className":22232,"style":461},[302],[15,22234,22236],{"className":22235},[59],[15,22237,11],{"className":22238},[59,60],[15,22240,318],{"className":22241},[317],[15,22243,22245],{"className":22244},[290],[15,22246,22248],{"className":22247,"style":506},[294],[15,22249],{},[15,22251],{"className":22252},[153,441],[15,22254],{"className":22255,"style":406},[157],[15,22257,244],{"className":22258},[59,60],[15,22260,774],{"className":22261},[59,60],[15,22263],{"className":22264,"style":158},[157],[15,22266,123],{"className":22267},[162],[15,22269],{"className":22270,"style":158},[157],[15,22272,22274,22277,22323,22326,22329,22332,22335],{"className":22273},[50],[15,22275],{"className":22276,"style":139},[54],[15,22278,22280,22283],{"className":22279},[59],[15,22281,199],{"className":22282,"style":277},[59,60],[15,22284,22286],{"className":22285},[281],[15,22287,22289,22315],{"className":22288},[285,286],[15,22290,22292,22312],{"className":22291},[290],[15,22293,22295],{"className":22294,"style":379},[294],[15,22296,22297,22300],{"style":298},[15,22298],{"className":22299,"style":303},[302],[15,22301,22303],{"className":22302},[307,308,309,310],[15,22304,22306,22309],{"className":22305},[59,310],[15,22307,10694],{"className":22308,"style":10782},[59,60,310],[15,22310,21893],{"className":22311},[59,60,310],[15,22313,318],{"className":22314},[317],[15,22316,22318],{"className":22317},[290],[15,22319,22321],{"className":22320,"style":7968},[294],[15,22322],{},[15,22324,113],{"className":22325},[146],[15,22327,206],{"className":22328,"style":334},[59,60],[15,22330,210],{"className":22331},[59],[15,22333,213],{"className":22334},[59,60],[15,22336,120],{"className":22337},[153],[11,22339,22340,22341,22446,22447,9400],{},"反向 KL 散度 ",[15,22342,22344,22376],{"className":22343,"translate":19},[18],[15,22345,22347],{"className":22346},[23],[25,22348,22349],{"xmlns":27},[29,22350,22351,22373],{},[32,22352,22353,22363,22365,22367,22369,22371],{},[195,22354,22355,22357],{},[35,22356,199],{},[32,22358,22359,22361],{},[35,22360,10694],{},[35,22362,21893],{},[110,22364,113],{"stretchy":112},[35,22366,213],{},[35,22368,210],{"mathvariant":209},[35,22370,206],{},[110,22372,120],{"stretchy":112},[39,22374,22375],{"encoding":41},"D_{KL}(Q\\|P)",[15,22377,22379],{"className":22378,"ariaHidden":46},[45],[15,22380,22382,22385,22431,22434,22437,22440,22443],{"className":22381},[50],[15,22383],{"className":22384,"style":139},[54],[15,22386,22388,22391],{"className":22387},[59],[15,22389,199],{"className":22390,"style":277},[59,60],[15,22392,22394],{"className":22393},[281],[15,22395,22397,22423],{"className":22396},[285,286],[15,22398,22400,22420],{"className":22399},[290],[15,22401,22403],{"className":22402,"style":379},[294],[15,22404,22405,22408],{"style":298},[15,22406],{"className":22407,"style":303},[302],[15,22409,22411],{"className":22410},[307,308,309,310],[15,22412,22414,22417],{"className":22413},[59,310],[15,22415,10694],{"className":22416,"style":10782},[59,60,310],[15,22418,21893],{"className":22419},[59,60,310],[15,22421,318],{"className":22422},[317],[15,22424,22426],{"className":22425},[290],[15,22427,22429],{"className":22428,"style":7968},[294],[15,22430],{},[15,22432,113],{"className":22433},[146],[15,22435,213],{"className":22436},[59,60],[15,22438,210],{"className":22439},[59],[15,22441,206],{"className":22442,"style":334},[59,60],[15,22444,120],{"className":22445},[153]," 对应斜共轭 ",[15,22448,22450,22476],{"className":22449,"translate":19},[18],[15,22451,22453],{"className":22452},[23],[25,22454,22455],{"xmlns":27},[29,22456,22457,22473],{},[32,22458,22459,22461,22463,22465,22467,22469,22471],{},[35,22460,769],{},[35,22462,37],{},[110,22464,113],{"stretchy":112},[115,22466,117],{},[35,22468,941],{"mathvariant":209},[35,22470,769],{},[110,22472,120],{"stretchy":112},[39,22474,22475],{"encoding":41},"t f(1\u002Ft)",[15,22477,22479],{"className":22478,"ariaHidden":46},[45],[15,22480,22482,22485,22488,22491,22494,22497,22500],{"className":22481},[50],[15,22483],{"className":22484,"style":139},[54],[15,22486,769],{"className":22487},[59,60],[15,22489,37],{"className":22490,"style":61},[59,60],[15,22492,113],{"className":22493},[146],[15,22495,8589],{"className":22496},[59],[15,22498,769],{"className":22499},[59,60],[15,22501,120],{"className":22502},[153],[15,22504,22506],{"className":22505,"translate":19},[180],[15,22507,22509,22631],{"className":22508,"translate":19},[18],[15,22510,22512],{"className":22511},[23],[25,22513,22514],{"xmlns":27,"display":189},[29,22515,22516,22628],{},[1243,22517,22518,22552],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,22519,22520,22534],{},[1252,22521,22522],{},[1255,22523,22524],{"scriptlevel":126,"displaystyle":46},[32,22525,22526,22528,22530,22532],{},[35,22527,37],{},[110,22529,113],{"stretchy":112},[35,22531,769],{},[110,22533,120],{"stretchy":112},[1252,22535,22536],{},[1255,22537,22538],{"scriptlevel":126,"displaystyle":46},[32,22539,22540,22542,22544,22546,22548,22550],{},[32,22541],{},[110,22543,123],{},[35,22545,769],{},[35,22547,4100],{},[110,22549,4103],{},[35,22551,769],{},[1249,22553,22554,22560],{},[1252,22555,22556],{},[1255,22557,22558],{"scriptlevel":126,"displaystyle":46},[32,22559],{},[1252,22561,22562],{},[1255,22563,22564],{"scriptlevel":126,"displaystyle":46},[32,22565,22566,22568,22570,22572,22588,22590,22592,22594,22596,22598,22600,22606,22608,22610,22616,22618,22620,22622,22624,22626],{},[32,22567],{},[110,22569,4286],{},[1297,22571,4283],{},[7553,22573,22574,22576,22586],{},[35,22575,37],{},[32,22577,22578,22580,22582,22584],{},[35,22579,7561],{},[35,22581,7564],{},[35,22583,7567],{},[35,22585,7570],{},[110,22587,7573],{"lspace":1247,"rspace":1247},[110,22589,113],{"stretchy":112},[35,22591,769],{},[110,22593,120],{"stretchy":112},[110,22595,123],{},[35,22597,769],{},[110,22599,3299],{},[238,22601,22602,22604],{},[115,22603,117],{},[35,22605,769],{},[35,22607,4100],{},[110,22609,4103],{},[238,22611,22612,22614],{},[115,22613,117],{},[35,22615,769],{},[110,22617,123],{},[110,22619,4813],{},[35,22621,4100],{},[110,22623,4103],{},[35,22625,769],{},[110,22627,551],{"separator":46},[39,22629,22630],{"encoding":41},"\\begin{aligned}\nf(t)&=t\\log t\\\\[2pt]\n&\\Longrightarrow\\ f^{*}_{skew}(t)\n=t\\cdot\\frac1t\\log\\frac1t=-\\log t,\n\\end{aligned}",[15,22632,22634],{"className":22633,"ariaHidden":46},[45],[15,22635,22637,22641],{"className":22636},[50],[15,22638],{"className":22639,"style":22640},[54],"height:3.7074em;vertical-align:-1.6037em;",[15,22642,22644],{"className":22643},[59],[15,22645,22647,22703],{"className":22646},[1243],[15,22648,22650],{"className":22649},[1360],[15,22651,22653,22694],{"className":22652},[285,286],[15,22654,22656,22691],{"className":22655},[290],[15,22657,22660,22682],{"className":22658,"style":22659},[294],"height:2.1037em;",[15,22661,22663,22667],{"style":22662},"top:-4.5852em;",[15,22664],{"className":22665,"style":22666},[302],"height:3.3214em;",[15,22668,22670,22673,22676,22679],{"className":22669},[59],[15,22671,37],{"className":22672,"style":61},[59,60],[15,22674,113],{"className":22675},[146],[15,22677,769],{"className":22678},[59,60],[15,22680,120],{"className":22681},[153],[15,22683,22685,22688],{"style":22684},"top:-2.4037em;",[15,22686],{"className":22687,"style":22666},[302],[15,22689],{"className":22690},[59],[15,22692,318],{"className":22693},[317],[15,22695,22697],{"className":22696},[290],[15,22698,22701],{"className":22699,"style":22700},[294],"height:1.6037em;",[15,22702],{},[15,22704,22706],{"className":22705},[1451],[15,22707,22709,23039],{"className":22708},[285,286],[15,22710,22712,23036],{"className":22711},[290],[15,22713,22715,22752],{"className":22714,"style":22659},[294],[15,22716,22717,22720],{"style":22662},[15,22718],{"className":22719,"style":22666},[302],[15,22721,22723,22726,22729,22732,22735,22738,22741,22746,22749],{"className":22722},[59],[15,22724],{"className":22725},[59],[15,22727],{"className":22728,"style":158},[157],[15,22730,123],{"className":22731},[162],[15,22733],{"className":22734,"style":158},[157],[15,22736,769],{"className":22737},[59,60],[15,22739],{"className":22740,"style":406},[157],[15,22742,4154,22744],{"className":22743},[1484],[15,22745,4158],{"style":4157},[15,22747],{"className":22748,"style":406},[157],[15,22750,769],{"className":22751},[59,60],[15,22753,22754,22757],{"style":22684},[15,22755],{"className":22756,"style":22666},[302],[15,22758,22760,22763,22766,22769,22772,22775,22841,22844,22847,22850,22853,22856,22859,22862,22865,22868,22871,22934,22937,22942,22945,23007,23010,23013,23016,23019,23022,23027,23030,23033],{"className":22759},[59],[15,22761],{"className":22762},[59],[15,22764],{"className":22765,"style":158},[157],[15,22767,4286],{"className":22768},[162],[15,22770,4283],{"className":22771},[157],[15,22773],{"className":22774,"style":158},[157],[15,22776,22778,22781],{"className":22777},[59],[15,22779,37],{"className":22780,"style":61},[59,60],[15,22782,22784],{"className":22783},[281],[15,22785,22787,22833],{"className":22786},[285,286],[15,22788,22790,22830],{"className":22789},[290],[15,22791,22793,22816],{"className":22792,"style":8248},[294],[15,22794,22795,22798],{"style":8251},[15,22796],{"className":22797,"style":303},[302],[15,22799,22801],{"className":22800},[307,308,309,310],[15,22802,22804,22807,22810,22813],{"className":22803},[59,310],[15,22805,7561],{"className":22806},[59,60,310],[15,22808,7564],{"className":22809,"style":8267},[59,60,310],[15,22811,7567],{"className":22812},[59,60,310],[15,22814,7570],{"className":22815,"style":8274},[59,60,310],[15,22817,22818,22821],{"style":8277},[15,22819],{"className":22820,"style":303},[302],[15,22822,22824],{"className":22823},[307,308,309,310],[15,22825,22827],{"className":22826},[59,310],[15,22828,7573],{"className":22829},[59,310],[15,22831,318],{"className":22832},[317],[15,22834,22836],{"className":22835},[290],[15,22837,22839],{"className":22838,"style":8299},[294],[15,22840],{},[15,22842,113],{"className":22843},[146],[15,22845,769],{"className":22846},[59,60],[15,22848,120],{"className":22849},[153],[15,22851],{"className":22852,"style":158},[157],[15,22854,123],{"className":22855},[162],[15,22857],{"className":22858,"style":158},[157],[15,22860,769],{"className":22861},[59,60],[15,22863],{"className":22864,"style":2587},[157],[15,22866,3299],{"className":22867},[2591],[15,22869],{"className":22870,"style":2587},[157],[15,22872,22874,22877,22931],{"className":22873},[59],[15,22875],{"className":22876},[146,441],[15,22878,22880],{"className":22879},[238],[15,22881,22883,22923],{"className":22882},[285,286],[15,22884,22886,22920],{"className":22885},[290],[15,22887,22890,22901,22909],{"className":22888,"style":22889},[294],"height:1.3214em;",[15,22891,22892,22895],{"style":457},[15,22893],{"className":22894,"style":461},[302],[15,22896,22898],{"className":22897},[59],[15,22899,769],{"className":22900},[59,60],[15,22902,22903,22906],{"style":473},[15,22904],{"className":22905,"style":461},[302],[15,22907],{"className":22908,"style":481},[480],[15,22910,22911,22914],{"style":484},[15,22912],{"className":22913,"style":461},[302],[15,22915,22917],{"className":22916},[59],[15,22918,117],{"className":22919},[59],[15,22921,318],{"className":22922},[317],[15,22924,22926],{"className":22925},[290],[15,22927,22929],{"className":22928,"style":3778},[294],[15,22930],{},[15,22932],{"className":22933},[153,441],[15,22935],{"className":22936,"style":406},[157],[15,22938,4154,22940],{"className":22939},[1484],[15,22941,4158],{"style":4157},[15,22943],{"className":22944,"style":406},[157],[15,22946,22948,22951,23004],{"className":22947},[59],[15,22949],{"className":22950},[146,441],[15,22952,22954],{"className":22953},[238],[15,22955,22957,22996],{"className":22956},[285,286],[15,22958,22960,22993],{"className":22959},[290],[15,22961,22963,22974,22982],{"className":22962,"style":22889},[294],[15,22964,22965,22968],{"style":457},[15,22966],{"className":22967,"style":461},[302],[15,22969,22971],{"className":22970},[59],[15,22972,769],{"className":22973},[59,60],[15,22975,22976,22979],{"style":473},[15,22977],{"className":22978,"style":461},[302],[15,22980],{"className":22981,"style":481},[480],[15,22983,22984,22987],{"style":484},[15,22985],{"className":22986,"style":461},[302],[15,22988,22990],{"className":22989},[59],[15,22991,117],{"className":22992},[59],[15,22994,318],{"className":22995},[317],[15,22997,22999],{"className":22998},[290],[15,23000,23002],{"className":23001,"style":3778},[294],[15,23003],{},[15,23005],{"className":23006},[153,441],[15,23008],{"className":23009,"style":158},[157],[15,23011,123],{"className":23012},[162],[15,23014],{"className":23015,"style":158},[157],[15,23017,4813],{"className":23018},[59],[15,23020],{"className":23021,"style":406},[157],[15,23023,4154,23025],{"className":23024},[1484],[15,23026,4158],{"style":4157},[15,23028],{"className":23029,"style":406},[157],[15,23031,769],{"className":23032},[59,60],[15,23034,551],{"className":23035},[573],[15,23037,318],{"className":23038},[317],[15,23040,23042],{"className":23041},[290],[15,23043,23045],{"className":23044,"style":22700},[294],[15,23046],{},[11,23048,23049],{},"所以",[15,23051,23053],{"className":23052,"translate":19},[180],[15,23054,23056,23132],{"className":23055,"translate":19},[18],[15,23057,23059],{"className":23058},[23],[25,23060,23061],{"xmlns":27,"display":189},[29,23062,23063,23129],{},[32,23064,23065,23067,23069,23071,23073,23075,23077,23079,23081,23083,23085,23087,23089,23095,23097,23099,23101,23103,23105,23107,23117,23119,23121,23123,23125,23127],{},[35,23066,37],{},[110,23068,113],{"stretchy":112},[35,23070,769],{},[110,23072,120],{"stretchy":112},[110,23074,123],{},[110,23076,4813],{},[35,23078,4100],{},[110,23080,4103],{},[35,23082,769],{},[1297,23084,4283],{},[110,23086,4286],{},[1297,23088,4283],{},[195,23090,23091,23093],{},[35,23092,199],{},[35,23094,37],{},[110,23096,113],{"stretchy":112},[35,23098,206],{},[35,23100,210],{"mathvariant":209},[35,23102,213],{},[110,23104,120],{"stretchy":112},[110,23106,123],{},[195,23108,23109,23111],{},[35,23110,199],{},[32,23112,23113,23115],{},[35,23114,10694],{},[35,23116,21893],{},[110,23118,113],{"stretchy":112},[35,23120,213],{},[35,23122,210],{"mathvariant":209},[35,23124,206],{},[110,23126,120],{"stretchy":112},[35,23128,4375],{"mathvariant":209},[39,23130,23131],{"encoding":41},"f(t)=-\\log t\n\\ \\Longrightarrow\\ D_f(P\\|Q)=D_{KL}(Q\\|P).",[15,23133,23135,23162,23200,23270],{"className":23134,"ariaHidden":46},[45],[15,23136,23138,23141,23144,23147,23150,23153,23156,23159],{"className":23137},[50],[15,23139],{"className":23140,"style":139},[54],[15,23142,37],{"className":23143,"style":61},[59,60],[15,23145,113],{"className":23146},[146],[15,23148,769],{"className":23149},[59,60],[15,23151,120],{"className":23152},[153],[15,23154],{"className":23155,"style":158},[157],[15,23157,123],{"className":23158},[162],[15,23160],{"className":23161,"style":158},[157],[15,23163,23165,23168,23171,23174,23179,23182,23185,23188,23191,23194,23197],{"className":23164},[50],[15,23166],{"className":23167,"style":55},[54],[15,23169,4813],{"className":23170},[59],[15,23172],{"className":23173,"style":406},[157],[15,23175,4154,23177],{"className":23176},[1484],[15,23178,4158],{"style":4157},[15,23180],{"className":23181,"style":406},[157],[15,23183,769],{"className":23184},[59,60],[15,23186,4283],{"className":23187},[157],[15,23189],{"className":23190,"style":158},[157],[15,23192,4286],{"className":23193},[162],[15,23195,4283],{"className":23196},[157],[15,23198],{"className":23199,"style":158},[157],[15,23201,23203,23206,23246,23249,23252,23255,23258,23261,23264,23267],{"className":23202},[50],[15,23204],{"className":23205,"style":270},[54],[15,23207,23209,23212],{"className":23208},[59],[15,23210,199],{"className":23211,"style":277},[59,60],[15,23213,23215],{"className":23214},[281],[15,23216,23218,23238],{"className":23217},[285,286],[15,23219,23221,23235],{"className":23220},[290],[15,23222,23224],{"className":23223,"style":295},[294],[15,23225,23226,23229],{"style":298},[15,23227],{"className":23228,"style":303},[302],[15,23230,23232],{"className":23231},[307,308,309,310],[15,23233,37],{"className":23234,"style":61},[59,60,310],[15,23236,318],{"className":23237},[317],[15,23239,23241],{"className":23240},[290],[15,23242,23244],{"className":23243,"style":325},[294],[15,23245],{},[15,23247,113],{"className":23248},[146],[15,23250,206],{"className":23251,"style":334},[59,60],[15,23253,210],{"className":23254},[59],[15,23256,213],{"className":23257},[59,60],[15,23259,120],{"className":23260},[153],[15,23262],{"className":23263,"style":158},[157],[15,23265,123],{"className":23266},[162],[15,23268],{"className":23269,"style":158},[157],[15,23271,23273,23276,23322,23325,23328,23331,23334,23337],{"className":23272},[50],[15,23274],{"className":23275,"style":139},[54],[15,23277,23279,23282],{"className":23278},[59],[15,23280,199],{"className":23281,"style":277},[59,60],[15,23283,23285],{"className":23284},[281],[15,23286,23288,23314],{"className":23287},[285,286],[15,23289,23291,23311],{"className":23290},[290],[15,23292,23294],{"className":23293,"style":379},[294],[15,23295,23296,23299],{"style":298},[15,23297],{"className":23298,"style":303},[302],[15,23300,23302],{"className":23301},[307,308,309,310],[15,23303,23305,23308],{"className":23304},[59,310],[15,23306,10694],{"className":23307,"style":10782},[59,60,310],[15,23309,21893],{"className":23310},[59,60,310],[15,23312,318],{"className":23313},[317],[15,23315,23317],{"className":23316},[290],[15,23318,23320],{"className":23319,"style":7968},[294],[15,23321],{},[15,23323,113],{"className":23324},[146],[15,23326,213],{"className":23327},[59,60],[15,23329,210],{"className":23330},[59],[15,23332,206],{"className":23333,"style":334},[59,60],[15,23335,120],{"className":23336},[153],[15,23338,4375],{"className":23339},[59],[11,23341,23342,23345,23346,23464,23465,23530,23531,23624],{},[1225,23343,23344],{},"对称化：Jeffreys 散度。"," 取 ",[15,23347,23349,23387],{"className":23348,"translate":19},[18],[15,23350,23352],{"className":23351},[23],[25,23353,23354],{"xmlns":27},[29,23355,23356,23384],{},[32,23357,23358,23360,23362,23364,23366,23368,23370,23372,23374,23376,23378,23380,23382],{},[35,23359,37],{},[110,23361,113],{"stretchy":112},[35,23363,769],{},[110,23365,120],{"stretchy":112},[110,23367,123],{},[110,23369,113],{"stretchy":112},[35,23371,769],{},[110,23373,4813],{},[115,23375,117],{},[110,23377,120],{"stretchy":112},[35,23379,4100],{},[110,23381,4103],{},[35,23383,769],{},[39,23385,23386],{"encoding":41},"f(t)=(t-1)\\log t",[15,23388,23390,23417,23438],{"className":23389,"ariaHidden":46},[45],[15,23391,23393,23396,23399,23402,23405,23408,23411,23414],{"className":23392},[50],[15,23394],{"className":23395,"style":139},[54],[15,23397,37],{"className":23398,"style":61},[59,60],[15,23400,113],{"className":23401},[146],[15,23403,769],{"className":23404},[59,60],[15,23406,120],{"className":23407},[153],[15,23409],{"className":23410,"style":158},[157],[15,23412,123],{"className":23413},[162],[15,23415],{"className":23416,"style":158},[157],[15,23418,23420,23423,23426,23429,23432,23435],{"className":23419},[50],[15,23421],{"className":23422,"style":139},[54],[15,23424,113],{"className":23425},[146],[15,23427,769],{"className":23428},[59,60],[15,23430],{"className":23431,"style":2587},[157],[15,23433,4813],{"className":23434},[2591],[15,23436],{"className":23437,"style":2587},[157],[15,23439,23441,23444,23447,23450,23453,23458,23461],{"className":23440},[50],[15,23442],{"className":23443,"style":139},[54],[15,23445,117],{"className":23446},[59],[15,23448,120],{"className":23449},[153],[15,23451],{"className":23452,"style":406},[157],[15,23454,4154,23456],{"className":23455},[1484],[15,23457,4158],{"style":4157},[15,23459],{"className":23460,"style":406},[157],[15,23462,769],{"className":23463},[59,60],"（它满足 ",[15,23466,23468,23491],{"className":23467,"translate":19},[18],[15,23469,23471],{"className":23470},[23],[25,23472,23473],{"xmlns":27},[29,23474,23475,23489],{},[32,23476,23477,23479,23481,23483,23485,23487],{},[35,23478,37],{},[110,23480,113],{"stretchy":112},[115,23482,117],{},[110,23484,120],{"stretchy":112},[110,23486,123],{},[115,23488,126],{},[39,23490,129],{"encoding":41},[15,23492,23494,23521],{"className":23493,"ariaHidden":46},[45],[15,23495,23497,23500,23503,23506,23509,23512,23515,23518],{"className":23496},[50],[15,23498],{"className":23499,"style":139},[54],[15,23501,37],{"className":23502,"style":61},[59,60],[15,23504,113],{"className":23505},[146],[15,23507,117],{"className":23508},[59],[15,23510,120],{"className":23511},[153],[15,23513],{"className":23514,"style":158},[157],[15,23516,123],{"className":23517},[162],[15,23519],{"className":23520,"style":158},[157],[15,23522,23524,23527],{"className":23523},[50],[15,23525],{"className":23526,"style":172},[54],[15,23528,126],{"className":23529},[59],"，且 ",[15,23532,23534,23570],{"className":23533,"translate":19},[18],[15,23535,23537],{"className":23536},[23],[25,23538,23539],{"xmlns":27},[29,23540,23541,23567],{},[32,23542,23543,23545,23547,23549,23551,23553,23555,23557,23559,23561,23563,23565],{},[35,23544,769],{},[35,23546,37],{},[110,23548,113],{"stretchy":112},[115,23550,117],{},[35,23552,941],{"mathvariant":209},[35,23554,769],{},[110,23556,120],{"stretchy":112},[110,23558,123],{},[35,23560,37],{},[110,23562,113],{"stretchy":112},[35,23564,769],{},[110,23566,120],{"stretchy":112},[39,23568,23569],{"encoding":41},"t f(1\u002Ft)=f(t)",[15,23571,23573,23606],{"className":23572,"ariaHidden":46},[45],[15,23574,23576,23579,23582,23585,23588,23591,23594,23597,23600,23603],{"className":23575},[50],[15,23577],{"className":23578,"style":139},[54],[15,23580,769],{"className":23581},[59,60],[15,23583,37],{"className":23584,"style":61},[59,60],[15,23586,113],{"className":23587},[146],[15,23589,8589],{"className":23590},[59],[15,23592,769],{"className":23593},[59,60],[15,23595,120],{"className":23596},[153],[15,23598],{"className":23599,"style":158},[157],[15,23601,123],{"className":23602},[162],[15,23604],{"className":23605,"style":158},[157],[15,23607,23609,23612,23615,23618,23621],{"className":23608},[50],[15,23610],{"className":23611,"style":139},[54],[15,23613,37],{"className":23614,"style":61},[59,60],[15,23616,113],{"className":23617},[146],[15,23619,769],{"className":23620},[59,60],[15,23622,120],{"className":23623},[153],"），则",[15,23626,23628],{"className":23627,"translate":19},[180],[15,23629,23631,23759],{"className":23630,"translate":19},[18],[15,23632,23634],{"className":23633},[23],[25,23635,23636],{"xmlns":27,"display":189},[29,23637,23638,23756],{},[32,23639,23640,23646,23648,23650,23652,23654,23656,23658,23660,23662,23664,23666,23668,23670,23672,23674,23680,23682,23684,23686,23689,23691,23701,23703,23705,23707,23709,23711,23713,23723,23725,23727,23729,23731,23733,23735,23737,23744,23746,23748,23750,23752,23754],{},[195,23641,23642,23644],{},[35,23643,199],{},[35,23645,37],{},[110,23647,113],{"stretchy":112},[35,23649,206],{},[35,23651,210],{"mathvariant":209},[35,23653,213],{},[110,23655,120],{"stretchy":112},[110,23657,123],{},[110,23659,1287],{},[110,23661,113],{"stretchy":112},[35,23663,11],{},[110,23665,4813],{},[35,23667,944],{},[110,23669,120],{"stretchy":112},[35,23671,4100],{},[110,23673,4103],{},[238,23675,23676,23678],{},[35,23677,11],{},[35,23679,944],{},[1297,23681,1299],{},[35,23683,244],{},[35,23685,774],{},[157,23687],{"linebreak":23688},"newline",[110,23690,123],{},[195,23692,23693,23695],{},[35,23694,199],{},[32,23696,23697,23699],{},[35,23698,10694],{},[35,23700,21893],{},[110,23702,113],{"stretchy":112},[35,23704,206],{},[35,23706,210],{"mathvariant":209},[35,23708,213],{},[110,23710,120],{"stretchy":112},[110,23712,2470],{},[195,23714,23715,23717],{},[35,23716,199],{},[32,23718,23719,23721],{},[35,23720,10694],{},[35,23722,21893],{},[110,23724,113],{"stretchy":112},[35,23726,213],{},[35,23728,210],{"mathvariant":209},[35,23730,206],{},[110,23732,120],{"stretchy":112},[110,23734,123],{},[110,23736,1015],{},[195,23738,23739,23741],{},[35,23740,199],{},[35,23742,23743],{},"J",[110,23745,113],{"stretchy":112},[35,23747,206],{},[110,23749,551],{"separator":46},[35,23751,213],{},[110,23753,120],{"stretchy":112},[110,23755,551],{"separator":46},[39,23757,23758],{"encoding":41},"D_f(P\\|Q)=\\int (p-q)\\log\\frac{p}{q}\\,dx \\\\\n=D_{KL}(P\\|Q)+D_{KL}(Q\\|P)=:D_J(P,Q),",[15,23760,23762,23832,23856,23950,23953,23965,24041,24118],{"className":23761,"ariaHidden":46},[45],[15,23763,23765,23768,23808,23811,23814,23817,23820,23823,23826,23829],{"className":23764},[50],[15,23766],{"className":23767,"style":270},[54],[15,23769,23771,23774],{"className":23770},[59],[15,23772,199],{"className":23773,"style":277},[59,60],[15,23775,23777],{"className":23776},[281],[15,23778,23780,23800],{"className":23779},[285,286],[15,23781,23783,23797],{"className":23782},[290],[15,23784,23786],{"className":23785,"style":295},[294],[15,23787,23788,23791],{"style":298},[15,23789],{"className":23790,"style":303},[302],[15,23792,23794],{"className":23793},[307,308,309,310],[15,23795,37],{"className":23796,"style":61},[59,60,310],[15,23798,318],{"className":23799},[317],[15,23801,23803],{"className":23802},[290],[15,23804,23806],{"className":23805,"style":325},[294],[15,23807],{},[15,23809,113],{"className":23810},[146],[15,23812,206],{"className":23813,"style":334},[59,60],[15,23815,210],{"className":23816},[59],[15,23818,213],{"className":23819},[59,60],[15,23821,120],{"className":23822},[153],[15,23824],{"className":23825,"style":158},[157],[15,23827,123],{"className":23828},[162],[15,23830],{"className":23831,"style":158},[157],[15,23833,23835,23838,23841,23844,23847,23850,23853],{"className":23834},[50],[15,23836],{"className":23837,"style":5777},[54],[15,23839,1287],{"className":23840,"style":1487},[1484,1485,1486],[15,23842,113],{"className":23843},[146],[15,23845,11],{"className":23846},[59,60],[15,23848],{"className":23849,"style":2587},[157],[15,23851,4813],{"className":23852},[2591],[15,23854],{"className":23855,"style":2587},[157],[15,23857,23859,23862,23865,23868,23871,23876,23879,23941,23944,23947],{"className":23858},[50],[15,23860],{"className":23861,"style":22010},[54],[15,23863,944],{"className":23864,"style":981},[59,60],[15,23866,120],{"className":23867},[153],[15,23869],{"className":23870,"style":406},[157],[15,23872,4154,23874],{"className":23873},[1484],[15,23875,4158],{"style":4157},[15,23877],{"className":23878,"style":406},[157],[15,23880,23882,23885,23938],{"className":23881},[59],[15,23883],{"className":23884},[146,441],[15,23886,23888],{"className":23887},[238],[15,23889,23891,23930],{"className":23890},[285,286],[15,23892,23894,23927],{"className":23893},[290],[15,23895,23897,23908,23916],{"className":23896,"style":3554},[294],[15,23898,23899,23902],{"style":457},[15,23900],{"className":23901,"style":461},[302],[15,23903,23905],{"className":23904},[59],[15,23906,944],{"className":23907,"style":981},[59,60],[15,23909,23910,23913],{"style":473},[15,23911],{"className":23912,"style":461},[302],[15,23914],{"className":23915,"style":481},[480],[15,23917,23918,23921],{"style":484},[15,23919],{"className":23920,"style":461},[302],[15,23922,23924],{"className":23923},[59],[15,23925,11],{"className":23926},[59,60],[15,23928,318],{"className":23929},[317],[15,23931,23933],{"className":23932},[290],[15,23934,23936],{"className":23935,"style":506},[294],[15,23937],{},[15,23939],{"className":23940},[153,441],[15,23942],{"className":23943,"style":406},[157],[15,23945,244],{"className":23946},[59,60],[15,23948,774],{"className":23949},[59,60],[15,23951],{"className":23952},[157,23688],[15,23954,23956,23959,23962],{"className":23955},[50],[15,23957],{"className":23958,"style":11003},[54],[15,23960,123],{"className":23961},[162],[15,23963],{"className":23964,"style":158},[157],[15,23966,23968,23971,24017,24020,24023,24026,24029,24032,24035,24038],{"className":23967},[50],[15,23969],{"className":23970,"style":139},[54],[15,23972,23974,23977],{"className":23973},[59],[15,23975,199],{"className":23976,"style":277},[59,60],[15,23978,23980],{"className":23979},[281],[15,23981,23983,24009],{"className":23982},[285,286],[15,23984,23986,24006],{"className":23985},[290],[15,23987,23989],{"className":23988,"style":379},[294],[15,23990,23991,23994],{"style":298},[15,23992],{"className":23993,"style":303},[302],[15,23995,23997],{"className":23996},[307,308,309,310],[15,23998,24000,24003],{"className":23999},[59,310],[15,24001,10694],{"className":24002,"style":10782},[59,60,310],[15,24004,21893],{"className":24005},[59,60,310],[15,24007,318],{"className":24008},[317],[15,24010,24012],{"className":24011},[290],[15,24013,24015],{"className":24014,"style":7968},[294],[15,24016],{},[15,24018,113],{"className":24019},[146],[15,24021,206],{"className":24022,"style":334},[59,60],[15,24024,210],{"className":24025},[59],[15,24027,213],{"className":24028},[59,60],[15,24030,120],{"className":24031},[153],[15,24033],{"className":24034,"style":2587},[157],[15,24036,2470],{"className":24037},[2591],[15,24039],{"className":24040,"style":2587},[157],[15,24042,24044,24047,24093,24096,24099,24102,24105,24108,24111,24115],{"className":24043},[50],[15,24045],{"className":24046,"style":139},[54],[15,24048,24050,24053],{"className":24049},[59],[15,24051,199],{"className":24052,"style":277},[59,60],[15,24054,24056],{"className":24055},[281],[15,24057,24059,24085],{"className":24058},[285,286],[15,24060,24062,24082],{"className":24061},[290],[15,24063,24065],{"className":24064,"style":379},[294],[15,24066,24067,24070],{"style":298},[15,24068],{"className":24069,"style":303},[302],[15,24071,24073],{"className":24072},[307,308,309,310],[15,24074,24076,24079],{"className":24075},[59,310],[15,24077,10694],{"className":24078,"style":10782},[59,60,310],[15,24080,21893],{"className":24081},[59,60,310],[15,24083,318],{"className":24084},[317],[15,24086,24088],{"className":24087},[290],[15,24089,24091],{"className":24090,"style":7968},[294],[15,24092],{},[15,24094,113],{"className":24095},[146],[15,24097,213],{"className":24098},[59,60],[15,24100,210],{"className":24101},[59],[15,24103,206],{"className":24104,"style":334},[59,60],[15,24106,120],{"className":24107},[153],[15,24109],{"className":24110,"style":158},[157],[15,24112,24114],{"className":24113},[162],"=:",[15,24116],{"className":24117,"style":158},[157],[15,24119,24121,24124,24165,24168,24171,24174,24177,24180,24183],{"className":24120},[50],[15,24122],{"className":24123,"style":139},[54],[15,24125,24127,24130],{"className":24126},[59],[15,24128,199],{"className":24129,"style":277},[59,60],[15,24131,24133],{"className":24132},[281],[15,24134,24136,24157],{"className":24135},[285,286],[15,24137,24139,24154],{"className":24138},[290],[15,24140,24142],{"className":24141,"style":379},[294],[15,24143,24144,24147],{"style":298},[15,24145],{"className":24146,"style":303},[302],[15,24148,24150],{"className":24149},[307,308,309,310],[15,24151,23743],{"className":24152,"style":24153},[59,60,310],"margin-right:0.0962em;",[15,24155,318],{"className":24156},[317],[15,24158,24160],{"className":24159},[290],[15,24161,24163],{"className":24162,"style":7968},[294],[15,24164],{},[15,24166,113],{"className":24167},[146],[15,24169,206],{"className":24170,"style":334},[59,60],[15,24172,551],{"className":24173},[573],[15,24175],{"className":24176,"style":406},[157],[15,24178,213],{"className":24179},[59,60],[15,24181,120],{"className":24182},[153],[15,24184,551],{"className":24185},[573],[11,24187,24188],{},"这是 KL 的两向之和，也是一个人为构造的对称 f-散度。",[11,24190,24191,24194,24195,24198,24199,24227,24228,24256,24257,24285,24286,24318,24319,24424,24425,24453,24454,24482,24483,24486],{},[1225,24192,24193],{},"意义。"," KL 是最基础的散度，等价于信息论中的",[1225,24196,24197],{},"相对熵","：若真实分布是 ",[15,24200,24202,24215],{"className":24201,"translate":19},[18],[15,24203,24205],{"className":24204},[23],[25,24206,24207],{"xmlns":27},[29,24208,24209,24213],{},[32,24210,24211],{},[35,24212,206],{},[39,24214,206],{"encoding":41},[15,24216,24218],{"className":24217,"ariaHidden":46},[45],[15,24219,24221,24224],{"className":24220},[50],[15,24222],{"className":24223,"style":664},[54],[15,24225,206],{"className":24226,"style":334},[59,60],"、而用 ",[15,24229,24231,24244],{"className":24230,"translate":19},[18],[15,24232,24234],{"className":24233},[23],[25,24235,24236],{"xmlns":27},[29,24237,24238,24242],{},[32,24239,24240],{},[35,24241,213],{},[39,24243,213],{"encoding":41},[15,24245,24247],{"className":24246,"ariaHidden":46},[45],[15,24248,24250,24253],{"className":24249},[50],[15,24251],{"className":24252,"style":566},[54],[15,24254,213],{"className":24255},[59,60]," 去编码来自 ",[15,24258,24260,24273],{"className":24259,"translate":19},[18],[15,24261,24263],{"className":24262},[23],[25,24264,24265],{"xmlns":27},[29,24266,24267,24271],{},[32,24268,24269],{},[35,24270,206],{},[39,24272,206],{"encoding":41},[15,24274,24276],{"className":24275,"ariaHidden":46},[45],[15,24277,24279,24282],{"className":24278},[50],[15,24280],{"className":24281,"style":664},[54],[15,24283,206],{"className":24284,"style":334},[59,60]," 的样本，那么 ",[15,24287,24289,24304],{"className":24288,"translate":19},[18],[15,24290,24292],{"className":24291},[23],[25,24293,24294],{"xmlns":27},[29,24295,24296,24302],{},[32,24297,24298,24300],{},[35,24299,4100],{},[110,24301,4103],{},[39,24303,21583],{"encoding":41},[15,24305,24307],{"className":24306,"ariaHidden":46},[45],[15,24308,24310,24313],{"className":24309},[50],[15,24311],{"className":24312,"style":55},[54],[15,24314,4154,24316],{"className":24315},[1484],[15,24317,4158],{"style":4157}," 以 2 为底时 ",[15,24320,24322,24354],{"className":24321,"translate":19},[18],[15,24323,24325],{"className":24324},[23],[25,24326,24327],{"xmlns":27},[29,24328,24329,24351],{},[32,24330,24331,24341,24343,24345,24347,24349],{},[195,24332,24333,24335],{},[35,24334,199],{},[32,24336,24337,24339],{},[35,24338,10694],{},[35,24340,21893],{},[110,24342,113],{"stretchy":112},[35,24344,206],{},[35,24346,210],{"mathvariant":209},[35,24348,213],{},[110,24350,120],{"stretchy":112},[39,24352,24353],{"encoding":41},"D_{KL}(P\\|Q)",[15,24355,24357],{"className":24356,"ariaHidden":46},[45],[15,24358,24360,24363,24409,24412,24415,24418,24421],{"className":24359},[50],[15,24361],{"className":24362,"style":139},[54],[15,24364,24366,24369],{"className":24365},[59],[15,24367,199],{"className":24368,"style":277},[59,60],[15,24370,24372],{"className":24371},[281],[15,24373,24375,24401],{"className":24374},[285,286],[15,24376,24378,24398],{"className":24377},[290],[15,24379,24381],{"className":24380,"style":379},[294],[15,24382,24383,24386],{"style":298},[15,24384],{"className":24385,"style":303},[302],[15,24387,24389],{"className":24388},[307,308,309,310],[15,24390,24392,24395],{"className":24391},[59,310],[15,24393,10694],{"className":24394,"style":10782},[59,60,310],[15,24396,21893],{"className":24397},[59,60,310],[15,24399,318],{"className":24400},[317],[15,24402,24404],{"className":24403},[290],[15,24405,24407],{"className":24406,"style":7968},[294],[15,24408],{},[15,24410,113],{"className":24411},[146],[15,24413,206],{"className":24414,"style":334},[59,60],[15,24416,210],{"className":24417},[59],[15,24419,213],{"className":24420},[59,60],[15,24422,120],{"className":24423},[153]," 正是用 ",[15,24426,24428,24441],{"className":24427,"translate":19},[18],[15,24429,24431],{"className":24430},[23],[25,24432,24433],{"xmlns":27},[29,24434,24435,24439],{},[32,24436,24437],{},[35,24438,213],{},[39,24440,213],{"encoding":41},[15,24442,24444],{"className":24443,"ariaHidden":46},[45],[15,24445,24447,24450],{"className":24446},[50],[15,24448],{"className":24449,"style":566},[54],[15,24451,213],{"className":24452},[59,60]," 编码比用 ",[15,24455,24457,24470],{"className":24456,"translate":19},[18],[15,24458,24460],{"className":24459},[23],[25,24461,24462],{"xmlns":27},[29,24463,24464,24468],{},[32,24465,24466],{},[35,24467,206],{},[39,24469,206],{"encoding":41},[15,24471,24473],{"className":24472,"ariaHidden":46},[45],[15,24474,24476,24479],{"className":24475},[50],[15,24477],{"className":24478,"style":664},[54],[15,24480,206],{"className":24481,"style":334},[59,60]," 编码",[1225,24484,24485],{},"多付出的比特数","，即",[15,24488,24490],{"className":24489,"translate":19},[180],[15,24491,24493,24635],{"className":24492,"translate":19},[18],[15,24494,24496],{"className":24495},[23],[25,24497,24498],{"xmlns":27,"display":189},[29,24499,24500,24632],{},[1243,24501,24502,24575],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,24503,24504,24530],{},[1252,24505,24506],{},[1255,24507,24508],{"scriptlevel":126,"displaystyle":46},[32,24509,24510,24520,24522,24524,24526,24528],{},[195,24511,24512,24514],{},[35,24513,199],{},[32,24515,24516,24518],{},[35,24517,10694],{},[35,24519,21893],{},[110,24521,113],{"stretchy":112},[35,24523,206],{},[35,24525,210],{"mathvariant":209},[35,24527,213],{},[110,24529,120],{"stretchy":112},[1252,24531,24532],{},[1255,24533,24534],{"scriptlevel":126,"displaystyle":46},[32,24535,24536,24538,24540],{},[32,24537],{},[110,24539,123],{},[6016,24541,24542,24572],{},[6016,24543,24544,24570],{},[32,24545,24546,24552,24554,24556,24558,24560,24562,24564,24566,24568],{},[195,24547,24548,24550],{},[35,24549,223],{"mathvariant":222},[35,24551,206],{},[110,24553,230],{"stretchy":112},[110,24555,4813],{},[35,24557,4100],{},[110,24559,4103],{},[35,24561,944],{},[110,24563,113],{"stretchy":112},[35,24565,598],{},[110,24567,120],{"stretchy":112},[110,24569,257],{"stretchy":112},[110,24571,6040],{"stretchy":46},[1297,24573,24574],{},"交叉熵",[1249,24576,24577,24583],{},[1252,24578,24579],{},[1255,24580,24581],{"scriptlevel":126,"displaystyle":46},[32,24582],{},[1252,24584,24585],{},[1255,24586,24587],{"scriptlevel":126,"displaystyle":46},[32,24588,24589,24591,24593,24595,24630],{},[32,24590],{},[157,24592],{"width":3262},[110,24594,4813],{},[6016,24596,24597,24627],{},[6016,24598,24599,24625],{},[32,24600,24601,24607,24609,24611,24613,24615,24617,24619,24621,24623],{},[195,24602,24603,24605],{},[35,24604,223],{"mathvariant":222},[35,24606,206],{},[110,24608,230],{"stretchy":112},[110,24610,4813],{},[35,24612,4100],{},[110,24614,4103],{},[35,24616,11],{},[110,24618,113],{"stretchy":112},[35,24620,598],{},[110,24622,120],{"stretchy":112},[110,24624,257],{"stretchy":112},[110,24626,6040],{"stretchy":46},[1297,24628,24629],{},"熵",[35,24631,4375],{"mathvariant":209},[39,24633,24634],{"encoding":41},"\\begin{aligned}\nD_{KL}(P\\|Q)\n&=\\underbrace{\\mathbb E_P[-\\log q(X)]}\n_{\\text{交叉熵}}\\\\[2pt]\n&\\qquad-\\underbrace{\\mathbb E_P[-\\log p(X)]}\n_{\\text{熵}} .\n\\end{aligned}",[15,24636,24638],{"className":24637,"ariaHidden":46},[45],[15,24639,24641,24645],{"className":24640},[50],[15,24642],{"className":24643,"style":24644},[54],"height:5.1327em;vertical-align:-2.3163em;",[15,24646,24648],{"className":24647},[59],[15,24649,24651,24755],{"className":24650},[1243],[15,24652,24654],{"className":24653},[1360],[15,24655,24657,24746],{"className":24656},[285,286],[15,24658,24660,24743],{"className":24659},[290],[15,24661,24664,24734],{"className":24662,"style":24663},[294],"height:2.8163em;",[15,24665,24667,24670],{"style":24666},"top:-4.9763em;",[15,24668],{"className":24669,"style":461},[302],[15,24671,24673,24719,24722,24725,24728,24731],{"className":24672},[59],[15,24674,24676,24679],{"className":24675},[59],[15,24677,199],{"className":24678,"style":277},[59,60],[15,24680,24682],{"className":24681},[281],[15,24683,24685,24711],{"className":24684},[285,286],[15,24686,24688,24708],{"className":24687},[290],[15,24689,24691],{"className":24690,"style":379},[294],[15,24692,24693,24696],{"style":298},[15,24694],{"className":24695,"style":303},[302],[15,24697,24699],{"className":24698},[307,308,309,310],[15,24700,24702,24705],{"className":24701},[59,310],[15,24703,10694],{"className":24704,"style":10782},[59,60,310],[15,24706,21893],{"className":24707},[59,60,310],[15,24709,318],{"className":24710},[317],[15,24712,24714],{"className":24713},[290],[15,24715,24717],{"className":24716,"style":7968},[294],[15,24718],{},[15,24720,113],{"className":24721},[146],[15,24723,206],{"className":24724,"style":334},[59,60],[15,24726,210],{"className":24727},[59],[15,24729,213],{"className":24730},[59,60],[15,24732,120],{"className":24733},[153],[15,24735,24737,24740],{"style":24736},"top:-2.26em;",[15,24738],{"className":24739,"style":461},[302],[15,24741],{"className":24742},[59],[15,24744,318],{"className":24745},[317],[15,24747,24749],{"className":24748},[290],[15,24750,24753],{"className":24751,"style":24752},[294],"height:2.3163em;",[15,24754],{},[15,24756,24758],{"className":24757},[1451],[15,24759,24761,25174],{"className":24760},[285,286],[15,24762,24764,25171],{"className":24763},[290],[15,24765,24767,24967],{"className":24766,"style":24663},[294],[15,24768,24769,24772],{"style":24666},[15,24770],{"className":24771,"style":461},[302],[15,24773,24775,24778,24781,24784,24787],{"className":24774},[59],[15,24776],{"className":24777},[59],[15,24779],{"className":24780,"style":158},[157],[15,24782,123],{"className":24783},[162],[15,24785],{"className":24786,"style":158},[157],[15,24788,24790],{"className":24789},[410,6016],[15,24791,24793,24958],{"className":24792},[285,286],[15,24794,24796,24955],{"className":24795},[290],[15,24797,24800,24818],{"className":24798,"style":24799},[294],"height:0.75em;",[15,24801,24803,24806],{"style":24802},"top:-1.4237em;",[15,24804],{"className":24805,"style":461},[302],[15,24807,24809],{"className":24808},[307,308,309,310],[15,24810,24812],{"className":24811},[59,310],[15,24813,24815],{"className":24814},[59,4598,310],[15,24816,24574],{"className":24817},[59,4602,310],[15,24819,24820,24823],{"style":11863},[15,24821],{"className":24822,"style":461},[302],[15,24824,24826],{"className":24825},[410,6016],[15,24827,24829,24946],{"className":24828},[285,286],[15,24830,24832,24943],{"className":24831},[290],[15,24833,24835,24866],{"className":24834,"style":24799},[294],[15,24836,24839,24842],{"className":24837,"style":24838},[6307],"top:-2.102em;",[15,24840],{"className":24841,"style":461},[302],[15,24843,24845,24852,24859],{"className":24844,"style":6316},[6315],[15,24846,24848],{"className":24847,"style":6321},[6320],[6323,24849,24850],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6329},[6331,24851],{"d":6333},[15,24853,24855],{"className":24854,"style":6321},[6337],[6323,24856,24857],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6340},[6331,24858],{"d":6343},[15,24860,24862],{"className":24861,"style":6321},[6347],[6323,24863,24864],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6350},[6331,24865],{"d":6353},[15,24867,24868,24871],{"style":11863},[15,24869],{"className":24870,"style":461},[302],[15,24872,24874,24914,24917,24920,24923,24928,24931,24934,24937,24940],{"className":24873},[59],[15,24875,24877,24880],{"className":24876},[59],[15,24878,223],{"className":24879},[59,366],[15,24881,24883],{"className":24882},[281],[15,24884,24886,24906],{"className":24885},[285,286],[15,24887,24889,24903],{"className":24888},[290],[15,24890,24892],{"className":24891,"style":379},[294],[15,24893,24894,24897],{"style":382},[15,24895],{"className":24896,"style":303},[302],[15,24898,24900],{"className":24899},[307,308,309,310],[15,24901,206],{"className":24902,"style":334},[59,60,310],[15,24904,318],{"className":24905},[317],[15,24907,24909],{"className":24908},[290],[15,24910,24912],{"className":24911,"style":7968},[294],[15,24913],{},[15,24915,230],{"className":24916},[146],[15,24918,4813],{"className":24919},[59],[15,24921],{"className":24922,"style":406},[157],[15,24924,4154,24926],{"className":24925},[1484],[15,24927,4158],{"style":4157},[15,24929],{"className":24930,"style":406},[157],[15,24932,944],{"className":24933,"style":981},[59,60],[15,24935,113],{"className":24936},[146],[15,24938,598],{"className":24939,"style":8887},[59,60],[15,24941,20390],{"className":24942},[153],[15,24944,318],{"className":24945},[317],[15,24947,24949],{"className":24948},[290],[15,24950,24953],{"className":24951,"style":24952},[294],"height:0.898em;",[15,24954],{},[15,24956,318],{"className":24957},[317],[15,24959,24961],{"className":24960},[290],[15,24962,24965],{"className":24963,"style":24964},[294],"height:1.5763em;",[15,24966],{},[15,24968,24969,24972],{"style":24736},[15,24970],{"className":24971,"style":461},[302],[15,24973,24975,24978,24981,24984,24987,24990,25165,25168],{"className":24974},[59],[15,24976],{"className":24977},[59],[15,24979],{"className":24980,"style":3634},[157],[15,24982],{"className":24983,"style":2587},[157],[15,24985,4813],{"className":24986},[2591],[15,24988],{"className":24989,"style":2587},[157],[15,24991,24993],{"className":24992},[410,6016],[15,24994,24996,25157],{"className":24995},[285,286],[15,24997,24999,25154],{"className":24998},[290],[15,25000,25002,25019],{"className":25001,"style":24799},[294],[15,25003,25004,25007],{"style":24802},[15,25005],{"className":25006,"style":461},[302],[15,25008,25010],{"className":25009},[307,308,309,310],[15,25011,25013],{"className":25012},[59,310],[15,25014,25016],{"className":25015},[59,4598,310],[15,25017,24629],{"className":25018},[59,4602,310],[15,25020,25021,25024],{"style":11863},[15,25022],{"className":25023,"style":461},[302],[15,25025,25027],{"className":25026},[410,6016],[15,25028,25030,25146],{"className":25029},[285,286],[15,25031,25033,25143],{"className":25032},[290],[15,25034,25036,25066],{"className":25035,"style":24799},[294],[15,25037,25039,25042],{"className":25038,"style":24838},[6307],[15,25040],{"className":25041,"style":461},[302],[15,25043,25045,25052,25059],{"className":25044,"style":6316},[6315],[15,25046,25048],{"className":25047,"style":6321},[6320],[6323,25049,25050],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6329},[6331,25051],{"d":6333},[15,25053,25055],{"className":25054,"style":6321},[6337],[6323,25056,25057],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6340},[6331,25058],{"d":6343},[15,25060,25062],{"className":25061,"style":6321},[6347],[6323,25063,25064],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6350},[6331,25065],{"d":6353},[15,25067,25068,25071],{"style":11863},[15,25069],{"className":25070,"style":461},[302],[15,25072,25074,25114,25117,25120,25123,25128,25131,25134,25137,25140],{"className":25073},[59],[15,25075,25077,25080],{"className":25076},[59],[15,25078,223],{"className":25079},[59,366],[15,25081,25083],{"className":25082},[281],[15,25084,25086,25106],{"className":25085},[285,286],[15,25087,25089,25103],{"className":25088},[290],[15,25090,25092],{"className":25091,"style":379},[294],[15,25093,25094,25097],{"style":382},[15,25095],{"className":25096,"style":303},[302],[15,25098,25100],{"className":25099},[307,308,309,310],[15,25101,206],{"className":25102,"style":334},[59,60,310],[15,25104,318],{"className":25105},[317],[15,25107,25109],{"className":25108},[290],[15,25110,25112],{"className":25111,"style":7968},[294],[15,25113],{},[15,25115,230],{"className":25116},[146],[15,25118,4813],{"className":25119},[59],[15,25121],{"className":25122,"style":406},[157],[15,25124,4154,25126],{"className":25125},[1484],[15,25127,4158],{"style":4157},[15,25129],{"className":25130,"style":406},[157],[15,25132,11],{"className":25133},[59,60],[15,25135,113],{"className":25136},[146],[15,25138,598],{"className":25139,"style":8887},[59,60],[15,25141,20390],{"className":25142},[153],[15,25144,318],{"className":25145},[317],[15,25147,25149],{"className":25148},[290],[15,25150,25152],{"className":25151,"style":24952},[294],[15,25153],{},[15,25155,318],{"className":25156},[317],[15,25158,25160],{"className":25159},[290],[15,25161,25163],{"className":25162,"style":24964},[294],[15,25164],{},[15,25166],{"className":25167,"style":406},[157],[15,25169,4375],{"className":25170},[59],[15,25172,318],{"className":25173},[317],[15,25175,25177],{"className":25176},[290],[15,25178,25180],{"className":25179,"style":24752},[294],[15,25181],{},[11,25183,25184,25185,25289,25290,3853,25318,25346,25347,25350,25351,25379,25380,25484,25485,3853,25513,25541,25542,25545],{},"在统计中它是最大似然估计的对数似然比的期望，决定了 Stein 引理里第二类错误的最优指数，也是 AIC\u002FBIC 这类模型选择的基石；在机器学习中它是最大似然训练、变分推断与知识蒸馏的目标。它的不对称性带来两种相反的行为：",[15,25186,25188,25219],{"className":25187,"translate":19},[18],[15,25189,25191],{"className":25190},[23],[25,25192,25193],{"xmlns":27},[29,25194,25195,25217],{},[32,25196,25197,25207,25209,25211,25213,25215],{},[195,25198,25199,25201],{},[35,25200,199],{},[32,25202,25203,25205],{},[35,25204,10694],{},[35,25206,21893],{},[110,25208,113],{"stretchy":112},[35,25210,206],{},[35,25212,210],{"mathvariant":209},[35,25214,213],{},[110,25216,120],{"stretchy":112},[39,25218,24353],{"encoding":41},[15,25220,25222],{"className":25221,"ariaHidden":46},[45],[15,25223,25225,25228,25274,25277,25280,25283,25286],{"className":25224},[50],[15,25226],{"className":25227,"style":139},[54],[15,25229,25231,25234],{"className":25230},[59],[15,25232,199],{"className":25233,"style":277},[59,60],[15,25235,25237],{"className":25236},[281],[15,25238,25240,25266],{"className":25239},[285,286],[15,25241,25243,25263],{"className":25242},[290],[15,25244,25246],{"className":25245,"style":379},[294],[15,25247,25248,25251],{"style":298},[15,25249],{"className":25250,"style":303},[302],[15,25252,25254],{"className":25253},[307,308,309,310],[15,25255,25257,25260],{"className":25256},[59,310],[15,25258,10694],{"className":25259,"style":10782},[59,60,310],[15,25261,21893],{"className":25262},[59,60,310],[15,25264,318],{"className":25265},[317],[15,25267,25269],{"className":25268},[290],[15,25270,25272],{"className":25271,"style":7968},[294],[15,25273],{},[15,25275,113],{"className":25276},[146],[15,25278,206],{"className":25279,"style":334},[59,60],[15,25281,210],{"className":25282},[59],[15,25284,213],{"className":25285},[59,60],[15,25287,120],{"className":25288},[153]," 要求 ",[15,25291,25293,25306],{"className":25292,"translate":19},[18],[15,25294,25296],{"className":25295},[23],[25,25297,25298],{"xmlns":27},[29,25299,25300,25304],{},[32,25301,25302],{},[35,25303,213],{},[39,25305,213],{"encoding":41},[15,25307,25309],{"className":25308,"ariaHidden":46},[45],[15,25310,25312,25315],{"className":25311},[50],[15,25313],{"className":25314,"style":566},[54],[15,25316,213],{"className":25317},[59,60],[15,25319,25321,25334],{"className":25320,"translate":19},[18],[15,25322,25324],{"className":25323},[23],[25,25325,25326],{"xmlns":27},[29,25327,25328,25332],{},[32,25329,25330],{},[35,25331,206],{},[39,25333,206],{"encoding":41},[15,25335,25337],{"className":25336,"ariaHidden":46},[45],[15,25338,25340,25343],{"className":25339},[50],[15,25341],{"className":25342,"style":664},[54],[15,25344,206],{"className":25345,"style":334},[59,60]," 有质量处不为零（",[1225,25348,25349],{},"零回避","，mass-covering，倾向覆盖 ",[15,25352,25354,25367],{"className":25353,"translate":19},[18],[15,25355,25357],{"className":25356},[23],[25,25358,25359],{"xmlns":27},[29,25360,25361,25365],{},[32,25362,25363],{},[35,25364,206],{},[39,25366,206],{"encoding":41},[15,25368,25370],{"className":25369,"ariaHidden":46},[45],[15,25371,25373,25376],{"className":25372},[50],[15,25374],{"className":25375,"style":664},[54],[15,25377,206],{"className":25378,"style":334},[59,60]," 的每一个模式），而 ",[15,25381,25383,25414],{"className":25382,"translate":19},[18],[15,25384,25386],{"className":25385},[23],[25,25387,25388],{"xmlns":27},[29,25389,25390,25412],{},[32,25391,25392,25402,25404,25406,25408,25410],{},[195,25393,25394,25396],{},[35,25395,199],{},[32,25397,25398,25400],{},[35,25399,10694],{},[35,25401,21893],{},[110,25403,113],{"stretchy":112},[35,25405,213],{},[35,25407,210],{"mathvariant":209},[35,25409,206],{},[110,25411,120],{"stretchy":112},[39,25413,22375],{"encoding":41},[15,25415,25417],{"className":25416,"ariaHidden":46},[45],[15,25418,25420,25423,25469,25472,25475,25478,25481],{"className":25419},[50],[15,25421],{"className":25422,"style":139},[54],[15,25424,25426,25429],{"className":25425},[59],[15,25427,199],{"className":25428,"style":277},[59,60],[15,25430,25432],{"className":25431},[281],[15,25433,25435,25461],{"className":25434},[285,286],[15,25436,25438,25458],{"className":25437},[290],[15,25439,25441],{"className":25440,"style":379},[294],[15,25442,25443,25446],{"style":298},[15,25444],{"className":25445,"style":303},[302],[15,25447,25449],{"className":25448},[307,308,309,310],[15,25450,25452,25455],{"className":25451},[59,310],[15,25453,10694],{"className":25454,"style":10782},[59,60,310],[15,25456,21893],{"className":25457},[59,60,310],[15,25459,318],{"className":25460},[317],[15,25462,25464],{"className":25463},[290],[15,25465,25467],{"className":25466,"style":7968},[294],[15,25468],{},[15,25470,113],{"className":25471},[146],[15,25473,213],{"className":25474},[59,60],[15,25476,210],{"className":25477},[59],[15,25479,206],{"className":25480,"style":334},[59,60],[15,25482,120],{"className":25483},[153]," 会把 ",[15,25486,25488,25501],{"className":25487,"translate":19},[18],[15,25489,25491],{"className":25490},[23],[25,25492,25493],{"xmlns":27},[29,25494,25495,25499],{},[32,25496,25497],{},[35,25498,213],{},[39,25500,213],{"encoding":41},[15,25502,25504],{"className":25503,"ariaHidden":46},[45],[15,25505,25507,25510],{"className":25506},[50],[15,25508],{"className":25509,"style":566},[54],[15,25511,213],{"className":25512},[59,60],[15,25514,25516,25529],{"className":25515,"translate":19},[18],[15,25517,25519],{"className":25518},[23],[25,25520,25521],{"xmlns":27},[29,25522,25523,25527],{},[32,25524,25525],{},[35,25526,206],{},[39,25528,206],{"encoding":41},[15,25530,25532],{"className":25531,"ariaHidden":46},[45],[15,25533,25535,25538],{"className":25534},[50],[15,25536],{"className":25537,"style":664},[54],[15,25539,206],{"className":25540,"style":334},[59,60]," 为零处压到零（",[1225,25543,25544],{},"零强制","，mode-seeking，倾向锁定单一模式）。GAN 的模式崩塌与变分推断的均值场近似，本质都由这一不对称性决定。",[2311,25547,25549],{"id":25548},"_32-js-散度","3.2 JS 散度",[11,25551,25552,25553,9400],{},"先回顾 JS 散度的定义，令 ",[15,25554,25556,25589],{"className":25555,"translate":19},[18],[15,25557,25559],{"className":25558},[23],[25,25560,25561],{"xmlns":27},[29,25562,25563,25586],{},[32,25564,25565,25568,25570,25576,25578,25580,25582,25584],{},[35,25566,25567],{},"M",[110,25569,123],{},[238,25571,25572,25574],{},[115,25573,117],{},[115,25575,2463],{},[110,25577,113],{"stretchy":112},[35,25579,206],{},[110,25581,2470],{},[35,25583,213],{},[110,25585,120],{"stretchy":112},[39,25587,25588],{"encoding":41},"M=\\frac12(P+Q)",[15,25590,25592,25611,25700],{"className":25591,"ariaHidden":46},[45],[15,25593,25595,25598,25602,25605,25608],{"className":25594},[50],[15,25596],{"className":25597,"style":664},[54],[15,25599,25567],{"className":25600,"style":25601},[59,60],"margin-right:0.109em;",[15,25603],{"className":25604,"style":158},[157],[15,25606,123],{"className":25607},[162],[15,25609],{"className":25610,"style":158},[157],[15,25612,25614,25617,25685,25688,25691,25694,25697],{"className":25613},[50],[15,25615],{"className":25616,"style":2505},[54],[15,25618,25620,25623,25682],{"className":25619},[59],[15,25621],{"className":25622},[146,441],[15,25624,25626],{"className":25625},[238],[15,25627,25629,25674],{"className":25628},[285,286],[15,25630,25632,25671],{"className":25631},[290],[15,25633,25635,25649,25657],{"className":25634,"style":2524},[294],[15,25636,25637,25640],{"style":2527},[15,25638],{"className":25639,"style":461},[302],[15,25641,25643],{"className":25642},[307,308,309,310],[15,25644,25646],{"className":25645},[59,310],[15,25647,2463],{"className":25648},[59,310],[15,25650,25651,25654],{"style":473},[15,25652],{"className":25653,"style":461},[302],[15,25655],{"className":25656,"style":481},[480],[15,25658,25659,25662],{"style":2550},[15,25660],{"className":25661,"style":461},[302],[15,25663,25665],{"className":25664},[307,308,309,310],[15,25666,25668],{"className":25667},[59,310],[15,25669,117],{"className":25670},[59,310],[15,25672,318],{"className":25673},[317],[15,25675,25677],{"className":25676},[290],[15,25678,25680],{"className":25679,"style":2572},[294],[15,25681],{},[15,25683],{"className":25684},[153,441],[15,25686,113],{"className":25687},[146],[15,25689,206],{"className":25690,"style":334},[59,60],[15,25692],{"className":25693,"style":2587},[157],[15,25695,2470],{"className":25696},[2591],[15,25698],{"className":25699,"style":2587},[157],[15,25701,25703,25706,25709],{"className":25702},[50],[15,25704],{"className":25705,"style":139},[54],[15,25707,213],{"className":25708},[59,60],[15,25710,120],{"className":25711},[153],[15,25713,25715],{"className":25714,"translate":19},[180],[15,25716,25718,25817],{"className":25717,"translate":19},[18],[15,25719,25721],{"className":25720},[23],[25,25722,25723],{"xmlns":27,"display":189},[29,25724,25725,25814],{},[32,25726,25727,25738,25740,25742,25744,25746,25748,25750,25756,25766,25768,25780,25782,25788,25798,25800,25812],{},[195,25728,25729,25731],{},[35,25730,199],{},[32,25732,25733,25735],{},[35,25734,23743],{},[35,25736,25737],{},"S",[110,25739,113],{"stretchy":112},[35,25741,206],{},[35,25743,210],{"mathvariant":209},[35,25745,213],{},[110,25747,120],{"stretchy":112},[110,25749,123],{},[238,25751,25752,25754],{},[115,25753,117],{},[115,25755,2463],{},[195,25757,25758,25760],{},[35,25759,199],{},[32,25761,25762,25764],{},[35,25763,10694],{},[35,25765,21893],{},[1297,25767,1304],{},[32,25769,25770,25772,25774,25776,25778],{},[110,25771,113],{"fence":46},[35,25773,206],{},[35,25775,210],{"mathvariant":209},[35,25777,25567],{},[110,25779,120],{"fence":46},[110,25781,2470],{},[238,25783,25784,25786],{},[115,25785,117],{},[115,25787,2463],{},[195,25789,25790,25792],{},[35,25791,199],{},[32,25793,25794,25796],{},[35,25795,10694],{},[35,25797,21893],{},[1297,25799,1304],{},[32,25801,25802,25804,25806,25808,25810],{},[110,25803,113],{"fence":46},[35,25805,213],{},[35,25807,210],{"mathvariant":209},[35,25809,25567],{},[110,25811,120],{"fence":46},[35,25813,4375],{"mathvariant":209},[39,25815,25816],{"encoding":41},"D_{JS}(P\\|Q)=\\frac12 D_{KL}\\!\\left(P\\|M\\right)\n+\\frac12 D_{KL}\\!\\left(Q\\|M\\right).",[15,25818,25820,25897,26045],{"className":25819,"ariaHidden":46},[45],[15,25821,25823,25826,25873,25876,25879,25882,25885,25888,25891,25894],{"className":25822},[50],[15,25824],{"className":25825,"style":139},[54],[15,25827,25829,25832],{"className":25828},[59],[15,25830,199],{"className":25831,"style":277},[59,60],[15,25833,25835],{"className":25834},[281],[15,25836,25838,25865],{"className":25837},[285,286],[15,25839,25841,25862],{"className":25840},[290],[15,25842,25844],{"className":25843,"style":379},[294],[15,25845,25846,25849],{"style":298},[15,25847],{"className":25848,"style":303},[302],[15,25850,25852],{"className":25851},[307,308,309,310],[15,25853,25855,25858],{"className":25854},[59,310],[15,25856,23743],{"className":25857,"style":24153},[59,60,310],[15,25859,25737],{"className":25860,"style":25861},[59,60,310],"margin-right:0.0576em;",[15,25863,318],{"className":25864},[317],[15,25866,25868],{"className":25867},[290],[15,25869,25871],{"className":25870,"style":7968},[294],[15,25872],{},[15,25874,113],{"className":25875},[146],[15,25877,206],{"className":25878,"style":334},[59,60],[15,25880,210],{"className":25881},[59],[15,25883,213],{"className":25884},[59,60],[15,25886,120],{"className":25887},[153],[15,25889],{"className":25890,"style":158},[157],[15,25892,123],{"className":25893},[162],[15,25895],{"className":25896,"style":158},[157],[15,25898,25900,25904,25966,26012,26015,26018,26036,26039,26042],{"className":25899},[50],[15,25901],{"className":25902,"style":25903},[54],"height:2.0074em;vertical-align:-0.686em;",[15,25905,25907,25910,25963],{"className":25906},[59],[15,25908],{"className":25909},[146,441],[15,25911,25913],{"className":25912},[238],[15,25914,25916,25955],{"className":25915},[285,286],[15,25917,25919,25952],{"className":25918},[290],[15,25920,25922,25933,25941],{"className":25921,"style":22889},[294],[15,25923,25924,25927],{"style":457},[15,25925],{"className":25926,"style":461},[302],[15,25928,25930],{"className":25929},[59],[15,25931,2463],{"className":25932},[59],[15,25934,25935,25938],{"style":473},[15,25936],{"className":25937,"style":461},[302],[15,25939],{"className":25940,"style":481},[480],[15,25942,25943,25946],{"style":484},[15,25944],{"className":25945,"style":461},[302],[15,25947,25949],{"className":25948},[59],[15,25950,117],{"className":25951},[59],[15,25953,318],{"className":25954},[317],[15,25956,25958],{"className":25957},[290],[15,25959,25961],{"className":25960,"style":3778},[294],[15,25962],{},[15,25964],{"className":25965},[153,441],[15,25967,25969,25972],{"className":25968},[59],[15,25970,199],{"className":25971,"style":277},[59,60],[15,25973,25975],{"className":25974},[281],[15,25976,25978,26004],{"className":25977},[285,286],[15,25979,25981,26001],{"className":25980},[290],[15,25982,25984],{"className":25983,"style":379},[294],[15,25985,25986,25989],{"style":298},[15,25987],{"className":25988,"style":303},[302],[15,25990,25992],{"className":25991},[307,308,309,310],[15,25993,25995,25998],{"className":25994},[59,310],[15,25996,10694],{"className":25997,"style":10782},[59,60,310],[15,25999,21893],{"className":26000},[59,60,310],[15,26002,318],{"className":26003},[317],[15,26005,26007],{"className":26006},[290],[15,26008,26010],{"className":26009,"style":7968},[294],[15,26011],{},[15,26013],{"className":26014,"style":1512},[157],[15,26016],{"className":26017,"style":406},[157],[15,26019,26021,26024,26027,26030,26033],{"className":26020},[410],[15,26022,113],{"className":26023,"style":415},[146,414],[15,26025,206],{"className":26026,"style":334},[59,60],[15,26028,210],{"className":26029},[59],[15,26031,25567],{"className":26032,"style":25601},[59,60],[15,26034,120],{"className":26035,"style":415},[153,414],[15,26037],{"className":26038,"style":2587},[157],[15,26040,2470],{"className":26041},[2591],[15,26043],{"className":26044,"style":2587},[157],[15,26046,26048,26051,26113,26159,26162,26165,26183,26186],{"className":26047},[50],[15,26049],{"className":26050,"style":25903},[54],[15,26052,26054,26057,26110],{"className":26053},[59],[15,26055],{"className":26056},[146,441],[15,26058,26060],{"className":26059},[238],[15,26061,26063,26102],{"className":26062},[285,286],[15,26064,26066,26099],{"className":26065},[290],[15,26067,26069,26080,26088],{"className":26068,"style":22889},[294],[15,26070,26071,26074],{"style":457},[15,26072],{"className":26073,"style":461},[302],[15,26075,26077],{"className":26076},[59],[15,26078,2463],{"className":26079},[59],[15,26081,26082,26085],{"style":473},[15,26083],{"className":26084,"style":461},[302],[15,26086],{"className":26087,"style":481},[480],[15,26089,26090,26093],{"style":484},[15,26091],{"className":26092,"style":461},[302],[15,26094,26096],{"className":26095},[59],[15,26097,117],{"className":26098},[59],[15,26100,318],{"className":26101},[317],[15,26103,26105],{"className":26104},[290],[15,26106,26108],{"className":26107,"style":3778},[294],[15,26109],{},[15,26111],{"className":26112},[153,441],[15,26114,26116,26119],{"className":26115},[59],[15,26117,199],{"className":26118,"style":277},[59,60],[15,26120,26122],{"className":26121},[281],[15,26123,26125,26151],{"className":26124},[285,286],[15,26126,26128,26148],{"className":26127},[290],[15,26129,26131],{"className":26130,"style":379},[294],[15,26132,26133,26136],{"style":298},[15,26134],{"className":26135,"style":303},[302],[15,26137,26139],{"className":26138},[307,308,309,310],[15,26140,26142,26145],{"className":26141},[59,310],[15,26143,10694],{"className":26144,"style":10782},[59,60,310],[15,26146,21893],{"className":26147},[59,60,310],[15,26149,318],{"className":26150},[317],[15,26152,26154],{"className":26153},[290],[15,26155,26157],{"className":26156,"style":7968},[294],[15,26158],{},[15,26160],{"className":26161,"style":1512},[157],[15,26163],{"className":26164,"style":406},[157],[15,26166,26168,26171,26174,26177,26180],{"className":26167},[410],[15,26169,113],{"className":26170,"style":415},[146,414],[15,26172,213],{"className":26173},[59,60],[15,26175,210],{"className":26176},[59],[15,26178,25567],{"className":26179,"style":25601},[59,60],[15,26181,120],{"className":26182,"style":415},[153,414],[15,26184],{"className":26185,"style":406},[157],[15,26187,4375],{"className":26188},[59],[11,26190,26191,26194,26195,26223,26224,26279,26280,26308,26309,26460],{},[1225,26192,26193],{},"它是单个 f-散度。"," 这一点很容易被误解。我们直接构造 ",[15,26196,26198,26211],{"className":26197,"translate":19},[18],[15,26199,26201],{"className":26200},[23],[25,26202,26203],{"xmlns":27},[29,26204,26205,26209],{},[32,26206,26207],{},[35,26208,37],{},[39,26210,37],{"encoding":41},[15,26212,26214],{"className":26213,"ariaHidden":46},[45],[15,26215,26217,26220],{"className":26216},[50],[15,26218],{"className":26219,"style":55},[54],[15,26221,37],{"className":26222,"style":61},[59,60],"：代入 ",[15,26225,26227,26247],{"className":26226,"translate":19},[18],[15,26228,26230],{"className":26229},[23],[25,26231,26232],{"xmlns":27},[29,26233,26234,26244],{},[32,26235,26236,26238,26240,26242],{},[35,26237,11],{},[110,26239,123],{},[35,26241,769],{},[35,26243,944],{},[39,26245,26246],{"encoding":41},"p=tq",[15,26248,26250,26268],{"className":26249,"ariaHidden":46},[45],[15,26251,26253,26256,26259,26262,26265],{"className":26252},[50],[15,26254],{"className":26255,"style":2276},[54],[15,26257,11],{"className":26258},[59,60],[15,26260],{"className":26261,"style":158},[157],[15,26263,123],{"className":26264},[162],[15,26266],{"className":26267,"style":158},[157],[15,26269,26271,26275],{"className":26270},[50],[15,26272],{"className":26273,"style":26274},[54],"height:0.8095em;vertical-align:-0.1944em;",[15,26276,26278],{"className":26277,"style":981},[59,60],"tq","，于是 ",[15,26281,26283,26296],{"className":26282,"translate":19},[18],[15,26284,26286],{"className":26285},[23],[25,26287,26288],{"xmlns":27},[29,26289,26290,26294],{},[32,26291,26292],{},[35,26293,25567],{},[39,26295,25567],{"encoding":41},[15,26297,26299],{"className":26298,"ariaHidden":46},[45],[15,26300,26302,26305],{"className":26301},[50],[15,26303],{"className":26304,"style":664},[54],[15,26306,25567],{"className":26307,"style":25601},[59,60]," 的密度为 ",[15,26310,26312,26347],{"className":26311,"translate":19},[18],[15,26313,26315],{"className":26314},[23],[25,26316,26317],{"xmlns":27},[29,26318,26319,26344],{},[32,26320,26321,26324,26326],{},[35,26322,26323],{},"m",[110,26325,123],{},[238,26327,26328,26342],{},[32,26329,26330,26332,26334,26336,26338,26340],{},[110,26331,113],{"stretchy":112},[35,26333,769],{},[110,26335,2470],{},[115,26337,117],{},[110,26339,120],{"stretchy":112},[35,26341,944],{},[115,26343,2463],{},[39,26345,26346],{"encoding":41},"m=\\frac{(t+1)q}{2}",[15,26348,26350,26368],{"className":26349,"ariaHidden":46},[45],[15,26351,26353,26356,26359,26362,26365],{"className":26352},[50],[15,26354],{"className":26355,"style":2345},[54],[15,26357,26323],{"className":26358},[59,60],[15,26360],{"className":26361,"style":158},[157],[15,26363,123],{"className":26364},[162],[15,26366],{"className":26367,"style":158},[157],[15,26369,26371,26375],{"className":26370},[50],[15,26372],{"className":26373,"style":26374},[54],"height:1.355em;vertical-align:-0.345em;",[15,26376,26378,26381,26457],{"className":26377},[59],[15,26379],{"className":26380},[146,441],[15,26382,26384],{"className":26383},[238],[15,26385,26387,26449],{"className":26386},[285,286],[15,26388,26390,26446],{"className":26389},[290],[15,26391,26394,26408,26416],{"className":26392,"style":26393},[294],"height:1.01em;",[15,26395,26396,26399],{"style":2527},[15,26397],{"className":26398,"style":461},[302],[15,26400,26402],{"className":26401},[307,308,309,310],[15,26403,26405],{"className":26404},[59,310],[15,26406,2463],{"className":26407},[59,310],[15,26409,26410,26413],{"style":473},[15,26411],{"className":26412,"style":461},[302],[15,26414],{"className":26415,"style":481},[480],[15,26417,26419,26422],{"style":26418},"top:-3.485em;",[15,26420],{"className":26421,"style":461},[302],[15,26423,26425],{"className":26424},[307,308,309,310],[15,26426,26428,26431,26434,26437,26440,26443],{"className":26427},[59,310],[15,26429,113],{"className":26430},[146,310],[15,26432,769],{"className":26433},[59,60,310],[15,26435,2470],{"className":26436},[2591,310],[15,26438,117],{"className":26439},[59,310],[15,26441,120],{"className":26442},[153,310],[15,26444,944],{"className":26445,"style":981},[59,60,310],[15,26447,318],{"className":26448},[317],[15,26450,26452],{"className":26451},[290],[15,26453,26455],{"className":26454,"style":2572},[294],[15,26456],{},[15,26458],{"className":26459},[153,441],"，逐项算：",[15,26462,26464],{"className":26463,"translate":19},[180],[15,26465,26467,26529],{"className":26466,"translate":19},[18],[15,26468,26470],{"className":26469},[23],[25,26471,26472],{"xmlns":27,"display":189},[29,26473,26474,26526],{},[32,26475,26476,26482,26484,26500,26502,26504,26510,26512,26524],{},[238,26477,26478,26480],{},[35,26479,11],{},[35,26481,26323],{},[110,26483,123],{},[238,26485,26486,26492],{},[32,26487,26488,26490],{},[115,26489,2463],{},[35,26491,769],{},[32,26493,26494,26496,26498],{},[35,26495,769],{},[110,26497,2470],{},[115,26499,117],{},[110,26501,551],{"separator":46},[157,26503],{"width":3262},[238,26505,26506,26508],{},[35,26507,944],{},[35,26509,26323],{},[110,26511,123],{},[238,26513,26514,26516],{},[115,26515,2463],{},[32,26517,26518,26520,26522],{},[35,26519,769],{},[110,26521,2470],{},[115,26523,117],{},[110,26525,551],{"separator":46},[39,26527,26528],{"encoding":41},"\\frac{p}{m}=\\frac{2t}{t+1},\\qquad\n\\frac{q}{m}=\\frac{2}{t+1},",[15,26530,26532,26610,26774],{"className":26531,"ariaHidden":46},[45],[15,26533,26535,26539,26601,26604,26607],{"className":26534},[50],[15,26536],{"className":26537,"style":26538},[54],"height:1.7936em;vertical-align:-0.686em;",[15,26540,26542,26545,26598],{"className":26541},[59],[15,26543],{"className":26544},[146,441],[15,26546,26548],{"className":26547},[238],[15,26549,26551,26590],{"className":26550},[285,286],[15,26552,26554,26587],{"className":26553},[290],[15,26555,26557,26568,26576],{"className":26556,"style":3554},[294],[15,26558,26559,26562],{"style":457},[15,26560],{"className":26561,"style":461},[302],[15,26563,26565],{"className":26564},[59],[15,26566,26323],{"className":26567},[59,60],[15,26569,26570,26573],{"style":473},[15,26571],{"className":26572,"style":461},[302],[15,26574],{"className":26575,"style":481},[480],[15,26577,26578,26581],{"style":484},[15,26579],{"className":26580,"style":461},[302],[15,26582,26584],{"className":26583},[59],[15,26585,11],{"className":26586},[59,60],[15,26588,318],{"className":26589},[317],[15,26591,26593],{"className":26592},[290],[15,26594,26596],{"className":26595,"style":3778},[294],[15,26597],{},[15,26599],{"className":26600},[153,441],[15,26602],{"className":26603,"style":158},[157],[15,26605,123],{"className":26606},[162],[15,26608],{"className":26609,"style":158},[157],[15,26611,26613,26617,26694,26697,26700,26703,26765,26768,26771],{"className":26612},[50],[15,26614],{"className":26615,"style":26616},[54],"height:2.0908em;vertical-align:-0.7693em;",[15,26618,26620,26623,26691],{"className":26619},[59],[15,26621],{"className":26622},[146,441],[15,26624,26626],{"className":26625},[238],[15,26627,26629,26683],{"className":26628},[285,286],[15,26630,26632,26680],{"className":26631},[290],[15,26633,26635,26658,26666],{"className":26634,"style":22889},[294],[15,26636,26637,26640],{"style":457},[15,26638],{"className":26639,"style":461},[302],[15,26641,26643,26646,26649,26652,26655],{"className":26642},[59],[15,26644,769],{"className":26645},[59,60],[15,26647],{"className":26648,"style":2587},[157],[15,26650,2470],{"className":26651},[2591],[15,26653],{"className":26654,"style":2587},[157],[15,26656,117],{"className":26657},[59],[15,26659,26660,26663],{"style":473},[15,26661],{"className":26662,"style":461},[302],[15,26664],{"className":26665,"style":481},[480],[15,26667,26668,26671],{"style":484},[15,26669],{"className":26670,"style":461},[302],[15,26672,26674,26677],{"className":26673},[59],[15,26675,2463],{"className":26676},[59],[15,26678,769],{"className":26679},[59,60],[15,26681,318],{"className":26682},[317],[15,26684,26686],{"className":26685},[290],[15,26687,26689],{"className":26688,"style":17015},[294],[15,26690],{},[15,26692],{"className":26693},[153,441],[15,26695,551],{"className":26696},[573],[15,26698],{"className":26699,"style":3634},[157],[15,26701],{"className":26702,"style":406},[157],[15,26704,26706,26709,26762],{"className":26705},[59],[15,26707],{"className":26708},[146,441],[15,26710,26712],{"className":26711},[238],[15,26713,26715,26754],{"className":26714},[285,286],[15,26716,26718,26751],{"className":26717},[290],[15,26719,26721,26732,26740],{"className":26720,"style":3554},[294],[15,26722,26723,26726],{"style":457},[15,26724],{"className":26725,"style":461},[302],[15,26727,26729],{"className":26728},[59],[15,26730,26323],{"className":26731},[59,60],[15,26733,26734,26737],{"style":473},[15,26735],{"className":26736,"style":461},[302],[15,26738],{"className":26739,"style":481},[480],[15,26741,26742,26745],{"style":484},[15,26743],{"className":26744,"style":461},[302],[15,26746,26748],{"className":26747},[59],[15,26749,944],{"className":26750,"style":981},[59,60],[15,26752,318],{"className":26753},[317],[15,26755,26757],{"className":26756},[290],[15,26758,26760],{"className":26759,"style":3778},[294],[15,26761],{},[15,26763],{"className":26764},[153,441],[15,26766],{"className":26767,"style":158},[157],[15,26769,123],{"className":26770},[162],[15,26772],{"className":26773,"style":158},[157],[15,26775,26777,26780,26854],{"className":26776},[50],[15,26778],{"className":26779,"style":26616},[54],[15,26781,26783,26786,26851],{"className":26782},[59],[15,26784],{"className":26785},[146,441],[15,26787,26789],{"className":26788},[238],[15,26790,26792,26843],{"className":26791},[285,286],[15,26793,26795,26840],{"className":26794},[290],[15,26796,26798,26821,26829],{"className":26797,"style":22889},[294],[15,26799,26800,26803],{"style":457},[15,26801],{"className":26802,"style":461},[302],[15,26804,26806,26809,26812,26815,26818],{"className":26805},[59],[15,26807,769],{"className":26808},[59,60],[15,26810],{"className":26811,"style":2587},[157],[15,26813,2470],{"className":26814},[2591],[15,26816],{"className":26817,"style":2587},[157],[15,26819,117],{"className":26820},[59],[15,26822,26823,26826],{"style":473},[15,26824],{"className":26825,"style":461},[302],[15,26827],{"className":26828,"style":481},[480],[15,26830,26831,26834],{"style":484},[15,26832],{"className":26833,"style":461},[302],[15,26835,26837],{"className":26836},[59],[15,26838,2463],{"className":26839},[59],[15,26841,318],{"className":26842},[317],[15,26844,26846],{"className":26845},[290],[15,26847,26849],{"className":26848,"style":17015},[294],[15,26850],{},[15,26852],{"className":26853},[153,441],[15,26855,551],{"className":26856},[573],[15,26858,26860],{"className":26859,"translate":19},[180],[15,26861,26863,27003],{"className":26862,"translate":19},[18],[15,26864,26866],{"className":26865},[23],[25,26867,26868],{"xmlns":27,"display":189},[29,26869,26870,27000],{},[1243,26871,26872,26952],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,26873,26874,26900],{},[1252,26875,26876],{},[1255,26877,26878],{"scriptlevel":126,"displaystyle":46},[32,26879,26880,26890,26892,26894,26896,26898],{},[195,26881,26882,26884],{},[35,26883,199],{},[32,26885,26886,26888],{},[35,26887,23743],{},[35,26889,25737],{},[110,26891,113],{"stretchy":112},[35,26893,206],{},[35,26895,210],{"mathvariant":209},[35,26897,213],{},[110,26899,120],{"stretchy":112},[1252,26901,26902],{},[1255,26903,26904],{"scriptlevel":126,"displaystyle":46},[32,26905,26906,26908,26910,26916,26918,26920,26922,26924,26930,26932,26938,26940,26942,26944,26946],{},[32,26907],{},[110,26909,123],{},[238,26911,26912,26914],{},[115,26913,117],{},[115,26915,2463],{},[110,26917,1287],{},[35,26919,11],{},[35,26921,4100],{},[110,26923,4103],{},[238,26925,26926,26928],{},[35,26927,11],{},[35,26929,26323],{},[110,26931,2470],{},[238,26933,26934,26936],{},[115,26935,117],{},[115,26937,2463],{},[110,26939,1287],{},[35,26941,944],{},[35,26943,4100],{},[110,26945,4103],{},[238,26947,26948,26950],{},[35,26949,944],{},[35,26951,26323],{},[1249,26953,26954,26960],{},[1252,26955,26956],{},[1255,26957,26958],{"scriptlevel":126,"displaystyle":46},[32,26959],{},[1252,26961,26962],{},[1255,26963,26964],{"scriptlevel":126,"displaystyle":46},[32,26965,26966,26968,26970,26972,26974,26976,26986,26988,26990,26992,26994,26996,26998],{},[32,26967],{},[110,26969,123],{},[110,26971,1287],{},[35,26973,944],{},[1297,26975,1299],{},[195,26977,26978,26980],{},[35,26979,37],{},[32,26981,26982,26984],{},[35,26983,23743],{},[35,26985,25737],{},[110,26987,113],{"stretchy":112},[35,26989,769],{},[110,26991,120],{"stretchy":112},[1297,26993,1299],{},[35,26995,244],{},[35,26997,774],{},[110,26999,551],{"separator":46},[39,27001,27002],{"encoding":41},"\\begin{aligned}\nD_{JS}(P\\|Q)\n&=\\frac12\\int p\\log\\frac{p}{m}\n+\\frac12\\int q\\log\\frac{q}{m}\\\\[2pt]\n&=\\int q\\,f_{JS}(t)\\,dx,\n\\end{aligned}",[15,27004,27006],{"className":27005,"ariaHidden":46},[45],[15,27007,27009,27013],{"className":27008},[50],[15,27010],{"className":27011,"style":27012},[54],"height:4.7445em;vertical-align:-2.1223em;",[15,27014,27016],{"className":27015},[59],[15,27017,27019,27122],{"className":27018},[1243],[15,27020,27022],{"className":27021},[1360],[15,27023,27025,27113],{"className":27024},[285,286],[15,27026,27028,27110],{"className":27027},[290],[15,27029,27032,27102],{"className":27030,"style":27031},[294],"height:2.6223em;",[15,27033,27035,27038],{"style":27034},"top:-4.6223em;",[15,27036],{"className":27037,"style":6273},[302],[15,27039,27041,27087,27090,27093,27096,27099],{"className":27040},[59],[15,27042,27044,27047],{"className":27043},[59],[15,27045,199],{"className":27046,"style":277},[59,60],[15,27048,27050],{"className":27049},[281],[15,27051,27053,27079],{"className":27052},[285,286],[15,27054,27056,27076],{"className":27055},[290],[15,27057,27059],{"className":27058,"style":379},[294],[15,27060,27061,27064],{"style":298},[15,27062],{"className":27063,"style":303},[302],[15,27065,27067],{"className":27066},[307,308,309,310],[15,27068,27070,27073],{"className":27069},[59,310],[15,27071,23743],{"className":27072,"style":24153},[59,60,310],[15,27074,25737],{"className":27075,"style":25861},[59,60,310],[15,27077,318],{"className":27078},[317],[15,27080,27082],{"className":27081},[290],[15,27083,27085],{"className":27084,"style":7968},[294],[15,27086],{},[15,27088,113],{"className":27089},[146],[15,27091,206],{"className":27092,"style":334},[59,60],[15,27094,210],{"className":27095},[59],[15,27097,213],{"className":27098},[59,60],[15,27100,120],{"className":27101},[153],[15,27103,27104,27107],{"style":1903},[15,27105],{"className":27106,"style":6273},[302],[15,27108],{"className":27109},[59],[15,27111,318],{"className":27112},[317],[15,27114,27116],{"className":27115},[290],[15,27117,27120],{"className":27118,"style":27119},[294],"height:2.1223em;",[15,27121],{},[15,27123,27125],{"className":27124},[1451],[15,27126,27128,27560],{"className":27127},[285,286],[15,27129,27131,27557],{"className":27130},[290],[15,27132,27134,27457],{"className":27133,"style":27031},[294],[15,27135,27136,27139],{"style":27034},[15,27137],{"className":27138,"style":6273},[302],[15,27140,27142,27145,27148,27151,27154,27216,27219,27222,27225,27228,27231,27236,27239,27301,27304,27307,27310,27372,27375,27378,27381,27384,27387,27392,27395],{"className":27141},[59],[15,27143],{"className":27144},[59],[15,27146],{"className":27147,"style":158},[157],[15,27149,123],{"className":27150},[162],[15,27152],{"className":27153,"style":158},[157],[15,27155,27157,27160,27213],{"className":27156},[59],[15,27158],{"className":27159},[146,441],[15,27161,27163],{"className":27162},[238],[15,27164,27166,27205],{"className":27165},[285,286],[15,27167,27169,27202],{"className":27168},[290],[15,27170,27172,27183,27191],{"className":27171,"style":22889},[294],[15,27173,27174,27177],{"style":457},[15,27175],{"className":27176,"style":461},[302],[15,27178,27180],{"className":27179},[59],[15,27181,2463],{"className":27182},[59],[15,27184,27185,27188],{"style":473},[15,27186],{"className":27187,"style":461},[302],[15,27189],{"className":27190,"style":481},[480],[15,27192,27193,27196],{"style":484},[15,27194],{"className":27195,"style":461},[302],[15,27197,27199],{"className":27198},[59],[15,27200,117],{"className":27201},[59],[15,27203,318],{"className":27204},[317],[15,27206,27208],{"className":27207},[290],[15,27209,27211],{"className":27210,"style":3778},[294],[15,27212],{},[15,27214],{"className":27215},[153,441],[15,27217],{"className":27218,"style":406},[157],[15,27220,1287],{"className":27221,"style":1487},[1484,1485,1486],[15,27223],{"className":27224,"style":406},[157],[15,27226,11],{"className":27227},[59,60],[15,27229],{"className":27230,"style":406},[157],[15,27232,4154,27234],{"className":27233},[1484],[15,27235,4158],{"style":4157},[15,27237],{"className":27238,"style":406},[157],[15,27240,27242,27245,27298],{"className":27241},[59],[15,27243],{"className":27244},[146,441],[15,27246,27248],{"className":27247},[238],[15,27249,27251,27290],{"className":27250},[285,286],[15,27252,27254,27287],{"className":27253},[290],[15,27255,27257,27268,27276],{"className":27256,"style":3554},[294],[15,27258,27259,27262],{"style":457},[15,27260],{"className":27261,"style":461},[302],[15,27263,27265],{"className":27264},[59],[15,27266,26323],{"className":27267},[59,60],[15,27269,27270,27273],{"style":473},[15,27271],{"className":27272,"style":461},[302],[15,27274],{"className":27275,"style":481},[480],[15,27277,27278,27281],{"style":484},[15,27279],{"className":27280,"style":461},[302],[15,27282,27284],{"className":27283},[59],[15,27285,11],{"className":27286},[59,60],[15,27288,318],{"className":27289},[317],[15,27291,27293],{"className":27292},[290],[15,27294,27296],{"className":27295,"style":3778},[294],[15,27297],{},[15,27299],{"className":27300},[153,441],[15,27302],{"className":27303,"style":2587},[157],[15,27305,2470],{"className":27306},[2591],[15,27308],{"className":27309,"style":2587},[157],[15,27311,27313,27316,27369],{"className":27312},[59],[15,27314],{"className":27315},[146,441],[15,27317,27319],{"className":27318},[238],[15,27320,27322,27361],{"className":27321},[285,286],[15,27323,27325,27358],{"className":27324},[290],[15,27326,27328,27339,27347],{"className":27327,"style":22889},[294],[15,27329,27330,27333],{"style":457},[15,27331],{"className":27332,"style":461},[302],[15,27334,27336],{"className":27335},[59],[15,27337,2463],{"className":27338},[59],[15,27340,27341,27344],{"style":473},[15,27342],{"className":27343,"style":461},[302],[15,27345],{"className":27346,"style":481},[480],[15,27348,27349,27352],{"style":484},[15,27350],{"className":27351,"style":461},[302],[15,27353,27355],{"className":27354},[59],[15,27356,117],{"className":27357},[59],[15,27359,318],{"className":27360},[317],[15,27362,27364],{"className":27363},[290],[15,27365,27367],{"className":27366,"style":3778},[294],[15,27368],{},[15,27370],{"className":27371},[153,441],[15,27373],{"className":27374,"style":406},[157],[15,27376,1287],{"className":27377,"style":1487},[1484,1485,1486],[15,27379],{"className":27380,"style":406},[157],[15,27382,944],{"className":27383,"style":981},[59,60],[15,27385],{"className":27386,"style":406},[157],[15,27388,4154,27390],{"className":27389},[1484],[15,27391,4158],{"style":4157},[15,27393],{"className":27394,"style":406},[157],[15,27396,27398,27401,27454],{"className":27397},[59],[15,27399],{"className":27400},[146,441],[15,27402,27404],{"className":27403},[238],[15,27405,27407,27446],{"className":27406},[285,286],[15,27408,27410,27443],{"className":27409},[290],[15,27411,27413,27424,27432],{"className":27412,"style":3554},[294],[15,27414,27415,27418],{"style":457},[15,27416],{"className":27417,"style":461},[302],[15,27419,27421],{"className":27420},[59],[15,27422,26323],{"className":27423},[59,60],[15,27425,27426,27429],{"style":473},[15,27427],{"className":27428,"style":461},[302],[15,27430],{"className":27431,"style":481},[480],[15,27433,27434,27437],{"style":484},[15,27435],{"className":27436,"style":461},[302],[15,27438,27440],{"className":27439},[59],[15,27441,944],{"className":27442,"style":981},[59,60],[15,27444,318],{"className":27445},[317],[15,27447,27449],{"className":27448},[290],[15,27450,27452],{"className":27451,"style":3778},[294],[15,27453],{},[15,27455],{"className":27456},[153,441],[15,27458,27459,27462],{"style":1903},[15,27460],{"className":27461,"style":6273},[302],[15,27463,27465,27468,27471,27474,27477,27480,27483,27486,27489,27536,27539,27542,27545,27548,27551,27554],{"className":27464},[59],[15,27466],{"className":27467},[59],[15,27469],{"className":27470,"style":158},[157],[15,27472,123],{"className":27473},[162],[15,27475],{"className":27476,"style":158},[157],[15,27478,1287],{"className":27479,"style":1487},[1484,1485,1486],[15,27481],{"className":27482,"style":406},[157],[15,27484,944],{"className":27485,"style":981},[59,60],[15,27487],{"className":27488,"style":406},[157],[15,27490,27492,27495],{"className":27491},[59],[15,27493,37],{"className":27494,"style":61},[59,60],[15,27496,27498],{"className":27497},[281],[15,27499,27501,27528],{"className":27500},[285,286],[15,27502,27504,27525],{"className":27503},[290],[15,27505,27507],{"className":27506,"style":379},[294],[15,27508,27510,27513],{"style":27509},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[15,27511],{"className":27512,"style":303},[302],[15,27514,27516],{"className":27515},[307,308,309,310],[15,27517,27519,27522],{"className":27518},[59,310],[15,27520,23743],{"className":27521,"style":24153},[59,60,310],[15,27523,25737],{"className":27524,"style":25861},[59,60,310],[15,27526,318],{"className":27527},[317],[15,27529,27531],{"className":27530},[290],[15,27532,27534],{"className":27533,"style":7968},[294],[15,27535],{},[15,27537,113],{"className":27538},[146],[15,27540,769],{"className":27541},[59,60],[15,27543,120],{"className":27544},[153],[15,27546],{"className":27547,"style":406},[157],[15,27549,244],{"className":27550},[59,60],[15,27552,774],{"className":27553},[59,60],[15,27555,551],{"className":27556},[573],[15,27558,318],{"className":27559},[317],[15,27561,27563],{"className":27562},[290],[15,27564,27566],{"className":27565,"style":27119},[294],[15,27567],{},[11,27569,27570],{},"其中",[15,27572,27574],{"className":27573,"translate":19},[180],[15,27575,27577,27661],{"className":27576,"translate":19},[18],[15,27578,27580],{"className":27579},[23],[25,27581,27582],{"xmlns":27,"display":189},[29,27583,27584,27658],{},[32,27585,27586,27596,27598,27600,27602,27604,27610,27656],{},[195,27587,27588,27590],{},[35,27589,37],{},[32,27591,27592,27594],{},[35,27593,23743],{},[35,27595,25737],{},[110,27597,113],{"stretchy":112},[35,27599,769],{},[110,27601,120],{"stretchy":112},[110,27603,123],{},[238,27605,27606,27608],{},[115,27607,117],{},[115,27609,2463],{},[32,27611,27612,27614,27616,27618,27620,27636,27638,27640,27642,27654],{},[110,27613,230],{"fence":46},[35,27615,769],{},[35,27617,4100],{},[110,27619,4103],{},[238,27621,27622,27628],{},[32,27623,27624,27626],{},[115,27625,2463],{},[35,27627,769],{},[32,27629,27630,27632,27634],{},[35,27631,769],{},[110,27633,2470],{},[115,27635,117],{},[110,27637,2470],{},[35,27639,4100],{},[110,27641,4103],{},[238,27643,27644,27646],{},[115,27645,2463],{},[32,27647,27648,27650,27652],{},[35,27649,769],{},[110,27651,2470],{},[115,27653,117],{},[110,27655,257],{"fence":46},[35,27657,4375],{"mathvariant":209},[39,27659,27660],{"encoding":41},"f_{JS}(t)=\\frac12\\left[\nt\\log\\frac{2t}{t+1}+\\log\\frac{2}{t+1}\\right].",[15,27662,27664,27734],{"className":27663,"ariaHidden":46},[45],[15,27665,27667,27670,27716,27719,27722,27725,27728,27731],{"className":27666},[50],[15,27668],{"className":27669,"style":139},[54],[15,27671,27673,27676],{"className":27672},[59],[15,27674,37],{"className":27675,"style":61},[59,60],[15,27677,27679],{"className":27678},[281],[15,27680,27682,27708],{"className":27681},[285,286],[15,27683,27685,27705],{"className":27684},[290],[15,27686,27688],{"className":27687,"style":379},[294],[15,27689,27690,27693],{"style":27509},[15,27691],{"className":27692,"style":303},[302],[15,27694,27696],{"className":27695},[307,308,309,310],[15,27697,27699,27702],{"className":27698},[59,310],[15,27700,23743],{"className":27701,"style":24153},[59,60,310],[15,27703,25737],{"className":27704,"style":25861},[59,60,310],[15,27706,318],{"className":27707},[317],[15,27709,27711],{"className":27710},[290],[15,27712,27714],{"className":27713,"style":7968},[294],[15,27715],{},[15,27717,113],{"className":27718},[146],[15,27720,769],{"className":27721},[59,60],[15,27723,120],{"className":27724},[153],[15,27726],{"className":27727,"style":158},[157],[15,27729,123],{"className":27730},[162],[15,27732],{"className":27733,"style":158},[157],[15,27735,27737,27740,27802,27805,28002,28005],{"className":27736},[50],[15,27738],{"className":27739,"style":359},[54],[15,27741,27743,27746,27799],{"className":27742},[59],[15,27744],{"className":27745},[146,441],[15,27747,27749],{"className":27748},[238],[15,27750,27752,27791],{"className":27751},[285,286],[15,27753,27755,27788],{"className":27754},[290],[15,27756,27758,27769,27777],{"className":27757,"style":22889},[294],[15,27759,27760,27763],{"style":457},[15,27761],{"className":27762,"style":461},[302],[15,27764,27766],{"className":27765},[59],[15,27767,2463],{"className":27768},[59],[15,27770,27771,27774],{"style":473},[15,27772],{"className":27773,"style":461},[302],[15,27775],{"className":27776,"style":481},[480],[15,27778,27779,27782],{"style":484},[15,27780],{"className":27781,"style":461},[302],[15,27783,27785],{"className":27784},[59],[15,27786,117],{"className":27787},[59],[15,27789,318],{"className":27790},[317],[15,27792,27794],{"className":27793},[290],[15,27795,27797],{"className":27796,"style":3778},[294],[15,27798],{},[15,27800],{"className":27801},[153,441],[15,27803],{"className":27804,"style":406},[157],[15,27806,27808,27814,27817,27820,27825,27828,27905,27908,27911,27914,27919,27922,27996],{"className":27807},[410],[15,27809,27811],{"className":27810,"style":415},[146,414],[15,27812,230],{"className":27813},[419,309],[15,27815,769],{"className":27816},[59,60],[15,27818],{"className":27819,"style":406},[157],[15,27821,4154,27823],{"className":27822},[1484],[15,27824,4158],{"style":4157},[15,27826],{"className":27827,"style":406},[157],[15,27829,27831,27834,27902],{"className":27830},[59],[15,27832],{"className":27833},[146,441],[15,27835,27837],{"className":27836},[238],[15,27838,27840,27894],{"className":27839},[285,286],[15,27841,27843,27891],{"className":27842},[290],[15,27844,27846,27869,27877],{"className":27845,"style":22889},[294],[15,27847,27848,27851],{"style":457},[15,27849],{"className":27850,"style":461},[302],[15,27852,27854,27857,27860,27863,27866],{"className":27853},[59],[15,27855,769],{"className":27856},[59,60],[15,27858],{"className":27859,"style":2587},[157],[15,27861,2470],{"className":27862},[2591],[15,27864],{"className":27865,"style":2587},[157],[15,27867,117],{"className":27868},[59],[15,27870,27871,27874],{"style":473},[15,27872],{"className":27873,"style":461},[302],[15,27875],{"className":27876,"style":481},[480],[15,27878,27879,27882],{"style":484},[15,27880],{"className":27881,"style":461},[302],[15,27883,27885,27888],{"className":27884},[59],[15,27886,2463],{"className":27887},[59],[15,27889,769],{"className":27890},[59,60],[15,27892,318],{"className":27893},[317],[15,27895,27897],{"className":27896},[290],[15,27898,27900],{"className":27899,"style":17015},[294],[15,27901],{},[15,27903],{"className":27904},[153,441],[15,27906],{"className":27907,"style":2587},[157],[15,27909,2470],{"className":27910},[2591],[15,27912],{"className":27913,"style":2587},[157],[15,27915,4154,27917],{"className":27916},[1484],[15,27918,4158],{"style":4157},[15,27920],{"className":27921,"style":406},[157],[15,27923,27925,27928,27993],{"className":27924},[59],[15,27926],{"className":27927},[146,441],[15,27929,27931],{"className":27930},[238],[15,27932,27934,27985],{"className":27933},[285,286],[15,27935,27937,27982],{"className":27936},[290],[15,27938,27940,27963,27971],{"className":27939,"style":22889},[294],[15,27941,27942,27945],{"style":457},[15,27943],{"className":27944,"style":461},[302],[15,27946,27948,27951,27954,27957,27960],{"className":27947},[59],[15,27949,769],{"className":27950},[59,60],[15,27952],{"className":27953,"style":2587},[157],[15,27955,2470],{"className":27956},[2591],[15,27958],{"className":27959,"style":2587},[157],[15,27961,117],{"className":27962},[59],[15,27964,27965,27968],{"style":473},[15,27966],{"className":27967,"style":461},[302],[15,27969],{"className":27970,"style":481},[480],[15,27972,27973,27976],{"style":484},[15,27974],{"className":27975,"style":461},[302],[15,27977,27979],{"className":27978},[59],[15,27980,2463],{"className":27981},[59],[15,27983,318],{"className":27984},[317],[15,27986,27988],{"className":27987},[290],[15,27989,27991],{"className":27990,"style":17015},[294],[15,27992],{},[15,27994],{"className":27995},[153,441],[15,27997,27999],{"className":27998,"style":415},[153,414],[15,28000,257],{"className":28001},[419,309],[15,28003],{"className":28004,"style":406},[157],[15,28006,4375],{"className":28007},[59],[11,28009,28010],{},"整理得",[15,28012,28014],{"className":28013,"translate":19},[180],[15,28015,28017,28109],{"className":28016,"translate":19},[18],[15,28018,28020],{"className":28019},[23],[25,28021,28022],{"xmlns":27,"display":189},[29,28023,28024,28106],{},[32,28025,28026],{},[28027,28028,28030],"menclose",{"notation":28029},"box",[1255,28031,28032],{"scriptlevel":126,"displaystyle":112},[1255,28033,28034],{"scriptlevel":126,"displaystyle":112},[1255,28035,28036],{"scriptlevel":126,"displaystyle":46},[32,28037,28038,28040,28050,28052,28054,28056,28058,28064,28066,28068,28070,28072,28074,28076,28078,28080,28082,28084,28086,28088,28090,28102,28104],{},[1297,28039,15904],{},[195,28041,28042,28044],{},[35,28043,37],{},[32,28045,28046,28048],{},[35,28047,23743],{},[35,28049,25737],{},[110,28051,113],{"stretchy":112},[35,28053,769],{},[110,28055,120],{"stretchy":112},[110,28057,123],{},[238,28059,28060,28062],{},[115,28061,117],{},[115,28063,2463],{},[110,28065,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,28067,769],{},[35,28069,4100],{},[110,28071,4103],{},[35,28073,769],{},[110,28075,4813],{},[110,28077,113],{"stretchy":112},[35,28079,769],{},[110,28081,2470],{},[115,28083,117],{},[110,28085,120],{"stretchy":112},[35,28087,4100],{},[110,28089,4103],{},[238,28091,28092,28100],{},[32,28093,28094,28096,28098],{},[35,28095,769],{},[110,28097,2470],{},[115,28099,117],{},[115,28101,2463],{},[110,28103,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1297,28105,15904],{},[39,28107,28108],{"encoding":41},"\\boxed{\\;\nf_{JS}(t)=\\frac12\\Big[\nt\\log t-(t+1)\\log\\frac{t+1}{2}\\Big]\n\\;}",[15,28110,28112],{"className":28111,"ariaHidden":46},[45],[15,28113,28115,28119],{"className":28114},[50],[15,28116],{"className":28117,"style":28118},[54],"height:2.6874em;vertical-align:-1.026em;",[15,28120,28122],{"className":28121},[59],[15,28123,28125,28439],{"className":28124},[285,286],[15,28126,28128,28436],{"className":28127},[290],[15,28129,28132,28425],{"className":28130,"style":28131},[294],"height:1.6614em;",[15,28133,28135,28139],{"style":28134},"top:-4.6874em;",[15,28136],{"className":28137,"style":28138},[302],"height:4.6874em;",[15,28140,28143],{"className":28141},[28142],"boxpad",[15,28144,28146],{"className":28145},[59],[15,28147,28149,28152,28198,28201,28204,28207,28210,28213,28216,28278,28284,28287,28290,28295,28298,28301,28304,28307,28310,28313,28316,28319,28322,28325,28328,28331,28334,28339,28342,28416,28422],{"className":28148},[59],[15,28150],{"className":28151,"style":158},[157],[15,28153,28155,28158],{"className":28154},[59],[15,28156,37],{"className":28157,"style":61},[59,60],[15,28159,28161],{"className":28160},[281],[15,28162,28164,28190],{"className":28163},[285,286],[15,28165,28167,28187],{"className":28166},[290],[15,28168,28170],{"className":28169,"style":379},[294],[15,28171,28172,28175],{"style":27509},[15,28173],{"className":28174,"style":303},[302],[15,28176,28178],{"className":28177},[307,308,309,310],[15,28179,28181,28184],{"className":28180},[59,310],[15,28182,23743],{"className":28183,"style":24153},[59,60,310],[15,28185,25737],{"className":28186,"style":25861},[59,60,310],[15,28188,318],{"className":28189},[317],[15,28191,28193],{"className":28192},[290],[15,28194,28196],{"className":28195,"style":7968},[294],[15,28197],{},[15,28199,113],{"className":28200},[146],[15,28202,769],{"className":28203},[59,60],[15,28205,120],{"className":28206},[153],[15,28208],{"className":28209,"style":158},[157],[15,28211,123],{"className":28212},[162],[15,28214],{"className":28215,"style":158},[157],[15,28217,28219,28222,28275],{"className":28218},[59],[15,28220],{"className":28221},[146,441],[15,28223,28225],{"className":28224},[238],[15,28226,28228,28267],{"className":28227},[285,286],[15,28229,28231,28264],{"className":28230},[290],[15,28232,28234,28245,28253],{"className":28233,"style":22889},[294],[15,28235,28236,28239],{"style":457},[15,28237],{"className":28238,"style":461},[302],[15,28240,28242],{"className":28241},[59],[15,28243,2463],{"className":28244},[59],[15,28246,28247,28250],{"style":473},[15,28248],{"className":28249,"style":461},[302],[15,28251],{"className":28252,"style":481},[480],[15,28254,28255,28258],{"style":484},[15,28256],{"className":28257,"style":461},[302],[15,28259,28261],{"className":28260},[59],[15,28262,117],{"className":28263},[59],[15,28265,318],{"className":28266},[317],[15,28268,28270],{"className":28269},[290],[15,28271,28273],{"className":28272,"style":3778},[294],[15,28274],{},[15,28276],{"className":28277},[153,441],[15,28279,28281],{"className":28280},[59],[15,28282,230],{"className":28283},[419,3720],[15,28285,769],{"className":28286},[59,60],[15,28288],{"className":28289,"style":406},[157],[15,28291,4154,28293],{"className":28292},[1484],[15,28294,4158],{"style":4157},[15,28296],{"className":28297,"style":406},[157],[15,28299,769],{"className":28300},[59,60],[15,28302],{"className":28303,"style":2587},[157],[15,28305,4813],{"className":28306},[2591],[15,28308],{"className":28309,"style":2587},[157],[15,28311,113],{"className":28312},[146],[15,28314,769],{"className":28315},[59,60],[15,28317],{"className":28318,"style":2587},[157],[15,28320,2470],{"className":28321},[2591],[15,28323],{"className":28324,"style":2587},[157],[15,28326,117],{"className":28327},[59],[15,28329,120],{"className":28330},[153],[15,28332],{"className":28333,"style":406},[157],[15,28335,4154,28337],{"className":28336},[1484],[15,28338,4158],{"style":4157},[15,28340],{"className":28341,"style":406},[157],[15,28343,28345,28348,28413],{"className":28344},[59],[15,28346],{"className":28347},[146,441],[15,28349,28351],{"className":28350},[238],[15,28352,28354,28405],{"className":28353},[285,286],[15,28355,28357,28402],{"className":28356},[290],[15,28358,28360,28371,28379],{"className":28359,"style":22889},[294],[15,28361,28362,28365],{"style":457},[15,28363],{"className":28364,"style":461},[302],[15,28366,28368],{"className":28367},[59],[15,28369,2463],{"className":28370},[59],[15,28372,28373,28376],{"style":473},[15,28374],{"className":28375,"style":461},[302],[15,28377],{"className":28378,"style":481},[480],[15,28380,28381,28384],{"style":484},[15,28382],{"className":28383,"style":461},[302],[15,28385,28387,28390,28393,28396,28399],{"className":28386},[59],[15,28388,769],{"className":28389},[59,60],[15,28391],{"className":28392,"style":2587},[157],[15,28394,2470],{"className":28395},[2591],[15,28397],{"className":28398,"style":2587},[157],[15,28400,117],{"className":28401},[59],[15,28403,318],{"className":28404},[317],[15,28406,28408],{"className":28407},[290],[15,28409,28411],{"className":28410,"style":3778},[294],[15,28412],{},[15,28414],{"className":28415},[153,441],[15,28417,28419],{"className":28418},[59],[15,28420,257],{"className":28421},[419,3720],[15,28423],{"className":28424,"style":158},[157],[15,28426,28428,28431],{"style":28427},"top:-3.6614em;",[15,28429],{"className":28430,"style":28138},[302],[15,28432],{"className":28433,"style":28435},[6315,28434],"fbox","height:2.6874em;border-style:solid;border-width:0.04em;",[15,28437,318],{"className":28438},[317],[15,28440,28442],{"className":28441},[290],[15,28443,28446],{"className":28444,"style":28445},[294],"height:1.026em;",[15,28447],{},[11,28449,28450,28451,28716],{},"它满足 ",[15,28452,28454,28510],{"className":28453,"translate":19},[18],[15,28455,28457],{"className":28456},[23],[25,28458,28459],{"xmlns":27},[29,28460,28461,28507],{},[32,28462,28463,28473,28475,28477,28479,28481,28487,28489,28491,28493,28495,28497,28499,28501,28503,28505],{},[195,28464,28465,28467],{},[35,28466,37],{},[32,28468,28469,28471],{},[35,28470,23743],{},[35,28472,25737],{},[110,28474,113],{"stretchy":112},[115,28476,117],{},[110,28478,120],{"stretchy":112},[110,28480,123],{},[238,28482,28483,28485],{},[115,28484,117],{},[115,28486,2463],{},[110,28488,230],{"stretchy":112},[115,28490,126],{},[110,28492,4813],{},[115,28494,2463],{},[35,28496,4100],{},[110,28498,4103],{},[115,28500,117],{},[110,28502,257],{"stretchy":112},[110,28504,123],{},[115,28506,126],{},[39,28508,28509],{"encoding":41},"f_{JS}(1)=\\frac12[0-2\\log1]=0",[15,28511,28513,28583,28672,28707],{"className":28512,"ariaHidden":46},[45],[15,28514,28516,28519,28565,28568,28571,28574,28577,28580],{"className":28515},[50],[15,28517],{"className":28518,"style":139},[54],[15,28520,28522,28525],{"className":28521},[59],[15,28523,37],{"className":28524,"style":61},[59,60],[15,28526,28528],{"className":28527},[281],[15,28529,28531,28557],{"className":28530},[285,286],[15,28532,28534,28554],{"className":28533},[290],[15,28535,28537],{"className":28536,"style":379},[294],[15,28538,28539,28542],{"style":27509},[15,28540],{"className":28541,"style":303},[302],[15,28543,28545],{"className":28544},[307,308,309,310],[15,28546,28548,28551],{"className":28547},[59,310],[15,28549,23743],{"className":28550,"style":24153},[59,60,310],[15,28552,25737],{"className":28553,"style":25861},[59,60,310],[15,28555,318],{"className":28556},[317],[15,28558,28560],{"className":28559},[290],[15,28561,28563],{"className":28562,"style":7968},[294],[15,28564],{},[15,28566,113],{"className":28567},[146],[15,28569,117],{"className":28570},[59],[15,28572,120],{"className":28573},[153],[15,28575],{"className":28576,"style":158},[157],[15,28578,123],{"className":28579},[162],[15,28581],{"className":28582,"style":158},[157],[15,28584,28586,28589,28657,28660,28663,28666,28669],{"className":28585},[50],[15,28587],{"className":28588,"style":2505},[54],[15,28590,28592,28595,28654],{"className":28591},[59],[15,28593],{"className":28594},[146,441],[15,28596,28598],{"className":28597},[238],[15,28599,28601,28646],{"className":28600},[285,286],[15,28602,28604,28643],{"className":28603},[290],[15,28605,28607,28621,28629],{"className":28606,"style":2524},[294],[15,28608,28609,28612],{"style":2527},[15,28610],{"className":28611,"style":461},[302],[15,28613,28615],{"className":28614},[307,308,309,310],[15,28616,28618],{"className":28617},[59,310],[15,28619,2463],{"className":28620},[59,310],[15,28622,28623,28626],{"style":473},[15,28624],{"className":28625,"style":461},[302],[15,28627],{"className":28628,"style":481},[480],[15,28630,28631,28634],{"style":2550},[15,28632],{"className":28633,"style":461},[302],[15,28635,28637],{"className":28636},[307,308,309,310],[15,28638,28640],{"className":28639},[59,310],[15,28641,117],{"className":28642},[59,310],[15,28644,318],{"className":28645},[317],[15,28647,28649],{"className":28648},[290],[15,28650,28652],{"className":28651,"style":2572},[294],[15,28653],{},[15,28655],{"className":28656},[153,441],[15,28658,230],{"className":28659},[146],[15,28661,126],{"className":28662},[59],[15,28664],{"className":28665,"style":2587},[157],[15,28667,4813],{"className":28668},[2591],[15,28670],{"className":28671,"style":2587},[157],[15,28673,28675,28678,28681,28684,28689,28692,28695,28698,28701,28704],{"className":28674},[50],[15,28676],{"className":28677,"style":139},[54],[15,28679,2463],{"className":28680},[59],[15,28682],{"className":28683,"style":406},[157],[15,28685,4154,28687],{"className":28686},[1484],[15,28688,4158],{"style":4157},[15,28690],{"className":28691,"style":406},[157],[15,28693,117],{"className":28694},[59],[15,28696,257],{"className":28697},[153],[15,28699],{"className":28700,"style":158},[157],[15,28702,123],{"className":28703},[162],[15,28705],{"className":28706,"style":158},[157],[15,28708,28710,28713],{"className":28709},[50],[15,28711],{"className":28712,"style":172},[54],[15,28714,126],{"className":28715},[59],"，且",[15,28718,28720],{"className":28719,"translate":19},[180],[15,28721,28723,28915],{"className":28722,"translate":19},[18],[15,28724,28726],{"className":28725},[23],[25,28727,28728],{"xmlns":27,"display":189},[29,28729,28730,28912],{},[1243,28731,28732,28796,28866],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,28733,28734,28758],{},[1252,28735,28736],{},[1255,28737,28738],{"scriptlevel":126,"displaystyle":46},[32,28739,28740,28752,28754,28756],{},[7553,28741,28742,28744,28750],{},[35,28743,37],{},[32,28745,28746,28748],{},[35,28747,23743],{},[35,28749,25737],{},[110,28751,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,28753,113],{"stretchy":112},[35,28755,769],{},[110,28757,120],{"stretchy":112},[1252,28759,28760],{},[1255,28761,28762],{"scriptlevel":126,"displaystyle":46},[32,28763,28764,28766,28768,28774,28776,28778,28794],{},[32,28765],{},[110,28767,123],{},[238,28769,28770,28772],{},[115,28771,117],{},[115,28773,2463],{},[35,28775,4100],{},[110,28777,4103],{},[238,28779,28780,28786],{},[32,28781,28782,28784],{},[115,28783,2463],{},[35,28785,769],{},[32,28787,28788,28790,28792],{},[35,28789,769],{},[110,28791,2470],{},[115,28793,117],{},[110,28795,551],{"separator":46},[1249,28797,28798,28826],{},[1252,28799,28800],{},[1255,28801,28802],{"scriptlevel":126,"displaystyle":46},[32,28803,28804,28820,28822,28824],{},[7553,28805,28806,28808,28814],{},[35,28807,37],{},[32,28809,28810,28812],{},[35,28811,23743],{},[35,28813,25737],{},[32,28815,28816,28818],{},[110,28817,6820],{"mathvariant":209},[110,28819,6820],{"mathvariant":209},[110,28821,113],{"stretchy":112},[35,28823,769],{},[110,28825,120],{"stretchy":112},[1252,28827,28828],{},[1255,28829,28830],{"scriptlevel":126,"displaystyle":46},[32,28831,28832,28834,28836,28842,28844,28850,28852,28864],{},[32,28833],{},[110,28835,123],{},[238,28837,28838,28840],{},[115,28839,117],{},[115,28841,2463],{},[110,28843,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[238,28845,28846,28848],{},[115,28847,117],{},[35,28849,769],{},[110,28851,4813],{},[238,28853,28854,28856],{},[115,28855,117],{},[32,28857,28858,28860,28862],{},[35,28859,769],{},[110,28861,2470],{},[115,28863,117],{},[110,28865,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,28867,28868,28874],{},[1252,28869,28870],{},[1255,28871,28872],{"scriptlevel":126,"displaystyle":46},[32,28873],{},[1252,28875,28876],{},[1255,28877,28878],{"scriptlevel":126,"displaystyle":46},[32,28879,28880,28882,28884,28886,28906,28908,28910],{},[32,28881],{},[157,28883],{"width":3262},[110,28885,123],{},[238,28887,28888,28890],{},[115,28889,117],{},[32,28891,28892,28894,28896,28898,28900,28902,28904],{},[115,28893,2463],{},[35,28895,769],{},[110,28897,113],{"stretchy":112},[35,28899,769],{},[110,28901,2470],{},[115,28903,117],{},[110,28905,120],{"stretchy":112},[110,28907,2903],{},[115,28909,126],{},[110,28911,551],{"separator":46},[39,28913,28914],{"encoding":41},"\\begin{aligned}\nf_{JS}'(t)&=\\frac12\\log\\frac{2t}{t+1},\\\\[2pt]\nf_{JS}''(t)&=\\frac12\\Big(\n\\frac1t-\\frac1{t+1}\\Big)\\\\\n&\\qquad=\\frac{1}{2t(t+1)}>0,\n\\end{aligned}",[15,28916,28918],{"className":28917,"ariaHidden":46},[45],[15,28919,28921,28925],{"className":28920},[50],[15,28922],{"className":28923,"style":28924},[54],"height:7.039em;vertical-align:-3.2695em;",[15,28926,28928],{"className":28927},[59],[15,28929,28931,29122],{"className":28930},[1243],[15,28932,28934],{"className":28933},[1360],[15,28935,28937,29113],{"className":28936},[285,286],[15,28938,28940,29110],{"className":28939},[290],[15,28941,28944,29023,29101],{"className":28942,"style":28943},[294],"height:3.7695em;",[15,28945,28947,28950],{"style":28946},"top:-5.7695em;",[15,28948],{"className":28949,"style":22666},[302],[15,28951,28953,29014,29017,29020],{"className":28952},[59],[15,28954,28956,28959],{"className":28955},[59],[15,28957,37],{"className":28958,"style":61},[59,60],[15,28960,28962],{"className":28961},[281],[15,28963,28965,29006],{"className":28964},[285,286],[15,28966,28968,29003],{"className":28967},[290],[15,28969,28972,28989],{"className":28970,"style":28971},[294],"height:0.8019em;",[15,28973,28974,28977],{"style":8251},[15,28975],{"className":28976,"style":303},[302],[15,28978,28980],{"className":28979},[307,308,309,310],[15,28981,28983,28986],{"className":28982},[59,310],[15,28984,23743],{"className":28985,"style":24153},[59,60,310],[15,28987,25737],{"className":28988,"style":25861},[59,60,310],[15,28990,28991,28994],{"style":8277},[15,28992],{"className":28993,"style":303},[302],[15,28995,28997],{"className":28996},[307,308,309,310],[15,28998,29000],{"className":28999},[59,310],[15,29001,6820],{"className":29002},[59,310],[15,29004,318],{"className":29005},[317],[15,29007,29009],{"className":29008},[290],[15,29010,29012],{"className":29011,"style":8299},[294],[15,29013],{},[15,29015,113],{"className":29016},[146],[15,29018,769],{"className":29019},[59,60],[15,29021,120],{"className":29022},[153],[15,29024,29026,29029],{"style":29025},"top:-3.3787em;",[15,29027],{"className":29028,"style":22666},[302],[15,29030,29032,29092,29095,29098],{"className":29031},[59],[15,29033,29035,29038],{"className":29034},[59],[15,29036,37],{"className":29037,"style":61},[59,60],[15,29039,29041],{"className":29040},[281],[15,29042,29044,29084],{"className":29043},[285,286],[15,29045,29047,29081],{"className":29046},[290],[15,29048,29050,29067],{"className":29049,"style":28971},[294],[15,29051,29052,29055],{"style":8251},[15,29053],{"className":29054,"style":303},[302],[15,29056,29058],{"className":29057},[307,308,309,310],[15,29059,29061,29064],{"className":29060},[59,310],[15,29062,23743],{"className":29063,"style":24153},[59,60,310],[15,29065,25737],{"className":29066,"style":25861},[59,60,310],[15,29068,29069,29072],{"style":8277},[15,29070],{"className":29071,"style":303},[302],[15,29073,29075],{"className":29074},[307,308,309,310],[15,29076,29078],{"className":29077},[59,310],[15,29079,21748],{"className":29080},[59,310],[15,29082,318],{"className":29083},[317],[15,29085,29087],{"className":29086},[290],[15,29088,29090],{"className":29089,"style":8299},[294],[15,29091],{},[15,29093,113],{"className":29094},[146],[15,29096,769],{"className":29097},[59,60],[15,29099,120],{"className":29100},[153],[15,29102,29104,29107],{"style":29103},"top:-0.9879em;",[15,29105],{"className":29106,"style":22666},[302],[15,29108],{"className":29109},[59],[15,29111,318],{"className":29112},[317],[15,29114,29116],{"className":29115},[290],[15,29117,29120],{"className":29118,"style":29119},[294],"height:3.2695em;",[15,29121],{},[15,29123,29125],{"className":29124},[1451],[15,29126,29128,29673],{"className":29127},[285,286],[15,29129,29131,29670],{"className":29130},[290],[15,29132,29134,29307,29546],{"className":29133,"style":28943},[294],[15,29135,29136,29139],{"style":28946},[15,29137],{"className":29138,"style":22666},[302],[15,29140,29142,29145,29148,29151,29154,29216,29219,29224,29227,29304],{"className":29141},[59],[15,29143],{"className":29144},[59],[15,29146],{"className":29147,"style":158},[157],[15,29149,123],{"className":29150},[162],[15,29152],{"className":29153,"style":158},[157],[15,29155,29157,29160,29213],{"className":29156},[59],[15,29158],{"className":29159},[146,441],[15,29161,29163],{"className":29162},[238],[15,29164,29166,29205],{"className":29165},[285,286],[15,29167,29169,29202],{"className":29168},[290],[15,29170,29172,29183,29191],{"className":29171,"style":22889},[294],[15,29173,29174,29177],{"style":457},[15,29175],{"className":29176,"style":461},[302],[15,29178,29180],{"className":29179},[59],[15,29181,2463],{"className":29182},[59],[15,29184,29185,29188],{"style":473},[15,29186],{"className":29187,"style":461},[302],[15,29189],{"className":29190,"style":481},[480],[15,29192,29193,29196],{"style":484},[15,29194],{"className":29195,"style":461},[302],[15,29197,29199],{"className":29198},[59],[15,29200,117],{"className":29201},[59],[15,29203,318],{"className":29204},[317],[15,29206,29208],{"className":29207},[290],[15,29209,29211],{"className":29210,"style":3778},[294],[15,29212],{},[15,29214],{"className":29215},[153,441],[15,29217],{"className":29218,"style":406},[157],[15,29220,4154,29222],{"className":29221},[1484],[15,29223,4158],{"style":4157},[15,29225],{"className":29226,"style":406},[157],[15,29228,29230,29233,29301],{"className":29229},[59],[15,29231],{"className":29232},[146,441],[15,29234,29236],{"className":29235},[238],[15,29237,29239,29293],{"className":29238},[285,286],[15,29240,29242,29290],{"className":29241},[290],[15,29243,29245,29268,29276],{"className":29244,"style":22889},[294],[15,29246,29247,29250],{"style":457},[15,29248],{"className":29249,"style":461},[302],[15,29251,29253,29256,29259,29262,29265],{"className":29252},[59],[15,29254,769],{"className":29255},[59,60],[15,29257],{"className":29258,"style":2587},[157],[15,29260,2470],{"className":29261},[2591],[15,29263],{"className":29264,"style":2587},[157],[15,29266,117],{"className":29267},[59],[15,29269,29270,29273],{"style":473},[15,29271],{"className":29272,"style":461},[302],[15,29274],{"className":29275,"style":481},[480],[15,29277,29278,29281],{"style":484},[15,29279],{"className":29280,"style":461},[302],[15,29282,29284,29287],{"className":29283},[59],[15,29285,2463],{"className":29286},[59],[15,29288,769],{"className":29289},[59,60],[15,29291,318],{"className":29292},[317],[15,29294,29296],{"className":29295},[290],[15,29297,29299],{"className":29298,"style":17015},[294],[15,29300],{},[15,29302],{"className":29303},[153,441],[15,29305,551],{"className":29306},[573],[15,29308,29309,29312],{"style":29025},[15,29310],{"className":29311,"style":22666},[302],[15,29313,29315,29318,29321,29324,29327,29389,29395,29457,29460,29463,29466,29540],{"className":29314},[59],[15,29316],{"className":29317},[59],[15,29319],{"className":29320,"style":158},[157],[15,29322,123],{"className":29323},[162],[15,29325],{"className":29326,"style":158},[157],[15,29328,29330,29333,29386],{"className":29329},[59],[15,29331],{"className":29332},[146,441],[15,29334,29336],{"className":29335},[238],[15,29337,29339,29378],{"className":29338},[285,286],[15,29340,29342,29375],{"className":29341},[290],[15,29343,29345,29356,29364],{"className":29344,"style":22889},[294],[15,29346,29347,29350],{"style":457},[15,29348],{"className":29349,"style":461},[302],[15,29351,29353],{"className":29352},[59],[15,29354,2463],{"className":29355},[59],[15,29357,29358,29361],{"style":473},[15,29359],{"className":29360,"style":461},[302],[15,29362],{"className":29363,"style":481},[480],[15,29365,29366,29369],{"style":484},[15,29367],{"className":29368,"style":461},[302],[15,29370,29372],{"className":29371},[59],[15,29373,117],{"className":29374},[59],[15,29376,318],{"className":29377},[317],[15,29379,29381],{"className":29380},[290],[15,29382,29384],{"className":29383,"style":3778},[294],[15,29385],{},[15,29387],{"className":29388},[153,441],[15,29390,29392],{"className":29391},[59],[15,29393,113],{"className":29394},[419,3720],[15,29396,29398,29401,29454],{"className":29397},[59],[15,29399],{"className":29400},[146,441],[15,29402,29404],{"className":29403},[238],[15,29405,29407,29446],{"className":29406},[285,286],[15,29408,29410,29443],{"className":29409},[290],[15,29411,29413,29424,29432],{"className":29412,"style":22889},[294],[15,29414,29415,29418],{"style":457},[15,29416],{"className":29417,"style":461},[302],[15,29419,29421],{"className":29420},[59],[15,29422,769],{"className":29423},[59,60],[15,29425,29426,29429],{"style":473},[15,29427],{"className":29428,"style":461},[302],[15,29430],{"className":29431,"style":481},[480],[15,29433,29434,29437],{"style":484},[15,29435],{"className":29436,"style":461},[302],[15,29438,29440],{"className":29439},[59],[15,29441,117],{"className":29442},[59],[15,29444,318],{"className":29445},[317],[15,29447,29449],{"className":29448},[290],[15,29450,29452],{"className":29451,"style":3778},[294],[15,29453],{},[15,29455],{"className":29456},[153,441],[15,29458],{"className":29459,"style":2587},[157],[15,29461,4813],{"className":29462},[2591],[15,29464],{"className":29465,"style":2587},[157],[15,29467,29469,29472,29537],{"className":29468},[59],[15,29470],{"className":29471},[146,441],[15,29473,29475],{"className":29474},[238],[15,29476,29478,29529],{"className":29477},[285,286],[15,29479,29481,29526],{"className":29480},[290],[15,29482,29484,29507,29515],{"className":29483,"style":22889},[294],[15,29485,29486,29489],{"style":457},[15,29487],{"className":29488,"style":461},[302],[15,29490,29492,29495,29498,29501,29504],{"className":29491},[59],[15,29493,769],{"className":29494},[59,60],[15,29496],{"className":29497,"style":2587},[157],[15,29499,2470],{"className":29500},[2591],[15,29502],{"className":29503,"style":2587},[157],[15,29505,117],{"className":29506},[59],[15,29508,29509,29512],{"style":473},[15,29510],{"className":29511,"style":461},[302],[15,29513],{"className":29514,"style":481},[480],[15,29516,29517,29520],{"style":484},[15,29518],{"className":29519,"style":461},[302],[15,29521,29523],{"className":29522},[59],[15,29524,117],{"className":29525},[59],[15,29527,318],{"className":29528},[317],[15,29530,29532],{"className":29531},[290],[15,29533,29535],{"className":29534,"style":17015},[294],[15,29536],{},[15,29538],{"className":29539},[153,441],[15,29541,29543],{"className":29542},[59],[15,29544,120],{"className":29545},[419,3720],[15,29547,29548,29551],{"style":29103},[15,29549],{"className":29550,"style":22666},[302],[15,29552,29554,29557,29560,29563,29566,29569,29655,29658,29661,29664,29667],{"className":29553},[59],[15,29555],{"className":29556},[59],[15,29558],{"className":29559,"style":3634},[157],[15,29561],{"className":29562,"style":158},[157],[15,29564,123],{"className":29565},[162],[15,29567],{"className":29568,"style":158},[157],[15,29570,29572,29575,29652],{"className":29571},[59],[15,29573],{"className":29574},[146,441],[15,29576,29578],{"className":29577},[238],[15,29579,29581,29644],{"className":29580},[285,286],[15,29582,29584,29641],{"className":29583},[290],[15,29585,29587,29622,29630],{"className":29586,"style":22889},[294],[15,29588,29589,29592],{"style":457},[15,29590],{"className":29591,"style":461},[302],[15,29593,29595,29598,29601,29604,29607,29610,29613,29616,29619],{"className":29594},[59],[15,29596,2463],{"className":29597},[59],[15,29599,769],{"className":29600},[59,60],[15,29602,113],{"className":29603},[146],[15,29605,769],{"className":29606},[59,60],[15,29608],{"className":29609,"style":2587},[157],[15,29611,2470],{"className":29612},[2591],[15,29614],{"className":29615,"style":2587},[157],[15,29617,117],{"className":29618},[59],[15,29620,120],{"className":29621},[153],[15,29623,29624,29627],{"style":473},[15,29625],{"className":29626,"style":461},[302],[15,29628],{"className":29629,"style":481},[480],[15,29631,29632,29635],{"style":484},[15,29633],{"className":29634,"style":461},[302],[15,29636,29638],{"className":29637},[59],[15,29639,117],{"className":29640},[59],[15,29642,318],{"className":29643},[317],[15,29645,29647],{"className":29646},[290],[15,29648,29650],{"className":29649,"style":1601},[294],[15,29651],{},[15,29653],{"className":29654},[153,441],[15,29656],{"className":29657,"style":158},[157],[15,29659,2903],{"className":29660},[162],[15,29662],{"className":29663,"style":158},[157],[15,29665,126],{"className":29666},[59],[15,29668,551],{"className":29669},[573],[15,29671,318],{"className":29672},[317],[15,29674,29676],{"className":29675},[290],[15,29677,29679],{"className":29678,"style":29119},[294],[15,29680],{},[11,29682,29683,29684,6494,29687,29882,29883,29933],{},"故凸；并且",[1225,29685,29686],{},"对称",[15,29688,29690,29742],{"className":29689,"translate":19},[18],[15,29691,29693],{"className":29692},[23],[25,29694,29695],{"xmlns":27},[29,29696,29697,29739],{},[32,29698,29699,29701,29711,29713,29715,29717,29719,29721,29723,29733,29735,29737],{},[35,29700,769],{},[195,29702,29703,29705],{},[35,29704,37],{},[32,29706,29707,29709],{},[35,29708,23743],{},[35,29710,25737],{},[110,29712,113],{"stretchy":112},[115,29714,117],{},[35,29716,941],{"mathvariant":209},[35,29718,769],{},[110,29720,120],{"stretchy":112},[110,29722,123],{},[195,29724,29725,29727],{},[35,29726,37],{},[32,29728,29729,29731],{},[35,29730,23743],{},[35,29732,25737],{},[110,29734,113],{"stretchy":112},[35,29736,769],{},[110,29738,120],{"stretchy":112},[39,29740,29741],{"encoding":41},"t f_{JS}(1\u002Ft)=f_{JS}(t)",[15,29743,29745,29821],{"className":29744,"ariaHidden":46},[45],[15,29746,29748,29751,29754,29800,29803,29806,29809,29812,29815,29818],{"className":29747},[50],[15,29749],{"className":29750,"style":139},[54],[15,29752,769],{"className":29753},[59,60],[15,29755,29757,29760],{"className":29756},[59],[15,29758,37],{"className":29759,"style":61},[59,60],[15,29761,29763],{"className":29762},[281],[15,29764,29766,29792],{"className":29765},[285,286],[15,29767,29769,29789],{"className":29768},[290],[15,29770,29772],{"className":29771,"style":379},[294],[15,29773,29774,29777],{"style":27509},[15,29775],{"className":29776,"style":303},[302],[15,29778,29780],{"className":29779},[307,308,309,310],[15,29781,29783,29786],{"className":29782},[59,310],[15,29784,23743],{"className":29785,"style":24153},[59,60,310],[15,29787,25737],{"className":29788,"style":25861},[59,60,310],[15,29790,318],{"className":29791},[317],[15,29793,29795],{"className":29794},[290],[15,29796,29798],{"className":29797,"style":7968},[294],[15,29799],{},[15,29801,113],{"className":29802},[146],[15,29804,8589],{"className":29805},[59],[15,29807,769],{"className":29808},[59,60],[15,29810,120],{"className":29811},[153],[15,29813],{"className":29814,"style":158},[157],[15,29816,123],{"className":29817},[162],[15,29819],{"className":29820,"style":158},[157],[15,29822,29824,29827,29873,29876,29879],{"className":29823},[50],[15,29825],{"className":29826,"style":139},[54],[15,29828,29830,29833],{"className":29829},[59],[15,29831,37],{"className":29832,"style":61},[59,60],[15,29834,29836],{"className":29835},[281],[15,29837,29839,29865],{"className":29838},[285,286],[15,29840,29842,29862],{"className":29841},[290],[15,29843,29845],{"className":29844,"style":379},[294],[15,29846,29847,29850],{"style":27509},[15,29848],{"className":29849,"style":303},[302],[15,29851,29853],{"className":29852},[307,308,309,310],[15,29854,29856,29859],{"className":29855},[59,310],[15,29857,23743],{"className":29858,"style":24153},[59,60,310],[15,29860,25737],{"className":29861,"style":25861},[59,60,310],[15,29863,318],{"className":29864},[317],[15,29866,29868],{"className":29867},[290],[15,29869,29871],{"className":29870,"style":7968},[294],[15,29872],{},[15,29874,113],{"className":29875},[146],[15,29877,769],{"className":29878},[59,60],[15,29880,120],{"className":29881},[153],"。因此当 ",[15,29884,29886,29903],{"className":29885,"translate":19},[18],[15,29887,29889],{"className":29888},[23],[25,29890,29891],{"xmlns":27},[29,29892,29893,29901],{},[32,29894,29895,29897,29899],{},[35,29896,206],{},[110,29898,714],{},[35,29900,213],{},[39,29902,719],{"encoding":41},[15,29904,29906,29924],{"className":29905,"ariaHidden":46},[45],[15,29907,29909,29912,29915,29918,29921],{"className":29908},[50],[15,29910],{"className":29911,"style":729},[54],[15,29913,206],{"className":29914,"style":334},[59,60],[15,29916],{"className":29917,"style":158},[157],[15,29919,714],{"className":29920},[162],[15,29922],{"className":29923,"style":158},[157],[15,29925,29927,29930],{"className":29926},[50],[15,29928],{"className":29929,"style":566},[54],[15,29931,213],{"className":29932},[59,60]," 时",[15,29935,29937],{"className":29936,"translate":19},[180],[15,29938,29940,30068],{"className":29939,"translate":19},[18],[15,29941,29943],{"className":29942},[23],[25,29944,29945],{"xmlns":27,"display":189},[29,29946,29947,30065],{},[32,29948,29949,29959,29961,29963,29965,29967,29969,29971,29985,29987,29989,29991,29993,29995,29997,30003,30009,30011,30013,30015,30017,30019,30021,30027,30033,30035,30037,30039,30041,30043,30045,30047,30049,30051,30053,30055,30057,30059,30061,30063],{},[195,29950,29951,29953],{},[35,29952,199],{},[32,29954,29955,29957],{},[35,29956,23743],{},[35,29958,25737],{},[110,29960,113],{"stretchy":112},[35,29962,206],{},[35,29964,210],{"mathvariant":209},[35,29966,213],{},[110,29968,120],{"stretchy":112},[110,29970,123],{},[195,29972,29973,29975],{},[35,29974,199],{},[195,29976,29977,29979],{},[35,29978,37],{},[32,29980,29981,29983],{},[35,29982,23743],{},[35,29984,25737],{},[110,29986,113],{"stretchy":112},[35,29988,206],{},[35,29990,210],{"mathvariant":209},[35,29992,213],{},[110,29994,120],{"stretchy":112},[110,29996,123],{},[238,29998,29999,30001],{},[115,30000,117],{},[115,30002,2463],{},[195,30004,30005,30007],{},[35,30006,199],{},[35,30008,37],{},[110,30010,113],{"stretchy":112},[35,30012,206],{},[35,30014,210],{"mathvariant":209},[35,30016,25567],{},[110,30018,120],{"stretchy":112},[110,30020,2470],{},[238,30022,30023,30025],{},[115,30024,117],{},[115,30026,2463],{},[195,30028,30029,30031],{},[35,30030,199],{},[35,30032,37],{},[110,30034,113],{"stretchy":112},[35,30036,213],{},[35,30038,210],{"mathvariant":209},[35,30040,25567],{},[110,30042,120],{"stretchy":112},[110,30044,551],{"separator":46},[157,30046],{"width":3262},[110,30048,113],{"stretchy":112},[35,30050,37],{},[110,30052,123],{},[35,30054,769],{},[35,30056,4100],{},[110,30058,4103],{},[35,30060,769],{},[110,30062,120],{"stretchy":112},[110,30064,551],{"separator":46},[39,30066,30067],{"encoding":41},"D_{JS}(P\\|Q)=D_{f_{JS}}(P\\|Q)\n=\\frac12D_f(P\\|M)\n+\\frac12D_f(Q\\|M),\\qquad(f=t\\log t),",[15,30069,30071,30147,30267,30399,30546],{"className":30070,"ariaHidden":46},[45],[15,30072,30074,30077,30123,30126,30129,30132,30135,30138,30141,30144],{"className":30073},[50],[15,30075],{"className":30076,"style":139},[54],[15,30078,30080,30083],{"className":30079},[59],[15,30081,199],{"className":30082,"style":277},[59,60],[15,30084,30086],{"className":30085},[281],[15,30087,30089,30115],{"className":30088},[285,286],[15,30090,30092,30112],{"className":30091},[290],[15,30093,30095],{"className":30094,"style":379},[294],[15,30096,30097,30100],{"style":298},[15,30098],{"className":30099,"style":303},[302],[15,30101,30103],{"className":30102},[307,308,309,310],[15,30104,30106,30109],{"className":30105},[59,310],[15,30107,23743],{"className":30108,"style":24153},[59,60,310],[15,30110,25737],{"className":30111,"style":25861},[59,60,310],[15,30113,318],{"className":30114},[317],[15,30116,30118],{"className":30117},[290],[15,30119,30121],{"className":30120,"style":7968},[294],[15,30122],{},[15,30124,113],{"className":30125},[146],[15,30127,206],{"className":30128,"style":334},[59,60],[15,30130,210],{"className":30131},[59],[15,30133,213],{"className":30134},[59,60],[15,30136,120],{"className":30137},[153],[15,30139],{"className":30140,"style":158},[157],[15,30142,123],{"className":30143},[162],[15,30145],{"className":30146,"style":158},[157],[15,30148,30150,30153,30243,30246,30249,30252,30255,30258,30261,30264],{"className":30149},[50],[15,30151],{"className":30152,"style":270},[54],[15,30154,30156,30159],{"className":30155},[59],[15,30157,199],{"className":30158,"style":277},[59,60],[15,30160,30162],{"className":30161},[281],[15,30163,30165,30235],{"className":30164},[285,286],[15,30166,30168,30232],{"className":30167},[290],[15,30169,30171],{"className":30170,"style":295},[294],[15,30172,30173,30176],{"style":298},[15,30174],{"className":30175,"style":303},[302],[15,30177,30179],{"className":30178},[307,308,309,310],[15,30180,30182],{"className":30181},[59,310],[15,30183,30185,30188],{"className":30184},[59,310],[15,30186,37],{"className":30187,"style":61},[59,60,310],[15,30189,30191],{"className":30190},[281],[15,30192,30194,30223],{"className":30193},[285,286],[15,30195,30197,30220],{"className":30196},[290],[15,30198,30200],{"className":30199,"style":6098},[294],[15,30201,30203,30207],{"style":30202},"top:-2.3567em;margin-left:-0.1076em;margin-right:0.0714em;",[15,30204],{"className":30205,"style":30206},[302],"height:2.5em;",[15,30208,30211],{"className":30209},[307,30210,9674,310],"reset-size3",[15,30212,30214,30217],{"className":30213},[59,310],[15,30215,23743],{"className":30216,"style":24153},[59,60,310],[15,30218,25737],{"className":30219,"style":25861},[59,60,310],[15,30221,318],{"className":30222},[317],[15,30224,30226],{"className":30225},[290],[15,30227,30230],{"className":30228,"style":30229},[294],"height:0.1433em;",[15,30231],{},[15,30233,318],{"className":30234},[317],[15,30236,30238],{"className":30237},[290],[15,30239,30241],{"className":30240,"style":325},[294],[15,30242],{},[15,30244,113],{"className":30245},[146],[15,30247,206],{"className":30248,"style":334},[59,60],[15,30250,210],{"className":30251},[59],[15,30253,213],{"className":30254},[59,60],[15,30256,120],{"className":30257},[153],[15,30259],{"className":30260,"style":158},[157],[15,30262,123],{"className":30263},[162],[15,30265],{"className":30266,"style":158},[157],[15,30268,30270,30273,30335,30375,30378,30381,30384,30387,30390,30393,30396],{"className":30269},[50],[15,30271],{"className":30272,"style":25903},[54],[15,30274,30276,30279,30332],{"className":30275},[59],[15,30277],{"className":30278},[146,441],[15,30280,30282],{"className":30281},[238],[15,30283,30285,30324],{"className":30284},[285,286],[15,30286,30288,30321],{"className":30287},[290],[15,30289,30291,30302,30310],{"className":30290,"style":22889},[294],[15,30292,30293,30296],{"style":457},[15,30294],{"className":30295,"style":461},[302],[15,30297,30299],{"className":30298},[59],[15,30300,2463],{"className":30301},[59],[15,30303,30304,30307],{"style":473},[15,30305],{"className":30306,"style":461},[302],[15,30308],{"className":30309,"style":481},[480],[15,30311,30312,30315],{"style":484},[15,30313],{"className":30314,"style":461},[302],[15,30316,30318],{"className":30317},[59],[15,30319,117],{"className":30320},[59],[15,30322,318],{"className":30323},[317],[15,30325,30327],{"className":30326},[290],[15,30328,30330],{"className":30329,"style":3778},[294],[15,30331],{},[15,30333],{"className":30334},[153,441],[15,30336,30338,30341],{"className":30337},[59],[15,30339,199],{"className":30340,"style":277},[59,60],[15,30342,30344],{"className":30343},[281],[15,30345,30347,30367],{"className":30346},[285,286],[15,30348,30350,30364],{"className":30349},[290],[15,30351,30353],{"className":30352,"style":295},[294],[15,30354,30355,30358],{"style":298},[15,30356],{"className":30357,"style":303},[302],[15,30359,30361],{"className":30360},[307,308,309,310],[15,30362,37],{"className":30363,"style":61},[59,60,310],[15,30365,318],{"className":30366},[317],[15,30368,30370],{"className":30369},[290],[15,30371,30373],{"className":30372,"style":325},[294],[15,30374],{},[15,30376,113],{"className":30377},[146],[15,30379,206],{"className":30380,"style":334},[59,60],[15,30382,210],{"className":30383},[59],[15,30385,25567],{"className":30386,"style":25601},[59,60],[15,30388,120],{"className":30389},[153],[15,30391],{"className":30392,"style":2587},[157],[15,30394,2470],{"className":30395},[2591],[15,30397],{"className":30398,"style":2587},[157],[15,30400,30402,30405,30467,30507,30510,30513,30516,30519,30522,30525,30528,30531,30534,30537,30540,30543],{"className":30401},[50],[15,30403],{"className":30404,"style":25903},[54],[15,30406,30408,30411,30464],{"className":30407},[59],[15,30409],{"className":30410},[146,441],[15,30412,30414],{"className":30413},[238],[15,30415,30417,30456],{"className":30416},[285,286],[15,30418,30420,30453],{"className":30419},[290],[15,30421,30423,30434,30442],{"className":30422,"style":22889},[294],[15,30424,30425,30428],{"style":457},[15,30426],{"className":30427,"style":461},[302],[15,30429,30431],{"className":30430},[59],[15,30432,2463],{"className":30433},[59],[15,30435,30436,30439],{"style":473},[15,30437],{"className":30438,"style":461},[302],[15,30440],{"className":30441,"style":481},[480],[15,30443,30444,30447],{"style":484},[15,30445],{"className":30446,"style":461},[302],[15,30448,30450],{"className":30449},[59],[15,30451,117],{"className":30452},[59],[15,30454,318],{"className":30455},[317],[15,30457,30459],{"className":30458},[290],[15,30460,30462],{"className":30461,"style":3778},[294],[15,30463],{},[15,30465],{"className":30466},[153,441],[15,30468,30470,30473],{"className":30469},[59],[15,30471,199],{"className":30472,"style":277},[59,60],[15,30474,30476],{"className":30475},[281],[15,30477,30479,30499],{"className":30478},[285,286],[15,30480,30482,30496],{"className":30481},[290],[15,30483,30485],{"className":30484,"style":295},[294],[15,30486,30487,30490],{"style":298},[15,30488],{"className":30489,"style":303},[302],[15,30491,30493],{"className":30492},[307,308,309,310],[15,30494,37],{"className":30495,"style":61},[59,60,310],[15,30497,318],{"className":30498},[317],[15,30500,30502],{"className":30501},[290],[15,30503,30505],{"className":30504,"style":325},[294],[15,30506],{},[15,30508,113],{"className":30509},[146],[15,30511,213],{"className":30512},[59,60],[15,30514,210],{"className":30515},[59],[15,30517,25567],{"className":30518,"style":25601},[59,60],[15,30520,120],{"className":30521},[153],[15,30523,551],{"className":30524},[573],[15,30526],{"className":30527,"style":3634},[157],[15,30529],{"className":30530,"style":406},[157],[15,30532,113],{"className":30533},[146],[15,30535,37],{"className":30536,"style":61},[59,60],[15,30538],{"className":30539,"style":158},[157],[15,30541,123],{"className":30542},[162],[15,30544],{"className":30545,"style":158},[157],[15,30547,30549,30552,30555,30558,30563,30566,30569,30572],{"className":30548},[50],[15,30550],{"className":30551,"style":139},[54],[15,30553,769],{"className":30554},[59,60],[15,30556],{"className":30557,"style":406},[157],[15,30559,4154,30561],{"className":30560},[1484],[15,30562,4158],{"style":4157},[15,30564],{"className":30565,"style":406},[157],[15,30567,769],{"className":30568},[59,60],[15,30570,120],{"className":30571},[153],[15,30573,551],{"className":30574},[573],[11,30576,30577,30578,30606,30607,30676,30677,30812],{},"两种写法完全一致：JS 既是「两个 f-散度（相对 ",[15,30579,30581,30594],{"className":30580,"translate":19},[18],[15,30582,30584],{"className":30583},[23],[25,30585,30586],{"xmlns":27},[29,30587,30588,30592],{},[32,30589,30590],{},[35,30591,25567],{},[39,30593,25567],{"encoding":41},[15,30595,30597],{"className":30596,"ariaHidden":46},[45],[15,30598,30600,30603],{"className":30599},[50],[15,30601],{"className":30602,"style":664},[54],[15,30604,25567],{"className":30605,"style":25601},[59,60],"）的平均」，也是「一个对称 f-散度」。原文「不是单一 ",[15,30608,30610,30627],{"className":30609,"translate":19},[18],[15,30611,30613],{"className":30612},[23],[25,30614,30615],{"xmlns":27},[29,30616,30617,30625],{},[32,30618,30619],{},[195,30620,30621,30623],{},[35,30622,199],{},[35,30624,37],{},[39,30626,4022],{"encoding":41},[15,30628,30630],{"className":30629,"ariaHidden":46},[45],[15,30631,30633,30636],{"className":30632},[50],[15,30634],{"className":30635,"style":4032},[54],[15,30637,30639,30642],{"className":30638},[59],[15,30640,199],{"className":30641,"style":277},[59,60],[15,30643,30645],{"className":30644},[281],[15,30646,30648,30668],{"className":30647},[285,286],[15,30649,30651,30665],{"className":30650},[290],[15,30652,30654],{"className":30653,"style":295},[294],[15,30655,30656,30659],{"style":298},[15,30657],{"className":30658,"style":303},[302],[15,30660,30662],{"className":30661},[307,308,309,310],[15,30663,37],{"className":30664,"style":61},[59,60,310],[15,30666,318],{"className":30667},[317],[15,30669,30671],{"className":30670},[290],[15,30672,30674],{"className":30673,"style":325},[294],[15,30675],{},"」的说法可修正为：",[1225,30678,30679,30680,30730,30731,30811],{},"在 ",[15,30681,30683,30700],{"className":30682,"translate":19},[18],[15,30684,30686],{"className":30685},[23],[25,30687,30688],{"xmlns":27},[29,30689,30690,30698],{},[32,30691,30692,30694,30696],{},[35,30693,206],{},[110,30695,714],{},[35,30697,213],{},[39,30699,719],{"encoding":41},[15,30701,30703,30721],{"className":30702,"ariaHidden":46},[45],[15,30704,30706,30709,30712,30715,30718],{"className":30705},[50],[15,30707],{"className":30708,"style":729},[54],[15,30710,206],{"className":30711,"style":334},[59,60],[15,30713],{"className":30714,"style":158},[157],[15,30716,714],{"className":30717},[162],[15,30719],{"className":30720,"style":158},[157],[15,30722,30724,30727],{"className":30723},[50],[15,30725],{"className":30726,"style":566},[54],[15,30728,213],{"className":30729},[59,60]," 时它是单一 ",[15,30732,30734,30756],{"className":30733,"translate":19},[18],[15,30735,30737],{"className":30736},[23],[25,30738,30739],{"xmlns":27},[29,30740,30741,30753],{},[32,30742,30743],{},[195,30744,30745,30747],{},[35,30746,37],{},[32,30748,30749,30751],{},[35,30750,23743],{},[35,30752,25737],{},[39,30754,30755],{"encoding":41},"f_{JS}",[15,30757,30759],{"className":30758,"ariaHidden":46},[45],[15,30760,30762,30765],{"className":30761},[50],[15,30763],{"className":30764,"style":55},[54],[15,30766,30768,30771],{"className":30767},[59],[15,30769,37],{"className":30770,"style":61},[59,60],[15,30772,30774],{"className":30773},[281],[15,30775,30777,30803],{"className":30776},[285,286],[15,30778,30780,30800],{"className":30779},[290],[15,30781,30783],{"className":30782,"style":379},[294],[15,30784,30785,30788],{"style":27509},[15,30786],{"className":30787,"style":303},[302],[15,30789,30791],{"className":30790},[307,308,309,310],[15,30792,30794,30797],{"className":30793},[59,310],[15,30795,23743],{"className":30796,"style":24153},[59,60,310],[15,30798,25737],{"className":30799,"style":25861},[59,60,310],[15,30801,318],{"className":30802},[317],[15,30804,30806],{"className":30805},[290],[15,30807,30809],{"className":30808,"style":7968},[294],[15,30810],{}," 的 f-散度","；一般情形则用下面的双变量形式。",[11,30814,30815,30818,30819,30860,30861,30976,30977,30980],{},[1225,30816,30817],{},"一般情形的双变量形式."," 当 ",[15,30820,30822,30839],{"className":30821,"translate":19},[18],[15,30823,30825],{"className":30824},[23],[25,30826,30827],{"xmlns":27},[29,30828,30829,30837],{},[32,30830,30831,30833,30835],{},[35,30832,206],{},[110,30834,551],{"separator":46},[35,30836,213],{},[39,30838,556],{"encoding":41},[15,30840,30842],{"className":30841,"ariaHidden":46},[45],[15,30843,30845,30848,30851,30854,30857],{"className":30844},[50],[15,30846],{"className":30847,"style":566},[54],[15,30849,206],{"className":30850,"style":334},[59,60],[15,30852,551],{"className":30853},[573],[15,30855],{"className":30856,"style":406},[157],[15,30858,213],{"className":30859},[59,60]," 支撑集可能分离时，",[15,30862,30864,30900],{"className":30863,"translate":19},[18],[15,30865,30867],{"className":30866},[23],[25,30868,30869],{"xmlns":27},[29,30870,30871,30897],{},[32,30872,30873,30875,30877,30879,30889,30891,30893,30895],{},[110,30874,113],{"stretchy":112},[35,30876,769],{},[110,30878,551],{"separator":46},[195,30880,30881,30883],{},[35,30882,37],{},[32,30884,30885,30887],{},[35,30886,23743],{},[35,30888,25737],{},[110,30890,113],{"stretchy":112},[35,30892,769],{},[110,30894,120],{"stretchy":112},[110,30896,120],{"stretchy":112},[39,30898,30899],{"encoding":41},"(t,f_{JS}(t))",[15,30901,30903],{"className":30902,"ariaHidden":46},[45],[15,30904,30906,30909,30912,30915,30918,30921,30967,30970,30973],{"className":30905},[50],[15,30907],{"className":30908,"style":139},[54],[15,30910,113],{"className":30911},[146],[15,30913,769],{"className":30914},[59,60],[15,30916,551],{"className":30917},[573],[15,30919],{"className":30920,"style":406},[157],[15,30922,30924,30927],{"className":30923},[59],[15,30925,37],{"className":30926,"style":61},[59,60],[15,30928,30930],{"className":30929},[281],[15,30931,30933,30959],{"className":30932},[285,286],[15,30934,30936,30956],{"className":30935},[290],[15,30937,30939],{"className":30938,"style":379},[294],[15,30940,30941,30944],{"style":27509},[15,30942],{"className":30943,"style":303},[302],[15,30945,30947],{"className":30946},[307,308,309,310],[15,30948,30950,30953],{"className":30949},[59,310],[15,30951,23743],{"className":30952,"style":24153},[59,60,310],[15,30954,25737],{"className":30955,"style":25861},[59,60,310],[15,30957,318],{"className":30958},[317],[15,30960,30962],{"className":30961},[290],[15,30963,30965],{"className":30964,"style":7968},[294],[15,30966],{},[15,30968,113],{"className":30969},[146],[15,30971,769],{"className":30972},[59,60],[15,30974,19047],{"className":30975},[153]," 的写法会漏掉奇异项。此时把 JS 写成 Csiszár 的",[1225,30978,30979],{},"双变量（齐次、联合凸）泛函","最稳妥：",[15,30982,30984],{"className":30983,"translate":19},[180],[15,30985,30987,31044],{"className":30986,"translate":19},[18],[15,30988,30990],{"className":30989},[23],[25,30991,30992],{"xmlns":27,"display":189},[29,30993,30994,31041],{},[32,30995,30996,31006,31008,31010,31012,31014,31016,31018,31020,31023,31025,31027,31029,31031,31033,31035,31037,31039],{},[195,30997,30998,31000],{},[35,30999,199],{},[32,31001,31002,31004],{},[35,31003,23743],{},[35,31005,25737],{},[110,31007,113],{"stretchy":112},[35,31009,206],{},[35,31011,210],{"mathvariant":209},[35,31013,213],{},[110,31015,120],{"stretchy":112},[110,31017,123],{},[110,31019,1287],{},[35,31021,31022],{},"φ",[110,31024,113],{"stretchy":112},[35,31026,11],{},[110,31028,551],{"separator":46},[35,31030,944],{},[110,31032,120],{"stretchy":112},[1297,31034,1299],{},[35,31036,244],{},[35,31038,2364],{},[110,31040,551],{"separator":46},[39,31042,31043],{"encoding":41},"D_{JS}(P\\|Q)=\\int \\varphi(p,q)\\,d\\mu,",[15,31045,31047,31123],{"className":31046,"ariaHidden":46},[45],[15,31048,31050,31053,31099,31102,31105,31108,31111,31114,31117,31120],{"className":31049},[50],[15,31051],{"className":31052,"style":139},[54],[15,31054,31056,31059],{"className":31055},[59],[15,31057,199],{"className":31058,"style":277},[59,60],[15,31060,31062],{"className":31061},[281],[15,31063,31065,31091],{"className":31064},[285,286],[15,31066,31068,31088],{"className":31067},[290],[15,31069,31071],{"className":31070,"style":379},[294],[15,31072,31073,31076],{"style":298},[15,31074],{"className":31075,"style":303},[302],[15,31077,31079],{"className":31078},[307,308,309,310],[15,31080,31082,31085],{"className":31081},[59,310],[15,31083,23743],{"className":31084,"style":24153},[59,60,310],[15,31086,25737],{"className":31087,"style":25861},[59,60,310],[15,31089,318],{"className":31090},[317],[15,31092,31094],{"className":31093},[290],[15,31095,31097],{"className":31096,"style":7968},[294],[15,31098],{},[15,31100,113],{"className":31101},[146],[15,31103,206],{"className":31104,"style":334},[59,60],[15,31106,210],{"className":31107},[59],[15,31109,213],{"className":31110},[59,60],[15,31112,120],{"className":31113},[153],[15,31115],{"className":31116,"style":158},[157],[15,31118,123],{"className":31119},[162],[15,31121],{"className":31122,"style":158},[157],[15,31124,31126,31129,31132,31135,31138,31141,31144,31147,31150,31153,31156,31159,31162,31165],{"className":31125},[50],[15,31127],{"className":31128,"style":5777},[54],[15,31130,1287],{"className":31131,"style":1487},[1484,1485,1486],[15,31133],{"className":31134,"style":406},[157],[15,31136,31022],{"className":31137},[59,60],[15,31139,113],{"className":31140},[146],[15,31142,11],{"className":31143},[59,60],[15,31145,551],{"className":31146},[573],[15,31148],{"className":31149,"style":406},[157],[15,31151,944],{"className":31152,"style":981},[59,60],[15,31154,120],{"className":31155},[153],[15,31157],{"className":31158,"style":406},[157],[15,31160,244],{"className":31161},[59,60],[15,31163,2364],{"className":31164},[59,60],[15,31166,551],{"className":31167},[573],[15,31169,31171],{"className":31170,"translate":19},[180],[15,31172,31174,31258],{"className":31173,"translate":19},[18],[15,31175,31177],{"className":31176},[23],[25,31178,31179],{"xmlns":27,"display":189},[29,31180,31181,31255],{},[32,31182,31183,31185,31187,31189,31191,31193,31195,31197,31203,31205,31207,31209,31211,31227,31229,31231,31233,31235,31251,31253],{},[35,31184,31022],{},[110,31186,113],{"stretchy":112},[35,31188,11],{},[110,31190,551],{"separator":46},[35,31192,944],{},[110,31194,120],{"stretchy":112},[110,31196,123],{},[238,31198,31199,31201],{},[115,31200,117],{},[115,31202,2463],{},[110,31204,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,31206,11],{},[35,31208,4100],{},[110,31210,4103],{},[238,31212,31213,31219],{},[32,31214,31215,31217],{},[115,31216,2463],{},[35,31218,11],{},[32,31220,31221,31223,31225],{},[35,31222,11],{},[110,31224,2470],{},[35,31226,944],{},[110,31228,2470],{},[35,31230,944],{},[35,31232,4100],{},[110,31234,4103],{},[238,31236,31237,31243],{},[32,31238,31239,31241],{},[115,31240,2463],{},[35,31242,944],{},[32,31244,31245,31247,31249],{},[35,31246,11],{},[110,31248,2470],{},[35,31250,944],{},[110,31252,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,31254,551],{"separator":46},[39,31256,31257],{"encoding":41},"\\varphi(p,q)=\\frac12\\Big[\np\\log\\frac{2p}{p+q}+q\\log\\frac{2q}{p+q}\\Big],",[15,31259,31261,31297,31472],{"className":31260,"ariaHidden":46},[45],[15,31262,31264,31267,31270,31273,31276,31279,31282,31285,31288,31291,31294],{"className":31263},[50],[15,31265],{"className":31266,"style":139},[54],[15,31268,31022],{"className":31269},[59,60],[15,31271,113],{"className":31272},[146],[15,31274,11],{"className":31275},[59,60],[15,31277,551],{"className":31278},[573],[15,31280],{"className":31281,"style":406},[157],[15,31283,944],{"className":31284,"style":981},[59,60],[15,31286,120],{"className":31287},[153],[15,31289],{"className":31290,"style":158},[157],[15,31292,123],{"className":31293},[162],[15,31295],{"className":31296,"style":158},[157],[15,31298,31300,31304,31366,31372,31375,31378,31383,31386,31463,31466,31469],{"className":31299},[50],[15,31301],{"className":31302,"style":31303},[54],"height:2.2019em;vertical-align:-0.8804em;",[15,31305,31307,31310,31363],{"className":31306},[59],[15,31308],{"className":31309},[146,441],[15,31311,31313],{"className":31312},[238],[15,31314,31316,31355],{"className":31315},[285,286],[15,31317,31319,31352],{"className":31318},[290],[15,31320,31322,31333,31341],{"className":31321,"style":22889},[294],[15,31323,31324,31327],{"style":457},[15,31325],{"className":31326,"style":461},[302],[15,31328,31330],{"className":31329},[59],[15,31331,2463],{"className":31332},[59],[15,31334,31335,31338],{"style":473},[15,31336],{"className":31337,"style":461},[302],[15,31339],{"className":31340,"style":481},[480],[15,31342,31343,31346],{"style":484},[15,31344],{"className":31345,"style":461},[302],[15,31347,31349],{"className":31348},[59],[15,31350,117],{"className":31351},[59],[15,31353,318],{"className":31354},[317],[15,31356,31358],{"className":31357},[290],[15,31359,31361],{"className":31360,"style":3778},[294],[15,31362],{},[15,31364],{"className":31365},[153,441],[15,31367,31369],{"className":31368},[59],[15,31370,230],{"className":31371},[419,3720],[15,31373,11],{"className":31374},[59,60],[15,31376],{"className":31377,"style":406},[157],[15,31379,4154,31381],{"className":31380},[1484],[15,31382,4158],{"style":4157},[15,31384],{"className":31385,"style":406},[157],[15,31387,31389,31392,31460],{"className":31388},[59],[15,31390],{"className":31391},[146,441],[15,31393,31395],{"className":31394},[238],[15,31396,31398,31452],{"className":31397},[285,286],[15,31399,31401,31449],{"className":31400},[290],[15,31402,31404,31427,31435],{"className":31403,"style":22889},[294],[15,31405,31406,31409],{"style":457},[15,31407],{"className":31408,"style":461},[302],[15,31410,31412,31415,31418,31421,31424],{"className":31411},[59],[15,31413,11],{"className":31414},[59,60],[15,31416],{"className":31417,"style":2587},[157],[15,31419,2470],{"className":31420},[2591],[15,31422],{"className":31423,"style":2587},[157],[15,31425,944],{"className":31426,"style":981},[59,60],[15,31428,31429,31432],{"style":473},[15,31430],{"className":31431,"style":461},[302],[15,31433],{"className":31434,"style":481},[480],[15,31436,31437,31440],{"style":484},[15,31438],{"className":31439,"style":461},[302],[15,31441,31443,31446],{"className":31442},[59],[15,31444,2463],{"className":31445},[59],[15,31447,11],{"className":31448},[59,60],[15,31450,318],{"className":31451},[317],[15,31453,31455],{"className":31454},[290],[15,31456,31458],{"className":31457,"style":506},[294],[15,31459],{},[15,31461],{"className":31462},[153,441],[15,31464],{"className":31465,"style":2587},[157],[15,31467,2470],{"className":31468},[2591],[15,31470],{"className":31471,"style":2587},[157],[15,31473,31475,31478,31481,31484,31489,31492,31569,31575],{"className":31474},[50],[15,31476],{"className":31477,"style":31303},[54],[15,31479,944],{"className":31480,"style":981},[59,60],[15,31482],{"className":31483,"style":406},[157],[15,31485,4154,31487],{"className":31486},[1484],[15,31488,4158],{"style":4157},[15,31490],{"className":31491,"style":406},[157],[15,31493,31495,31498,31566],{"className":31494},[59],[15,31496],{"className":31497},[146,441],[15,31499,31501],{"className":31500},[238],[15,31502,31504,31558],{"className":31503},[285,286],[15,31505,31507,31555],{"className":31506},[290],[15,31508,31510,31533,31541],{"className":31509,"style":22889},[294],[15,31511,31512,31515],{"style":457},[15,31513],{"className":31514,"style":461},[302],[15,31516,31518,31521,31524,31527,31530],{"className":31517},[59],[15,31519,11],{"className":31520},[59,60],[15,31522],{"className":31523,"style":2587},[157],[15,31525,2470],{"className":31526},[2591],[15,31528],{"className":31529,"style":2587},[157],[15,31531,944],{"className":31532,"style":981},[59,60],[15,31534,31535,31538],{"style":473},[15,31536],{"className":31537,"style":461},[302],[15,31539],{"className":31540,"style":481},[480],[15,31542,31543,31546],{"style":484},[15,31544],{"className":31545,"style":461},[302],[15,31547,31549,31552],{"className":31548},[59],[15,31550,2463],{"className":31551},[59],[15,31553,944],{"className":31554,"style":981},[59,60],[15,31556,318],{"className":31557},[317],[15,31559,31561],{"className":31560},[290],[15,31562,31564],{"className":31563,"style":506},[294],[15,31565],{},[15,31567],{"className":31568},[153,441],[15,31570,31572],{"className":31571},[59],[15,31573,257],{"className":31574},[419,3720],[15,31576,551],{"className":31577},[573],[11,31579,31580,668,31609,31661,31662,31714,31715,31872,31873,31959,31960,32083],{},[15,31581,31583,31597],{"className":31582,"translate":19},[18],[15,31584,31586],{"className":31585},[23],[25,31587,31588],{"xmlns":27},[29,31589,31590,31594],{},[32,31591,31592],{},[35,31593,31022],{},[39,31595,31596],{"encoding":41},"\\varphi",[15,31598,31600],{"className":31599,"ariaHidden":46},[45],[15,31601,31603,31606],{"className":31602},[50],[15,31604],{"className":31605,"style":2276},[54],[15,31607,31022],{"className":31608},[59,60],[15,31610,31612,31634],{"className":31611,"translate":19},[18],[15,31613,31615],{"className":31614},[23],[25,31616,31617],{"xmlns":27},[29,31618,31619,31631],{},[32,31620,31621,31623,31625,31627,31629],{},[110,31622,113],{"stretchy":112},[35,31624,11],{},[110,31626,551],{"separator":46},[35,31628,944],{},[110,31630,120],{"stretchy":112},[39,31632,31633],{"encoding":41},"(p,q)",[15,31635,31637],{"className":31636,"ariaHidden":46},[45],[15,31638,31640,31643,31646,31649,31652,31655,31658],{"className":31639},[50],[15,31641],{"className":31642,"style":139},[54],[15,31644,113],{"className":31645},[146],[15,31647,11],{"className":31648},[59,60],[15,31650,551],{"className":31651},[573],[15,31653],{"className":31654,"style":406},[157],[15,31656,944],{"className":31657,"style":981},[59,60],[15,31659,120],{"className":31660},[153]," 联合凸且一次齐次。在 ",[15,31663,31665,31683],{"className":31664,"translate":19},[18],[15,31666,31668],{"className":31667},[23],[25,31669,31670],{"xmlns":27},[29,31671,31672,31680],{},[32,31673,31674,31676,31678],{},[35,31675,944],{},[110,31677,2903],{},[115,31679,126],{},[39,31681,31682],{"encoding":41},"q>0",[15,31684,31686,31705],{"className":31685,"ariaHidden":46},[45],[15,31687,31689,31693,31696,31699,31702],{"className":31688},[50],[15,31690],{"className":31691,"style":31692},[54],"height:0.7335em;vertical-align:-0.1944em;",[15,31694,944],{"className":31695,"style":981},[59,60],[15,31697],{"className":31698,"style":158},[157],[15,31700,2903],{"className":31701},[162],[15,31703],{"className":31704,"style":158},[157],[15,31706,31708,31711],{"className":31707},[50],[15,31709],{"className":31710,"style":172},[54],[15,31712,126],{"className":31713},[59]," 处 ",[15,31716,31718,31766],{"className":31717,"translate":19},[18],[15,31719,31721],{"className":31720},[23],[25,31722,31723],{"xmlns":27},[29,31724,31725,31763],{},[32,31726,31727,31729,31731,31733,31735,31737,31739,31741,31743,31745,31747,31757,31759,31761],{},[35,31728,31022],{},[110,31730,113],{"stretchy":112},[35,31732,769],{},[35,31734,944],{},[110,31736,551],{"separator":46},[35,31738,944],{},[110,31740,120],{"stretchy":112},[110,31742,123],{},[35,31744,944],{},[1297,31746,1299],{},[195,31748,31749,31751],{},[35,31750,37],{},[32,31752,31753,31755],{},[35,31754,23743],{},[35,31756,25737],{},[110,31758,113],{"stretchy":112},[35,31760,769],{},[110,31762,120],{"stretchy":112},[39,31764,31765],{"encoding":41},"\\varphi(tq,q)=q\\,f_{JS}(t)",[15,31767,31769,31805],{"className":31768,"ariaHidden":46},[45],[15,31770,31772,31775,31778,31781,31784,31787,31790,31793,31796,31799,31802],{"className":31771},[50],[15,31773],{"className":31774,"style":139},[54],[15,31776,31022],{"className":31777},[59,60],[15,31779,113],{"className":31780},[146],[15,31782,26278],{"className":31783,"style":981},[59,60],[15,31785,551],{"className":31786},[573],[15,31788],{"className":31789,"style":406},[157],[15,31791,944],{"className":31792,"style":981},[59,60],[15,31794,120],{"className":31795},[153],[15,31797],{"className":31798,"style":158},[157],[15,31800,123],{"className":31801},[162],[15,31803],{"className":31804,"style":158},[157],[15,31806,31808,31811,31814,31817,31863,31866,31869],{"className":31807},[50],[15,31809],{"className":31810,"style":139},[54],[15,31812,944],{"className":31813,"style":981},[59,60],[15,31815],{"className":31816,"style":406},[157],[15,31818,31820,31823],{"className":31819},[59],[15,31821,37],{"className":31822,"style":61},[59,60],[15,31824,31826],{"className":31825},[281],[15,31827,31829,31855],{"className":31828},[285,286],[15,31830,31832,31852],{"className":31831},[290],[15,31833,31835],{"className":31834,"style":379},[294],[15,31836,31837,31840],{"style":27509},[15,31838],{"className":31839,"style":303},[302],[15,31841,31843],{"className":31842},[307,308,309,310],[15,31844,31846,31849],{"className":31845},[59,310],[15,31847,23743],{"className":31848,"style":24153},[59,60,310],[15,31850,25737],{"className":31851,"style":25861},[59,60,310],[15,31853,318],{"className":31854},[317],[15,31856,31858],{"className":31857},[290],[15,31859,31861],{"className":31860,"style":7968},[294],[15,31862],{},[15,31864,113],{"className":31865},[146],[15,31867,769],{"className":31868},[59,60],[15,31870,120],{"className":31871},[153],"，两者一致；在 ",[15,31874,31876,31902],{"className":31875,"translate":19},[18],[15,31877,31879],{"className":31878},[23],[25,31880,31881],{"xmlns":27},[29,31882,31883,31899],{},[32,31884,31885,31887,31889,31891,31893,31895,31897],{},[35,31886,944],{},[110,31888,123],{},[115,31890,126],{},[110,31892,551],{"separator":46},[35,31894,11],{},[110,31896,2903],{},[115,31898,126],{},[39,31900,31901],{"encoding":41},"q=0,p>0",[15,31903,31905,31923,31950],{"className":31904,"ariaHidden":46},[45],[15,31906,31908,31911,31914,31917,31920],{"className":31907},[50],[15,31909],{"className":31910,"style":2276},[54],[15,31912,944],{"className":31913,"style":981},[59,60],[15,31915],{"className":31916,"style":158},[157],[15,31918,123],{"className":31919},[162],[15,31921],{"className":31922,"style":158},[157],[15,31924,31926,31929,31932,31935,31938,31941,31944,31947],{"className":31925},[50],[15,31927],{"className":31928,"style":9358},[54],[15,31930,126],{"className":31931},[59],[15,31933,551],{"className":31934},[573],[15,31936],{"className":31937,"style":406},[157],[15,31939,11],{"className":31940},[59,60],[15,31942],{"className":31943,"style":158},[157],[15,31945,2903],{"className":31946},[162],[15,31948],{"className":31949,"style":158},[157],[15,31951,31953,31956],{"className":31952},[50],[15,31954],{"className":31955,"style":172},[54],[15,31957,126],{"className":31958},[59]," 处奇异项 ",[15,31961,31963,31989],{"className":31962,"translate":19},[18],[15,31964,31966],{"className":31965},[23],[25,31967,31968],{"xmlns":27},[29,31969,31970,31986],{},[32,31971,31972,31978,31980,31982,31984],{},[238,31973,31974,31976],{},[115,31975,117],{},[115,31977,2463],{},[35,31979,11],{},[35,31981,4100],{},[110,31983,4103],{},[115,31985,2463],{},[39,31987,31988],{"encoding":41},"\\frac12 p\\log 2",[15,31990,31992],{"className":31991,"ariaHidden":46},[45],[15,31993,31995,31998,32066,32069,32072,32077,32080],{"className":31994},[50],[15,31996],{"className":31997,"style":2505},[54],[15,31999,32001,32004,32063],{"className":32000},[59],[15,32002],{"className":32003},[146,441],[15,32005,32007],{"className":32006},[238],[15,32008,32010,32055],{"className":32009},[285,286],[15,32011,32013,32052],{"className":32012},[290],[15,32014,32016,32030,32038],{"className":32015,"style":2524},[294],[15,32017,32018,32021],{"style":2527},[15,32019],{"className":32020,"style":461},[302],[15,32022,32024],{"className":32023},[307,308,309,310],[15,32025,32027],{"className":32026},[59,310],[15,32028,2463],{"className":32029},[59,310],[15,32031,32032,32035],{"style":473},[15,32033],{"className":32034,"style":461},[302],[15,32036],{"className":32037,"style":481},[480],[15,32039,32040,32043],{"style":2550},[15,32041],{"className":32042,"style":461},[302],[15,32044,32046],{"className":32045},[307,308,309,310],[15,32047,32049],{"className":32048},[59,310],[15,32050,117],{"className":32051},[59,310],[15,32053,318],{"className":32054},[317],[15,32056,32058],{"className":32057},[290],[15,32059,32061],{"className":32060,"style":2572},[294],[15,32062],{},[15,32064],{"className":32065},[153,441],[15,32067,11],{"className":32068},[59,60],[15,32070],{"className":32071,"style":406},[157],[15,32073,4154,32075],{"className":32074},[1484],[15,32076,4158],{"style":4157},[15,32078],{"className":32079,"style":406},[157],[15,32081,2463],{"className":32082},[59]," 会被保留下来（这正是 1.1 节讨论的「支撑不重叠」约定）。",[11,32085,32086,32089,32090,32169,32170,15795,32173,32224,32225,32458,32459,32487,32488,32516,32517,32705,32706,32801],{},[1225,32087,32088],{},"有界性。"," 注意 ",[15,32091,32093,32114],{"className":32092,"translate":19},[18],[15,32094,32096],{"className":32095},[23],[25,32097,32098],{"xmlns":27},[29,32099,32100,32112],{},[32,32101,32102],{},[195,32103,32104,32106],{},[35,32105,37],{},[32,32107,32108,32110],{},[35,32109,23743],{},[35,32111,25737],{},[39,32113,30755],{"encoding":41},[15,32115,32117],{"className":32116,"ariaHidden":46},[45],[15,32118,32120,32123],{"className":32119},[50],[15,32121],{"className":32122,"style":55},[54],[15,32124,32126,32129],{"className":32125},[59],[15,32127,37],{"className":32128,"style":61},[59,60],[15,32130,32132],{"className":32131},[281],[15,32133,32135,32161],{"className":32134},[285,286],[15,32136,32138,32158],{"className":32137},[290],[15,32139,32141],{"className":32140,"style":379},[294],[15,32142,32143,32146],{"style":27509},[15,32144],{"className":32145,"style":303},[302],[15,32147,32149],{"className":32148},[307,308,309,310],[15,32150,32152,32155],{"className":32151},[59,310],[15,32153,23743],{"className":32154,"style":24153},[59,60,310],[15,32156,25737],{"className":32157,"style":25861},[59,60,310],[15,32159,318],{"className":32160},[317],[15,32162,32164],{"className":32163},[290],[15,32165,32167],{"className":32166,"style":7968},[294],[15,32168],{}," 逐点",[1225,32171,32172],{},"无界",[15,32174,32176,32194],{"className":32175,"translate":19},[18],[15,32177,32179],{"className":32178},[23],[25,32180,32181],{"xmlns":27},[29,32182,32183,32191],{},[32,32184,32185,32187,32189],{},[35,32186,769],{},[110,32188,1029],{},[35,32190,1024],{"mathvariant":209},[39,32192,32193],{"encoding":41},"t\\to\\infty",[15,32195,32197,32215],{"className":32196,"ariaHidden":46},[45],[15,32198,32200,32203,32206,32209,32212],{"className":32199},[50],[15,32201],{"className":32202,"style":5343},[54],[15,32204,769],{"className":32205},[59,60],[15,32207],{"className":32208,"style":158},[157],[15,32210,1029],{"className":32211},[162],[15,32213],{"className":32214,"style":158},[157],[15,32216,32218,32221],{"className":32217},[50],[15,32219],{"className":32220,"style":2345},[54],[15,32222,1024],{"className":32223},[59]," 时 ",[15,32226,32228,32276],{"className":32227,"translate":19},[18],[15,32229,32231],{"className":32230},[23],[25,32232,32233],{"xmlns":27},[29,32234,32235,32273],{},[32,32236,32237,32247,32249,32251,32253,32255,32261,32263,32265,32267,32269,32271],{},[195,32238,32239,32241],{},[35,32240,37],{},[32,32242,32243,32245],{},[35,32244,23743],{},[35,32246,25737],{},[110,32248,113],{"stretchy":112},[35,32250,769],{},[110,32252,120],{"stretchy":112},[110,32254,8869],{},[238,32256,32257,32259],{},[115,32258,117],{},[115,32260,2463],{},[35,32262,769],{},[35,32264,4100],{},[110,32266,4103],{},[115,32268,2463],{},[110,32270,1029],{},[35,32272,1024],{"mathvariant":209},[39,32274,32275],{"encoding":41},"f_{JS}(t)\\sim\\frac12 t\\log 2\\to\\infty",[15,32277,32279,32349,32449],{"className":32278,"ariaHidden":46},[45],[15,32280,32282,32285,32331,32334,32337,32340,32343,32346],{"className":32281},[50],[15,32283],{"className":32284,"style":139},[54],[15,32286,32288,32291],{"className":32287},[59],[15,32289,37],{"className":32290,"style":61},[59,60],[15,32292,32294],{"className":32293},[281],[15,32295,32297,32323],{"className":32296},[285,286],[15,32298,32300,32320],{"className":32299},[290],[15,32301,32303],{"className":32302,"style":379},[294],[15,32304,32305,32308],{"style":27509},[15,32306],{"className":32307,"style":303},[302],[15,32309,32311],{"className":32310},[307,308,309,310],[15,32312,32314,32317],{"className":32313},[59,310],[15,32315,23743],{"className":32316,"style":24153},[59,60,310],[15,32318,25737],{"className":32319,"style":25861},[59,60,310],[15,32321,318],{"className":32322},[317],[15,32324,32326],{"className":32325},[290],[15,32327,32329],{"className":32328,"style":7968},[294],[15,32330],{},[15,32332,113],{"className":32333},[146],[15,32335,769],{"className":32336},[59,60],[15,32338,120],{"className":32339},[153],[15,32341],{"className":32342,"style":158},[157],[15,32344,8869],{"className":32345},[162],[15,32347],{"className":32348,"style":158},[157],[15,32350,32352,32355,32423,32426,32429,32434,32437,32440,32443,32446],{"className":32351},[50],[15,32353],{"className":32354,"style":2505},[54],[15,32356,32358,32361,32420],{"className":32357},[59],[15,32359],{"className":32360},[146,441],[15,32362,32364],{"className":32363},[238],[15,32365,32367,32412],{"className":32366},[285,286],[15,32368,32370,32409],{"className":32369},[290],[15,32371,32373,32387,32395],{"className":32372,"style":2524},[294],[15,32374,32375,32378],{"style":2527},[15,32376],{"className":32377,"style":461},[302],[15,32379,32381],{"className":32380},[307,308,309,310],[15,32382,32384],{"className":32383},[59,310],[15,32385,2463],{"className":32386},[59,310],[15,32388,32389,32392],{"style":473},[15,32390],{"className":32391,"style":461},[302],[15,32393],{"className":32394,"style":481},[480],[15,32396,32397,32400],{"style":2550},[15,32398],{"className":32399,"style":461},[302],[15,32401,32403],{"className":32402},[307,308,309,310],[15,32404,32406],{"className":32405},[59,310],[15,32407,117],{"className":32408},[59,310],[15,32410,318],{"className":32411},[317],[15,32413,32415],{"className":32414},[290],[15,32416,32418],{"className":32417,"style":2572},[294],[15,32419],{},[15,32421],{"className":32422},[153,441],[15,32424,769],{"className":32425},[59,60],[15,32427],{"className":32428,"style":406},[157],[15,32430,4154,32432],{"className":32431},[1484],[15,32433,4158],{"style":4157},[15,32435],{"className":32436,"style":406},[157],[15,32438,2463],{"className":32439},[59],[15,32441],{"className":32442,"style":158},[157],[15,32444,1029],{"className":32445},[162],[15,32447],{"className":32448,"style":158},[157],[15,32450,32452,32455],{"className":32451},[50],[15,32453],{"className":32454,"style":2345},[54],[15,32456,1024],{"className":32457},[59],"），但积分有界，因为 ",[15,32460,32462,32475],{"className":32461,"translate":19},[18],[15,32463,32465],{"className":32464},[23],[25,32466,32467],{"xmlns":27},[29,32468,32469,32473],{},[32,32470,32471],{},[35,32472,769],{},[39,32474,769],{"encoding":41},[15,32476,32478],{"className":32477,"ariaHidden":46},[45],[15,32479,32481,32484],{"className":32480},[50],[15,32482],{"className":32483,"style":5343},[54],[15,32485,769],{"className":32486},[59,60]," 大的地方 ",[15,32489,32491,32504],{"className":32490,"translate":19},[18],[15,32492,32494],{"className":32493},[23],[25,32495,32496],{"xmlns":27},[29,32497,32498,32502],{},[32,32499,32500],{},[35,32501,944],{},[39,32503,944],{"encoding":41},[15,32505,32507],{"className":32506,"ariaHidden":46},[45],[15,32508,32510,32513],{"className":32509},[50],[15,32511],{"className":32512,"style":2276},[54],[15,32514,944],{"className":32515,"style":981},[59,60]," 小、权重趋于 0。严格地用两 KL 形式：",[15,32518,32520,32578],{"className":32519,"translate":19},[18],[15,32521,32523],{"className":32522},[23],[25,32524,32525],{"xmlns":27},[29,32526,32527,32575],{},[32,32528,32529,32531,32533,32535,32537,32539,32541,32543,32545,32547,32549,32551,32557,32559,32561,32563,32565,32567,32569,32571,32573],{},[115,32530,2463],{},[35,32532,11],{},[35,32534,941],{"mathvariant":209},[110,32536,113],{"stretchy":112},[35,32538,11],{},[110,32540,2470],{},[35,32542,944],{},[110,32544,120],{"stretchy":112},[110,32546,9952],{},[115,32548,2463],{},[110,32550,10990],{},[32,32552,32553,32555],{},[35,32554,10694],{"mathvariant":209},[35,32556,21893],{"mathvariant":209},[110,32558,113],{"stretchy":112},[35,32560,206],{},[35,32562,210],{"mathvariant":209},[35,32564,25567],{},[110,32566,120],{"stretchy":112},[110,32568,9952],{},[35,32570,4100],{},[110,32572,4103],{},[115,32574,2463],{},[39,32576,32577],{"encoding":41},"2p\u002F(p+q)\\le 2\\Rightarrow \\mathrm{KL}(P\\|M)\\le\\log2",[15,32579,32581,32611,32632,32650,32688],{"className":32580,"ariaHidden":46},[45],[15,32582,32584,32587,32590,32593,32596,32599,32602,32605,32608],{"className":32583},[50],[15,32585],{"className":32586,"style":139},[54],[15,32588,2463],{"className":32589},[59],[15,32591,11],{"className":32592},[59,60],[15,32594,941],{"className":32595},[59],[15,32597,113],{"className":32598},[146],[15,32600,11],{"className":32601},[59,60],[15,32603],{"className":32604,"style":2587},[157],[15,32606,2470],{"className":32607},[2591],[15,32609],{"className":32610,"style":2587},[157],[15,32612,32614,32617,32620,32623,32626,32629],{"className":32613},[50],[15,32615],{"className":32616,"style":139},[54],[15,32618,944],{"className":32619,"style":981},[59,60],[15,32621,120],{"className":32622},[153],[15,32624],{"className":32625,"style":158},[157],[15,32627,9952],{"className":32628},[162],[15,32630],{"className":32631,"style":158},[157],[15,32633,32635,32638,32641,32644,32647],{"className":32634},[50],[15,32636],{"className":32637,"style":172},[54],[15,32639,2463],{"className":32640},[59],[15,32642],{"className":32643,"style":158},[157],[15,32645,10990],{"className":32646},[162],[15,32648],{"className":32649,"style":158},[157],[15,32651,32653,32656,32664,32667,32670,32673,32676,32679,32682,32685],{"className":32652},[50],[15,32654],{"className":32655,"style":139},[54],[15,32657,32659],{"className":32658},[59],[15,32660,32663],{"className":32661},[59,32662],"mathrm","KL",[15,32665,113],{"className":32666},[146],[15,32668,206],{"className":32669,"style":334},[59,60],[15,32671,210],{"className":32672},[59],[15,32674,25567],{"className":32675,"style":25601},[59,60],[15,32677,120],{"className":32678},[153],[15,32680],{"className":32681,"style":158},[157],[15,32683,9952],{"className":32684},[162],[15,32686],{"className":32687,"style":158},[157],[15,32689,32691,32694,32699,32702],{"className":32690},[50],[15,32692],{"className":32693,"style":55},[54],[15,32695,4154,32697],{"className":32696},[1484],[15,32698,4158],{"style":4157},[15,32700],{"className":32701,"style":406},[157],[15,32703,2463],{"className":32704},[59],"，同理 ",[15,32707,32709,32745],{"className":32708,"translate":19},[18],[15,32710,32712],{"className":32711},[23],[25,32713,32714],{"xmlns":27},[29,32715,32716,32742],{},[32,32717,32718,32724,32726,32728,32730,32732,32734,32736,32738,32740],{},[32,32719,32720,32722],{},[35,32721,10694],{"mathvariant":209},[35,32723,21893],{"mathvariant":209},[110,32725,113],{"stretchy":112},[35,32727,213],{},[35,32729,210],{"mathvariant":209},[35,32731,25567],{},[110,32733,120],{"stretchy":112},[110,32735,9952],{},[35,32737,4100],{},[110,32739,4103],{},[115,32741,2463],{},[39,32743,32744],{"encoding":41},"\\mathrm{KL}(Q\\|M)\\le\\log2",[15,32746,32748,32784],{"className":32747,"ariaHidden":46},[45],[15,32749,32751,32754,32760,32763,32766,32769,32772,32775,32778,32781],{"className":32750},[50],[15,32752],{"className":32753,"style":139},[54],[15,32755,32757],{"className":32756},[59],[15,32758,32663],{"className":32759},[59,32662],[15,32761,113],{"className":32762},[146],[15,32764,213],{"className":32765},[59,60],[15,32767,210],{"className":32768},[59],[15,32770,25567],{"className":32771,"style":25601},[59,60],[15,32773,120],{"className":32774},[153],[15,32776],{"className":32777,"style":158},[157],[15,32779,9952],{"className":32780},[162],[15,32782],{"className":32783,"style":158},[157],[15,32785,32787,32790,32795,32798],{"className":32786},[50],[15,32788],{"className":32789,"style":55},[54],[15,32791,4154,32793],{"className":32792},[1484],[15,32794,4158],{"style":4157},[15,32796],{"className":32797,"style":406},[157],[15,32799,2463],{"className":32800},[59],"，故",[15,32803,32805],{"className":32804,"translate":19},[180],[15,32806,32808,32966],{"className":32807,"translate":19},[18],[15,32809,32811],{"className":32810},[23],[25,32812,32813],{"xmlns":27,"display":189},[29,32814,32815,32963],{},[1243,32816,32817,32905],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,32818,32819,32849],{},[1252,32820,32821],{},[1255,32822,32823],{"scriptlevel":126,"displaystyle":46},[32,32824,32825,32827,32829,32839,32841,32843,32845,32847],{},[115,32826,126],{},[110,32828,9952],{},[195,32830,32831,32833],{},[35,32832,199],{},[32,32834,32835,32837],{},[35,32836,23743],{},[35,32838,25737],{},[110,32840,113],{"stretchy":112},[35,32842,206],{},[35,32844,210],{"mathvariant":209},[35,32846,213],{},[110,32848,120],{"stretchy":112},[1252,32850,32851],{},[1255,32852,32853],{"scriptlevel":126,"displaystyle":46},[32,32854,32855,32857,32859,32865,32871,32873,32875,32877,32879,32881,32883,32889,32895,32897,32899,32901,32903],{},[32,32856],{},[110,32858,123],{},[238,32860,32861,32863],{},[115,32862,117],{},[115,32864,2463],{},[32,32866,32867,32869],{},[35,32868,10694],{"mathvariant":209},[35,32870,21893],{"mathvariant":209},[110,32872,113],{"stretchy":112},[35,32874,206],{},[35,32876,210],{"mathvariant":209},[35,32878,25567],{},[110,32880,120],{"stretchy":112},[110,32882,2470],{},[238,32884,32885,32887],{},[115,32886,117],{},[115,32888,2463],{},[32,32890,32891,32893],{},[35,32892,10694],{"mathvariant":209},[35,32894,21893],{"mathvariant":209},[110,32896,113],{"stretchy":112},[35,32898,213],{},[35,32900,210],{"mathvariant":209},[35,32902,25567],{},[110,32904,120],{"stretchy":112},[1249,32906,32907,32913],{},[1252,32908,32909],{},[1255,32910,32911],{"scriptlevel":126,"displaystyle":46},[32,32912],{},[1252,32914,32915],{},[1255,32916,32917],{"scriptlevel":126,"displaystyle":46},[32,32918,32919,32921,32923,32929,32931,32933,32935,32937,32943,32945,32947,32949,32951,32953,32955,32957,32960],{},[32,32920],{},[110,32922,9952],{},[238,32924,32925,32927],{},[115,32926,117],{},[115,32928,2463],{},[35,32930,4100],{},[110,32932,4103],{},[115,32934,2463],{},[110,32936,2470],{},[238,32938,32939,32941],{},[115,32940,117],{},[115,32942,2463],{},[35,32944,4100],{},[110,32946,4103],{},[115,32948,2463],{},[110,32950,123],{},[35,32952,4100],{},[110,32954,4103],{},[115,32956,2463],{},[110,32958,32959],{},"≈",[115,32961,32962],{},"0.693.",[39,32964,32965],{"encoding":41},"\\begin{aligned}\n0\\le D_{JS}(P\\|Q)\n&=\\frac12\\mathrm{KL}(P\\|M)\n+\\frac12\\mathrm{KL}(Q\\|M)\\\\[2pt]\n&\\le \\frac12\\log 2+\\frac12\\log 2\n=\\log 2\\approx 0.693 .\n\\end{aligned}",[15,32967,32969],{"className":32968,"ariaHidden":46},[45],[15,32970,32972,32976],{"className":32971},[50],[15,32973],{"className":32974,"style":32975},[54],"height:4.3149em;vertical-align:-1.9074em;",[15,32977,32979],{"className":32978},[59],[15,32980,32982,33097],{"className":32981},[1243],[15,32983,32985],{"className":32984},[1360],[15,32986,32988,33088],{"className":32987},[285,286],[15,32989,32991,33085],{"className":32990},[290],[15,32992,32995,33077],{"className":32993,"style":32994},[294],"height:2.4074em;",[15,32996,32998,33001],{"style":32997},"top:-4.4074em;",[15,32999],{"className":33000,"style":22666},[302],[15,33002,33004,33007,33010,33013,33016,33062,33065,33068,33071,33074],{"className":33003},[59],[15,33005,126],{"className":33006},[59],[15,33008],{"className":33009,"style":158},[157],[15,33011,9952],{"className":33012},[162],[15,33014],{"className":33015,"style":158},[157],[15,33017,33019,33022],{"className":33018},[59],[15,33020,199],{"className":33021,"style":277},[59,60],[15,33023,33025],{"className":33024},[281],[15,33026,33028,33054],{"className":33027},[285,286],[15,33029,33031,33051],{"className":33030},[290],[15,33032,33034],{"className":33033,"style":379},[294],[15,33035,33036,33039],{"style":298},[15,33037],{"className":33038,"style":303},[302],[15,33040,33042],{"className":33041},[307,308,309,310],[15,33043,33045,33048],{"className":33044},[59,310],[15,33046,23743],{"className":33047,"style":24153},[59,60,310],[15,33049,25737],{"className":33050,"style":25861},[59,60,310],[15,33052,318],{"className":33053},[317],[15,33055,33057],{"className":33056},[290],[15,33058,33060],{"className":33059,"style":7968},[294],[15,33061],{},[15,33063,113],{"className":33064},[146],[15,33066,206],{"className":33067,"style":334},[59,60],[15,33069,210],{"className":33070},[59],[15,33072,213],{"className":33073},[59,60],[15,33075,120],{"className":33076},[153],[15,33078,33079,33082],{"style":1903},[15,33080],{"className":33081,"style":22666},[302],[15,33083],{"className":33084},[59],[15,33086,318],{"className":33087},[317],[15,33089,33091],{"className":33090},[290],[15,33092,33095],{"className":33093,"style":33094},[294],"height:1.9074em;",[15,33096],{},[15,33098,33100],{"className":33099},[1451],[15,33101,33103,33520],{"className":33102},[285,286],[15,33104,33106,33517],{"className":33105},[290],[15,33107,33109,33304],{"className":33108,"style":32994},[294],[15,33110,33111,33114],{"style":32997},[15,33112],{"className":33113,"style":22666},[302],[15,33115,33117,33120,33123,33126,33129,33191,33197,33200,33203,33206,33209,33212,33215,33218,33221,33283,33289,33292,33295,33298,33301],{"className":33116},[59],[15,33118],{"className":33119},[59],[15,33121],{"className":33122,"style":158},[157],[15,33124,123],{"className":33125},[162],[15,33127],{"className":33128,"style":158},[157],[15,33130,33132,33135,33188],{"className":33131},[59],[15,33133],{"className":33134},[146,441],[15,33136,33138],{"className":33137},[238],[15,33139,33141,33180],{"className":33140},[285,286],[15,33142,33144,33177],{"className":33143},[290],[15,33145,33147,33158,33166],{"className":33146,"style":22889},[294],[15,33148,33149,33152],{"style":457},[15,33150],{"className":33151,"style":461},[302],[15,33153,33155],{"className":33154},[59],[15,33156,2463],{"className":33157},[59],[15,33159,33160,33163],{"style":473},[15,33161],{"className":33162,"style":461},[302],[15,33164],{"className":33165,"style":481},[480],[15,33167,33168,33171],{"style":484},[15,33169],{"className":33170,"style":461},[302],[15,33172,33174],{"className":33173},[59],[15,33175,117],{"className":33176},[59],[15,33178,318],{"className":33179},[317],[15,33181,33183],{"className":33182},[290],[15,33184,33186],{"className":33185,"style":3778},[294],[15,33187],{},[15,33189],{"className":33190},[153,441],[15,33192,33194],{"className":33193},[59],[15,33195,32663],{"className":33196},[59,32662],[15,33198,113],{"className":33199},[146],[15,33201,206],{"className":33202,"style":334},[59,60],[15,33204,210],{"className":33205},[59],[15,33207,25567],{"className":33208,"style":25601},[59,60],[15,33210,120],{"className":33211},[153],[15,33213],{"className":33214,"style":2587},[157],[15,33216,2470],{"className":33217},[2591],[15,33219],{"className":33220,"style":2587},[157],[15,33222,33224,33227,33280],{"className":33223},[59],[15,33225],{"className":33226},[146,441],[15,33228,33230],{"className":33229},[238],[15,33231,33233,33272],{"className":33232},[285,286],[15,33234,33236,33269],{"className":33235},[290],[15,33237,33239,33250,33258],{"className":33238,"style":22889},[294],[15,33240,33241,33244],{"style":457},[15,33242],{"className":33243,"style":461},[302],[15,33245,33247],{"className":33246},[59],[15,33248,2463],{"className":33249},[59],[15,33251,33252,33255],{"style":473},[15,33253],{"className":33254,"style":461},[302],[15,33256],{"className":33257,"style":481},[480],[15,33259,33260,33263],{"style":484},[15,33261],{"className":33262,"style":461},[302],[15,33264,33266],{"className":33265},[59],[15,33267,117],{"className":33268},[59],[15,33270,318],{"className":33271},[317],[15,33273,33275],{"className":33274},[290],[15,33276,33278],{"className":33277,"style":3778},[294],[15,33279],{},[15,33281],{"className":33282},[153,441],[15,33284,33286],{"className":33285},[59],[15,33287,32663],{"className":33288},[59,32662],[15,33290,113],{"className":33291},[146],[15,33293,213],{"className":33294},[59,60],[15,33296,210],{"className":33297},[59],[15,33299,25567],{"className":33300,"style":25601},[59,60],[15,33302,120],{"className":33303},[153],[15,33305,33306,33309],{"style":1903},[15,33307],{"className":33308,"style":22666},[302],[15,33310,33312,33315,33318,33321,33324,33386,33389,33394,33397,33400,33403,33406,33409,33471,33474,33479,33482,33485,33488,33491,33494,33499,33502,33505,33508,33511,33514],{"className":33311},[59],[15,33313],{"className":33314},[59],[15,33316],{"className":33317,"style":158},[157],[15,33319,9952],{"className":33320},[162],[15,33322],{"className":33323,"style":158},[157],[15,33325,33327,33330,33383],{"className":33326},[59],[15,33328],{"className":33329},[146,441],[15,33331,33333],{"className":33332},[238],[15,33334,33336,33375],{"className":33335},[285,286],[15,33337,33339,33372],{"className":33338},[290],[15,33340,33342,33353,33361],{"className":33341,"style":22889},[294],[15,33343,33344,33347],{"style":457},[15,33345],{"className":33346,"style":461},[302],[15,33348,33350],{"className":33349},[59],[15,33351,2463],{"className":33352},[59],[15,33354,33355,33358],{"style":473},[15,33356],{"className":33357,"style":461},[302],[15,33359],{"className":33360,"style":481},[480],[15,33362,33363,33366],{"style":484},[15,33364],{"className":33365,"style":461},[302],[15,33367,33369],{"className":33368},[59],[15,33370,117],{"className":33371},[59],[15,33373,318],{"className":33374},[317],[15,33376,33378],{"className":33377},[290],[15,33379,33381],{"className":33380,"style":3778},[294],[15,33382],{},[15,33384],{"className":33385},[153,441],[15,33387],{"className":33388,"style":406},[157],[15,33390,4154,33392],{"className":33391},[1484],[15,33393,4158],{"style":4157},[15,33395],{"className":33396,"style":406},[157],[15,33398,2463],{"className":33399},[59],[15,33401],{"className":33402,"style":2587},[157],[15,33404,2470],{"className":33405},[2591],[15,33407],{"className":33408,"style":2587},[157],[15,33410,33412,33415,33468],{"className":33411},[59],[15,33413],{"className":33414},[146,441],[15,33416,33418],{"className":33417},[238],[15,33419,33421,33460],{"className":33420},[285,286],[15,33422,33424,33457],{"className":33423},[290],[15,33425,33427,33438,33446],{"className":33426,"style":22889},[294],[15,33428,33429,33432],{"style":457},[15,33430],{"className":33431,"style":461},[302],[15,33433,33435],{"className":33434},[59],[15,33436,2463],{"className":33437},[59],[15,33439,33440,33443],{"style":473},[15,33441],{"className":33442,"style":461},[302],[15,33444],{"className":33445,"style":481},[480],[15,33447,33448,33451],{"style":484},[15,33449],{"className":33450,"style":461},[302],[15,33452,33454],{"className":33453},[59],[15,33455,117],{"className":33456},[59],[15,33458,318],{"className":33459},[317],[15,33461,33463],{"className":33462},[290],[15,33464,33466],{"className":33465,"style":3778},[294],[15,33467],{},[15,33469],{"className":33470},[153,441],[15,33472],{"className":33473,"style":406},[157],[15,33475,4154,33477],{"className":33476},[1484],[15,33478,4158],{"style":4157},[15,33480],{"className":33481,"style":406},[157],[15,33483,2463],{"className":33484},[59],[15,33486],{"className":33487,"style":158},[157],[15,33489,123],{"className":33490},[162],[15,33492],{"className":33493,"style":158},[157],[15,33495,4154,33497],{"className":33496},[1484],[15,33498,4158],{"style":4157},[15,33500],{"className":33501,"style":406},[157],[15,33503,2463],{"className":33504},[59],[15,33506],{"className":33507,"style":158},[157],[15,33509,32959],{"className":33510},[162],[15,33512],{"className":33513,"style":158},[157],[15,33515,32962],{"className":33516},[59],[15,33518,318],{"className":33519},[317],[15,33521,33523],{"className":33522},[290],[15,33524,33526],{"className":33525,"style":33094},[294],[15,33527],{},[11,33529,33530,33531,33583],{},"等号成立当且仅当 ",[15,33532,33534,33553],{"className":33533,"translate":19},[18],[15,33535,33537],{"className":33536},[23],[25,33538,33539],{"xmlns":27},[29,33540,33541,33550],{},[32,33542,33543,33545,33548],{},[35,33544,206],{},[110,33546,33547],{},"⊥",[35,33549,213],{},[39,33551,33552],{"encoding":41},"P\\perp Q",[15,33554,33556,33574],{"className":33555,"ariaHidden":46},[45],[15,33557,33559,33562,33565,33568,33571],{"className":33558},[50],[15,33560],{"className":33561,"style":12597},[54],[15,33563,206],{"className":33564,"style":334},[59,60],[15,33566],{"className":33567,"style":158},[157],[15,33569,33547],{"className":33570},[162],[15,33572],{"className":33573,"style":158},[157],[15,33575,33577,33580],{"className":33576},[50],[15,33578],{"className":33579,"style":566},[54],[15,33581,213],{"className":33582},[59,60],"（支撑集不重叠）。有界是 JS 相对 KL 的最大优点（梯度消失则是它最大的缺点，二者互为因果）。",[11,33585,33586,33588,33589,33618,33619,33652,33653,33681,33682,33710,33711,33739,33740,33768,33769,2409,33797,33825,33826,9400],{},[1225,33587,24193],{}," JS 有一个很直观的信息论解释：先掷一枚公平硬币 ",[15,33590,33592,33606],{"className":33591,"translate":19},[18],[15,33593,33595],{"className":33594},[23],[25,33596,33597],{"xmlns":27},[29,33598,33599,33604],{},[32,33600,33601],{},[35,33602,33603],{},"Z",[39,33605,33603],{"encoding":41},[15,33607,33609],{"className":33608,"ariaHidden":46},[45],[15,33610,33612,33615],{"className":33611},[50],[15,33613],{"className":33614,"style":664},[54],[15,33616,33603],{"className":33617,"style":10782},[59,60],"（正反面各 ",[15,33620,33622,33640],{"className":33621,"translate":19},[18],[15,33623,33625],{"className":33624},[23],[25,33626,33627],{"xmlns":27},[29,33628,33629,33637],{},[32,33630,33631,33633,33635],{},[115,33632,117],{},[35,33634,941],{"mathvariant":209},[115,33636,2463],{},[39,33638,33639],{"encoding":41},"1\u002F2",[15,33641,33643],{"className":33642,"ariaHidden":46},[45],[15,33644,33646,33649],{"className":33645},[50],[15,33647],{"className":33648,"style":139},[54],[15,33650,33639],{"className":33651},[59],"），正面时从 ",[15,33654,33656,33669],{"className":33655,"translate":19},[18],[15,33657,33659],{"className":33658},[23],[25,33660,33661],{"xmlns":27},[29,33662,33663,33667],{},[32,33664,33665],{},[35,33666,206],{},[39,33668,206],{"encoding":41},[15,33670,33672],{"className":33671,"ariaHidden":46},[45],[15,33673,33675,33678],{"className":33674},[50],[15,33676],{"className":33677,"style":664},[54],[15,33679,206],{"className":33680,"style":334},[59,60]," 取样、反面时从 ",[15,33683,33685,33698],{"className":33684,"translate":19},[18],[15,33686,33688],{"className":33687},[23],[25,33689,33690],{"xmlns":27},[29,33691,33692,33696],{},[32,33693,33694],{},[35,33695,213],{},[39,33697,213],{"encoding":41},[15,33699,33701],{"className":33700,"ariaHidden":46},[45],[15,33702,33704,33707],{"className":33703},[50],[15,33705],{"className":33706,"style":566},[54],[15,33708,213],{"className":33709},[59,60]," 取样，得到观测 ",[15,33712,33714,33727],{"className":33713,"translate":19},[18],[15,33715,33717],{"className":33716},[23],[25,33718,33719],{"xmlns":27},[29,33720,33721,33725],{},[32,33722,33723],{},[35,33724,598],{},[39,33726,598],{"encoding":41},[15,33728,33730],{"className":33729,"ariaHidden":46},[45],[15,33731,33733,33736],{"className":33732},[50],[15,33734],{"className":33735,"style":664},[54],[15,33737,598],{"className":33738,"style":8887},[59,60],"；则 JS 正是「看一眼 ",[15,33741,33743,33756],{"className":33742,"translate":19},[18],[15,33744,33746],{"className":33745},[23],[25,33747,33748],{"xmlns":27},[29,33749,33750,33754],{},[32,33751,33752],{},[35,33753,598],{},[39,33755,598],{"encoding":41},[15,33757,33759],{"className":33758,"ariaHidden":46},[45],[15,33760,33762,33765],{"className":33761},[50],[15,33763],{"className":33764,"style":664},[54],[15,33766,598],{"className":33767,"style":8887},[59,60]," 能否判断硬币正反」所蕴含的信息量，即 ",[15,33770,33772,33785],{"className":33771,"translate":19},[18],[15,33773,33775],{"className":33774},[23],[25,33776,33777],{"xmlns":27},[29,33778,33779,33783],{},[32,33780,33781],{},[35,33782,33603],{},[39,33784,33603],{"encoding":41},[15,33786,33788],{"className":33787,"ariaHidden":46},[45],[15,33789,33791,33794],{"className":33790},[50],[15,33792],{"className":33793,"style":664},[54],[15,33795,33603],{"className":33796,"style":10782},[59,60],[15,33798,33800,33813],{"className":33799,"translate":19},[18],[15,33801,33803],{"className":33802},[23],[25,33804,33805],{"xmlns":27},[29,33806,33807,33811],{},[32,33808,33809],{},[35,33810,598],{},[39,33812,598],{"encoding":41},[15,33814,33816],{"className":33815,"ariaHidden":46},[45],[15,33817,33819,33822],{"className":33818},[50],[15,33820],{"className":33821,"style":664},[54],[15,33823,598],{"className":33824,"style":8887},[59,60]," 的",[1225,33827,33828],{},"互信息",[15,33830,33832],{"className":33831,"translate":19},[180],[15,33833,33835,33914],{"className":33834,"translate":19},[18],[15,33836,33838],{"className":33837},[23],[25,33839,33840],{"xmlns":27,"display":189},[29,33841,33842,33911],{},[32,33843,33844,33854,33856,33858,33860,33862,33864,33866,33869,33871,33873,33876,33878,33880,33882,33885,33887,33889,33891,33893,33895,33897,33899,33901,33903,33905,33907,33909],{},[195,33845,33846,33848],{},[35,33847,199],{},[32,33849,33850,33852],{},[35,33851,23743],{},[35,33853,25737],{},[110,33855,113],{"stretchy":112},[35,33857,206],{},[35,33859,210],{"mathvariant":209},[35,33861,213],{},[110,33863,120],{"stretchy":112},[110,33865,123],{},[35,33867,33868],{},"I",[110,33870,113],{"stretchy":112},[35,33872,33603],{},[110,33874,33875],{"separator":46},";",[35,33877,598],{},[110,33879,120],{"stretchy":112},[110,33881,123],{},[35,33883,33884],{},"H",[110,33886,113],{"stretchy":112},[35,33888,598],{},[110,33890,120],{"stretchy":112},[110,33892,4813],{},[35,33894,33884],{},[110,33896,113],{"stretchy":112},[35,33898,598],{},[1297,33900,1299],{},[35,33902,4808],{"mathvariant":209},[1297,33904,1299],{},[35,33906,33603],{},[110,33908,120],{"stretchy":112},[35,33910,4375],{"mathvariant":209},[39,33912,33913],{"encoding":41},"D_{JS}(P\\|Q)=I(Z;X)=H(X)-H(X\\,|\\,Z).",[15,33915,33917,33993,34029,34057],{"className":33916,"ariaHidden":46},[45],[15,33918,33920,33923,33969,33972,33975,33978,33981,33984,33987,33990],{"className":33919},[50],[15,33921],{"className":33922,"style":139},[54],[15,33924,33926,33929],{"className":33925},[59],[15,33927,199],{"className":33928,"style":277},[59,60],[15,33930,33932],{"className":33931},[281],[15,33933,33935,33961],{"className":33934},[285,286],[15,33936,33938,33958],{"className":33937},[290],[15,33939,33941],{"className":33940,"style":379},[294],[15,33942,33943,33946],{"style":298},[15,33944],{"className":33945,"style":303},[302],[15,33947,33949],{"className":33948},[307,308,309,310],[15,33950,33952,33955],{"className":33951},[59,310],[15,33953,23743],{"className":33954,"style":24153},[59,60,310],[15,33956,25737],{"className":33957,"style":25861},[59,60,310],[15,33959,318],{"className":33960},[317],[15,33962,33964],{"className":33963},[290],[15,33965,33967],{"className":33966,"style":7968},[294],[15,33968],{},[15,33970,113],{"className":33971},[146],[15,33973,206],{"className":33974,"style":334},[59,60],[15,33976,210],{"className":33977},[59],[15,33979,213],{"className":33980},[59,60],[15,33982,120],{"className":33983},[153],[15,33985],{"className":33986,"style":158},[157],[15,33988,123],{"className":33989},[162],[15,33991],{"className":33992,"style":158},[157],[15,33994,33996,33999,34002,34005,34008,34011,34014,34017,34020,34023,34026],{"className":33995},[50],[15,33997],{"className":33998,"style":139},[54],[15,34000,33868],{"className":34001,"style":8887},[59,60],[15,34003,113],{"className":34004},[146],[15,34006,33603],{"className":34007,"style":10782},[59,60],[15,34009,33875],{"className":34010},[573],[15,34012],{"className":34013,"style":406},[157],[15,34015,598],{"className":34016,"style":8887},[59,60],[15,34018,120],{"className":34019},[153],[15,34021],{"className":34022,"style":158},[157],[15,34024,123],{"className":34025},[162],[15,34027],{"className":34028,"style":158},[157],[15,34030,34032,34035,34039,34042,34045,34048,34051,34054],{"className":34031},[50],[15,34033],{"className":34034,"style":139},[54],[15,34036,33884],{"className":34037,"style":34038},[59,60],"margin-right:0.0813em;",[15,34040,113],{"className":34041},[146],[15,34043,598],{"className":34044,"style":8887},[59,60],[15,34046,120],{"className":34047},[153],[15,34049],{"className":34050,"style":2587},[157],[15,34052,4813],{"className":34053},[2591],[15,34055],{"className":34056,"style":2587},[157],[15,34058,34060,34063,34066,34069,34072,34075,34078,34081,34084,34087],{"className":34059},[50],[15,34061],{"className":34062,"style":139},[54],[15,34064,33884],{"className":34065,"style":34038},[59,60],[15,34067,113],{"className":34068},[146],[15,34070,598],{"className":34071,"style":8887},[59,60],[15,34073],{"className":34074,"style":406},[157],[15,34076,4808],{"className":34077},[59],[15,34079],{"className":34080,"style":406},[157],[15,34082,33603],{"className":34083,"style":10782},[59,60],[15,34085,120],{"className":34086},[153],[15,34088,4375],{"className":34089},[59],[11,34091,34092,34093,34121,34122,34154,34155,34283,34284,34325,34326,34464,34465,34506],{},"由于 ",[15,34094,34096,34109],{"className":34095,"translate":19},[18],[15,34097,34099],{"className":34098},[23],[25,34100,34101],{"xmlns":27},[29,34102,34103,34107],{},[32,34104,34105],{},[35,34106,33603],{},[39,34108,33603],{"encoding":41},[15,34110,34112],{"className":34111,"ariaHidden":46},[45],[15,34113,34115,34118],{"className":34114},[50],[15,34116],{"className":34117,"style":664},[54],[15,34119,33603],{"className":34120,"style":10782},[59,60]," 是概率 ",[15,34123,34125,34142],{"className":34124,"translate":19},[18],[15,34126,34128],{"className":34127},[23],[25,34129,34130],{"xmlns":27},[29,34131,34132,34140],{},[32,34133,34134,34136,34138],{},[115,34135,117],{},[35,34137,941],{"mathvariant":209},[115,34139,2463],{},[39,34141,33639],{"encoding":41},[15,34143,34145],{"className":34144,"ariaHidden":46},[45],[15,34146,34148,34151],{"className":34147},[50],[15,34149],{"className":34150,"style":139},[54],[15,34152,33639],{"className":34153},[59]," 的伯努利变量，",[15,34156,34158,34200],{"className":34157,"translate":19},[18],[15,34159,34161],{"className":34160},[23],[25,34162,34163],{"xmlns":27},[29,34164,34165,34197],{},[32,34166,34167,34169,34171,34173,34175,34177,34179,34181,34183,34185,34187,34189,34191,34193,34195],{},[35,34168,33868],{},[110,34170,113],{"stretchy":112},[35,34172,33603],{},[110,34174,33875],{"separator":46},[35,34176,598],{},[110,34178,120],{"stretchy":112},[110,34180,9952],{},[35,34182,33884],{},[110,34184,113],{"stretchy":112},[35,34186,33603],{},[110,34188,120],{"stretchy":112},[110,34190,123],{},[35,34192,4100],{},[110,34194,4103],{},[115,34196,2463],{},[39,34198,34199],{"encoding":41},"I(Z;X)\\le H(Z)=\\log 2",[15,34201,34203,34239,34266],{"className":34202,"ariaHidden":46},[45],[15,34204,34206,34209,34212,34215,34218,34221,34224,34227,34230,34233,34236],{"className":34205},[50],[15,34207],{"className":34208,"style":139},[54],[15,34210,33868],{"className":34211,"style":8887},[59,60],[15,34213,113],{"className":34214},[146],[15,34216,33603],{"className":34217,"style":10782},[59,60],[15,34219,33875],{"className":34220},[573],[15,34222],{"className":34223,"style":406},[157],[15,34225,598],{"className":34226,"style":8887},[59,60],[15,34228,120],{"className":34229},[153],[15,34231],{"className":34232,"style":158},[157],[15,34234,9952],{"className":34235},[162],[15,34237],{"className":34238,"style":158},[157],[15,34240,34242,34245,34248,34251,34254,34257,34260,34263],{"className":34241},[50],[15,34243],{"className":34244,"style":139},[54],[15,34246,33884],{"className":34247,"style":34038},[59,60],[15,34249,113],{"className":34250},[146],[15,34252,33603],{"className":34253,"style":10782},[59,60],[15,34255,120],{"className":34256},[153],[15,34258],{"className":34259,"style":158},[157],[15,34261,123],{"className":34262},[162],[15,34264],{"className":34265,"style":158},[157],[15,34267,34269,34272,34277,34280],{"className":34268},[50],[15,34270],{"className":34271,"style":55},[54],[15,34273,4154,34275],{"className":34274},[1484],[15,34276,4158],{"style":4157},[15,34278],{"className":34279,"style":406},[157],[15,34281,2463],{"className":34282},[59],"，有界性由此而来，",[15,34285,34287,34305],{"className":34286,"translate":19},[18],[15,34288,34290],{"className":34289},[23],[25,34291,34292],{"xmlns":27},[29,34293,34294,34302],{},[32,34295,34296,34298,34300],{},[35,34297,4100],{},[110,34299,4103],{},[115,34301,2463],{},[39,34303,34304],{"encoding":41},"\\log 2",[15,34306,34308],{"className":34307,"ariaHidden":46},[45],[15,34309,34311,34314,34319,34322],{"className":34310},[50],[15,34312],{"className":34313,"style":55},[54],[15,34315,4154,34317],{"className":34316},[1484],[15,34318,4158],{"style":4157},[15,34320],{"className":34321,"style":406},[157],[15,34323,2463],{"className":34324},[59]," 恰好对应「最多只能获得 1 比特」这一直觉。JS 对称、有界且 ",[15,34327,34329,34354],{"className":34328,"translate":19},[18],[15,34330,34332],{"className":34331},[23],[25,34333,34334],{"xmlns":27},[29,34335,34336,34351],{},[32,34337,34338],{},[34339,34340,34341],"msqrt",{},[195,34342,34343,34345],{},[35,34344,199],{},[32,34346,34347,34349],{},[35,34348,23743],{},[35,34350,25737],{},[39,34352,34353],{"encoding":41},"\\sqrt{D_{JS}}",[15,34355,34357],{"className":34356,"ariaHidden":46},[45],[15,34358,34360,34364],{"className":34359},[50],[15,34361],{"className":34362,"style":34363},[54],"height:1.04em;vertical-align:-0.1883em;",[15,34365,34368],{"className":34366},[59,34367],"sqrt",[15,34369,34371,34455],{"className":34370},[285,286],[15,34372,34374,34452],{"className":34373},[290],[15,34375,34378,34434],{"className":34376,"style":34377},[294],"height:0.8517em;",[15,34379,34381,34384],{"className":34380,"style":11863},[6307],[15,34382],{"className":34383,"style":461},[302],[15,34385,34388],{"className":34386,"style":34387},[59],"padding-left:0.833em;",[15,34389,34391,34394],{"className":34390},[59],[15,34392,199],{"className":34393,"style":277},[59,60],[15,34395,34397],{"className":34396},[281],[15,34398,34400,34426],{"className":34399},[285,286],[15,34401,34403,34423],{"className":34402},[290],[15,34404,34406],{"className":34405,"style":379},[294],[15,34407,34408,34411],{"style":298},[15,34409],{"className":34410,"style":303},[302],[15,34412,34414],{"className":34413},[307,308,309,310],[15,34415,34417,34420],{"className":34416},[59,310],[15,34418,23743],{"className":34419,"style":24153},[59,60,310],[15,34421,25737],{"className":34422,"style":25861},[59,60,310],[15,34424,318],{"className":34425},[317],[15,34427,34429],{"className":34428},[290],[15,34430,34432],{"className":34431,"style":7968},[294],[15,34433],{},[15,34435,34437,34440],{"style":34436},"top:-2.8117em;",[15,34438],{"className":34439,"style":461},[302],[15,34441,34445],{"className":34442,"style":34444},[34443],"hide-tail","min-width:0.853em;height:1.08em;",[6323,34446,34449],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},"1.08em","0 0 400000 1080",[6331,34450],{"d":34451},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[15,34453,318],{"className":34454},[317],[15,34456,34458],{"className":34457},[290],[15,34459,34462],{"className":34460,"style":34461},[294],"height:0.1883em;",[15,34463],{}," 仍是度量，因此在文本\u002F分布聚类、模型比较与原始 GAN 目标里被广泛使用；代价同样来自「有界」与上面这个混合结构——真差异越大 JS 越接近饱和的 ",[15,34466,34468,34486],{"className":34467,"translate":19},[18],[15,34469,34471],{"className":34470},[23],[25,34472,34473],{"xmlns":27},[29,34474,34475,34483],{},[32,34476,34477,34479,34481],{},[35,34478,4100],{},[110,34480,4103],{},[115,34482,2463],{},[39,34484,34485],{"encoding":41},"\\log2",[15,34487,34489],{"className":34488,"ariaHidden":46},[45],[15,34490,34492,34495,34500,34503],{"className":34491},[50],[15,34493],{"className":34494,"style":55},[54],[15,34496,4154,34498],{"className":34497},[1484],[15,34499,4158],{"style":4157},[15,34501],{"className":34502,"style":406},[157],[15,34504,2463],{"className":34505},[59],"，梯度随之消失，这正是 WGAN 等替代方案的动机。",[2311,34508,34510],{"id":34509},"_33-全变差","3.3 全变差",[11,34512,21473],{},[15,34514,34516],{"className":34515,"translate":19},[180],[15,34517,34519,34557],{"className":34518,"translate":19},[18],[15,34520,34522],{"className":34521},[23],[25,34523,34524],{"xmlns":27,"display":189},[29,34525,34526,34554],{},[32,34527,34528,34530,34532,34534,34536,34538,34544,34546,34548,34550,34552],{},[35,34529,37],{},[110,34531,113],{"stretchy":112},[35,34533,769],{},[110,34535,120],{"stretchy":112},[110,34537,123],{},[238,34539,34540,34542],{},[115,34541,117],{},[115,34543,2463],{},[35,34545,4808],{"mathvariant":209},[35,34547,769],{},[110,34549,4813],{},[115,34551,117],{},[35,34553,4808],{"mathvariant":209},[39,34555,34556],{"encoding":41},"f(t)=\\frac12|t-1|",[15,34558,34560,34587,34670],{"className":34559,"ariaHidden":46},[45],[15,34561,34563,34566,34569,34572,34575,34578,34581,34584],{"className":34562},[50],[15,34564],{"className":34565,"style":139},[54],[15,34567,37],{"className":34568,"style":61},[59,60],[15,34570,113],{"className":34571},[146],[15,34573,769],{"className":34574},[59,60],[15,34576,120],{"className":34577},[153],[15,34579],{"className":34580,"style":158},[157],[15,34582,123],{"className":34583},[162],[15,34585],{"className":34586,"style":158},[157],[15,34588,34590,34593,34655,34658,34661,34664,34667],{"className":34589},[50],[15,34591],{"className":34592,"style":25903},[54],[15,34594,34596,34599,34652],{"className":34595},[59],[15,34597],{"className":34598},[146,441],[15,34600,34602],{"className":34601},[238],[15,34603,34605,34644],{"className":34604},[285,286],[15,34606,34608,34641],{"className":34607},[290],[15,34609,34611,34622,34630],{"className":34610,"style":22889},[294],[15,34612,34613,34616],{"style":457},[15,34614],{"className":34615,"style":461},[302],[15,34617,34619],{"className":34618},[59],[15,34620,2463],{"className":34621},[59],[15,34623,34624,34627],{"style":473},[15,34625],{"className":34626,"style":461},[302],[15,34628],{"className":34629,"style":481},[480],[15,34631,34632,34635],{"style":484},[15,34633],{"className":34634,"style":461},[302],[15,34636,34638],{"className":34637},[59],[15,34639,117],{"className":34640},[59],[15,34642,318],{"className":34643},[317],[15,34645,34647],{"className":34646},[290],[15,34648,34650],{"className":34649,"style":3778},[294],[15,34651],{},[15,34653],{"className":34654},[153,441],[15,34656,4808],{"className":34657},[59],[15,34659,769],{"className":34660},[59,60],[15,34662],{"className":34663,"style":2587},[157],[15,34665,4813],{"className":34666},[2591],[15,34668],{"className":34669,"style":2587},[157],[15,34671,34673,34676],{"className":34672},[50],[15,34674],{"className":34675,"style":139},[54],[15,34677,34679],{"className":34678},[59],"1∣",[11,34681,34682,34683,34748],{},"则 ",[15,34684,34686,34709],{"className":34685,"translate":19},[18],[15,34687,34689],{"className":34688},[23],[25,34690,34691],{"xmlns":27},[29,34692,34693,34707],{},[32,34694,34695,34697,34699,34701,34703,34705],{},[35,34696,37],{},[110,34698,113],{"stretchy":112},[115,34700,117],{},[110,34702,120],{"stretchy":112},[110,34704,123],{},[115,34706,126],{},[39,34708,129],{"encoding":41},[15,34710,34712,34739],{"className":34711,"ariaHidden":46},[45],[15,34713,34715,34718,34721,34724,34727,34730,34733,34736],{"className":34714},[50],[15,34716],{"className":34717,"style":139},[54],[15,34719,37],{"className":34720,"style":61},[59,60],[15,34722,113],{"className":34723},[146],[15,34725,117],{"className":34726},[59],[15,34728,120],{"className":34729},[153],[15,34731],{"className":34732,"style":158},[157],[15,34734,123],{"className":34735},[162],[15,34737],{"className":34738,"style":158},[157],[15,34740,34742,34745],{"className":34741},[50],[15,34743],{"className":34744,"style":172},[54],[15,34746,126],{"className":34747},[59]," 且凸（绝对值是凸函数），代入：",[15,34750,34752],{"className":34751,"translate":19},[180],[15,34753,34755,34866],{"className":34754,"translate":19},[18],[15,34756,34758],{"className":34757},[23],[25,34759,34760],{"xmlns":27,"display":189},[29,34761,34762,34863],{},[32,34763,34764,34770,34772,34774,34776,34778,34780,34782,34788,34790,34792,34808,34810,34812,34814,34820,34822,34824,34826,34828,34830,34832,34834,34836,34838,34840,34851,34853,34855,34857,34859,34861],{},[195,34765,34766,34768],{},[35,34767,199],{},[35,34769,37],{},[110,34771,113],{"stretchy":112},[35,34773,206],{},[35,34775,210],{"mathvariant":209},[35,34777,213],{},[110,34779,120],{"stretchy":112},[110,34781,123],{},[238,34783,34784,34786],{},[115,34785,117],{},[115,34787,2463],{},[110,34789,1287],{},[35,34791,944],{},[32,34793,34794,34796,34802,34804,34806],{},[110,34795,4808],{"fence":46},[238,34797,34798,34800],{},[35,34799,11],{},[35,34801,944],{},[110,34803,4813],{},[115,34805,117],{},[110,34807,4808],{"fence":46},[35,34809,244],{},[35,34811,774],{},[110,34813,123],{},[238,34815,34816,34818],{},[115,34817,117],{},[115,34819,2463],{},[110,34821,1287],{},[35,34823,4808],{"mathvariant":209},[35,34825,11],{},[110,34827,4813],{},[35,34829,944],{},[35,34831,4808],{"mathvariant":209},[1297,34833,1299],{},[35,34835,244],{},[35,34837,774],{},[110,34839,123],{},[195,34841,34842,34844],{},[35,34843,199],{},[32,34845,34846,34848],{},[35,34847,5392],{},[35,34849,34850],{},"V",[110,34852,113],{"stretchy":112},[35,34854,206],{},[35,34856,210],{"mathvariant":209},[35,34858,213],{},[110,34860,120],{"stretchy":112},[35,34862,4375],{"mathvariant":209},[39,34864,34865],{"encoding":41},"D_f(P\\|Q)\n=\\frac12\\int q\\left|\\frac{p}{q}-1\\right|dx\n=\\frac12\\int |p-q|\\,dx\n=D_{TV}(P\\|Q).",[15,34867,34869,34939,35197,35289,35319],{"className":34868,"ariaHidden":46},[45],[15,34870,34872,34875,34915,34918,34921,34924,34927,34930,34933,34936],{"className":34871},[50],[15,34873],{"className":34874,"style":270},[54],[15,34876,34878,34881],{"className":34877},[59],[15,34879,199],{"className":34880,"style":277},[59,60],[15,34882,34884],{"className":34883},[281],[15,34885,34887,34907],{"className":34886},[285,286],[15,34888,34890,34904],{"className":34889},[290],[15,34891,34893],{"className":34892,"style":295},[294],[15,34894,34895,34898],{"style":298},[15,34896],{"className":34897,"style":303},[302],[15,34899,34901],{"className":34900},[307,308,309,310],[15,34902,37],{"className":34903,"style":61},[59,60,310],[15,34905,318],{"className":34906},[317],[15,34908,34910],{"className":34909},[290],[15,34911,34913],{"className":34912,"style":325},[294],[15,34914],{},[15,34916,113],{"className":34917},[146],[15,34919,206],{"className":34920,"style":334},[59,60],[15,34922,210],{"className":34923},[59],[15,34925,213],{"className":34926},[59,60],[15,34928,120],{"className":34929},[153],[15,34931],{"className":34932,"style":158},[157],[15,34934,123],{"className":34935},[162],[15,34937],{"className":34938,"style":158},[157],[15,34940,34942,34945,35007,35010,35013,35016,35019,35022,35179,35182,35185,35188,35191,35194],{"className":34941},[50],[15,34943],{"className":34944,"style":359},[54],[15,34946,34948,34951,35004],{"className":34947},[59],[15,34949],{"className":34950},[146,441],[15,34952,34954],{"className":34953},[238],[15,34955,34957,34996],{"className":34956},[285,286],[15,34958,34960,34993],{"className":34959},[290],[15,34961,34963,34974,34982],{"className":34962,"style":22889},[294],[15,34964,34965,34968],{"style":457},[15,34966],{"className":34967,"style":461},[302],[15,34969,34971],{"className":34970},[59],[15,34972,2463],{"className":34973},[59],[15,34975,34976,34979],{"style":473},[15,34977],{"className":34978,"style":461},[302],[15,34980],{"className":34981,"style":481},[480],[15,34983,34984,34987],{"style":484},[15,34985],{"className":34986,"style":461},[302],[15,34988,34990],{"className":34989},[59],[15,34991,117],{"className":34992},[59],[15,34994,318],{"className":34995},[317],[15,34997,34999],{"className":34998},[290],[15,35000,35002],{"className":35001,"style":3778},[294],[15,35003],{},[15,35005],{"className":35006},[153,441],[15,35008],{"className":35009,"style":406},[157],[15,35011,1287],{"className":35012,"style":1487},[1484,1485,1486],[15,35014],{"className":35015,"style":406},[157],[15,35017,944],{"className":35018,"style":981},[59,60],[15,35020],{"className":35021,"style":406},[157],[15,35023,35025,35068,35130,35133,35136,35139,35142],{"className":35024},[410],[15,35026,35028],{"className":35027},[146],[15,35029,35031],{"className":35030},[419,14829],[15,35032,35034,35060],{"className":35033},[285,286],[15,35035,35037,35057],{"className":35036},[290],[15,35038,35040],{"className":35039,"style":1370},[294],[15,35041,35042,35046],{"style":1373},[15,35043],{"className":35044,"style":35045},[302],"height:4.4em;",[15,35047,35049],{"style":35048},"width:0.333em;height:2.4em;",[6323,35050,35054],{"xmlns":6325,"width":35051,"height":35052,"viewBox":35053},"0.333em","2.4em","0 0 333 2400",[6331,35055],{"d":35056},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[15,35058,318],{"className":35059},[317],[15,35061,35063],{"className":35062},[290],[15,35064,35066],{"className":35065,"style":1445},[294],[15,35067],{},[15,35069,35071,35074,35127],{"className":35070},[59],[15,35072],{"className":35073},[146,441],[15,35075,35077],{"className":35076},[238],[15,35078,35080,35119],{"className":35079},[285,286],[15,35081,35083,35116],{"className":35082},[290],[15,35084,35086,35097,35105],{"className":35085,"style":3554},[294],[15,35087,35088,35091],{"style":457},[15,35089],{"className":35090,"style":461},[302],[15,35092,35094],{"className":35093},[59],[15,35095,944],{"className":35096,"style":981},[59,60],[15,35098,35099,35102],{"style":473},[15,35100],{"className":35101,"style":461},[302],[15,35103],{"className":35104,"style":481},[480],[15,35106,35107,35110],{"style":484},[15,35108],{"className":35109,"style":461},[302],[15,35111,35113],{"className":35112},[59],[15,35114,11],{"className":35115},[59,60],[15,35117,318],{"className":35118},[317],[15,35120,35122],{"className":35121},[290],[15,35123,35125],{"className":35124,"style":506},[294],[15,35126],{},[15,35128],{"className":35129},[153,441],[15,35131],{"className":35132,"style":2587},[157],[15,35134,4813],{"className":35135},[2591],[15,35137],{"className":35138,"style":2587},[157],[15,35140,117],{"className":35141},[59],[15,35143,35145],{"className":35144},[153],[15,35146,35148],{"className":35147},[419,14829],[15,35149,35151,35171],{"className":35150},[285,286],[15,35152,35154,35168],{"className":35153},[290],[15,35155,35157],{"className":35156,"style":1370},[294],[15,35158,35159,35162],{"style":1373},[15,35160],{"className":35161,"style":35045},[302],[15,35163,35164],{"style":35048},[6323,35165,35166],{"xmlns":6325,"width":35051,"height":35052,"viewBox":35053},[6331,35167],{"d":35056},[15,35169,318],{"className":35170},[317],[15,35172,35174],{"className":35173},[290],[15,35175,35177],{"className":35176,"style":1445},[294],[15,35178],{},[15,35180],{"className":35181,"style":406},[157],[15,35183,244],{"className":35184},[59,60],[15,35186,774],{"className":35187},[59,60],[15,35189],{"className":35190,"style":158},[157],[15,35192,123],{"className":35193},[162],[15,35195],{"className":35196,"style":158},[157],[15,35198,35200,35203,35265,35268,35271,35274,35277,35280,35283,35286],{"className":35199},[50],[15,35201],{"className":35202,"style":5777},[54],[15,35204,35206,35209,35262],{"className":35205},[59],[15,35207],{"className":35208},[146,441],[15,35210,35212],{"className":35211},[238],[15,35213,35215,35254],{"className":35214},[285,286],[15,35216,35218,35251],{"className":35217},[290],[15,35219,35221,35232,35240],{"className":35220,"style":22889},[294],[15,35222,35223,35226],{"style":457},[15,35224],{"className":35225,"style":461},[302],[15,35227,35229],{"className":35228},[59],[15,35230,2463],{"className":35231},[59],[15,35233,35234,35237],{"style":473},[15,35235],{"className":35236,"style":461},[302],[15,35238],{"className":35239,"style":481},[480],[15,35241,35242,35245],{"style":484},[15,35243],{"className":35244,"style":461},[302],[15,35246,35248],{"className":35247},[59],[15,35249,117],{"className":35250},[59],[15,35252,318],{"className":35253},[317],[15,35255,35257],{"className":35256},[290],[15,35258,35260],{"className":35259,"style":3778},[294],[15,35261],{},[15,35263],{"className":35264},[153,441],[15,35266],{"className":35267,"style":406},[157],[15,35269,1287],{"className":35270,"style":1487},[1484,1485,1486],[15,35272],{"className":35273,"style":406},[157],[15,35275,4808],{"className":35276},[59],[15,35278,11],{"className":35279},[59,60],[15,35281],{"className":35282,"style":2587},[157],[15,35284,4813],{"className":35285},[2591],[15,35287],{"className":35288,"style":2587},[157],[15,35290,35292,35295,35298,35301,35304,35307,35310,35313,35316],{"className":35291},[50],[15,35293],{"className":35294,"style":139},[54],[15,35296,944],{"className":35297,"style":981},[59,60],[15,35299,4808],{"className":35300},[59],[15,35302],{"className":35303,"style":406},[157],[15,35305,244],{"className":35306},[59,60],[15,35308,774],{"className":35309},[59,60],[15,35311],{"className":35312,"style":158},[157],[15,35314,123],{"className":35315},[162],[15,35317],{"className":35318,"style":158},[157],[15,35320,35322,35325,35371,35374,35377,35380,35383,35386],{"className":35321},[50],[15,35323],{"className":35324,"style":139},[54],[15,35326,35328,35331],{"className":35327},[59],[15,35329,199],{"className":35330,"style":277},[59,60],[15,35332,35334],{"className":35333},[281],[15,35335,35337,35363],{"className":35336},[285,286],[15,35338,35340,35360],{"className":35339},[290],[15,35341,35343],{"className":35342,"style":379},[294],[15,35344,35345,35348],{"style":298},[15,35346],{"className":35347,"style":303},[302],[15,35349,35351],{"className":35350},[307,308,309,310],[15,35352,35354,35357],{"className":35353},[59,310],[15,35355,5392],{"className":35356,"style":334},[59,60,310],[15,35358,34850],{"className":35359,"style":2587},[59,60,310],[15,35361,318],{"className":35362},[317],[15,35364,35366],{"className":35365},[290],[15,35367,35369],{"className":35368,"style":7968},[294],[15,35370],{},[15,35372,113],{"className":35373},[146],[15,35375,206],{"className":35376,"style":334},[59,60],[15,35378,210],{"className":35379},[59],[15,35381,213],{"className":35382},[59,60],[15,35384,120],{"className":35385},[153],[15,35387,4375],{"className":35388},[59],[11,35390,35391,35392,35657,35658,35783],{},"一般测度上 ",[15,35393,35395,35468],{"className":35394,"translate":19},[18],[15,35396,35398],{"className":35397},[23],[25,35399,35400],{"xmlns":27},[29,35401,35402,35465],{},[32,35403,35404,35414,35416,35418,35420,35422,35424,35426,35443,35445,35447,35449,35451,35453,35455,35457,35459,35461,35463],{},[195,35405,35406,35408],{},[35,35407,199],{},[32,35409,35410,35412],{},[35,35411,5392],{},[35,35413,34850],{},[110,35415,113],{"stretchy":112},[35,35417,206],{},[110,35419,551],{"separator":46},[35,35421,213],{},[110,35423,120],{"stretchy":112},[110,35425,123],{},[195,35427,35428,35435],{},[32,35429,35430,35433],{},[35,35431,35432],{},"sup",[110,35434,4103],{},[32,35436,35437,35439,35441],{},[35,35438,603],{},[110,35440,5909],{},[35,35442,603],{"mathvariant":597},[35,35444,4808],{"mathvariant":209},[35,35446,206],{},[110,35448,113],{"stretchy":112},[35,35450,603],{},[110,35452,120],{"stretchy":112},[110,35454,4813],{},[35,35456,213],{},[110,35458,113],{"stretchy":112},[35,35460,603],{},[110,35462,120],{"stretchy":112},[35,35464,4808],{"mathvariant":209},[39,35466,35467],{"encoding":41},"D_{TV}(P,Q)=\\sup_{A\\in\\mathcal A}|P(A)-Q(A)|",[15,35469,35471,35550,35636],{"className":35470,"ariaHidden":46},[45],[15,35472,35474,35477,35523,35526,35529,35532,35535,35538,35541,35544,35547],{"className":35473},[50],[15,35475],{"className":35476,"style":139},[54],[15,35478,35480,35483],{"className":35479},[59],[15,35481,199],{"className":35482,"style":277},[59,60],[15,35484,35486],{"className":35485},[281],[15,35487,35489,35515],{"className":35488},[285,286],[15,35490,35492,35512],{"className":35491},[290],[15,35493,35495],{"className":35494,"style":379},[294],[15,35496,35497,35500],{"style":298},[15,35498],{"className":35499,"style":303},[302],[15,35501,35503],{"className":35502},[307,308,309,310],[15,35504,35506,35509],{"className":35505},[59,310],[15,35507,5392],{"className":35508,"style":334},[59,60,310],[15,35510,34850],{"className":35511,"style":2587},[59,60,310],[15,35513,318],{"className":35514},[317],[15,35516,35518],{"className":35517},[290],[15,35519,35521],{"className":35520,"style":7968},[294],[15,35522],{},[15,35524,113],{"className":35525},[146],[15,35527,206],{"className":35528,"style":334},[59,60],[15,35530,551],{"className":35531},[573],[15,35533],{"className":35534,"style":406},[157],[15,35536,213],{"className":35537},[59,60],[15,35539,120],{"className":35540},[153],[15,35542],{"className":35543,"style":158},[157],[15,35545,123],{"className":35546},[162],[15,35548],{"className":35549,"style":158},[157],[15,35551,35553,35557,35609,35612,35615,35618,35621,35624,35627,35630,35633],{"className":35552},[50],[15,35554],{"className":35555,"style":35556},[54],"height:1.0215em;vertical-align:-0.2715em;",[15,35558,35560,35563],{"className":35559},[1484],[15,35561,35432],{"className":35562},[1484],[15,35564,35566],{"className":35565},[281],[15,35567,35569,35600],{"className":35568},[285,286],[15,35570,35572,35597],{"className":35571},[290],[15,35573,35576],{"className":35574,"style":35575},[294],"height:0.2342em;",[15,35577,35579,35582],{"style":35578},"top:-2.4559em;margin-right:0.05em;",[15,35580],{"className":35581,"style":303},[302],[15,35583,35585],{"className":35584},[307,308,309,310],[15,35586,35588,35591,35594],{"className":35587},[59,310],[15,35589,603],{"className":35590},[59,60,310],[15,35592,5909],{"className":35593},[162,310],[15,35595,603],{"className":35596},[59,624,310],[15,35598,318],{"className":35599},[317],[15,35601,35603],{"className":35602},[290],[15,35604,35607],{"className":35605,"style":35606},[294],"height:0.2715em;",[15,35608],{},[15,35610],{"className":35611,"style":406},[157],[15,35613,4808],{"className":35614},[59],[15,35616,206],{"className":35617,"style":334},[59,60],[15,35619,113],{"className":35620},[146],[15,35622,603],{"className":35623},[59,60],[15,35625,120],{"className":35626},[153],[15,35628],{"className":35629,"style":2587},[157],[15,35631,4813],{"className":35632},[2591],[15,35634],{"className":35635,"style":2587},[157],[15,35637,35639,35642,35645,35648,35651,35654],{"className":35638},[50],[15,35640],{"className":35641,"style":139},[54],[15,35643,213],{"className":35644},[59,60],[15,35646,113],{"className":35647},[146],[15,35649,603],{"className":35650},[59,60],[15,35652,120],{"className":35653},[153],[15,35655,4808],{"className":35656},[59],"；两个表达式相等（这是全变差的对偶刻画）。注意 ",[15,35659,35661,35695],{"className":35660,"translate":19},[18],[15,35662,35664],{"className":35663},[23],[25,35665,35666],{"xmlns":27},[29,35667,35668,35692],{},[32,35669,35670,35680,35682,35684,35686,35688,35690],{},[195,35671,35672,35674],{},[35,35673,199],{},[32,35675,35676,35678],{},[35,35677,5392],{},[35,35679,34850],{},[110,35681,5909],{},[110,35683,230],{"stretchy":112},[115,35685,126],{},[110,35687,551],{"separator":46},[115,35689,117],{},[110,35691,257],{"stretchy":112},[39,35693,35694],{"encoding":41},"D_{TV}\\in[0,1]",[15,35696,35698,35759],{"className":35697,"ariaHidden":46},[45],[15,35699,35701,35704,35750,35753,35756],{"className":35700},[50],[15,35702],{"className":35703,"style":15961},[54],[15,35705,35707,35710],{"className":35706},[59],[15,35708,199],{"className":35709,"style":277},[59,60],[15,35711,35713],{"className":35712},[281],[15,35714,35716,35742],{"className":35715},[285,286],[15,35717,35719,35739],{"className":35718},[290],[15,35720,35722],{"className":35721,"style":379},[294],[15,35723,35724,35727],{"style":298},[15,35725],{"className":35726,"style":303},[302],[15,35728,35730],{"className":35729},[307,308,309,310],[15,35731,35733,35736],{"className":35732},[59,310],[15,35734,5392],{"className":35735,"style":334},[59,60,310],[15,35737,34850],{"className":35738,"style":2587},[59,60,310],[15,35740,318],{"className":35741},[317],[15,35743,35745],{"className":35744},[290],[15,35746,35748],{"className":35747,"style":7968},[294],[15,35749],{},[15,35751],{"className":35752,"style":158},[157],[15,35754,5909],{"className":35755},[162],[15,35757],{"className":35758,"style":158},[157],[15,35760,35762,35765,35768,35771,35774,35777,35780],{"className":35761},[50],[15,35763],{"className":35764,"style":139},[54],[15,35766,230],{"className":35767},[146],[15,35769,126],{"className":35770},[59],[15,35772,551],{"className":35773},[573],[15,35775],{"className":35776,"style":406},[157],[15,35778,117],{"className":35779},[59],[15,35781,257],{"className":35782},[153],"，总有界。",[11,35785,35786,9400,35789,36175],{},[1225,35787,35788],{},"斜共轭",[15,35790,35792,35856],{"className":35791,"translate":19},[18],[15,35793,35795],{"className":35794},[23],[25,35796,35797],{"xmlns":27},[29,35798,35799,35853],{},[32,35800,35801,35803,35805,35811,35813,35819,35821,35823,35825,35827,35833,35835,35837,35839,35841,35843,35845,35847,35849,35851],{},[35,35802,769],{},[110,35804,3299],{},[238,35806,35807,35809],{},[115,35808,117],{},[115,35810,2463],{},[35,35812,4808],{"mathvariant":209},[238,35814,35815,35817],{},[115,35816,117],{},[35,35818,769],{},[110,35820,4813],{},[115,35822,117],{},[35,35824,4808],{"mathvariant":209},[110,35826,123],{},[238,35828,35829,35831],{},[115,35830,117],{},[115,35832,2463],{},[35,35834,4808],{"mathvariant":209},[115,35836,117],{},[110,35838,4813],{},[35,35840,769],{},[35,35842,4808],{"mathvariant":209},[110,35844,123],{},[35,35846,37],{},[110,35848,113],{"stretchy":112},[35,35850,769],{},[110,35852,120],{"stretchy":112},[39,35854,35855],{"encoding":41},"t\\cdot\\frac12|\\frac1t-1|=\\frac12|1-t|=f(t)",[15,35857,35859,35877,36031,36049,36136,36157],{"className":35858,"ariaHidden":46},[45],[15,35860,35862,35865,35868,35871,35874],{"className":35861},[50],[15,35863],{"className":35864,"style":5343},[54],[15,35866,769],{"className":35867},[59,60],[15,35869],{"className":35870,"style":2587},[157],[15,35872,3299],{"className":35873},[2591],[15,35875],{"className":35876,"style":2587},[157],[15,35878,35880,35883,35951,35954,36022,36025,36028],{"className":35879},[50],[15,35881],{"className":35882,"style":2505},[54],[15,35884,35886,35889,35948],{"className":35885},[59],[15,35887],{"className":35888},[146,441],[15,35890,35892],{"className":35891},[238],[15,35893,35895,35940],{"className":35894},[285,286],[15,35896,35898,35937],{"className":35897},[290],[15,35899,35901,35915,35923],{"className":35900,"style":2524},[294],[15,35902,35903,35906],{"style":2527},[15,35904],{"className":35905,"style":461},[302],[15,35907,35909],{"className":35908},[307,308,309,310],[15,35910,35912],{"className":35911},[59,310],[15,35913,2463],{"className":35914},[59,310],[15,35916,35917,35920],{"style":473},[15,35918],{"className":35919,"style":461},[302],[15,35921],{"className":35922,"style":481},[480],[15,35924,35925,35928],{"style":2550},[15,35926],{"className":35927,"style":461},[302],[15,35929,35931],{"className":35930},[307,308,309,310],[15,35932,35934],{"className":35933},[59,310],[15,35935,117],{"className":35936},[59,310],[15,35938,318],{"className":35939},[317],[15,35941,35943],{"className":35942},[290],[15,35944,35946],{"className":35945,"style":2572},[294],[15,35947],{},[15,35949],{"className":35950},[153,441],[15,35952,4808],{"className":35953},[59],[15,35955,35957,35960,36019],{"className":35956},[59],[15,35958],{"className":35959},[146,441],[15,35961,35963],{"className":35962},[238],[15,35964,35966,36011],{"className":35965},[285,286],[15,35967,35969,36008],{"className":35968},[290],[15,35970,35972,35986,35994],{"className":35971,"style":2524},[294],[15,35973,35974,35977],{"style":2527},[15,35975],{"className":35976,"style":461},[302],[15,35978,35980],{"className":35979},[307,308,309,310],[15,35981,35983],{"className":35982},[59,310],[15,35984,769],{"className":35985},[59,60,310],[15,35987,35988,35991],{"style":473},[15,35989],{"className":35990,"style":461},[302],[15,35992],{"className":35993,"style":481},[480],[15,35995,35996,35999],{"style":2550},[15,35997],{"className":35998,"style":461},[302],[15,36000,36002],{"className":36001},[307,308,309,310],[15,36003,36005],{"className":36004},[59,310],[15,36006,117],{"className":36007},[59,310],[15,36009,318],{"className":36010},[317],[15,36012,36014],{"className":36013},[290],[15,36015,36017],{"className":36016,"style":2572},[294],[15,36018],{},[15,36020],{"className":36021},[153,441],[15,36023],{"className":36024,"style":2587},[157],[15,36026,4813],{"className":36027},[2591],[15,36029],{"className":36030,"style":2587},[157],[15,36032,36034,36037,36040,36043,36046],{"className":36033},[50],[15,36035],{"className":36036,"style":139},[54],[15,36038,34679],{"className":36039},[59],[15,36041],{"className":36042,"style":158},[157],[15,36044,123],{"className":36045},[162],[15,36047],{"className":36048,"style":158},[157],[15,36050,36052,36055,36123,36127,36130,36133],{"className":36051},[50],[15,36053],{"className":36054,"style":2505},[54],[15,36056,36058,36061,36120],{"className":36057},[59],[15,36059],{"className":36060},[146,441],[15,36062,36064],{"className":36063},[238],[15,36065,36067,36112],{"className":36066},[285,286],[15,36068,36070,36109],{"className":36069},[290],[15,36071,36073,36087,36095],{"className":36072,"style":2524},[294],[15,36074,36075,36078],{"style":2527},[15,36076],{"className":36077,"style":461},[302],[15,36079,36081],{"className":36080},[307,308,309,310],[15,36082,36084],{"className":36083},[59,310],[15,36085,2463],{"className":36086},[59,310],[15,36088,36089,36092],{"style":473},[15,36090],{"className":36091,"style":461},[302],[15,36093],{"className":36094,"style":481},[480],[15,36096,36097,36100],{"style":2550},[15,36098],{"className":36099,"style":461},[302],[15,36101,36103],{"className":36102},[307,308,309,310],[15,36104,36106],{"className":36105},[59,310],[15,36107,117],{"className":36108},[59,310],[15,36110,318],{"className":36111},[317],[15,36113,36115],{"className":36114},[290],[15,36116,36118],{"className":36117,"style":2572},[294],[15,36119],{},[15,36121],{"className":36122},[153,441],[15,36124,36126],{"className":36125},[59],"∣1",[15,36128],{"className":36129,"style":2587},[157],[15,36131,4813],{"className":36132},[2591],[15,36134],{"className":36135,"style":2587},[157],[15,36137,36139,36142,36145,36148,36151,36154],{"className":36138},[50],[15,36140],{"className":36141,"style":139},[54],[15,36143,769],{"className":36144},[59,60],[15,36146,4808],{"className":36147},[59],[15,36149],{"className":36150,"style":158},[157],[15,36152,123],{"className":36153},[162],[15,36155],{"className":36156,"style":158},[157],[15,36158,36160,36163,36166,36169,36172],{"className":36159},[50],[15,36161],{"className":36162,"style":139},[54],[15,36164,37],{"className":36165,"style":61},[59,60],[15,36167,113],{"className":36168},[146],[15,36170,769],{"className":36171},[59,60],[15,36173,120],{"className":36174},[153],"，所以 TV 是对称的。",[11,36177,36178,36180,36181,36184],{},[1225,36179,24193],{}," 全变差是概率测度空间上真正的",[1225,36182,36183],{},"度量","（对称、满足三角不等式），它等于两个分布在一件事上能给出的最大概率差：",[15,36186,36188],{"className":36187,"translate":19},[180],[15,36189,36191,36265],{"className":36190,"translate":19},[18],[15,36192,36194],{"className":36193},[23],[25,36195,36196],{"xmlns":27,"display":189},[29,36197,36198,36262],{},[32,36199,36200,36210,36212,36214,36216,36218,36220,36222,36238,36240,36242,36244,36246,36248,36250,36252,36254,36256,36258,36260],{},[195,36201,36202,36204],{},[35,36203,199],{},[32,36205,36206,36208],{},[35,36207,5392],{},[35,36209,34850],{},[110,36211,113],{"stretchy":112},[35,36213,206],{},[110,36215,551],{"separator":46},[35,36217,213],{},[110,36219,120],{"stretchy":112},[110,36221,123],{},[6016,36223,36224,36230],{},[32,36225,36226,36228],{},[35,36227,35432],{},[110,36229,4103],{},[32,36231,36232,36234,36236],{},[35,36233,603],{},[110,36235,5909],{},[35,36237,603],{"mathvariant":597},[110,36239,4808],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,36241,206],{},[110,36243,113],{"stretchy":112},[35,36245,603],{},[110,36247,120],{"stretchy":112},[110,36249,4813],{},[35,36251,213],{},[110,36253,113],{"stretchy":112},[35,36255,603],{},[110,36257,120],{"stretchy":112},[110,36259,4808],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,36261,4375],{"mathvariant":209},[39,36263,36264],{"encoding":41},"D_{TV}(P,Q)\n=\\sup_{A\\in\\mathcal A}\\big|P(A)-Q(A)\\big| .",[15,36266,36268,36347,36473],{"className":36267,"ariaHidden":46},[45],[15,36269,36271,36274,36320,36323,36326,36329,36332,36335,36338,36341,36344],{"className":36270},[50],[15,36272],{"className":36273,"style":139},[54],[15,36275,36277,36280],{"className":36276},[59],[15,36278,199],{"className":36279,"style":277},[59,60],[15,36281,36283],{"className":36282},[281],[15,36284,36286,36312],{"className":36285},[285,286],[15,36287,36289,36309],{"className":36288},[290],[15,36290,36292],{"className":36291,"style":379},[294],[15,36293,36294,36297],{"style":298},[15,36295],{"className":36296,"style":303},[302],[15,36298,36300],{"className":36299},[307,308,309,310],[15,36301,36303,36306],{"className":36302},[59,310],[15,36304,5392],{"className":36305,"style":334},[59,60,310],[15,36307,34850],{"className":36308,"style":2587},[59,60,310],[15,36310,318],{"className":36311},[317],[15,36313,36315],{"className":36314},[290],[15,36316,36318],{"className":36317,"style":7968},[294],[15,36319],{},[15,36321,113],{"className":36322},[146],[15,36324,206],{"className":36325,"style":334},[59,60],[15,36327,551],{"className":36328},[573],[15,36330],{"className":36331,"style":406},[157],[15,36333,213],{"className":36334},[59,60],[15,36336,120],{"className":36337},[153],[15,36339],{"className":36340,"style":158},[157],[15,36342,123],{"className":36343},[162],[15,36345],{"className":36346,"style":158},[157],[15,36348,36350,36354,36409,36412,36452,36455,36458,36461,36464,36467,36470],{"className":36349},[50],[15,36351],{"className":36352,"style":36353},[54],"height:1.8161em;vertical-align:-0.9661em;",[15,36355,36357],{"className":36356},[1484,13716],[15,36358,36360,36400],{"className":36359},[285,286],[15,36361,36363,36397],{"className":36362},[290],[15,36364,36366,36387],{"className":36365,"style":2345},[294],[15,36367,36369,36372],{"style":36368},"top:-2.1612em;margin-left:0em;",[15,36370],{"className":36371,"style":461},[302],[15,36373,36375],{"className":36374},[307,308,309,310],[15,36376,36378,36381,36384],{"className":36377},[59,310],[15,36379,603],{"className":36380},[59,60,310],[15,36382,5909],{"className":36383},[162,310],[15,36385,603],{"className":36386},[59,624,310],[15,36388,36389,36392],{"style":11863},[15,36390],{"className":36391,"style":461},[302],[15,36393,36394],{},[15,36395,35432],{"className":36396},[1484],[15,36398,318],{"className":36399},[317],[15,36401,36403],{"className":36402},[290],[15,36404,36407],{"className":36405,"style":36406},[294],"height:0.9661em;",[15,36408],{},[15,36410],{"className":36411,"style":406},[157],[15,36413,36415],{"className":36414},[59],[15,36416,36418],{"className":36417},[419,14829],[15,36419,36421,36444],{"className":36420},[285,286],[15,36422,36424,36441],{"className":36423},[290],[15,36425,36427],{"className":36426,"style":14839},[294],[15,36428,36429,36432],{"style":14842},[15,36430],{"className":36431,"style":14846},[302],[15,36433,36435],{"style":36434},"width:0.333em;height:1.2em;",[6323,36436,36438],{"xmlns":6325,"width":35051,"height":9450,"viewBox":36437},"0 0 333 1200",[6331,36439],{"d":36440},"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",[15,36442,318],{"className":36443},[317],[15,36445,36447],{"className":36446},[290],[15,36448,36450],{"className":36449,"style":14866},[294],[15,36451],{},[15,36453,206],{"className":36454,"style":334},[59,60],[15,36456,113],{"className":36457},[146],[15,36459,603],{"className":36460},[59,60],[15,36462,120],{"className":36463},[153],[15,36465],{"className":36466,"style":2587},[157],[15,36468,4813],{"className":36469},[2591],[15,36471],{"className":36472,"style":2587},[157],[15,36474,36476,36479,36482,36485,36488,36491,36528],{"className":36475},[50],[15,36477],{"className":36478,"style":20563},[54],[15,36480,213],{"className":36481},[59,60],[15,36483,113],{"className":36484},[146],[15,36486,603],{"className":36487},[59,60],[15,36489,120],{"className":36490},[153],[15,36492,36494],{"className":36493},[59],[15,36495,36497],{"className":36496},[419,14829],[15,36498,36500,36520],{"className":36499},[285,286],[15,36501,36503,36517],{"className":36502},[290],[15,36504,36506],{"className":36505,"style":14839},[294],[15,36507,36508,36511],{"style":14842},[15,36509],{"className":36510,"style":14846},[302],[15,36512,36513],{"style":36434},[6323,36514,36515],{"xmlns":6325,"width":35051,"height":9450,"viewBox":36437},[6331,36516],{"d":36440},[15,36518,318],{"className":36519},[317],[15,36521,36523],{"className":36522},[290],[15,36524,36526],{"className":36525,"style":14866},[294],[15,36527],{},[15,36529,4375],{"className":36530},[59],[11,36532,36533,36534,2409,36562,36590,36591,36785,36786,36789,36790,36842,36843,37145],{},"它还有一个判决论解释：在等先验下用最优检验区分 ",[15,36535,36537,36550],{"className":36536,"translate":19},[18],[15,36538,36540],{"className":36539},[23],[25,36541,36542],{"xmlns":27},[29,36543,36544,36548],{},[32,36545,36546],{},[35,36547,206],{},[39,36549,206],{"encoding":41},[15,36551,36553],{"className":36552,"ariaHidden":46},[45],[15,36554,36556,36559],{"className":36555},[50],[15,36557],{"className":36558,"style":664},[54],[15,36560,206],{"className":36561,"style":334},[59,60],[15,36563,36565,36578],{"className":36564,"translate":19},[18],[15,36566,36568],{"className":36567},[23],[25,36569,36570],{"xmlns":27},[29,36571,36572,36576],{},[32,36573,36574],{},[35,36575,213],{},[39,36577,213],{"encoding":41},[15,36579,36581],{"className":36580,"ariaHidden":46},[45],[15,36582,36584,36587],{"className":36583},[50],[15,36585],{"className":36586,"style":566},[54],[15,36588,213],{"className":36589},[59,60]," 时，最小平均错误率为 ",[15,36592,36594,36632],{"className":36593,"translate":19},[18],[15,36595,36597],{"className":36596},[23],[25,36598,36599],{"xmlns":27},[29,36600,36601,36629],{},[32,36602,36603,36611,36613,36615,36617,36627],{},[1255,36604,36605],{"scriptlevel":126,"displaystyle":112},[238,36606,36607,36609],{},[115,36608,117],{},[115,36610,2463],{},[110,36612,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,36614,117],{},[110,36616,4813],{},[195,36618,36619,36621],{},[35,36620,199],{},[32,36622,36623,36625],{},[35,36624,5392],{},[35,36626,34850],{},[110,36628,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[39,36630,36631],{"encoding":41},"\\tfrac12\\big(1-D_{TV}\\big)",[15,36633,36635,36727],{"className":36634,"ariaHidden":46},[45],[15,36636,36638,36641,36709,36715,36718,36721,36724],{"className":36637},[50],[15,36639],{"className":36640,"style":20563},[54],[15,36642,36644,36647,36706],{"className":36643},[59],[15,36645],{"className":36646},[146,441],[15,36648,36650],{"className":36649},[238],[15,36651,36653,36698],{"className":36652},[285,286],[15,36654,36656,36695],{"className":36655},[290],[15,36657,36659,36673,36681],{"className":36658,"style":2524},[294],[15,36660,36661,36664],{"style":2527},[15,36662],{"className":36663,"style":461},[302],[15,36665,36667],{"className":36666},[307,308,309,310],[15,36668,36670],{"className":36669},[59,310],[15,36671,2463],{"className":36672},[59,310],[15,36674,36675,36678],{"style":473},[15,36676],{"className":36677,"style":461},[302],[15,36679],{"className":36680,"style":481},[480],[15,36682,36683,36686],{"style":2550},[15,36684],{"className":36685,"style":461},[302],[15,36687,36689],{"className":36688},[307,308,309,310],[15,36690,36692],{"className":36691},[59,310],[15,36693,117],{"className":36694},[59,310],[15,36696,318],{"className":36697},[317],[15,36699,36701],{"className":36700},[290],[15,36702,36704],{"className":36703,"style":2572},[294],[15,36705],{},[15,36707],{"className":36708},[153,441],[15,36710,36712],{"className":36711},[59],[15,36713,113],{"className":36714},[419,9674],[15,36716,117],{"className":36717},[59],[15,36719],{"className":36720,"style":2587},[157],[15,36722,4813],{"className":36723},[2591],[15,36725],{"className":36726,"style":2587},[157],[15,36728,36730,36733,36779],{"className":36729},[50],[15,36731],{"className":36732,"style":20563},[54],[15,36734,36736,36739],{"className":36735},[59],[15,36737,199],{"className":36738,"style":277},[59,60],[15,36740,36742],{"className":36741},[281],[15,36743,36745,36771],{"className":36744},[285,286],[15,36746,36748,36768],{"className":36747},[290],[15,36749,36751],{"className":36750,"style":379},[294],[15,36752,36753,36756],{"style":298},[15,36754],{"className":36755,"style":303},[302],[15,36757,36759],{"className":36758},[307,308,309,310],[15,36760,36762,36765],{"className":36761},[59,310],[15,36763,5392],{"className":36764,"style":334},[59,60,310],[15,36766,34850],{"className":36767,"style":2587},[59,60,310],[15,36769,318],{"className":36770},[317],[15,36772,36774],{"className":36773},[290],[15,36775,36777],{"className":36776,"style":7968},[294],[15,36778],{},[15,36780,36782],{"className":36781},[59],[15,36783,120],{"className":36784},[419,9674],"，因此 TV 直接度量了",[1225,36787,36788],{},"可分性","，「TV 小」就等于「几乎分不开」。TV 是这里所有 f-散度中最「弱」的标尺（总在 ",[15,36791,36793,36815],{"className":36792,"translate":19},[18],[15,36794,36796],{"className":36795},[23],[25,36797,36798],{"xmlns":27},[29,36799,36800,36812],{},[32,36801,36802,36804,36806,36808,36810],{},[110,36803,230],{"stretchy":112},[115,36805,126],{},[110,36807,551],{"separator":46},[115,36809,117],{},[110,36811,257],{"stretchy":112},[39,36813,36814],{"encoding":41},"[0,1]",[15,36816,36818],{"className":36817,"ariaHidden":46},[45],[15,36819,36821,36824,36827,36830,36833,36836,36839],{"className":36820},[50],[15,36822],{"className":36823,"style":139},[54],[15,36825,230],{"className":36826},[146],[15,36828,126],{"className":36829},[59],[15,36831,551],{"className":36832},[573],[15,36834],{"className":36835,"style":406},[157],[15,36837,117],{"className":36838},[59],[15,36840,257],{"className":36841},[153]," 内），但按 Csiszár 定理它与 KL 诱导同一个拓扑，所以常常已经够用；在一维实直线上它退化为 Kolmogorov 距离 ",[15,36844,36846,36911],{"className":36845,"translate":19},[18],[15,36847,36849],{"className":36848},[23],[25,36850,36851],{"xmlns":27},[29,36852,36853,36908],{},[32,36854,36855,36865,36867,36877,36879,36886,36888,36890,36892,36894,36900,36902,36904,36906],{},[195,36856,36857,36859],{},[35,36858,199],{},[32,36860,36861,36863],{},[35,36862,5392],{},[35,36864,34850],{},[110,36866,123],{},[195,36868,36869,36875],{},[32,36870,36871,36873],{},[35,36872,35432],{},[110,36874,4103],{},[35,36876,774],{},[35,36878,4808],{"mathvariant":209},[195,36880,36881,36884],{},[35,36882,36883],{},"F",[35,36885,206],{},[110,36887,113],{"stretchy":112},[35,36889,774],{},[110,36891,120],{"stretchy":112},[110,36893,4813],{},[195,36895,36896,36898],{},[35,36897,36883],{},[35,36899,213],{},[110,36901,113],{"stretchy":112},[35,36903,774],{},[110,36905,120],{"stretchy":112},[35,36907,4808],{"mathvariant":209},[39,36909,36910],{"encoding":41},"D_{TV}=\\sup_x|F_P(x)-F_Q(x)|",[15,36912,36914,36975,37087],{"className":36913,"ariaHidden":46},[45],[15,36915,36917,36920,36966,36969,36972],{"className":36916},[50],[15,36918],{"className":36919,"style":15961},[54],[15,36921,36923,36926],{"className":36922},[59],[15,36924,199],{"className":36925,"style":277},[59,60],[15,36927,36929],{"className":36928},[281],[15,36930,36932,36958],{"className":36931},[285,286],[15,36933,36935,36955],{"className":36934},[290],[15,36936,36938],{"className":36937,"style":379},[294],[15,36939,36940,36943],{"style":298},[15,36941],{"className":36942,"style":303},[302],[15,36944,36946],{"className":36945},[307,308,309,310],[15,36947,36949,36952],{"className":36948},[59,310],[15,36950,5392],{"className":36951,"style":334},[59,60,310],[15,36953,34850],{"className":36954,"style":2587},[59,60,310],[15,36956,318],{"className":36957},[317],[15,36959,36961],{"className":36960},[290],[15,36962,36964],{"className":36963,"style":7968},[294],[15,36965],{},[15,36967],{"className":36968,"style":158},[157],[15,36970,123],{"className":36971},[162],[15,36973],{"className":36974,"style":158},[157],[15,36976,36978,36981,37023,37026,37029,37069,37072,37075,37078,37081,37084],{"className":36977},[50],[15,36979],{"className":36980,"style":139},[54],[15,36982,36984,36987],{"className":36983},[1484],[15,36985,35432],{"className":36986},[1484],[15,36988,36990],{"className":36989},[281],[15,36991,36993,37014],{"className":36992},[285,286],[15,36994,36996,37011],{"className":36995},[290],[15,36997,37000],{"className":36998,"style":36999},[294],"height:0.0573em;",[15,37001,37002,37005],{"style":35578},[15,37003],{"className":37004,"style":303},[302],[15,37006,37008],{"className":37007},[307,308,309,310],[15,37009,774],{"className":37010},[59,60,310],[15,37012,318],{"className":37013},[317],[15,37015,37017],{"className":37016},[290],[15,37018,37021],{"className":37019,"style":37020},[294],"height:0.2441em;",[15,37022],{},[15,37024],{"className":37025,"style":406},[157],[15,37027,4808],{"className":37028},[59],[15,37030,37032,37035],{"className":37031},[59],[15,37033,36883],{"className":37034,"style":334},[59,60],[15,37036,37038],{"className":37037},[281],[15,37039,37041,37061],{"className":37040},[285,286],[15,37042,37044,37058],{"className":37043},[290],[15,37045,37047],{"className":37046,"style":379},[294],[15,37048,37049,37052],{"style":11136},[15,37050],{"className":37051,"style":303},[302],[15,37053,37055],{"className":37054},[307,308,309,310],[15,37056,206],{"className":37057,"style":334},[59,60,310],[15,37059,318],{"className":37060},[317],[15,37062,37064],{"className":37063},[290],[15,37065,37067],{"className":37066,"style":7968},[294],[15,37068],{},[15,37070,113],{"className":37071},[146],[15,37073,774],{"className":37074},[59,60],[15,37076,120],{"className":37077},[153],[15,37079],{"className":37080,"style":2587},[157],[15,37082,4813],{"className":37083},[2591],[15,37085],{"className":37086,"style":2587},[157],[15,37088,37090,37093,37133,37136,37139,37142],{"className":37089},[50],[15,37091],{"className":37092,"style":270},[54],[15,37094,37096,37099],{"className":37095},[59],[15,37097,36883],{"className":37098,"style":334},[59,60],[15,37100,37102],{"className":37101},[281],[15,37103,37105,37125],{"className":37104},[285,286],[15,37106,37108,37122],{"className":37107},[290],[15,37109,37111],{"className":37110,"style":379},[294],[15,37112,37113,37116],{"style":11136},[15,37114],{"className":37115,"style":303},[302],[15,37117,37119],{"className":37118},[307,308,309,310],[15,37120,213],{"className":37121},[59,60,310],[15,37123,318],{"className":37124},[317],[15,37126,37128],{"className":37127},[290],[15,37129,37131],{"className":37130,"style":325},[294],[15,37132],{},[15,37134,113],{"className":37135},[146],[15,37137,774],{"className":37138},[59,60],[15,37140,120],{"className":37141},[153],[15,37143,4808],{"className":37144},[59],"。马尔可夫链的混合时间、耦合构造与统计距离（total variation distance）都以它为核心。",[2311,37147,37149],{"id":37148},"_34-卡方散度","3.4 卡方散度",[11,37151,21473],{},[15,37153,37155],{"className":37154,"translate":19},[180],[15,37156,37158,37194],{"className":37157,"translate":19},[18],[15,37159,37161],{"className":37160},[23],[25,37162,37163],{"xmlns":27,"display":189},[29,37164,37165,37191],{},[32,37166,37167,37169,37171,37173,37175,37177,37179,37181,37183,37185],{},[35,37168,37],{},[110,37170,113],{"stretchy":112},[35,37172,769],{},[110,37174,120],{"stretchy":112},[110,37176,123],{},[110,37178,113],{"stretchy":112},[35,37180,769],{},[110,37182,4813],{},[115,37184,117],{},[6814,37186,37187,37189],{},[110,37188,120],{"stretchy":112},[115,37190,2463],{},[39,37192,37193],{"encoding":41},"f(t)=(t-1)^2",[15,37195,37197,37224,37245],{"className":37196,"ariaHidden":46},[45],[15,37198,37200,37203,37206,37209,37212,37215,37218,37221],{"className":37199},[50],[15,37201],{"className":37202,"style":139},[54],[15,37204,37],{"className":37205,"style":61},[59,60],[15,37207,113],{"className":37208},[146],[15,37210,769],{"className":37211},[59,60],[15,37213,120],{"className":37214},[153],[15,37216],{"className":37217,"style":158},[157],[15,37219,123],{"className":37220},[162],[15,37222],{"className":37223,"style":158},[157],[15,37225,37227,37230,37233,37236,37239,37242],{"className":37226},[50],[15,37228],{"className":37229,"style":139},[54],[15,37231,113],{"className":37232},[146],[15,37234,769],{"className":37235},[59,60],[15,37237],{"className":37238,"style":2587},[157],[15,37240,4813],{"className":37241},[2591],[15,37243],{"className":37244,"style":2587},[157],[15,37246,37248,37252,37255],{"className":37247},[50],[15,37249],{"className":37250,"style":37251},[54],"height:1.1141em;vertical-align:-0.25em;",[15,37253,117],{"className":37254},[59],[15,37256,37258,37261],{"className":37257},[153],[15,37259,120],{"className":37260},[153],[15,37262,37264],{"className":37263},[281],[15,37265,37267],{"className":37266},[285],[15,37268,37270],{"className":37269},[290],[15,37271,37273],{"className":37272,"style":19735},[294],[15,37274,37275,37278],{"style":8277},[15,37276],{"className":37277,"style":303},[302],[15,37279,37281],{"className":37280},[307,308,309,310],[15,37282,2463],{"className":37283},[59,310],[11,37285,34682,37286,37351],{},[15,37287,37289,37312],{"className":37288,"translate":19},[18],[15,37290,37292],{"className":37291},[23],[25,37293,37294],{"xmlns":27},[29,37295,37296,37310],{},[32,37297,37298,37300,37302,37304,37306,37308],{},[35,37299,37],{},[110,37301,113],{"stretchy":112},[115,37303,117],{},[110,37305,120],{"stretchy":112},[110,37307,123],{},[115,37309,126],{},[39,37311,129],{"encoding":41},[15,37313,37315,37342],{"className":37314,"ariaHidden":46},[45],[15,37316,37318,37321,37324,37327,37330,37333,37336,37339],{"className":37317},[50],[15,37319],{"className":37320,"style":139},[54],[15,37322,37],{"className":37323,"style":61},[59,60],[15,37325,113],{"className":37326},[146],[15,37328,117],{"className":37329},[59],[15,37331,120],{"className":37332},[153],[15,37334],{"className":37335,"style":158},[157],[15,37337,123],{"className":37338},[162],[15,37340],{"className":37341,"style":158},[157],[15,37343,37345,37348],{"className":37344},[50],[15,37346],{"className":37347,"style":172},[54],[15,37349,126],{"className":37350},[59],"、凸，代入：",[15,37353,37355],{"className":37354,"translate":19},[180],[15,37356,37358,37465],{"className":37357,"translate":19},[18],[15,37359,37361],{"className":37360},[23],[25,37362,37363],{"xmlns":27,"display":189},[29,37364,37365,37462],{},[32,37366,37367,37373,37375,37377,37379,37381,37383,37385,37387,37389,37409,37411,37413,37415,37417,37437,37439,37441,37443,37445,37452,37454,37456,37458,37460],{},[195,37368,37369,37371],{},[35,37370,199],{},[35,37372,37],{},[110,37374,113],{"stretchy":112},[35,37376,206],{},[35,37378,210],{"mathvariant":209},[35,37380,213],{},[110,37382,120],{"stretchy":112},[110,37384,123],{},[110,37386,1287],{},[35,37388,944],{},[6814,37390,37391,37407],{},[32,37392,37393,37395,37401,37403,37405],{},[110,37394,113],{"fence":46},[238,37396,37397,37399],{},[35,37398,11],{},[35,37400,944],{},[110,37402,4813],{},[115,37404,117],{},[110,37406,120],{"fence":46},[115,37408,2463],{},[35,37410,244],{},[35,37412,774],{},[110,37414,123],{},[110,37416,1287],{},[238,37418,37419,37435],{},[32,37420,37421,37423,37425,37427,37429],{},[110,37422,113],{"stretchy":112},[35,37424,11],{},[110,37426,4813],{},[35,37428,944],{},[6814,37430,37431,37433],{},[110,37432,120],{"stretchy":112},[115,37434,2463],{},[35,37436,944],{},[1297,37438,1299],{},[35,37440,244],{},[35,37442,774],{},[110,37444,123],{},[6814,37446,37447,37450],{},[35,37448,37449],{},"χ",[115,37451,2463],{},[110,37453,113],{"stretchy":112},[35,37455,206],{},[35,37457,210],{"mathvariant":209},[35,37459,213],{},[110,37461,120],{"stretchy":112},[39,37463,37464],{"encoding":41},"D_f(P\\|Q)=\\int q\\left(\\frac{p}{q}-1\\right)^2dx\n=\\int \\frac{(p-q)^2}{q}\\,dx\n=\\chi^2(P\\|Q)",[15,37466,37468,37538,37692,37830],{"className":37467,"ariaHidden":46},[45],[15,37469,37471,37474,37514,37517,37520,37523,37526,37529,37532,37535],{"className":37470},[50],[15,37472],{"className":37473,"style":270},[54],[15,37475,37477,37480],{"className":37476},[59],[15,37478,199],{"className":37479,"style":277},[59,60],[15,37481,37483],{"className":37482},[281],[15,37484,37486,37506],{"className":37485},[285,286],[15,37487,37489,37503],{"className":37488},[290],[15,37490,37492],{"className":37491,"style":295},[294],[15,37493,37494,37497],{"style":298},[15,37495],{"className":37496,"style":303},[302],[15,37498,37500],{"className":37499},[307,308,309,310],[15,37501,37],{"className":37502,"style":61},[59,60,310],[15,37504,318],{"className":37505},[317],[15,37507,37509],{"className":37508},[290],[15,37510,37512],{"className":37511,"style":325},[294],[15,37513],{},[15,37515,113],{"className":37516},[146],[15,37518,206],{"className":37519,"style":334},[59,60],[15,37521,210],{"className":37522},[59],[15,37524,213],{"className":37525},[59,60],[15,37527,120],{"className":37528},[153],[15,37530],{"className":37531,"style":158},[157],[15,37533,123],{"className":37534},[162],[15,37536],{"className":37537,"style":158},[157],[15,37539,37541,37545,37548,37551,37554,37557,37674,37677,37680,37683,37686,37689],{"className":37540},[50],[15,37542],{"className":37543,"style":37544},[54],"height:2.604em;vertical-align:-0.95em;",[15,37546,1287],{"className":37547,"style":1487},[1484,1485,1486],[15,37549],{"className":37550,"style":406},[157],[15,37552,944],{"className":37553,"style":981},[59,60],[15,37555],{"className":37556,"style":406},[157],[15,37558,37560,37649],{"className":37559},[410],[15,37561,37563,37569,37631,37634,37637,37640,37643],{"className":37562},[410],[15,37564,37566],{"className":37565,"style":415},[146,414],[15,37567,113],{"className":37568},[419,309],[15,37570,37572,37575,37628],{"className":37571},[59],[15,37573],{"className":37574},[146,441],[15,37576,37578],{"className":37577},[238],[15,37579,37581,37620],{"className":37580},[285,286],[15,37582,37584,37617],{"className":37583},[290],[15,37585,37587,37598,37606],{"className":37586,"style":3554},[294],[15,37588,37589,37592],{"style":457},[15,37590],{"className":37591,"style":461},[302],[15,37593,37595],{"className":37594},[59],[15,37596,944],{"className":37597,"style":981},[59,60],[15,37599,37600,37603],{"style":473},[15,37601],{"className":37602,"style":461},[302],[15,37604],{"className":37605,"style":481},[480],[15,37607,37608,37611],{"style":484},[15,37609],{"className":37610,"style":461},[302],[15,37612,37614],{"className":37613},[59],[15,37615,11],{"className":37616},[59,60],[15,37618,318],{"className":37619},[317],[15,37621,37623],{"className":37622},[290],[15,37624,37626],{"className":37625,"style":506},[294],[15,37627],{},[15,37629],{"className":37630},[153,441],[15,37632],{"className":37633,"style":2587},[157],[15,37635,4813],{"className":37636},[2591],[15,37638],{"className":37639,"style":2587},[157],[15,37641,117],{"className":37642},[59],[15,37644,37646],{"className":37645,"style":415},[153,414],[15,37647,120],{"className":37648},[419,309],[15,37650,37652],{"className":37651},[281],[15,37653,37655],{"className":37654},[285],[15,37656,37658],{"className":37657},[290],[15,37659,37662],{"className":37660,"style":37661},[294],"height:1.654em;",[15,37663,37665,37668],{"style":37664},"top:-3.9029em;margin-right:0.05em;",[15,37666],{"className":37667,"style":303},[302],[15,37669,37671],{"className":37670},[307,308,309,310],[15,37672,2463],{"className":37673},[59,310],[15,37675],{"className":37676,"style":406},[157],[15,37678,244],{"className":37679},[59,60],[15,37681,774],{"className":37682},[59,60],[15,37684],{"className":37685,"style":158},[157],[15,37687,123],{"className":37688},[162],[15,37690],{"className":37691,"style":158},[157],[15,37693,37695,37699,37702,37705,37812,37815,37818,37821,37824,37827],{"className":37694},[50],[15,37696],{"className":37697,"style":37698},[54],"height:2.3715em;vertical-align:-0.8804em;",[15,37700,1287],{"className":37701,"style":1487},[1484,1485,1486],[15,37703],{"className":37704,"style":406},[157],[15,37706,37708,37711,37809],{"className":37707},[59],[15,37709],{"className":37710},[146,441],[15,37712,37714],{"className":37713},[238],[15,37715,37717,37801],{"className":37716},[285,286],[15,37718,37720,37798],{"className":37719},[290],[15,37721,37724,37735,37743],{"className":37722,"style":37723},[294],"height:1.4911em;",[15,37725,37726,37729],{"style":457},[15,37727],{"className":37728,"style":461},[302],[15,37730,37732],{"className":37731},[59],[15,37733,944],{"className":37734,"style":981},[59,60],[15,37736,37737,37740],{"style":473},[15,37738],{"className":37739,"style":461},[302],[15,37741],{"className":37742,"style":481},[480],[15,37744,37745,37748],{"style":484},[15,37746],{"className":37747,"style":461},[302],[15,37749,37751,37754,37757,37760,37763,37766,37769],{"className":37750},[59],[15,37752,113],{"className":37753},[146],[15,37755,11],{"className":37756},[59,60],[15,37758],{"className":37759,"style":2587},[157],[15,37761,4813],{"className":37762},[2591],[15,37764],{"className":37765,"style":2587},[157],[15,37767,944],{"className":37768,"style":981},[59,60],[15,37770,37772,37775],{"className":37771},[153],[15,37773,120],{"className":37774},[153],[15,37776,37778],{"className":37777},[281],[15,37779,37781],{"className":37780},[285],[15,37782,37784],{"className":37783},[290],[15,37785,37787],{"className":37786,"style":20028},[294],[15,37788,37789,37792],{"style":6865},[15,37790],{"className":37791,"style":303},[302],[15,37793,37795],{"className":37794},[307,308,309,310],[15,37796,2463],{"className":37797},[59,310],[15,37799,318],{"className":37800},[317],[15,37802,37804],{"className":37803},[290],[15,37805,37807],{"className":37806,"style":506},[294],[15,37808],{},[15,37810],{"className":37811},[153,441],[15,37813],{"className":37814,"style":406},[157],[15,37816,244],{"className":37817},[59,60],[15,37819,774],{"className":37820},[59,60],[15,37822],{"className":37823,"style":158},[157],[15,37825,123],{"className":37826},[162],[15,37828],{"className":37829,"style":158},[157],[15,37831,37833,37836,37865,37868,37871,37874,37877],{"className":37832},[50],[15,37834],{"className":37835,"style":37251},[54],[15,37837,37839,37842],{"className":37838},[59],[15,37840,37449],{"className":37841},[59,60],[15,37843,37845],{"className":37844},[281],[15,37846,37848],{"className":37847},[285],[15,37849,37851],{"className":37850},[290],[15,37852,37854],{"className":37853,"style":19735},[294],[15,37855,37856,37859],{"style":8277},[15,37857],{"className":37858,"style":303},[302],[15,37860,37862],{"className":37861},[307,308,309,310],[15,37863,2463],{"className":37864},[59,310],[15,37866,113],{"className":37867},[146],[15,37869,206],{"className":37870,"style":334},[59,60],[15,37872,210],{"className":37873},[59],[15,37875,213],{"className":37876},[59,60],[15,37878,120],{"className":37879},[153],[11,37881,37882,37883,37886],{},"这是",[1225,37884,37885],{},"皮尔逊（Pearson）卡方散度","。它非对称、无界。其斜共轭是",[15,37888,37890],{"className":37889,"translate":19},[180],[15,37891,37893,37969],{"className":37892,"translate":19},[18],[15,37894,37896],{"className":37895},[23],[25,37897,37898],{"xmlns":27,"display":189},[29,37899,37900,37966],{},[32,37901,37902,37904,37906,37908,37910,37912,37914,37916,37918,37920,37922,37942,37944,37964],{},[35,37903,769],{},[1297,37905,1299],{},[35,37907,37],{},[110,37909,113],{"stretchy":112},[115,37911,117],{},[35,37913,941],{"mathvariant":209},[35,37915,769],{},[110,37917,120],{"stretchy":112},[110,37919,123],{},[35,37921,769],{},[6814,37923,37924,37940],{},[32,37925,37926,37928,37934,37936,37938],{},[110,37927,113],{"fence":46},[238,37929,37930,37932],{},[115,37931,117],{},[35,37933,769],{},[110,37935,4813],{},[115,37937,117],{},[110,37939,120],{"fence":46},[115,37941,2463],{},[110,37943,123],{},[238,37945,37946,37962],{},[32,37947,37948,37950,37952,37954,37956],{},[110,37949,113],{"stretchy":112},[35,37951,769],{},[110,37953,4813],{},[115,37955,117],{},[6814,37957,37958,37960],{},[110,37959,120],{"stretchy":112},[115,37961,2463],{},[35,37963,769],{},[110,37965,551],{"separator":46},[39,37967,37968],{"encoding":41},"t\\,f(1\u002Ft)=t\\left(\\frac1t-1\\right)^2\n=\\frac{(t-1)^2}{t},",[15,37970,37972,38008,38144],{"className":37971,"ariaHidden":46},[45],[15,37973,37975,37978,37981,37984,37987,37990,37993,37996,37999,38002,38005],{"className":37974},[50],[15,37976],{"className":37977,"style":139},[54],[15,37979,769],{"className":37980},[59,60],[15,37982],{"className":37983,"style":406},[157],[15,37985,37],{"className":37986,"style":61},[59,60],[15,37988,113],{"className":37989},[146],[15,37991,8589],{"className":37992},[59],[15,37994,769],{"className":37995},[59,60],[15,37997,120],{"className":37998},[153],[15,38000],{"className":38001,"style":158},[157],[15,38003,123],{"className":38004},[162],[15,38006],{"className":38007,"style":158},[157],[15,38009,38011,38014,38017,38020,38135,38138,38141],{"className":38010},[50],[15,38012],{"className":38013,"style":37544},[54],[15,38015,769],{"className":38016},[59,60],[15,38018],{"className":38019,"style":406},[157],[15,38021,38023,38112],{"className":38022},[410],[15,38024,38026,38032,38094,38097,38100,38103,38106],{"className":38025},[410],[15,38027,38029],{"className":38028,"style":415},[146,414],[15,38030,113],{"className":38031},[419,309],[15,38033,38035,38038,38091],{"className":38034},[59],[15,38036],{"className":38037},[146,441],[15,38039,38041],{"className":38040},[238],[15,38042,38044,38083],{"className":38043},[285,286],[15,38045,38047,38080],{"className":38046},[290],[15,38048,38050,38061,38069],{"className":38049,"style":22889},[294],[15,38051,38052,38055],{"style":457},[15,38053],{"className":38054,"style":461},[302],[15,38056,38058],{"className":38057},[59],[15,38059,769],{"className":38060},[59,60],[15,38062,38063,38066],{"style":473},[15,38064],{"className":38065,"style":461},[302],[15,38067],{"className":38068,"style":481},[480],[15,38070,38071,38074],{"style":484},[15,38072],{"className":38073,"style":461},[302],[15,38075,38077],{"className":38076},[59],[15,38078,117],{"className":38079},[59],[15,38081,318],{"className":38082},[317],[15,38084,38086],{"className":38085},[290],[15,38087,38089],{"className":38088,"style":3778},[294],[15,38090],{},[15,38092],{"className":38093},[153,441],[15,38095],{"className":38096,"style":2587},[157],[15,38098,4813],{"className":38099},[2591],[15,38101],{"className":38102,"style":2587},[157],[15,38104,117],{"className":38105},[59],[15,38107,38109],{"className":38108,"style":415},[153,414],[15,38110,120],{"className":38111},[419,309],[15,38113,38115],{"className":38114},[281],[15,38116,38118],{"className":38117},[285],[15,38119,38121],{"className":38120},[290],[15,38122,38124],{"className":38123,"style":37661},[294],[15,38125,38126,38129],{"style":37664},[15,38127],{"className":38128,"style":303},[302],[15,38130,38132],{"className":38131},[307,308,309,310],[15,38133,2463],{"className":38134},[59,310],[15,38136],{"className":38137,"style":158},[157],[15,38139,123],{"className":38140},[162],[15,38142],{"className":38143,"style":158},[157],[15,38145,38147,38151,38257],{"className":38146},[50],[15,38148],{"className":38149,"style":38150},[54],"height:2.1771em;vertical-align:-0.686em;",[15,38152,38154,38157,38254],{"className":38153},[59],[15,38155],{"className":38156},[146,441],[15,38158,38160],{"className":38159},[238],[15,38161,38163,38246],{"className":38162},[285,286],[15,38164,38166,38243],{"className":38165},[290],[15,38167,38169,38180,38188],{"className":38168,"style":37723},[294],[15,38170,38171,38174],{"style":457},[15,38172],{"className":38173,"style":461},[302],[15,38175,38177],{"className":38176},[59],[15,38178,769],{"className":38179},[59,60],[15,38181,38182,38185],{"style":473},[15,38183],{"className":38184,"style":461},[302],[15,38186],{"className":38187,"style":481},[480],[15,38189,38190,38193],{"style":484},[15,38191],{"className":38192,"style":461},[302],[15,38194,38196,38199,38202,38205,38208,38211,38214],{"className":38195},[59],[15,38197,113],{"className":38198},[146],[15,38200,769],{"className":38201},[59,60],[15,38203],{"className":38204,"style":2587},[157],[15,38206,4813],{"className":38207},[2591],[15,38209],{"className":38210,"style":2587},[157],[15,38212,117],{"className":38213},[59],[15,38215,38217,38220],{"className":38216},[153],[15,38218,120],{"className":38219},[153],[15,38221,38223],{"className":38222},[281],[15,38224,38226],{"className":38225},[285],[15,38227,38229],{"className":38228},[290],[15,38230,38232],{"className":38231,"style":20028},[294],[15,38233,38234,38237],{"style":6865},[15,38235],{"className":38236,"style":303},[302],[15,38238,38240],{"className":38239},[307,308,309,310],[15,38241,2463],{"className":38242},[59,310],[15,38244,318],{"className":38245},[317],[15,38247,38249],{"className":38248},[290],[15,38250,38252],{"className":38251,"style":3778},[294],[15,38253],{},[15,38255],{"className":38256},[153,441],[15,38258,551],{"className":38259},[573],[11,38261,38262,38263,6494,38266,18708,38548,38632],{},"对应 ",[1225,38264,38265],{},"Neyman 卡方散度",[15,38267,38269,38330],{"className":38268,"translate":19},[18],[15,38270,38272],{"className":38271},[23],[25,38273,38274],{"xmlns":27},[29,38275,38276,38327],{},[32,38277,38278,38287,38289,38291,38293,38295,38297,38299,38301,38321,38323,38325],{},[7553,38279,38280,38282,38285],{},[35,38281,37449],{},[35,38283,38284],{},"N",[115,38286,2463],{},[110,38288,113],{"stretchy":112},[35,38290,206],{},[35,38292,210],{"mathvariant":209},[35,38294,213],{},[110,38296,120],{"stretchy":112},[110,38298,123],{},[110,38300,1287],{},[238,38302,38303,38319],{},[32,38304,38305,38307,38309,38311,38313],{},[110,38306,113],{"stretchy":112},[35,38308,944],{},[110,38310,4813],{},[35,38312,11],{},[6814,38314,38315,38317],{},[110,38316,120],{"stretchy":112},[115,38318,2463],{},[35,38320,11],{},[1297,38322,1299],{},[35,38324,244],{},[35,38326,774],{},[39,38328,38329],{"encoding":41},"\\chi_N^2(P\\|Q)=\\int\\frac{(q-p)^2}{p}\\,dx",[15,38331,38333,38417],{"className":38332,"ariaHidden":46},[45],[15,38334,38336,38340,38393,38396,38399,38402,38405,38408,38411,38414],{"className":38335},[50],[15,38337],{"className":38338,"style":38339},[54],"height:1.0894em;vertical-align:-0.2753em;",[15,38341,38343,38346],{"className":38342},[59],[15,38344,37449],{"className":38345},[59,60],[15,38347,38349],{"className":38348},[281],[15,38350,38352,38384],{"className":38351},[285,286],[15,38353,38355,38381],{"className":38354},[290],[15,38356,38358,38370],{"className":38357,"style":20028},[294],[15,38359,38361,38364],{"style":38360},"top:-2.4247em;margin-left:0em;margin-right:0.05em;",[15,38362],{"className":38363,"style":303},[302],[15,38365,38367],{"className":38366},[307,308,309,310],[15,38368,38284],{"className":38369,"style":25601},[59,60,310],[15,38371,38372,38375],{"style":6865},[15,38373],{"className":38374,"style":303},[302],[15,38376,38378],{"className":38377},[307,308,309,310],[15,38379,2463],{"className":38380},[59,310],[15,38382,318],{"className":38383},[317],[15,38385,38387],{"className":38386},[290],[15,38388,38391],{"className":38389,"style":38390},[294],"height:0.2753em;",[15,38392],{},[15,38394,113],{"className":38395},[146],[15,38397,206],{"className":38398,"style":334},[59,60],[15,38400,210],{"className":38401},[59],[15,38403,213],{"className":38404},[59,60],[15,38406,120],{"className":38407},[153],[15,38409],{"className":38410,"style":158},[157],[15,38412,123],{"className":38413},[162],[15,38415],{"className":38416,"style":158},[157],[15,38418,38420,38424,38427,38430,38539,38542,38545],{"className":38419},[50],[15,38421],{"className":38422,"style":38423},[54],"height:1.59em;vertical-align:-0.4811em;",[15,38425,1287],{"className":38426,"style":5617},[1484,1485,5616],[15,38428],{"className":38429,"style":406},[157],[15,38431,38433,38436,38536],{"className":38432},[59],[15,38434],{"className":38435},[146,441],[15,38437,38439],{"className":38438},[238],[15,38440,38442,38528],{"className":38441},[285,286],[15,38443,38445,38525],{"className":38444},[290],[15,38446,38449,38463,38471],{"className":38447,"style":38448},[294],"height:1.1089em;",[15,38450,38451,38454],{"style":2527},[15,38452],{"className":38453,"style":461},[302],[15,38455,38457],{"className":38456},[307,308,309,310],[15,38458,38460],{"className":38459},[59,310],[15,38461,11],{"className":38462},[59,60,310],[15,38464,38465,38468],{"style":473},[15,38466],{"className":38467,"style":461},[302],[15,38469],{"className":38470,"style":481},[480],[15,38472,38473,38476],{"style":26418},[15,38474],{"className":38475,"style":461},[302],[15,38477,38479],{"className":38478},[307,308,309,310],[15,38480,38482,38485,38488,38491,38494],{"className":38481},[59,310],[15,38483,113],{"className":38484},[146,310],[15,38486,944],{"className":38487,"style":981},[59,60,310],[15,38489,4813],{"className":38490},[2591,310],[15,38492,11],{"className":38493},[59,60,310],[15,38495,38497,38500],{"className":38496},[153,310],[15,38498,120],{"className":38499},[153,310],[15,38501,38503],{"className":38502},[281],[15,38504,38506],{"className":38505},[285],[15,38507,38509],{"className":38508},[290],[15,38510,38513],{"className":38511,"style":38512},[294],"height:0.8913em;",[15,38514,38516,38519],{"style":38515},"top:-2.931em;margin-right:0.0714em;",[15,38517],{"className":38518,"style":30206},[302],[15,38520,38522],{"className":38521},[307,30210,9674,310],[15,38523,2463],{"className":38524},[59,310],[15,38526,318],{"className":38527},[317],[15,38529,38531],{"className":38530},[290],[15,38532,38534],{"className":38533,"style":2739},[294],[15,38535],{},[15,38537],{"className":38538},[153,441],[15,38540],{"className":38541,"style":406},[157],[15,38543,244],{"className":38544},[59,60],[15,38546,774],{"className":38547},[59,60],[15,38549,38551,38579],{"className":38550,"translate":19},[18],[15,38552,38554],{"className":38553},[23],[25,38555,38556],{"xmlns":27},[29,38557,38558,38576],{},[32,38559,38560,38566,38568,38570,38572,38574],{},[6814,38561,38562,38564],{},[35,38563,37449],{},[115,38565,2463],{},[110,38567,113],{"stretchy":112},[35,38569,213],{},[35,38571,210],{"mathvariant":209},[35,38573,206],{},[110,38575,120],{"stretchy":112},[39,38577,38578],{"encoding":41},"\\chi^2(Q\\|P)",[15,38580,38582],{"className":38581,"ariaHidden":46},[45],[15,38583,38585,38588,38617,38620,38623,38626,38629],{"className":38584},[50],[15,38586],{"className":38587,"style":20003},[54],[15,38589,38591,38594],{"className":38590},[59],[15,38592,37449],{"className":38593},[59,60],[15,38595,38597],{"className":38596},[281],[15,38598,38600],{"className":38599},[285],[15,38601,38603],{"className":38602},[290],[15,38604,38606],{"className":38605,"style":20028},[294],[15,38607,38608,38611],{"style":6865},[15,38609],{"className":38610,"style":303},[302],[15,38612,38614],{"className":38613},[307,308,309,310],[15,38615,2463],{"className":38616},[59,310],[15,38618,113],{"className":38619},[146],[15,38621,213],{"className":38622},[59,60],[15,38624,210],{"className":38625},[59],[15,38627,206],{"className":38628,"style":334},[59,60],[15,38630,120],{"className":38631},[153],"：皮尔逊卡方的\"反向兄弟\"。",[11,38634,38635,38636,38785,38786,38948,38949,39264,39265,39503,39504,39585],{},"卡方散度的重要性在于它是「二阶」散度：小偏差下（",[15,38637,38639,38669],{"className":38638,"translate":19},[18],[15,38640,38642],{"className":38641},[23],[25,38643,38644],{"xmlns":27},[29,38645,38646,38666],{},[32,38647,38648,38654,38656,38658,38660,38663],{},[238,38649,38650,38652],{},[35,38651,11],{},[35,38653,944],{},[110,38655,123],{},[115,38657,117],{},[110,38659,2470],{},[35,38661,38662],{},"ε",[35,38664,38665],{},"h",[39,38667,38668],{"encoding":41},"\\frac{p}{q}=1+\\varepsilon h",[15,38670,38672,38755,38773],{"className":38671,"ariaHidden":46},[45],[15,38673,38675,38678,38746,38749,38752],{"className":38674},[50],[15,38676],{"className":38677,"style":3084},[54],[15,38679,38681,38684,38743],{"className":38680},[59],[15,38682],{"className":38683},[146,441],[15,38685,38687],{"className":38686},[238],[15,38688,38690,38735],{"className":38689},[285,286],[15,38691,38693,38732],{"className":38692},[290],[15,38694,38696,38710,38718],{"className":38695,"style":3103},[294],[15,38697,38698,38701],{"style":2527},[15,38699],{"className":38700,"style":461},[302],[15,38702,38704],{"className":38703},[307,308,309,310],[15,38705,38707],{"className":38706},[59,310],[15,38708,944],{"className":38709,"style":981},[59,60,310],[15,38711,38712,38715],{"style":473},[15,38713],{"className":38714,"style":461},[302],[15,38716],{"className":38717,"style":481},[480],[15,38719,38720,38723],{"style":2853},[15,38721],{"className":38722,"style":461},[302],[15,38724,38726],{"className":38725},[307,308,309,310],[15,38727,38729],{"className":38728},[59,310],[15,38730,11],{"className":38731},[59,60,310],[15,38733,318],{"className":38734},[317],[15,38736,38738],{"className":38737},[290],[15,38739,38741],{"className":38740,"style":2739},[294],[15,38742],{},[15,38744],{"className":38745},[153,441],[15,38747],{"className":38748,"style":158},[157],[15,38750,123],{"className":38751},[162],[15,38753],{"className":38754,"style":158},[157],[15,38756,38758,38761,38764,38767,38770],{"className":38757},[50],[15,38759],{"className":38760,"style":12578},[54],[15,38762,117],{"className":38763},[59],[15,38765],{"className":38766,"style":2587},[157],[15,38768,2470],{"className":38769},[2591],[15,38771],{"className":38772,"style":2587},[157],[15,38774,38776,38779,38782],{"className":38775},[50],[15,38777],{"className":38778,"style":12597},[54],[15,38780,38662],{"className":38781},[59,60],[15,38783,38665],{"className":38784},[59,60]," 展开）有 ",[15,38787,38789,38821],{"className":38788,"translate":19},[18],[15,38790,38792],{"className":38791},[23],[25,38793,38794],{"xmlns":27},[29,38795,38796,38818],{},[32,38797,38798,38804,38806,38812],{},[32,38799,38800,38802],{},[35,38801,10694],{"mathvariant":209},[35,38803,21893],{"mathvariant":209},[110,38805,32959],{},[238,38807,38808,38810],{},[115,38809,117],{},[115,38811,2463],{},[6814,38813,38814,38816],{},[35,38815,37449],{},[115,38817,2463],{},[39,38819,38820],{"encoding":41},"\\mathrm{KL}\\approx\\frac12\\chi^2",[15,38822,38824,38845],{"className":38823,"ariaHidden":46},[45],[15,38825,38827,38830,38836,38839,38842],{"className":38826},[50],[15,38828],{"className":38829,"style":664},[54],[15,38831,38833],{"className":38832},[59],[15,38834,32663],{"className":38835},[59,32662],[15,38837],{"className":38838,"style":158},[157],[15,38840,32959],{"className":38841},[162],[15,38843],{"className":38844,"style":158},[157],[15,38846,38848,38851,38919],{"className":38847},[50],[15,38849],{"className":38850,"style":2505},[54],[15,38852,38854,38857,38916],{"className":38853},[59],[15,38855],{"className":38856},[146,441],[15,38858,38860],{"className":38859},[238],[15,38861,38863,38908],{"className":38862},[285,286],[15,38864,38866,38905],{"className":38865},[290],[15,38867,38869,38883,38891],{"className":38868,"style":2524},[294],[15,38870,38871,38874],{"style":2527},[15,38872],{"className":38873,"style":461},[302],[15,38875,38877],{"className":38876},[307,308,309,310],[15,38878,38880],{"className":38879},[59,310],[15,38881,2463],{"className":38882},[59,310],[15,38884,38885,38888],{"style":473},[15,38886],{"className":38887,"style":461},[302],[15,38889],{"className":38890,"style":481},[480],[15,38892,38893,38896],{"style":2550},[15,38894],{"className":38895,"style":461},[302],[15,38897,38899],{"className":38898},[307,308,309,310],[15,38900,38902],{"className":38901},[59,310],[15,38903,117],{"className":38904},[59,310],[15,38906,318],{"className":38907},[317],[15,38909,38911],{"className":38910},[290],[15,38912,38914],{"className":38913,"style":2572},[294],[15,38915],{},[15,38917],{"className":38918},[153,441],[15,38920,38922,38925],{"className":38921},[59],[15,38923,37449],{"className":38924},[59,60],[15,38926,38928],{"className":38927},[281],[15,38929,38931],{"className":38930},[285],[15,38932,38934],{"className":38933},[290],[15,38935,38937],{"className":38936,"style":20028},[294],[15,38938,38939,38942],{"style":6865},[15,38940],{"className":38941,"style":303},[302],[15,38943,38945],{"className":38944},[307,308,309,310],[15,38946,2463],{"className":38947},[59,310],"、本文约定的 ",[15,38950,38952,38999],{"className":38951,"translate":19},[18],[15,38953,38955],{"className":38954},[23],[25,38956,38957],{"xmlns":27},[29,38958,38959,38996],{},[32,38960,38961,38963,38965,38969,38971,38975,38981,38983,38990],{},[110,38962,1287],{},[110,38964,113],{"stretchy":112},[34339,38966,38967],{},[35,38968,11],{},[110,38970,4813],{},[34339,38972,38973],{},[35,38974,944],{},[6814,38976,38977,38979],{},[110,38978,120],{"stretchy":112},[115,38980,2463],{},[110,38982,32959],{},[238,38984,38985,38987],{},[115,38986,117],{},[115,38988,38989],{},"4",[6814,38991,38992,38994],{},[35,38993,37449],{},[115,38995,2463],{},[39,38997,38998],{"encoding":41},"\\int(\\sqrt p-\\sqrt q)^2\\approx\\frac14\\chi^2",[15,39000,39002,39071,39161],{"className":39001,"ariaHidden":46},[45],[15,39003,39005,39009,39012,39015,39062,39065,39068],{"className":39004},[50],[15,39006],{"className":39007,"style":39008},[54],"height:1.1419em;vertical-align:-0.3369em;",[15,39010,1287],{"className":39011,"style":5617},[1484,1485,5616],[15,39013,113],{"className":39014},[146],[15,39016,39018],{"className":39017},[59,34367],[15,39019,39021,39053],{"className":39020},[285,286],[15,39022,39024,39050],{"className":39023},[290],[15,39025,39028,39037],{"className":39026,"style":39027},[294],"height:0.7031em;",[15,39029,39031,39034],{"className":39030,"style":11863},[6307],[15,39032],{"className":39033,"style":461},[302],[15,39035,11],{"className":39036,"style":34387},[59,60],[15,39038,39040,39043],{"style":39039},"top:-2.6631em;",[15,39041],{"className":39042,"style":461},[302],[15,39044,39046],{"className":39045,"style":34444},[34443],[6323,39047,39048],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,39049],{"d":34451},[15,39051,318],{"className":39052},[317],[15,39054,39056],{"className":39055},[290],[15,39057,39060],{"className":39058,"style":39059},[294],"height:0.3369em;",[15,39061],{},[15,39063],{"className":39064,"style":2587},[157],[15,39066,4813],{"className":39067},[2591],[15,39069],{"className":39070,"style":2587},[157],[15,39072,39074,39078,39123,39152,39155,39158],{"className":39073},[50],[15,39075],{"className":39076,"style":39077},[54],"height:1.151em;vertical-align:-0.3369em;",[15,39079,39081],{"className":39080},[59,34367],[15,39082,39084,39115],{"className":39083},[285,286],[15,39085,39087,39112],{"className":39086},[290],[15,39088,39090,39100],{"className":39089,"style":39027},[294],[15,39091,39093,39096],{"className":39092,"style":11863},[6307],[15,39094],{"className":39095,"style":461},[302],[15,39097,944],{"className":39098,"style":39099},[59,60],"margin-right:0.0359em;padding-left:0.833em;",[15,39101,39102,39105],{"style":39039},[15,39103],{"className":39104,"style":461},[302],[15,39106,39108],{"className":39107,"style":34444},[34443],[6323,39109,39110],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,39111],{"d":34451},[15,39113,318],{"className":39114},[317],[15,39116,39118],{"className":39117},[290],[15,39119,39121],{"className":39120,"style":39059},[294],[15,39122],{},[15,39124,39126,39129],{"className":39125},[153],[15,39127,120],{"className":39128},[153],[15,39130,39132],{"className":39131},[281],[15,39133,39135],{"className":39134},[285],[15,39136,39138],{"className":39137},[290],[15,39139,39141],{"className":39140,"style":20028},[294],[15,39142,39143,39146],{"style":6865},[15,39144],{"className":39145,"style":303},[302],[15,39147,39149],{"className":39148},[307,308,309,310],[15,39150,2463],{"className":39151},[59,310],[15,39153],{"className":39154,"style":158},[157],[15,39156,32959],{"className":39157},[162],[15,39159],{"className":39160,"style":158},[157],[15,39162,39164,39167,39235],{"className":39163},[50],[15,39165],{"className":39166,"style":2505},[54],[15,39168,39170,39173,39232],{"className":39169},[59],[15,39171],{"className":39172},[146,441],[15,39174,39176],{"className":39175},[238],[15,39177,39179,39224],{"className":39178},[285,286],[15,39180,39182,39221],{"className":39181},[290],[15,39183,39185,39199,39207],{"className":39184,"style":2524},[294],[15,39186,39187,39190],{"style":2527},[15,39188],{"className":39189,"style":461},[302],[15,39191,39193],{"className":39192},[307,308,309,310],[15,39194,39196],{"className":39195},[59,310],[15,39197,38989],{"className":39198},[59,310],[15,39200,39201,39204],{"style":473},[15,39202],{"className":39203,"style":461},[302],[15,39205],{"className":39206,"style":481},[480],[15,39208,39209,39212],{"style":2550},[15,39210],{"className":39211,"style":461},[302],[15,39213,39215],{"className":39214},[307,308,309,310],[15,39216,39218],{"className":39217},[59,310],[15,39219,117],{"className":39220},[59,310],[15,39222,318],{"className":39223},[317],[15,39225,39227],{"className":39226},[290],[15,39228,39230],{"className":39229,"style":2572},[294],[15,39231],{},[15,39233],{"className":39234},[153,441],[15,39236,39238,39241],{"className":39237},[59],[15,39239,37449],{"className":39240},[59,60],[15,39242,39244],{"className":39243},[281],[15,39245,39247],{"className":39246},[285],[15,39248,39250],{"className":39249},[290],[15,39251,39253],{"className":39252,"style":20028},[294],[15,39254,39255,39258],{"style":6865},[15,39256],{"className":39257,"style":303},[302],[15,39259,39261],{"className":39260},[307,308,309,310],[15,39262,2463],{"className":39263},[59,310],"、Bhattacharyya 约定的 ",[15,39266,39268,39313],{"className":39267,"translate":19},[18],[15,39269,39271],{"className":39270},[23],[25,39272,39273],{"xmlns":27},[29,39274,39275,39310],{},[32,39276,39277,39283,39285,39287,39289,39292,39295,39297,39304],{},[6814,39278,39279,39281],{},[35,39280,33884],{},[115,39282,2463],{},[110,39284,123],{},[115,39286,117],{},[110,39288,4813],{},[35,39290,39291],{},"B",[35,39293,39294],{},"C",[110,39296,32959],{},[238,39298,39299,39301],{},[115,39300,117],{},[115,39302,39303],{},"8",[6814,39305,39306,39308],{},[35,39307,37449],{},[115,39309,2463],{},[39,39311,39312],{"encoding":41},"H^2=1-BC\\approx\\frac18\\chi^2",[15,39314,39316,39360,39378,39400],{"className":39315,"ariaHidden":46},[45],[15,39317,39319,39322,39351,39354,39357],{"className":39318},[50],[15,39320],{"className":39321,"style":20028},[54],[15,39323,39325,39328],{"className":39324},[59],[15,39326,33884],{"className":39327,"style":34038},[59,60],[15,39329,39331],{"className":39330},[281],[15,39332,39334],{"className":39333},[285],[15,39335,39337],{"className":39336},[290],[15,39338,39340],{"className":39339,"style":20028},[294],[15,39341,39342,39345],{"style":6865},[15,39343],{"className":39344,"style":303},[302],[15,39346,39348],{"className":39347},[307,308,309,310],[15,39349,2463],{"className":39350},[59,310],[15,39352],{"className":39353,"style":158},[157],[15,39355,123],{"className":39356},[162],[15,39358],{"className":39359,"style":158},[157],[15,39361,39363,39366,39369,39372,39375],{"className":39362},[50],[15,39364],{"className":39365,"style":12578},[54],[15,39367,117],{"className":39368},[59],[15,39370],{"className":39371,"style":2587},[157],[15,39373,4813],{"className":39374},[2591],[15,39376],{"className":39377,"style":2587},[157],[15,39379,39381,39384,39388,39391,39394,39397],{"className":39380},[50],[15,39382],{"className":39383,"style":664},[54],[15,39385,39291],{"className":39386,"style":39387},[59,60],"margin-right:0.0502em;",[15,39389,39294],{"className":39390,"style":10782},[59,60],[15,39392],{"className":39393,"style":158},[157],[15,39395,32959],{"className":39396},[162],[15,39398],{"className":39399,"style":158},[157],[15,39401,39403,39406,39474],{"className":39402},[50],[15,39404],{"className":39405,"style":2505},[54],[15,39407,39409,39412,39471],{"className":39408},[59],[15,39410],{"className":39411},[146,441],[15,39413,39415],{"className":39414},[238],[15,39416,39418,39463],{"className":39417},[285,286],[15,39419,39421,39460],{"className":39420},[290],[15,39422,39424,39438,39446],{"className":39423,"style":2524},[294],[15,39425,39426,39429],{"style":2527},[15,39427],{"className":39428,"style":461},[302],[15,39430,39432],{"className":39431},[307,308,309,310],[15,39433,39435],{"className":39434},[59,310],[15,39436,39303],{"className":39437},[59,310],[15,39439,39440,39443],{"style":473},[15,39441],{"className":39442,"style":461},[302],[15,39444],{"className":39445,"style":481},[480],[15,39447,39448,39451],{"style":2550},[15,39449],{"className":39450,"style":461},[302],[15,39452,39454],{"className":39453},[307,308,309,310],[15,39455,39457],{"className":39456},[59,310],[15,39458,117],{"className":39459},[59,310],[15,39461,318],{"className":39462},[317],[15,39464,39466],{"className":39465},[290],[15,39467,39469],{"className":39468,"style":2572},[294],[15,39470],{},[15,39472],{"className":39473},[153,441],[15,39475,39477,39480],{"className":39476},[59],[15,39478,37449],{"className":39479},[59,60],[15,39481,39483],{"className":39482},[281],[15,39484,39486],{"className":39485},[285],[15,39487,39489],{"className":39488},[290],[15,39490,39492],{"className":39491,"style":20028},[294],[15,39493,39494,39497],{"style":6865},[15,39495],{"className":39496,"style":303},[302],[15,39498,39500],{"className":39499},[307,308,309,310],[15,39501,2463],{"className":39502},[59,310],"（见 4.6 节的局部展开），因此它是所有 f-散度在局部的「公因子」——只是在 ",[15,39505,39507,39535],{"className":39506,"translate":19},[18],[15,39508,39510],{"className":39509},[23],[25,39511,39512],{"xmlns":27},[29,39513,39514,39532],{},[32,39515,39516,39526,39528,39530],{},[6814,39517,39518,39520],{},[35,39519,37],{},[32,39521,39522,39524],{},[110,39523,6820],{"mathvariant":209},[110,39525,6820],{"mathvariant":209},[110,39527,113],{"stretchy":112},[115,39529,117],{},[110,39531,120],{"stretchy":112},[39,39533,39534],{"encoding":41},"f''(1)",[15,39536,39538],{"className":39537,"ariaHidden":46},[45],[15,39539,39541,39544,39576,39579,39582],{"className":39540},[50],[15,39542],{"className":39543,"style":6843},[54],[15,39545,39547,39550],{"className":39546},[59],[15,39548,37],{"className":39549,"style":61},[59,60],[15,39551,39553],{"className":39552},[281],[15,39554,39556],{"className":39555},[285],[15,39557,39559],{"className":39558},[290],[15,39560,39562],{"className":39561,"style":6862},[294],[15,39563,39564,39567],{"style":6865},[15,39565],{"className":39566,"style":303},[302],[15,39568,39570],{"className":39569},[307,308,309,310],[15,39571,39573],{"className":39572},[59,310],[15,39574,21748],{"className":39575},[59,310],[15,39577,113],{"className":39578},[146],[15,39580,117],{"className":39581},[59],[15,39583,120],{"className":39584},[153]," 意义下的「单位」不同。",[11,39587,39588,39590,39591,39923,39924,39952,39953,2745,39981,40065,40066,40094,40095,40123,40124,40152,40153,40181,40182,40210,40211,40214,40215,40373,40374,40434],{},[1225,39589,24193],{}," 卡方散度是 Pearson 拟合优度统计量 ",[15,39592,39594,39644],{"className":39593,"translate":19},[18],[15,39595,39597],{"className":39596},[23],[25,39598,39599],{"xmlns":27},[29,39600,39601,39641],{},[32,39602,39603,39609],{},[195,39604,39605,39607],{},[110,39606,13461],{},[35,39608,11963],{},[238,39610,39611,39635],{},[32,39612,39613,39615,39621,39623,39629],{},[110,39614,113],{"stretchy":112},[195,39616,39617,39619],{},[35,39618,19221],{},[35,39620,11963],{},[110,39622,4813],{},[195,39624,39625,39627],{},[35,39626,223],{},[35,39628,11963],{},[6814,39630,39631,39633],{},[110,39632,120],{"stretchy":112},[115,39634,2463],{},[195,39636,39637,39639],{},[35,39638,223],{},[35,39640,11963],{},[39,39642,39643],{"encoding":41},"\\sum_i\\frac{(O_i-E_i)^2}{E_i}",[15,39645,39647],{"className":39646,"ariaHidden":46},[45],[15,39648,39650,39654,39698,39701],{"className":39649},[50],[15,39651],{"className":39652,"style":39653},[54],"height:1.554em;vertical-align:-0.4451em;",[15,39655,39657,39661],{"className":39656},[1484],[15,39658,13461],{"className":39659,"style":39660},[1484,1485,5616],"position:relative;top:0em;",[15,39662,39664],{"className":39663},[281],[15,39665,39667,39689],{"className":39666},[285,286],[15,39668,39670,39686],{"className":39669},[290],[15,39671,39674],{"className":39672,"style":39673},[294],"height:0.162em;",[15,39675,39677,39680],{"style":39676},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[15,39678],{"className":39679,"style":303},[302],[15,39681,39683],{"className":39682},[307,308,309,310],[15,39684,11963],{"className":39685},[59,60,310],[15,39687,318],{"className":39688},[317],[15,39690,39692],{"className":39691},[290],[15,39693,39696],{"className":39694,"style":39695},[294],"height:0.2997em;",[15,39697],{},[15,39699],{"className":39700,"style":406},[157],[15,39702,39704,39707,39920],{"className":39703},[59],[15,39705],{"className":39706},[146,441],[15,39708,39710],{"className":39709},[238],[15,39711,39713,39911],{"className":39712},[285,286],[15,39714,39716,39908],{"className":39715},[290],[15,39717,39719,39773,39781],{"className":39718,"style":38448},[294],[15,39720,39721,39724],{"style":2527},[15,39722],{"className":39723,"style":461},[302],[15,39725,39727],{"className":39726},[307,308,309,310],[15,39728,39730],{"className":39729},[59,310],[15,39731,39733,39736],{"className":39732},[59,310],[15,39734,223],{"className":39735,"style":25861},[59,60,310],[15,39737,39739],{"className":39738},[281],[15,39740,39742,39764],{"className":39741},[285,286],[15,39743,39745,39761],{"className":39744},[290],[15,39746,39749],{"className":39747,"style":39748},[294],"height:0.3281em;",[15,39750,39752,39755],{"style":39751},"top:-2.357em;margin-left:-0.0576em;margin-right:0.0714em;",[15,39753],{"className":39754,"style":30206},[302],[15,39756,39758],{"className":39757},[307,30210,9674,310],[15,39759,11963],{"className":39760},[59,60,310],[15,39762,318],{"className":39763},[317],[15,39765,39767],{"className":39766},[290],[15,39768,39771],{"className":39769,"style":39770},[294],"height:0.143em;",[15,39772],{},[15,39774,39775,39778],{"style":473},[15,39776],{"className":39777,"style":461},[302],[15,39779],{"className":39780,"style":481},[480],[15,39782,39783,39786],{"style":26418},[15,39784],{"className":39785,"style":461},[302],[15,39787,39789],{"className":39788},[307,308,309,310],[15,39790,39792,39795,39836,39839,39879],{"className":39791},[59,310],[15,39793,113],{"className":39794},[146,310],[15,39796,39798,39801],{"className":39797},[59,310],[15,39799,19221],{"className":39800,"style":277},[59,60,310],[15,39802,39804],{"className":39803},[281],[15,39805,39807,39828],{"className":39806},[285,286],[15,39808,39810,39825],{"className":39809},[290],[15,39811,39813],{"className":39812,"style":39748},[294],[15,39814,39816,39819],{"style":39815},"top:-2.357em;margin-left:-0.0278em;margin-right:0.0714em;",[15,39817],{"className":39818,"style":30206},[302],[15,39820,39822],{"className":39821},[307,30210,9674,310],[15,39823,11963],{"className":39824},[59,60,310],[15,39826,318],{"className":39827},[317],[15,39829,39831],{"className":39830},[290],[15,39832,39834],{"className":39833,"style":39770},[294],[15,39835],{},[15,39837,4813],{"className":39838},[2591,310],[15,39840,39842,39845],{"className":39841},[59,310],[15,39843,223],{"className":39844,"style":25861},[59,60,310],[15,39846,39848],{"className":39847},[281],[15,39849,39851,39871],{"className":39850},[285,286],[15,39852,39854,39868],{"className":39853},[290],[15,39855,39857],{"className":39856,"style":39748},[294],[15,39858,39859,39862],{"style":39751},[15,39860],{"className":39861,"style":30206},[302],[15,39863,39865],{"className":39864},[307,30210,9674,310],[15,39866,11963],{"className":39867},[59,60,310],[15,39869,318],{"className":39870},[317],[15,39872,39874],{"className":39873},[290],[15,39875,39877],{"className":39876,"style":39770},[294],[15,39878],{},[15,39880,39882,39885],{"className":39881},[153,310],[15,39883,120],{"className":39884},[153,310],[15,39886,39888],{"className":39887},[281],[15,39889,39891],{"className":39890},[285],[15,39892,39894],{"className":39893},[290],[15,39895,39897],{"className":39896,"style":38512},[294],[15,39898,39899,39902],{"style":38515},[15,39900],{"className":39901,"style":30206},[302],[15,39903,39905],{"className":39904},[307,30210,9674,310],[15,39906,2463],{"className":39907},[59,310],[15,39909,318],{"className":39910},[317],[15,39912,39914],{"className":39913},[290],[15,39915,39918],{"className":39916,"style":39917},[294],"height:0.4451em;",[15,39919],{},[15,39921],{"className":39922},[153,441]," 的总体（无限样本）版本：把观测频率看作 ",[15,39925,39927,39940],{"className":39926,"translate":19},[18],[15,39928,39930],{"className":39929},[23],[25,39931,39932],{"xmlns":27},[29,39933,39934,39938],{},[32,39935,39936],{},[35,39937,206],{},[39,39939,206],{"encoding":41},[15,39941,39943],{"className":39942,"ariaHidden":46},[45],[15,39944,39946,39949],{"className":39945},[50],[15,39947],{"className":39948,"style":664},[54],[15,39950,206],{"className":39951,"style":334},[59,60],"、期望频率看作 ",[15,39954,39956,39969],{"className":39955,"translate":19},[18],[15,39957,39959],{"className":39958},[23],[25,39960,39961],{"xmlns":27},[29,39962,39963,39967],{},[32,39964,39965],{},[35,39966,213],{},[39,39968,213],{"encoding":41},[15,39970,39972],{"className":39971,"ariaHidden":46},[45],[15,39973,39975,39978],{"className":39974},[50],[15,39976],{"className":39977,"style":566},[54],[15,39979,213],{"className":39980},[59,60],[15,39982,39984,40012],{"className":39983,"translate":19},[18],[15,39985,39987],{"className":39986},[23],[25,39988,39989],{"xmlns":27},[29,39990,39991,40009],{},[32,39992,39993,39999,40001,40003,40005,40007],{},[6814,39994,39995,39997],{},[35,39996,37449],{},[115,39998,2463],{},[110,40000,113],{"stretchy":112},[35,40002,206],{},[35,40004,210],{"mathvariant":209},[35,40006,213],{},[110,40008,120],{"stretchy":112},[39,40010,40011],{"encoding":41},"\\chi^2(P\\|Q)",[15,40013,40015],{"className":40014,"ariaHidden":46},[45],[15,40016,40018,40021,40050,40053,40056,40059,40062],{"className":40017},[50],[15,40019],{"className":40020,"style":20003},[54],[15,40022,40024,40027],{"className":40023},[59],[15,40025,37449],{"className":40026},[59,60],[15,40028,40030],{"className":40029},[281],[15,40031,40033],{"className":40032},[285],[15,40034,40036],{"className":40035},[290],[15,40037,40039],{"className":40038,"style":20028},[294],[15,40040,40041,40044],{"style":6865},[15,40042],{"className":40043,"style":303},[302],[15,40045,40047],{"className":40046},[307,308,309,310],[15,40048,2463],{"className":40049},[59,310],[15,40051,113],{"className":40052},[146],[15,40054,206],{"className":40055,"style":334},[59,60],[15,40057,210],{"className":40058},[59],[15,40060,213],{"className":40061},[59,60],[15,40063,120],{"className":40064},[153]," 就是「",[15,40067,40069,40082],{"className":40068,"translate":19},[18],[15,40070,40072],{"className":40071},[23],[25,40073,40074],{"xmlns":27},[29,40075,40076,40080],{},[32,40077,40078],{},[35,40079,206],{},[39,40081,206],{"encoding":41},[15,40083,40085],{"className":40084,"ariaHidden":46},[45],[15,40086,40088,40091],{"className":40087},[50],[15,40089],{"className":40090,"style":664},[54],[15,40092,206],{"className":40093,"style":334},[59,60]," 是否来自 ",[15,40096,40098,40111],{"className":40097,"translate":19},[18],[15,40099,40101],{"className":40100},[23],[25,40102,40103],{"xmlns":27},[29,40104,40105,40109],{},[32,40106,40107],{},[35,40108,213],{},[39,40110,213],{"encoding":41},[15,40112,40114],{"className":40113,"ariaHidden":46},[45],[15,40115,40117,40120],{"className":40116},[50],[15,40118],{"className":40119,"style":566},[54],[15,40121,213],{"className":40122},[59,60],"」的标准化偏差，因此它是独立性检验、拟合优度检验与特征选择的自然尺度。它的分母 ",[15,40125,40127,40140],{"className":40126,"translate":19},[18],[15,40128,40130],{"className":40129},[23],[25,40131,40132],{"xmlns":27},[29,40133,40134,40138],{},[32,40135,40136],{},[35,40137,944],{},[39,40139,944],{"encoding":41},[15,40141,40143],{"className":40142,"ariaHidden":46},[45],[15,40144,40146,40149],{"className":40145},[50],[15,40147],{"className":40148,"style":2276},[54],[15,40150,944],{"className":40151,"style":981},[59,60]," 使它对「",[15,40154,40156,40169],{"className":40155,"translate":19},[18],[15,40157,40159],{"className":40158},[23],[25,40160,40161],{"xmlns":27},[29,40162,40163,40167],{},[32,40164,40165],{},[35,40166,213],{},[39,40168,213],{"encoding":41},[15,40170,40172],{"className":40171,"ariaHidden":46},[45],[15,40173,40175,40178],{"className":40174},[50],[15,40176],{"className":40177,"style":566},[54],[15,40179,213],{"className":40180},[59,60]," 很小而 ",[15,40183,40185,40198],{"className":40184,"translate":19},[18],[15,40186,40188],{"className":40187},[23],[25,40189,40190],{"xmlns":27},[29,40191,40192,40196],{},[32,40193,40194],{},[35,40195,206],{},[39,40197,206],{"encoding":41},[15,40199,40201],{"className":40200,"ariaHidden":46},[45],[15,40202,40204,40207],{"className":40203},[50],[15,40205],{"className":40206,"style":664},[54],[15,40208,206],{"className":40209,"style":334},[59,60]," 不小」的稀有区域极度敏感（",[1225,40212,40213],{},"尾部敏感","）：这既是它能捕捉稀有事件的优点，也是它容易被少量异常值带偏的缺点。在 f-GAN 家族里它对应最小二乘 GAN（LSGAN）：因为 ",[15,40216,40218,40259],{"className":40217,"translate":19},[18],[15,40219,40221],{"className":40220},[23],[25,40222,40223],{"xmlns":27},[29,40224,40225,40256],{},[32,40226,40227,40233,40235,40238,40240,40242,40244,40246,40252,40254],{},[6814,40228,40229,40231],{},[35,40230,37],{},[110,40232,7573],{},[110,40234,113],{"stretchy":112},[35,40236,40237],{},"y",[110,40239,120],{"stretchy":112},[110,40241,123],{},[35,40243,40237],{},[110,40245,2470],{},[6814,40247,40248,40250],{},[35,40249,40237],{},[115,40251,2463],{},[35,40253,941],{"mathvariant":209},[115,40255,38989],{},[39,40257,40258],{"encoding":41},"f^*(y)=y+y^2\u002F4",[15,40260,40262,40315,40334],{"className":40261,"ariaHidden":46},[45],[15,40263,40265,40268,40297,40300,40303,40306,40309,40312],{"className":40264},[50],[15,40266],{"className":40267,"style":139},[54],[15,40269,40271,40274],{"className":40270},[59],[15,40272,37],{"className":40273,"style":61},[59,60],[15,40275,40277],{"className":40276},[281],[15,40278,40280],{"className":40279},[285],[15,40281,40283],{"className":40282},[290],[15,40284,40286],{"className":40285,"style":8499},[294],[15,40287,40288,40291],{"style":6865},[15,40289],{"className":40290,"style":303},[302],[15,40292,40294],{"className":40293},[307,308,309,310],[15,40295,7573],{"className":40296},[2591,310],[15,40298,113],{"className":40299},[146],[15,40301,40237],{"className":40302,"style":981},[59,60],[15,40304,120],{"className":40305},[153],[15,40307],{"className":40308,"style":158},[157],[15,40310,123],{"className":40311},[162],[15,40313],{"className":40314,"style":158},[157],[15,40316,40318,40322,40325,40328,40331],{"className":40317},[50],[15,40319],{"className":40320,"style":40321},[54],"height:0.7778em;vertical-align:-0.1944em;",[15,40323,40237],{"className":40324,"style":981},[59,60],[15,40326],{"className":40327,"style":2587},[157],[15,40329,2470],{"className":40330},[2591],[15,40332],{"className":40333,"style":2587},[157],[15,40335,40337,40340,40369],{"className":40336},[50],[15,40338],{"className":40339,"style":20003},[54],[15,40341,40343,40346],{"className":40342},[59],[15,40344,40237],{"className":40345,"style":981},[59,60],[15,40347,40349],{"className":40348},[281],[15,40350,40352],{"className":40351},[285],[15,40353,40355],{"className":40354},[290],[15,40356,40358],{"className":40357,"style":20028},[294],[15,40359,40360,40363],{"style":6865},[15,40361],{"className":40362,"style":303},[302],[15,40364,40366],{"className":40365},[307,308,309,310],[15,40367,2463],{"className":40368},[59,310],[15,40370,40372],{"className":40371},[59],"\u002F4"," 是二次的，判别器梯度不会像 JS 那样饱和；在鲁棒统计与核方法中，",[15,40375,40377,40395],{"className":40376,"translate":19},[18],[15,40378,40380],{"className":40379},[23],[25,40381,40382],{"xmlns":27},[29,40383,40384,40392],{},[32,40385,40386],{},[6814,40387,40388,40390],{},[35,40389,37449],{},[115,40391,2463],{},[39,40393,40394],{"encoding":41},"\\chi^2",[15,40396,40398],{"className":40397,"ariaHidden":46},[45],[15,40399,40401,40405],{"className":40400},[50],[15,40402],{"className":40403,"style":40404},[54],"height:1.0085em;vertical-align:-0.1944em;",[15,40406,40408,40411],{"className":40407},[59],[15,40409,37449],{"className":40410},[59,60],[15,40412,40414],{"className":40413},[281],[15,40415,40417],{"className":40416},[285],[15,40418,40420],{"className":40419},[290],[15,40421,40423],{"className":40422,"style":20028},[294],[15,40424,40425,40428],{"style":6865},[15,40426],{"className":40427,"style":303},[302],[15,40429,40431],{"className":40430},[307,308,309,310],[15,40432,2463],{"className":40433},[59,310]," 距离还给出了带权核的另一种「局部」相似度。",[2311,40436,40438],{"id":40437},"_35-hellinger-平方","3.5 Hellinger 平方",[11,40440,21473],{},[15,40442,40444],{"className":40443,"translate":19},[180],[15,40445,40447,40485],{"className":40446,"translate":19},[18],[15,40448,40450],{"className":40449},[23],[25,40451,40452],{"xmlns":27,"display":189},[29,40453,40454,40482],{},[32,40455,40456,40458,40460,40462,40464,40466,40468,40472,40474,40476],{},[35,40457,37],{},[110,40459,113],{"stretchy":112},[35,40461,769],{},[110,40463,120],{"stretchy":112},[110,40465,123],{},[110,40467,113],{"stretchy":112},[34339,40469,40470],{},[35,40471,769],{},[110,40473,4813],{},[115,40475,117],{},[6814,40477,40478,40480],{},[110,40479,120],{"stretchy":112},[115,40481,2463],{},[39,40483,40484],{"encoding":41},"f(t)=(\\sqrt{t}-1)^2",[15,40486,40488,40515,40584],{"className":40487,"ariaHidden":46},[45],[15,40489,40491,40494,40497,40500,40503,40506,40509,40512],{"className":40490},[50],[15,40492],{"className":40493,"style":139},[54],[15,40495,37],{"className":40496,"style":61},[59,60],[15,40498,113],{"className":40499},[146],[15,40501,769],{"className":40502},[59,60],[15,40504,120],{"className":40505},[153],[15,40507],{"className":40508,"style":158},[157],[15,40510,123],{"className":40511},[162],[15,40513],{"className":40514,"style":158},[157],[15,40516,40518,40522,40525,40575,40578,40581],{"className":40517},[50],[15,40519],{"className":40520,"style":40521},[54],"height:1.1914em;vertical-align:-0.25em;",[15,40523,113],{"className":40524},[146],[15,40526,40528],{"className":40527},[59,34367],[15,40529,40531,40566],{"className":40530},[285,286],[15,40532,40534,40563],{"className":40533},[290],[15,40535,40538,40550],{"className":40536,"style":40537},[294],"height:0.9414em;",[15,40539,40541,40544],{"className":40540,"style":11863},[6307],[15,40542],{"className":40543,"style":461},[302],[15,40545,40547],{"className":40546,"style":34387},[59],[15,40548,769],{"className":40549},[59,60],[15,40551,40553,40556],{"style":40552},"top:-2.9014em;",[15,40554],{"className":40555,"style":461},[302],[15,40557,40559],{"className":40558,"style":34444},[34443],[6323,40560,40561],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,40562],{"d":34451},[15,40564,318],{"className":40565},[317],[15,40567,40569],{"className":40568},[290],[15,40570,40573],{"className":40571,"style":40572},[294],"height:0.0986em;",[15,40574],{},[15,40576],{"className":40577,"style":2587},[157],[15,40579,4813],{"className":40580},[2591],[15,40582],{"className":40583,"style":2587},[157],[15,40585,40587,40590,40593],{"className":40586},[50],[15,40588],{"className":40589,"style":37251},[54],[15,40591,117],{"className":40592},[59],[15,40594,40596,40599],{"className":40595},[153],[15,40597,120],{"className":40598},[153],[15,40600,40602],{"className":40601},[281],[15,40603,40605],{"className":40604},[285],[15,40606,40608],{"className":40607},[290],[15,40609,40611],{"className":40610,"style":19735},[294],[15,40612,40613,40616],{"style":8277},[15,40614],{"className":40615,"style":303},[302],[15,40617,40619],{"className":40618},[307,308,309,310],[15,40620,2463],{"className":40621},[59,310],[11,40623,34682,40624,5645,40689,40937],{},[15,40625,40627,40650],{"className":40626,"translate":19},[18],[15,40628,40630],{"className":40629},[23],[25,40631,40632],{"xmlns":27},[29,40633,40634,40648],{},[32,40635,40636,40638,40640,40642,40644,40646],{},[35,40637,37],{},[110,40639,113],{"stretchy":112},[115,40641,117],{},[110,40643,120],{"stretchy":112},[110,40645,123],{},[115,40647,126],{},[39,40649,129],{"encoding":41},[15,40651,40653,40680],{"className":40652,"ariaHidden":46},[45],[15,40654,40656,40659,40662,40665,40668,40671,40674,40677],{"className":40655},[50],[15,40657],{"className":40658,"style":139},[54],[15,40660,37],{"className":40661,"style":61},[59,60],[15,40663,113],{"className":40664},[146],[15,40666,117],{"className":40667},[59],[15,40669,120],{"className":40670},[153],[15,40672],{"className":40673,"style":158},[157],[15,40675,123],{"className":40676},[162],[15,40678],{"className":40679,"style":158},[157],[15,40681,40683,40686],{"className":40682},[50],[15,40684],{"className":40685,"style":172},[54],[15,40687,126],{"className":40688},[59],[15,40690,40692,40747],{"className":40691,"translate":19},[18],[15,40693,40695],{"className":40694},[23],[25,40696,40697],{"xmlns":27},[29,40698,40699,40744],{},[32,40700,40701,40711,40713,40715,40717,40719,40740,40742],{},[6814,40702,40703,40705],{},[35,40704,37],{},[32,40706,40707,40709],{},[110,40708,6820],{"mathvariant":209},[110,40710,6820],{"mathvariant":209},[110,40712,113],{"stretchy":112},[35,40714,769],{},[110,40716,120],{"stretchy":112},[110,40718,123],{},[238,40720,40721,40723],{},[115,40722,117],{},[32,40724,40725,40727],{},[115,40726,2463],{},[6814,40728,40729,40731],{},[35,40730,769],{},[32,40732,40733,40736,40738],{},[115,40734,40735],{},"3",[35,40737,941],{"mathvariant":209},[115,40739,2463],{},[110,40741,2903],{},[115,40743,126],{},[39,40745,40746],{"encoding":41},"f''(t)=\\frac{1}{2t^{3\u002F2}}>0",[15,40748,40750,40806,40928],{"className":40749,"ariaHidden":46},[45],[15,40751,40753,40756,40788,40791,40794,40797,40800,40803],{"className":40752},[50],[15,40754],{"className":40755,"style":6843},[54],[15,40757,40759,40762],{"className":40758},[59],[15,40760,37],{"className":40761,"style":61},[59,60],[15,40763,40765],{"className":40764},[281],[15,40766,40768],{"className":40767},[285],[15,40769,40771],{"className":40770},[290],[15,40772,40774],{"className":40773,"style":6862},[294],[15,40775,40776,40779],{"style":6865},[15,40777],{"className":40778,"style":303},[302],[15,40780,40782],{"className":40781},[307,308,309,310],[15,40783,40785],{"className":40784},[59,310],[15,40786,21748],{"className":40787},[59,310],[15,40789,113],{"className":40790},[146],[15,40792,769],{"className":40793},[59,60],[15,40795,120],{"className":40796},[153],[15,40798],{"className":40799,"style":158},[157],[15,40801,123],{"className":40802},[162],[15,40804],{"className":40805,"style":158},[157],[15,40807,40809,40813,40919,40922,40925],{"className":40808},[50],[15,40810],{"className":40811,"style":40812},[54],"height:1.2305em;vertical-align:-0.3854em;",[15,40814,40816,40819,40916],{"className":40815},[59],[15,40817],{"className":40818},[146,441],[15,40820,40822],{"className":40821},[238],[15,40823,40825,40907],{"className":40824},[285,286],[15,40826,40828,40904],{"className":40827},[290],[15,40829,40831,40882,40890],{"className":40830,"style":2524},[294],[15,40832,40834,40837],{"style":40833},"top:-2.6146em;",[15,40835],{"className":40836,"style":461},[302],[15,40838,40840],{"className":40839},[307,308,309,310],[15,40841,40843,40846],{"className":40842},[59,310],[15,40844,2463],{"className":40845},[59,310],[15,40847,40849,40852],{"className":40848},[59,310],[15,40850,769],{"className":40851},[59,60,310],[15,40853,40855],{"className":40854},[281],[15,40856,40858],{"className":40857},[285],[15,40859,40861],{"className":40860},[290],[15,40862,40865],{"className":40863,"style":40864},[294],"height:0.822em;",[15,40866,40868,40872],{"style":40867},"top:-2.822em;margin-right:0.0714em;",[15,40869],{"className":40870,"style":40871},[302],"height:2.5357em;",[15,40873,40875],{"className":40874},[307,30210,9674,310],[15,40876,40878],{"className":40877},[59,310],[15,40879,40881],{"className":40880},[59,310],"3\u002F2",[15,40883,40884,40887],{"style":473},[15,40885],{"className":40886,"style":461},[302],[15,40888],{"className":40889,"style":481},[480],[15,40891,40892,40895],{"style":2550},[15,40893],{"className":40894,"style":461},[302],[15,40896,40898],{"className":40897},[307,308,309,310],[15,40899,40901],{"className":40900},[59,310],[15,40902,117],{"className":40903},[59,310],[15,40905,318],{"className":40906},[317],[15,40908,40910],{"className":40909},[290],[15,40911,40914],{"className":40912,"style":40913},[294],"height:0.3854em;",[15,40915],{},[15,40917],{"className":40918},[153,441],[15,40920],{"className":40921,"style":158},[157],[15,40923,2903],{"className":40924},[162],[15,40926],{"className":40927,"style":158},[157],[15,40929,40931,40934],{"className":40930},[50],[15,40932],{"className":40933,"style":172},[54],[15,40935,126],{"className":40936},[59]," 凸，代入：",[15,40939,40941],{"className":40940,"translate":19},[180],[15,40942,40944,41034],{"className":40943,"translate":19},[18],[15,40945,40947],{"className":40946},[23],[25,40948,40949],{"xmlns":27,"display":189},[29,40950,40951,41031],{},[32,40952,40953,40959,40961,40963,40965,40967,40969,40971,40973,40975,40997,40999,41001,41003,41005,41007,41011,41013,41017,41023,41025,41027,41029],{},[195,40954,40955,40957],{},[35,40956,199],{},[35,40958,37],{},[110,40960,113],{"stretchy":112},[35,40962,206],{},[35,40964,210],{"mathvariant":209},[35,40966,213],{},[110,40968,120],{"stretchy":112},[110,40970,123],{},[110,40972,1287],{},[35,40974,944],{},[6814,40976,40977,40995],{},[32,40978,40979,40981,40989,40991,40993],{},[110,40980,113],{"fence":46},[34339,40982,40983],{},[238,40984,40985,40987],{},[35,40986,11],{},[35,40988,944],{},[110,40990,4813],{},[115,40992,117],{},[110,40994,120],{"fence":46},[115,40996,2463],{},[35,40998,244],{},[35,41000,774],{},[110,41002,123],{},[110,41004,1287],{},[110,41006,113],{"stretchy":112},[34339,41008,41009],{},[35,41010,11],{},[110,41012,4813],{},[34339,41014,41015],{},[35,41016,944],{},[6814,41018,41019,41021],{},[110,41020,120],{"stretchy":112},[115,41022,2463],{},[1297,41024,1299],{},[35,41026,244],{},[35,41028,774],{},[35,41030,4375],{"mathvariant":209},[39,41032,41033],{"encoding":41},"D_f(P\\|Q)\n=\\int q\\left(\\sqrt{\\frac{p}{q}}-1\\right)^2dx\n=\\int (\\sqrt{p}-\\sqrt{q})^2\\,dx .",[15,41035,41037,41107,41312,41382],{"className":41036,"ariaHidden":46},[45],[15,41038,41040,41043,41083,41086,41089,41092,41095,41098,41101,41104],{"className":41039},[50],[15,41041],{"className":41042,"style":270},[54],[15,41044,41046,41049],{"className":41045},[59],[15,41047,199],{"className":41048,"style":277},[59,60],[15,41050,41052],{"className":41051},[281],[15,41053,41055,41075],{"className":41054},[285,286],[15,41056,41058,41072],{"className":41057},[290],[15,41059,41061],{"className":41060,"style":295},[294],[15,41062,41063,41066],{"style":298},[15,41064],{"className":41065,"style":303},[302],[15,41067,41069],{"className":41068},[307,308,309,310],[15,41070,37],{"className":41071,"style":61},[59,60,310],[15,41073,318],{"className":41074},[317],[15,41076,41078],{"className":41077},[290],[15,41079,41081],{"className":41080,"style":325},[294],[15,41082],{},[15,41084,113],{"className":41085},[146],[15,41087,206],{"className":41088,"style":334},[59,60],[15,41090,210],{"className":41091},[59],[15,41093,213],{"className":41094},[59,60],[15,41096,120],{"className":41097},[153],[15,41099],{"className":41100,"style":158},[157],[15,41102,123],{"className":41103},[162],[15,41105],{"className":41106,"style":158},[157],[15,41108,41110,41114,41117,41120,41123,41126,41294,41297,41300,41303,41306,41309],{"className":41109},[50],[15,41111],{"className":41112,"style":41113},[54],"height:2.6466em;vertical-align:-0.9926em;",[15,41115,1287],{"className":41116,"style":1487},[1484,1485,1486],[15,41118],{"className":41119,"style":406},[157],[15,41121,944],{"className":41122,"style":981},[59,60],[15,41124],{"className":41125,"style":406},[157],[15,41127,41129,41271],{"className":41128},[410],[15,41130,41132,41138,41253,41256,41259,41262,41265],{"className":41131},[410],[15,41133,41135],{"className":41134,"style":415},[146,414],[15,41136,113],{"className":41137},[419,309],[15,41139,41141],{"className":41140},[59,34367],[15,41142,41144,41244],{"className":41143},[285,286],[15,41145,41147,41241],{"className":41146},[290],[15,41148,41151,41224],{"className":41149,"style":41150},[294],"height:1.4474em;",[15,41152,41155,41158],{"className":41153,"style":41154},[6307],"top:-4.4em;",[15,41156],{"className":41157,"style":35045},[302],[15,41159,41162],{"className":41160,"style":41161},[59],"padding-left:1em;",[15,41163,41165,41168,41221],{"className":41164},[59],[15,41166],{"className":41167},[146,441],[15,41169,41171],{"className":41170},[238],[15,41172,41174,41213],{"className":41173},[285,286],[15,41175,41177,41210],{"className":41176},[290],[15,41178,41180,41191,41199],{"className":41179,"style":3554},[294],[15,41181,41182,41185],{"style":457},[15,41183],{"className":41184,"style":461},[302],[15,41186,41188],{"className":41187},[59],[15,41189,944],{"className":41190,"style":981},[59,60],[15,41192,41193,41196],{"style":473},[15,41194],{"className":41195,"style":461},[302],[15,41197],{"className":41198,"style":481},[480],[15,41200,41201,41204],{"style":484},[15,41202],{"className":41203,"style":461},[302],[15,41205,41207],{"className":41206},[59],[15,41208,11],{"className":41209},[59,60],[15,41211,318],{"className":41212},[317],[15,41214,41216],{"className":41215},[290],[15,41217,41219],{"className":41218,"style":506},[294],[15,41220],{},[15,41222],{"className":41223},[153,441],[15,41225,41227,41230],{"style":41226},"top:-3.4074em;",[15,41228],{"className":41229,"style":35045},[302],[15,41231,41234],{"className":41232,"style":41233},[34443],"min-width:1.02em;height:2.48em;",[6323,41235,41238],{"xmlns":6325,"width":6326,"height":41236,"viewBox":41237,"preserveAspectRatio":6329},"2.48em","0 0 400000 2592",[6331,41239],{"d":41240},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[15,41242,318],{"className":41243},[317],[15,41245,41247],{"className":41246},[290],[15,41248,41251],{"className":41249,"style":41250},[294],"height:0.9926em;",[15,41252],{},[15,41254],{"className":41255,"style":2587},[157],[15,41257,4813],{"className":41258},[2591],[15,41260],{"className":41261,"style":2587},[157],[15,41263,117],{"className":41264},[59],[15,41266,41268],{"className":41267,"style":415},[153,414],[15,41269,120],{"className":41270},[419,309],[15,41272,41274],{"className":41273},[281],[15,41275,41277],{"className":41276},[285],[15,41278,41280],{"className":41279},[290],[15,41281,41283],{"className":41282,"style":37661},[294],[15,41284,41285,41288],{"style":37664},[15,41286],{"className":41287,"style":303},[302],[15,41289,41291],{"className":41290},[307,308,309,310],[15,41292,2463],{"className":41293},[59,310],[15,41295],{"className":41296,"style":406},[157],[15,41298,244],{"className":41299},[59,60],[15,41301,774],{"className":41302},[59,60],[15,41304],{"className":41305,"style":158},[157],[15,41307,123],{"className":41308},[162],[15,41310],{"className":41311,"style":158},[157],[15,41313,41315,41318,41321,41324,41373,41376,41379],{"className":41314},[50],[15,41316],{"className":41317,"style":5777},[54],[15,41319,1287],{"className":41320,"style":1487},[1484,1485,1486],[15,41322,113],{"className":41323},[146],[15,41325,41327],{"className":41326},[59,34367],[15,41328,41330,41364],{"className":41329},[285,286],[15,41331,41333,41361],{"className":41332},[290],[15,41334,41336,41348],{"className":41335,"style":6862},[294],[15,41337,41339,41342],{"className":41338,"style":11863},[6307],[15,41340],{"className":41341,"style":461},[302],[15,41343,41345],{"className":41344,"style":34387},[59],[15,41346,11],{"className":41347},[59,60],[15,41349,41351,41354],{"style":41350},"top:-2.7119em;",[15,41352],{"className":41353,"style":461},[302],[15,41355,41357],{"className":41356,"style":34444},[34443],[6323,41358,41359],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41360],{"d":34451},[15,41362,318],{"className":41363},[317],[15,41365,41367],{"className":41366},[290],[15,41368,41371],{"className":41369,"style":41370},[294],"height:0.2881em;",[15,41372],{},[15,41374],{"className":41375,"style":2587},[157],[15,41377,4813],{"className":41378},[2591],[15,41380],{"className":41381,"style":2587},[157],[15,41383,41385,41389,41436,41465,41468,41471,41474],{"className":41384},[50],[15,41386],{"className":41387,"style":41388},[54],"height:1.1522em;vertical-align:-0.2881em;",[15,41390,41392],{"className":41391},[59,34367],[15,41393,41395,41428],{"className":41394},[285,286],[15,41396,41398,41425],{"className":41397},[290],[15,41399,41401,41413],{"className":41400,"style":6862},[294],[15,41402,41404,41407],{"className":41403,"style":11863},[6307],[15,41405],{"className":41406,"style":461},[302],[15,41408,41410],{"className":41409,"style":34387},[59],[15,41411,944],{"className":41412,"style":981},[59,60],[15,41414,41415,41418],{"style":41350},[15,41416],{"className":41417,"style":461},[302],[15,41419,41421],{"className":41420,"style":34444},[34443],[6323,41422,41423],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41424],{"d":34451},[15,41426,318],{"className":41427},[317],[15,41429,41431],{"className":41430},[290],[15,41432,41434],{"className":41433,"style":41370},[294],[15,41435],{},[15,41437,41439,41442],{"className":41438},[153],[15,41440,120],{"className":41441},[153],[15,41443,41445],{"className":41444},[281],[15,41446,41448],{"className":41447},[285],[15,41449,41451],{"className":41450},[290],[15,41452,41454],{"className":41453,"style":19735},[294],[15,41455,41456,41459],{"style":8277},[15,41457],{"className":41458,"style":303},[302],[15,41460,41462],{"className":41461},[307,308,309,310],[15,41463,2463],{"className":41464},[59,310],[15,41466],{"className":41467,"style":406},[157],[15,41469,244],{"className":41470},[59,60],[15,41472,774],{"className":41473},[59,60],[15,41475,4375],{"className":41476},[59],[11,41478,41479,41480,41638],{},"记 Bhattacharyya 系数 ",[15,41481,41483,41527],{"className":41482,"translate":19},[18],[15,41484,41486],{"className":41485},[23],[25,41487,41488],{"xmlns":27},[29,41489,41490,41524],{},[32,41491,41492,41494,41496,41498,41500,41502,41504,41506,41508,41510,41518,41520,41522],{},[35,41493,39291],{},[35,41495,39294],{},[110,41497,113],{"stretchy":112},[35,41499,206],{},[110,41501,551],{"separator":46},[35,41503,213],{},[110,41505,120],{"stretchy":112},[110,41507,123],{},[110,41509,1287],{},[34339,41511,41512],{},[32,41513,41514,41516],{},[35,41515,11],{},[35,41517,944],{},[1297,41519,1299],{},[35,41521,244],{},[35,41523,774],{},[39,41525,41526],{"encoding":41},"BC(P,Q)=\\int\\sqrt{pq}\\,dx",[15,41528,41530,41569],{"className":41529,"ariaHidden":46},[45],[15,41531,41533,41536,41539,41542,41545,41548,41551,41554,41557,41560,41563,41566],{"className":41532},[50],[15,41534],{"className":41535,"style":139},[54],[15,41537,39291],{"className":41538,"style":39387},[59,60],[15,41540,39294],{"className":41541,"style":10782},[59,60],[15,41543,113],{"className":41544},[146],[15,41546,206],{"className":41547,"style":334},[59,60],[15,41549,551],{"className":41550},[573],[15,41552],{"className":41553,"style":406},[157],[15,41555,213],{"className":41556},[59,60],[15,41558,120],{"className":41559},[153],[15,41561],{"className":41562,"style":158},[157],[15,41564,123],{"className":41565},[162],[15,41567],{"className":41568,"style":158},[157],[15,41570,41572,41575,41578,41581,41629,41632,41635],{"className":41571},[50],[15,41573],{"className":41574,"style":39008},[54],[15,41576,1287],{"className":41577,"style":5617},[1484,1485,5616],[15,41579],{"className":41580,"style":406},[157],[15,41582,41584],{"className":41583},[59,34367],[15,41585,41587,41621],{"className":41586},[285,286],[15,41588,41590,41618],{"className":41589},[290],[15,41591,41593,41606],{"className":41592,"style":39027},[294],[15,41594,41596,41599],{"className":41595,"style":11863},[6307],[15,41597],{"className":41598,"style":461},[302],[15,41600,41602],{"className":41601,"style":34387},[59],[15,41603,41605],{"className":41604,"style":981},[59,60],"pq",[15,41607,41608,41611],{"style":39039},[15,41609],{"className":41610,"style":461},[302],[15,41612,41614],{"className":41613,"style":34444},[34443],[6323,41615,41616],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41617],{"d":34451},[15,41619,318],{"className":41620},[317],[15,41622,41624],{"className":41623},[290],[15,41625,41627],{"className":41626,"style":39059},[294],[15,41628],{},[15,41630],{"className":41631,"style":406},[157],[15,41633,244],{"className":41634},[59,60],[15,41636,774],{"className":41637},[59,60],"，则",[15,41640,41642],{"className":41641,"translate":19},[180],[15,41643,41645,41721],{"className":41644,"translate":19},[18],[15,41646,41648],{"className":41647},[23],[25,41649,41650],{"xmlns":27,"display":189},[29,41651,41652,41718],{},[32,41653,41654,41656,41658,41662,41664,41668,41674,41676,41678,41680,41682,41684,41686,41688,41690,41692,41700,41702,41704,41706,41708,41710,41712,41714,41716],{},[110,41655,1287],{},[110,41657,113],{"stretchy":112},[34339,41659,41660],{},[35,41661,11],{},[110,41663,4813],{},[34339,41665,41666],{},[35,41667,944],{},[6814,41669,41670,41672],{},[110,41671,120],{"stretchy":112},[115,41673,2463],{},[110,41675,123],{},[110,41677,1287],{},[35,41679,11],{},[110,41681,2470],{},[110,41683,1287],{},[35,41685,944],{},[110,41687,4813],{},[115,41689,2463],{},[110,41691,1287],{},[34339,41693,41694],{},[32,41695,41696,41698],{},[35,41697,11],{},[35,41699,944],{},[110,41701,123],{},[115,41703,2463],{},[110,41705,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,41707,117],{},[110,41709,4813],{},[35,41711,39291],{},[35,41713,39294],{},[110,41715,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,41717,4375],{"mathvariant":209},[39,41719,41720],{"encoding":41},"\\int(\\sqrt p-\\sqrt q)^2\n=\\int p+\\int q-2\\int\\sqrt{pq}\n=2\\big(1-BC\\big).",[15,41722,41724,41789,41877,41901,41925,41999,42026],{"className":41723,"ariaHidden":46},[45],[15,41725,41727,41730,41733,41736,41780,41783,41786],{"className":41726},[50],[15,41728],{"className":41729,"style":5777},[54],[15,41731,1287],{"className":41732,"style":1487},[1484,1485,1486],[15,41734,113],{"className":41735},[146],[15,41737,41739],{"className":41738},[59,34367],[15,41740,41742,41772],{"className":41741},[285,286],[15,41743,41745,41769],{"className":41744},[290],[15,41746,41748,41757],{"className":41747,"style":6862},[294],[15,41749,41751,41754],{"className":41750,"style":11863},[6307],[15,41752],{"className":41753,"style":461},[302],[15,41755,11],{"className":41756,"style":34387},[59,60],[15,41758,41759,41762],{"style":41350},[15,41760],{"className":41761,"style":461},[302],[15,41763,41765],{"className":41764,"style":34444},[34443],[6323,41766,41767],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41768],{"d":34451},[15,41770,318],{"className":41771},[317],[15,41773,41775],{"className":41774},[290],[15,41776,41778],{"className":41777,"style":41370},[294],[15,41779],{},[15,41781],{"className":41782,"style":2587},[157],[15,41784,4813],{"className":41785},[2591],[15,41787],{"className":41788,"style":2587},[157],[15,41790,41792,41795,41839,41868,41871,41874],{"className":41791},[50],[15,41793],{"className":41794,"style":41388},[54],[15,41796,41798],{"className":41797},[59,34367],[15,41799,41801,41831],{"className":41800},[285,286],[15,41802,41804,41828],{"className":41803},[290],[15,41805,41807,41816],{"className":41806,"style":6862},[294],[15,41808,41810,41813],{"className":41809,"style":11863},[6307],[15,41811],{"className":41812,"style":461},[302],[15,41814,944],{"className":41815,"style":39099},[59,60],[15,41817,41818,41821],{"style":41350},[15,41819],{"className":41820,"style":461},[302],[15,41822,41824],{"className":41823,"style":34444},[34443],[6323,41825,41826],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41827],{"d":34451},[15,41829,318],{"className":41830},[317],[15,41832,41834],{"className":41833},[290],[15,41835,41837],{"className":41836,"style":41370},[294],[15,41838],{},[15,41840,41842,41845],{"className":41841},[153],[15,41843,120],{"className":41844},[153],[15,41846,41848],{"className":41847},[281],[15,41849,41851],{"className":41850},[285],[15,41852,41854],{"className":41853},[290],[15,41855,41857],{"className":41856,"style":19735},[294],[15,41858,41859,41862],{"style":8277},[15,41860],{"className":41861,"style":303},[302],[15,41863,41865],{"className":41864},[307,308,309,310],[15,41866,2463],{"className":41867},[59,310],[15,41869],{"className":41870,"style":158},[157],[15,41872,123],{"className":41873},[162],[15,41875],{"className":41876,"style":158},[157],[15,41878,41880,41883,41886,41889,41892,41895,41898],{"className":41879},[50],[15,41881],{"className":41882,"style":5777},[54],[15,41884,1287],{"className":41885,"style":1487},[1484,1485,1486],[15,41887],{"className":41888,"style":406},[157],[15,41890,11],{"className":41891},[59,60],[15,41893],{"className":41894,"style":2587},[157],[15,41896,2470],{"className":41897},[2591],[15,41899],{"className":41900,"style":2587},[157],[15,41902,41904,41907,41910,41913,41916,41919,41922],{"className":41903},[50],[15,41905],{"className":41906,"style":5777},[54],[15,41908,1287],{"className":41909,"style":1487},[1484,1485,1486],[15,41911],{"className":41912,"style":406},[157],[15,41914,944],{"className":41915,"style":981},[59,60],[15,41917],{"className":41918,"style":2587},[157],[15,41920,4813],{"className":41921},[2591],[15,41923],{"className":41924,"style":2587},[157],[15,41926,41928,41931,41934,41937,41940,41943,41990,41993,41996],{"className":41927},[50],[15,41929],{"className":41930,"style":5777},[54],[15,41932,2463],{"className":41933},[59],[15,41935],{"className":41936,"style":406},[157],[15,41938,1287],{"className":41939,"style":1487},[1484,1485,1486],[15,41941],{"className":41942,"style":406},[157],[15,41944,41946],{"className":41945},[59,34367],[15,41947,41949,41982],{"className":41948},[285,286],[15,41950,41952,41979],{"className":41951},[290],[15,41953,41955,41967],{"className":41954,"style":6862},[294],[15,41956,41958,41961],{"className":41957,"style":11863},[6307],[15,41959],{"className":41960,"style":461},[302],[15,41962,41964],{"className":41963,"style":34387},[59],[15,41965,41605],{"className":41966,"style":981},[59,60],[15,41968,41969,41972],{"style":41350},[15,41970],{"className":41971,"style":461},[302],[15,41973,41975],{"className":41974,"style":34444},[34443],[6323,41976,41977],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,41978],{"d":34451},[15,41980,318],{"className":41981},[317],[15,41983,41985],{"className":41984},[290],[15,41986,41988],{"className":41987,"style":41370},[294],[15,41989],{},[15,41991],{"className":41992,"style":158},[157],[15,41994,123],{"className":41995},[162],[15,41997],{"className":41998,"style":158},[157],[15,42000,42002,42005,42008,42014,42017,42020,42023],{"className":42001},[50],[15,42003],{"className":42004,"style":20563},[54],[15,42006,2463],{"className":42007},[59],[15,42009,42011],{"className":42010},[59],[15,42012,113],{"className":42013},[419,9674],[15,42015,117],{"className":42016},[59],[15,42018],{"className":42019,"style":2587},[157],[15,42021,4813],{"className":42022},[2591],[15,42024],{"className":42025,"style":2587},[157],[15,42027,42029,42032,42035,42038,42044],{"className":42028},[50],[15,42030],{"className":42031,"style":20563},[54],[15,42033,39291],{"className":42034,"style":39387},[59,60],[15,42036,39294],{"className":42037,"style":10782},[59,60],[15,42039,42041],{"className":42040},[59],[15,42042,120],{"className":42043},[419,9674],[15,42045,4375],{"className":42046},[59],[11,42048,42049,42050,42109],{},"文献里对 ",[15,42051,42053,42071],{"className":42052,"translate":19},[18],[15,42054,42056],{"className":42055},[23],[25,42057,42058],{"xmlns":27},[29,42059,42060,42068],{},[32,42061,42062],{},[6814,42063,42064,42066],{},[35,42065,33884],{},[115,42067,2463],{},[39,42069,42070],{"encoding":41},"H^2",[15,42072,42074],{"className":42073,"ariaHidden":46},[45],[15,42075,42077,42080],{"className":42076},[50],[15,42078],{"className":42079,"style":20028},[54],[15,42081,42083,42086],{"className":42082},[59],[15,42084,33884],{"className":42085,"style":34038},[59,60],[15,42087,42089],{"className":42088},[281],[15,42090,42092],{"className":42091},[285],[15,42093,42095],{"className":42094},[290],[15,42096,42098],{"className":42097,"style":20028},[294],[15,42099,42100,42103],{"style":6865},[15,42101],{"className":42102,"style":303},[302],[15,42104,42106],{"className":42105},[307,308,309,310],[15,42107,2463],{"className":42108},[59,310]," 有两种约定：",[15,42111,42113],{"className":42112,"translate":19},[180],[15,42114,42116,42222],{"className":42115,"translate":19},[18],[15,42117,42119],{"className":42118},[23],[25,42120,42121],{"xmlns":27,"display":189},[29,42122,42123,42219],{},[1243,42124,42125,42160],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,42126,42127,42140],{},[1252,42128,42129],{},[1255,42130,42131],{"scriptlevel":126,"displaystyle":46},[7553,42132,42133,42135,42138],{},[35,42134,33884],{},[1297,42136,42137],{},"Bhattacharyya",[115,42139,2463],{},[1252,42141,42142],{},[1255,42143,42144],{"scriptlevel":126,"displaystyle":46},[32,42145,42146,42148,42150,42152,42154,42156,42158],{},[32,42147],{},[110,42149,123],{},[115,42151,117],{},[110,42153,4813],{},[35,42155,39291],{},[35,42157,39294],{},[110,42159,551],{"separator":46},[1249,42161,42162,42181],{},[1252,42163,42164],{},[1255,42165,42166],{"scriptlevel":126,"displaystyle":46},[7553,42167,42168,42170,42179],{},[35,42169,33884],{},[32,42171,42172,42175,42177],{},[1297,42173,42174],{},"this",[1297,42176,1299],{},[35,42178,37],{},[115,42180,2463],{},[1252,42182,42183],{},[1255,42184,42185],{"scriptlevel":126,"displaystyle":46},[32,42186,42187,42189,42191,42193,42195,42197,42199,42201,42203,42205,42207,42209,42217],{},[32,42188],{},[110,42190,123],{},[115,42192,2463],{},[110,42194,113],{"stretchy":112},[115,42196,117],{},[110,42198,4813],{},[35,42200,39291],{},[35,42202,39294],{},[110,42204,120],{"stretchy":112},[110,42206,123],{},[115,42208,2463],{},[7553,42210,42211,42213,42215],{},[35,42212,33884],{},[1297,42214,42137],{},[115,42216,2463],{},[35,42218,4375],{"mathvariant":209},[39,42220,42221],{"encoding":41},"\\begin{aligned}\nH^2_{\\text{Bhattacharyya}}&=1-BC,\\\\[2pt]\nH^2_{\\text{this}\\,f}&=2(1-BC)\n=2H^2_{\\text{Bhattacharyya}} .\n\\end{aligned}",[15,42223,42225],{"className":42224,"ariaHidden":46},[45],[15,42226,42228,42232],{"className":42227},[50],[15,42229],{"className":42230,"style":42231},[54],"height:2.9713em;vertical-align:-1.2357em;",[15,42233,42235],{"className":42234},[59],[15,42236,42238,42404],{"className":42237},[1243],[15,42239,42241],{"className":42240},[1360],[15,42242,42244,42395],{"className":42243},[285,286],[15,42245,42247,42392],{"className":42246},[290],[15,42248,42251,42319],{"className":42249,"style":42250},[294],"height:1.7357em;",[15,42252,42254,42257],{"style":42253},"top:-3.8716em;",[15,42255],{"className":42256,"style":461},[302],[15,42258,42260],{"className":42259},[59],[15,42261,42263,42266],{"className":42262},[59],[15,42264,33884],{"className":42265,"style":34038},[59,60],[15,42267,42269],{"className":42268},[281],[15,42270,42272,42310],{"className":42271},[285,286],[15,42273,42275,42307],{"className":42274},[290],[15,42276,42278,42296],{"className":42277,"style":19735},[294],[15,42279,42281,42284],{"style":42280},"top:-2.453em;margin-left:-0.0813em;margin-right:0.05em;",[15,42282],{"className":42283,"style":303},[302],[15,42285,42287],{"className":42286},[307,308,309,310],[15,42288,42290],{"className":42289},[59,310],[15,42291,42293],{"className":42292},[59,4598,310],[15,42294,42137],{"className":42295},[59,310],[15,42297,42298,42301],{"style":8277},[15,42299],{"className":42300,"style":303},[302],[15,42302,42304],{"className":42303},[307,308,309,310],[15,42305,2463],{"className":42306},[59,310],[15,42308,318],{"className":42309},[317],[15,42311,42313],{"className":42312},[290],[15,42314,42317],{"className":42315,"style":42316},[294],"height:0.3831em;",[15,42318],{},[15,42320,42322,42325],{"style":42321},"top:-2.1474em;",[15,42323],{"className":42324,"style":461},[302],[15,42326,42328],{"className":42327},[59],[15,42329,42331,42334],{"className":42330},[59],[15,42332,33884],{"className":42333,"style":34038},[59,60],[15,42335,42337],{"className":42336},[281],[15,42338,42340,42384],{"className":42339},[285,286],[15,42341,42343,42381],{"className":42342},[290],[15,42344,42346,42370],{"className":42345,"style":19735},[294],[15,42347,42348,42351],{"style":42280},[15,42349],{"className":42350,"style":303},[302],[15,42352,42354],{"className":42353},[307,308,309,310],[15,42355,42357,42363,42367],{"className":42356},[59,310],[15,42358,42360],{"className":42359},[59,4598,310],[15,42361,42174],{"className":42362},[59,310],[15,42364],{"className":42365,"style":42366},[157,310],"margin-right:0.1952em;",[15,42368,37],{"className":42369,"style":61},[59,60,310],[15,42371,42372,42375],{"style":8277},[15,42373],{"className":42374,"style":303},[302],[15,42376,42378],{"className":42377},[307,308,309,310],[15,42379,2463],{"className":42380},[59,310],[15,42382,318],{"className":42383},[317],[15,42385,42387],{"className":42386},[290],[15,42388,42390],{"className":42389,"style":42316},[294],[15,42391],{},[15,42393,318],{"className":42394},[317],[15,42396,42398],{"className":42397},[290],[15,42399,42402],{"className":42400,"style":42401},[294],"height:1.2357em;",[15,42403],{},[15,42405,42407],{"className":42406},[1451],[15,42408,42410,42579],{"className":42409},[285,286],[15,42411,42413,42576],{"className":42412},[290],[15,42414,42416,42457],{"className":42415,"style":42250},[294],[15,42417,42418,42421],{"style":42253},[15,42419],{"className":42420,"style":461},[302],[15,42422,42424,42427,42430,42433,42436,42439,42442,42445,42448,42451,42454],{"className":42423},[59],[15,42425],{"className":42426},[59],[15,42428],{"className":42429,"style":158},[157],[15,42431,123],{"className":42432},[162],[15,42434],{"className":42435,"style":158},[157],[15,42437,117],{"className":42438},[59],[15,42440],{"className":42441,"style":2587},[157],[15,42443,4813],{"className":42444},[2591],[15,42446],{"className":42447,"style":2587},[157],[15,42449,39291],{"className":42450,"style":39387},[59,60],[15,42452,39294],{"className":42453,"style":10782},[59,60],[15,42455,551],{"className":42456},[573],[15,42458,42459,42462],{"style":42321},[15,42460],{"className":42461,"style":461},[302],[15,42463,42465,42468,42471,42474,42477,42480,42483,42486,42489,42492,42495,42498,42501,42504,42507,42510,42513,42516,42573],{"className":42464},[59],[15,42466],{"className":42467},[59],[15,42469],{"className":42470,"style":158},[157],[15,42472,123],{"className":42473},[162],[15,42475],{"className":42476,"style":158},[157],[15,42478,2463],{"className":42479},[59],[15,42481,113],{"className":42482},[146],[15,42484,117],{"className":42485},[59],[15,42487],{"className":42488,"style":2587},[157],[15,42490,4813],{"className":42491},[2591],[15,42493],{"className":42494,"style":2587},[157],[15,42496,39291],{"className":42497,"style":39387},[59,60],[15,42499,39294],{"className":42500,"style":10782},[59,60],[15,42502,120],{"className":42503},[153],[15,42505],{"className":42506,"style":158},[157],[15,42508,123],{"className":42509},[162],[15,42511],{"className":42512,"style":158},[157],[15,42514,2463],{"className":42515},[59],[15,42517,42519,42522],{"className":42518},[59],[15,42520,33884],{"className":42521,"style":34038},[59,60],[15,42523,42525],{"className":42524},[281],[15,42526,42528,42565],{"className":42527},[285,286],[15,42529,42531,42562],{"className":42530},[290],[15,42532,42534,42551],{"className":42533,"style":19735},[294],[15,42535,42536,42539],{"style":42280},[15,42537],{"className":42538,"style":303},[302],[15,42540,42542],{"className":42541},[307,308,309,310],[15,42543,42545],{"className":42544},[59,310],[15,42546,42548],{"className":42547},[59,4598,310],[15,42549,42137],{"className":42550},[59,310],[15,42552,42553,42556],{"style":8277},[15,42554],{"className":42555,"style":303},[302],[15,42557,42559],{"className":42558},[307,308,309,310],[15,42560,2463],{"className":42561},[59,310],[15,42563,318],{"className":42564},[317],[15,42566,42568],{"className":42567},[290],[15,42569,42571],{"className":42570,"style":42316},[294],[15,42572],{},[15,42574,4375],{"className":42575},[59],[15,42577,318],{"className":42578},[317],[15,42580,42582],{"className":42581},[290],[15,42583,42585],{"className":42584,"style":42401},[294],[15,42586],{},[11,42588,42589,42590,42765,42766,18141,43101,43159,43160,43204],{},"本文采用 ",[15,42591,42593,42631],{"className":42592,"translate":19},[18],[15,42594,42596],{"className":42595},[23],[25,42597,42598],{"xmlns":27},[29,42599,42600,42628],{},[32,42601,42602,42604,42606,42608,42610,42612,42614,42618,42620,42622],{},[35,42603,37],{},[110,42605,113],{"stretchy":112},[35,42607,769],{},[110,42609,120],{"stretchy":112},[110,42611,123],{},[110,42613,113],{"stretchy":112},[34339,42615,42616],{},[35,42617,769],{},[110,42619,4813],{},[115,42621,117],{},[6814,42623,42624,42626],{},[110,42625,120],{"stretchy":112},[115,42627,2463],{},[39,42629,42630],{"encoding":41},"f(t)=(\\sqrt t-1)^2",[15,42632,42634,42661,42727],{"className":42633,"ariaHidden":46},[45],[15,42635,42637,42640,42643,42646,42649,42652,42655,42658],{"className":42636},[50],[15,42638],{"className":42639,"style":139},[54],[15,42641,37],{"className":42642,"style":61},[59,60],[15,42644,113],{"className":42645},[146],[15,42647,769],{"className":42648},[59,60],[15,42650,120],{"className":42651},[153],[15,42653],{"className":42654,"style":158},[157],[15,42656,123],{"className":42657},[162],[15,42659],{"className":42660,"style":158},[157],[15,42662,42664,42668,42671,42718,42721,42724],{"className":42663},[50],[15,42665],{"className":42666,"style":42667},[54],"height:1.1425em;vertical-align:-0.25em;",[15,42669,113],{"className":42670},[146],[15,42672,42674],{"className":42673},[59,34367],[15,42675,42677,42709],{"className":42676},[285,286],[15,42678,42680,42706],{"className":42679},[290],[15,42681,42684,42693],{"className":42682,"style":42683},[294],"height:0.8925em;",[15,42685,42687,42690],{"className":42686,"style":11863},[6307],[15,42688],{"className":42689,"style":461},[302],[15,42691,769],{"className":42692,"style":34387},[59,60],[15,42694,42696,42699],{"style":42695},"top:-2.8525em;",[15,42697],{"className":42698,"style":461},[302],[15,42700,42702],{"className":42701,"style":34444},[34443],[6323,42703,42704],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,42705],{"d":34451},[15,42707,318],{"className":42708},[317],[15,42710,42712],{"className":42711},[290],[15,42713,42716],{"className":42714,"style":42715},[294],"height:0.1475em;",[15,42717],{},[15,42719],{"className":42720,"style":2587},[157],[15,42722,4813],{"className":42723},[2591],[15,42725],{"className":42726,"style":2587},[157],[15,42728,42730,42733,42736],{"className":42729},[50],[15,42731],{"className":42732,"style":20003},[54],[15,42734,117],{"className":42735},[59],[15,42737,42739,42742],{"className":42738},[153],[15,42740,120],{"className":42741},[153],[15,42743,42745],{"className":42744},[281],[15,42746,42748],{"className":42747},[285],[15,42749,42751],{"className":42750},[290],[15,42752,42754],{"className":42753,"style":20028},[294],[15,42755,42756,42759],{"style":6865},[15,42757],{"className":42758,"style":303},[302],[15,42760,42762],{"className":42761},[307,308,309,310],[15,42763,2463],{"className":42764},[59,310],"，故 ",[15,42767,42769,42821],{"className":42768,"translate":19},[18],[15,42770,42772],{"className":42771},[23],[25,42773,42774],{"xmlns":27},[29,42775,42776,42818],{},[32,42777,42778,42784,42786,42788,42796,42798,42800,42802,42806,42808,42812],{},[195,42779,42780,42782],{},[35,42781,199],{},[35,42783,37],{},[110,42785,123],{},[115,42787,2463],{},[7553,42789,42790,42792,42794],{},[35,42791,33884],{},[1297,42793,42137],{},[115,42795,2463],{},[110,42797,123],{},[110,42799,1287],{},[110,42801,113],{"stretchy":112},[34339,42803,42804],{},[35,42805,11],{},[110,42807,4813],{},[34339,42809,42810],{},[35,42811,944],{},[6814,42813,42814,42816],{},[110,42815,120],{"stretchy":112},[115,42817,2463],{},[39,42819,42820],{"encoding":41},"D_f=2H^2_{\\text{Bhattacharyya}}=\\int(\\sqrt p-\\sqrt q)^2",[15,42822,42824,42879,42957,43022],{"className":42823,"ariaHidden":46},[45],[15,42825,42827,42830,42870,42873,42876],{"className":42826},[50],[15,42828],{"className":42829,"style":4032},[54],[15,42831,42833,42836],{"className":42832},[59],[15,42834,199],{"className":42835,"style":277},[59,60],[15,42837,42839],{"className":42838},[281],[15,42840,42842,42862],{"className":42841},[285,286],[15,42843,42845,42859],{"className":42844},[290],[15,42846,42848],{"className":42847,"style":295},[294],[15,42849,42850,42853],{"style":298},[15,42851],{"className":42852,"style":303},[302],[15,42854,42856],{"className":42855},[307,308,309,310],[15,42857,37],{"className":42858,"style":61},[59,60,310],[15,42860,318],{"className":42861},[317],[15,42863,42865],{"className":42864},[290],[15,42866,42868],{"className":42867,"style":325},[294],[15,42869],{},[15,42871],{"className":42872,"style":158},[157],[15,42874,123],{"className":42875},[162],[15,42877],{"className":42878,"style":158},[157],[15,42880,42882,42886,42889,42948,42951,42954],{"className":42881},[50],[15,42883],{"className":42884,"style":42885},[54],"height:1.2333em;vertical-align:-0.4192em;",[15,42887,2463],{"className":42888},[59],[15,42890,42892,42895],{"className":42891},[59],[15,42893,33884],{"className":42894,"style":34038},[59,60],[15,42896,42898],{"className":42897},[281],[15,42899,42901,42939],{"className":42900},[285,286],[15,42902,42904,42936],{"className":42903},[290],[15,42905,42907,42925],{"className":42906,"style":20028},[294],[15,42908,42910,42913],{"style":42909},"top:-2.4169em;margin-left:-0.0813em;margin-right:0.05em;",[15,42911],{"className":42912,"style":303},[302],[15,42914,42916],{"className":42915},[307,308,309,310],[15,42917,42919],{"className":42918},[59,310],[15,42920,42922],{"className":42921},[59,4598,310],[15,42923,42137],{"className":42924},[59,310],[15,42926,42927,42930],{"style":6865},[15,42928],{"className":42929,"style":303},[302],[15,42931,42933],{"className":42932},[307,308,309,310],[15,42934,2463],{"className":42935},[59,310],[15,42937,318],{"className":42938},[317],[15,42940,42942],{"className":42941},[290],[15,42943,42946],{"className":42944,"style":42945},[294],"height:0.4192em;",[15,42947],{},[15,42949],{"className":42950,"style":158},[157],[15,42952,123],{"className":42953},[162],[15,42955],{"className":42956,"style":158},[157],[15,42958,42960,42963,42966,42969,43013,43016,43019],{"className":42959},[50],[15,42961],{"className":42962,"style":39008},[54],[15,42964,1287],{"className":42965,"style":5617},[1484,1485,5616],[15,42967,113],{"className":42968},[146],[15,42970,42972],{"className":42971},[59,34367],[15,42973,42975,43005],{"className":42974},[285,286],[15,42976,42978,43002],{"className":42977},[290],[15,42979,42981,42990],{"className":42980,"style":39027},[294],[15,42982,42984,42987],{"className":42983,"style":11863},[6307],[15,42985],{"className":42986,"style":461},[302],[15,42988,11],{"className":42989,"style":34387},[59,60],[15,42991,42992,42995],{"style":39039},[15,42993],{"className":42994,"style":461},[302],[15,42996,42998],{"className":42997,"style":34444},[34443],[6323,42999,43000],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,43001],{"d":34451},[15,43003,318],{"className":43004},[317],[15,43006,43008],{"className":43007},[290],[15,43009,43011],{"className":43010,"style":39059},[294],[15,43012],{},[15,43014],{"className":43015,"style":2587},[157],[15,43017,4813],{"className":43018},[2591],[15,43020],{"className":43021,"style":2587},[157],[15,43023,43025,43028,43072],{"className":43024},[50],[15,43026],{"className":43027,"style":39077},[54],[15,43029,43031],{"className":43030},[59,34367],[15,43032,43034,43064],{"className":43033},[285,286],[15,43035,43037,43061],{"className":43036},[290],[15,43038,43040,43049],{"className":43039,"style":39027},[294],[15,43041,43043,43046],{"className":43042,"style":11863},[6307],[15,43044],{"className":43045,"style":461},[302],[15,43047,944],{"className":43048,"style":39099},[59,60],[15,43050,43051,43054],{"style":39039},[15,43052],{"className":43053,"style":461},[302],[15,43055,43057],{"className":43056,"style":34444},[34443],[6323,43058,43059],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,43060],{"d":34451},[15,43062,318],{"className":43063},[317],[15,43065,43067],{"className":43066},[290],[15,43068,43070],{"className":43069,"style":39059},[294],[15,43071],{},[15,43073,43075,43078],{"className":43074},[153],[15,43076,120],{"className":43077},[153],[15,43079,43081],{"className":43080},[281],[15,43082,43084],{"className":43083},[285],[15,43085,43087],{"className":43086},[290],[15,43088,43090],{"className":43089,"style":20028},[294],[15,43091,43092,43095],{"style":6865},[15,43093],{"className":43094,"style":303},[302],[15,43096,43098],{"className":43097},[307,308,309,310],[15,43099,2463],{"className":43100},[59,310],[15,43102,43104,43121],{"className":43103,"translate":19},[18],[15,43105,43107],{"className":43106},[23],[25,43108,43109],{"xmlns":27},[29,43110,43111,43119],{},[32,43112,43113],{},[6814,43114,43115,43117],{},[35,43116,33884],{},[115,43118,2463],{},[39,43120,42070],{"encoding":41},[15,43122,43124],{"className":43123,"ariaHidden":46},[45],[15,43125,43127,43130],{"className":43126},[50],[15,43128],{"className":43129,"style":20028},[54],[15,43131,43133,43136],{"className":43132},[59],[15,43134,33884],{"className":43135,"style":34038},[59,60],[15,43137,43139],{"className":43138},[281],[15,43140,43142],{"className":43141},[285],[15,43143,43145],{"className":43144},[290],[15,43146,43148],{"className":43147,"style":20028},[294],[15,43149,43150,43153],{"style":6865},[15,43151],{"className":43152,"style":303},[302],[15,43154,43156],{"className":43155},[307,308,309,310],[15,43157,2463],{"className":43158},[59,310]," 有界（",[15,43161,43163,43179],{"className":43162,"translate":19},[18],[15,43164,43166],{"className":43165},[23],[25,43167,43168],{"xmlns":27},[29,43169,43170,43176],{},[32,43171,43172,43174],{},[110,43173,9952],{},[115,43175,2463],{},[39,43177,43178],{"encoding":41},"\\le 2",[15,43180,43182,43195],{"className":43181,"ariaHidden":46},[45],[15,43183,43185,43189,43192],{"className":43184},[50],[15,43186],{"className":43187,"style":43188},[54],"height:0.7719em;vertical-align:-0.136em;",[15,43190,9952],{"className":43191},[162],[15,43193],{"className":43194,"style":158},[157],[15,43196,43198,43201],{"className":43197},[50],[15,43199],{"className":43200,"style":172},[54],[15,43202,2463],{"className":43203},[59],"）。对称性可直接验算：",[15,43206,43208],{"className":43207,"translate":19},[180],[15,43209,43211,43387],{"className":43210,"translate":19},[18],[15,43212,43214],{"className":43213},[23],[25,43215,43216],{"xmlns":27,"display":189},[29,43217,43218,43384],{},[1243,43219,43220,43278,43322],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,43221,43222,43244],{},[1252,43223,43224],{},[1255,43225,43226],{"scriptlevel":126,"displaystyle":46},[32,43227,43228,43230,43232,43234,43236,43238,43240,43242],{},[35,43229,769],{},[1297,43231,1299],{},[35,43233,37],{},[110,43235,113],{"stretchy":112},[115,43237,117],{},[35,43239,941],{"mathvariant":209},[35,43241,769],{},[110,43243,120],{"stretchy":112},[1252,43245,43246],{},[1255,43247,43248],{"scriptlevel":126,"displaystyle":46},[32,43249,43250,43252,43254,43256],{},[32,43251],{},[110,43253,123],{},[35,43255,769],{},[6814,43257,43258,43276],{},[32,43259,43260,43262,43270,43272,43274],{},[110,43261,113],{"fence":46},[238,43263,43264,43266],{},[115,43265,117],{},[34339,43267,43268],{},[35,43269,769],{},[110,43271,4813],{},[115,43273,117],{},[110,43275,120],{"fence":46},[115,43277,2463],{},[1249,43279,43280,43286],{},[1252,43281,43282],{},[1255,43283,43284],{"scriptlevel":126,"displaystyle":46},[32,43285],{},[1252,43287,43288],{},[1255,43289,43290],{"scriptlevel":126,"displaystyle":46},[32,43291,43292,43294,43296,43298,43300,43306,43308,43316,43318,43320],{},[32,43293],{},[110,43295,123],{},[35,43297,769],{},[110,43299,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[238,43301,43302,43304],{},[115,43303,117],{},[35,43305,769],{},[110,43307,4813],{},[238,43309,43310,43312],{},[115,43311,2463],{},[34339,43313,43314],{},[35,43315,769],{},[110,43317,2470],{},[115,43319,117],{},[110,43321,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,43323,43324,43330],{},[1252,43325,43326],{},[1255,43327,43328],{"scriptlevel":126,"displaystyle":46},[32,43329],{},[1252,43331,43332],{},[1255,43333,43334],{"scriptlevel":126,"displaystyle":46},[32,43335,43336,43338,43340,43342,43344,43346,43350,43352,43354,43356,43358,43362,43364,43366,43372,43374,43376,43378,43380,43382],{},[32,43337],{},[110,43339,123],{},[115,43341,117],{},[110,43343,4813],{},[115,43345,2463],{},[34339,43347,43348],{},[35,43349,769],{},[110,43351,2470],{},[35,43353,769],{},[110,43355,123],{},[110,43357,113],{"stretchy":112},[34339,43359,43360],{},[35,43361,769],{},[110,43363,4813],{},[115,43365,117],{},[6814,43367,43368,43370],{},[110,43369,120],{"stretchy":112},[115,43371,2463],{},[110,43373,123],{},[35,43375,37],{},[110,43377,113],{"stretchy":112},[35,43379,769],{},[110,43381,120],{"stretchy":112},[110,43383,551],{"separator":46},[39,43385,43386],{"encoding":41},"\\begin{aligned}\nt\\,f(1\u002Ft)\n&=t\\left(\\frac{1}{\\sqrt t}-1\\right)^2\\\\\n&=t\\Big(\\frac1t-\\frac{2}{\\sqrt t}+1\\Big)\\\\[2pt]\n&=1-2\\sqrt t+t=(\\sqrt t-1)^2=f(t),\n\\end{aligned}",[15,43388,43390],{"className":43389,"ariaHidden":46},[45],[15,43391,43393,43397],{"className":43392},[50],[15,43394],{"className":43395,"style":43396},[54],"height:6.7569em;vertical-align:-3.1284em;",[15,43398,43400],{"className":43399},[59],[15,43401,43403,43477],{"className":43402},[1243],[15,43404,43406],{"className":43405},[1360],[15,43407,43409,43468],{"className":43408},[285,286],[15,43410,43412,43465],{"className":43411},[290],[15,43413,43416,43447,43456],{"className":43414,"style":43415},[294],"height:3.6284em;",[15,43417,43419,43423],{"style":43418},"top:-5.6284em;",[15,43420],{"className":43421,"style":43422},[302],"height:3.654em;",[15,43424,43426,43429,43432,43435,43438,43441,43444],{"className":43425},[59],[15,43427,769],{"className":43428},[59,60],[15,43430],{"className":43431,"style":406},[157],[15,43433,37],{"className":43434,"style":61},[59,60],[15,43436,113],{"className":43437},[146],[15,43439,8589],{"className":43440},[59],[15,43442,769],{"className":43443},[59,60],[15,43445,120],{"className":43446},[153],[15,43448,43450,43453],{"style":43449},"top:-3.057em;",[15,43451],{"className":43452,"style":43422},[302],[15,43454],{"className":43455},[59],[15,43457,43459,43462],{"style":43458},"top:-0.8856em;",[15,43460],{"className":43461,"style":43422},[302],[15,43463],{"className":43464},[59],[15,43466,318],{"className":43467},[317],[15,43469,43471],{"className":43470},[290],[15,43472,43475],{"className":43473,"style":43474},[294],"height:3.1284em;",[15,43476],{},[15,43478,43480],{"className":43479},[1451],[15,43481,43483,44109],{"className":43482},[285,286],[15,43484,43486,44106],{"className":43485},[290],[15,43487,43489,43673,43894],{"className":43488,"style":43415},[294],[15,43490,43491,43494],{"style":43418},[15,43492],{"className":43493,"style":43422},[302],[15,43495,43497,43500,43503,43506,43509,43512,43515],{"className":43496},[59],[15,43498],{"className":43499},[59],[15,43501],{"className":43502,"style":158},[157],[15,43504,123],{"className":43505},[162],[15,43507],{"className":43508,"style":158},[157],[15,43510,769],{"className":43511},[59,60],[15,43513],{"className":43514,"style":406},[157],[15,43516,43518,43650],{"className":43517},[410],[15,43519,43521,43527,43632,43635,43638,43641,43644],{"className":43520},[410],[15,43522,43524],{"className":43523,"style":415},[146,414],[15,43525,113],{"className":43526},[419,309],[15,43528,43530,43533,43629],{"className":43529},[59],[15,43531],{"className":43532},[146,441],[15,43534,43536],{"className":43535},[238],[15,43537,43539,43620],{"className":43538},[285,286],[15,43540,43542,43617],{"className":43541},[290],[15,43543,43545,43598,43606],{"className":43544,"style":22889},[294],[15,43546,43548,43551],{"style":43547},"top:-2.2175em;",[15,43549],{"className":43550,"style":461},[302],[15,43552,43554],{"className":43553},[59],[15,43555,43557],{"className":43556},[59,34367],[15,43558,43560,43590],{"className":43559},[285,286],[15,43561,43563,43587],{"className":43562},[290],[15,43564,43566,43575],{"className":43565,"style":42683},[294],[15,43567,43569,43572],{"className":43568,"style":11863},[6307],[15,43570],{"className":43571,"style":461},[302],[15,43573,769],{"className":43574,"style":34387},[59,60],[15,43576,43577,43580],{"style":42695},[15,43578],{"className":43579,"style":461},[302],[15,43581,43583],{"className":43582,"style":34444},[34443],[6323,43584,43585],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,43586],{"d":34451},[15,43588,318],{"className":43589},[317],[15,43591,43593],{"className":43592},[290],[15,43594,43596],{"className":43595,"style":42715},[294],[15,43597],{},[15,43599,43600,43603],{"style":473},[15,43601],{"className":43602,"style":461},[302],[15,43604],{"className":43605,"style":481},[480],[15,43607,43608,43611],{"style":484},[15,43609],{"className":43610,"style":461},[302],[15,43612,43614],{"className":43613},[59],[15,43615,117],{"className":43616},[59],[15,43618,318],{"className":43619},[317],[15,43621,43623],{"className":43622},[290],[15,43624,43627],{"className":43625,"style":43626},[294],"height:0.93em;",[15,43628],{},[15,43630],{"className":43631},[153,441],[15,43633],{"className":43634,"style":2587},[157],[15,43636,4813],{"className":43637},[2591],[15,43639],{"className":43640,"style":2587},[157],[15,43642,117],{"className":43643},[59],[15,43645,43647],{"className":43646,"style":415},[153,414],[15,43648,120],{"className":43649},[419,309],[15,43651,43653],{"className":43652},[281],[15,43654,43656],{"className":43655},[285],[15,43657,43659],{"className":43658},[290],[15,43660,43662],{"className":43661,"style":37661},[294],[15,43663,43664,43667],{"style":37664},[15,43665],{"className":43666,"style":303},[302],[15,43668,43670],{"className":43669},[307,308,309,310],[15,43671,2463],{"className":43672},[59,310],[15,43674,43675,43678],{"style":43449},[15,43676],{"className":43677,"style":43422},[302],[15,43679,43681,43684,43687,43690,43693,43696,43702,43764,43767,43770,43773,43876,43879,43882,43885,43888],{"className":43680},[59],[15,43682],{"className":43683},[59],[15,43685],{"className":43686,"style":158},[157],[15,43688,123],{"className":43689},[162],[15,43691],{"className":43692,"style":158},[157],[15,43694,769],{"className":43695},[59,60],[15,43697,43699],{"className":43698},[59],[15,43700,113],{"className":43701},[419,3720],[15,43703,43705,43708,43761],{"className":43704},[59],[15,43706],{"className":43707},[146,441],[15,43709,43711],{"className":43710},[238],[15,43712,43714,43753],{"className":43713},[285,286],[15,43715,43717,43750],{"className":43716},[290],[15,43718,43720,43731,43739],{"className":43719,"style":22889},[294],[15,43721,43722,43725],{"style":457},[15,43723],{"className":43724,"style":461},[302],[15,43726,43728],{"className":43727},[59],[15,43729,769],{"className":43730},[59,60],[15,43732,43733,43736],{"style":473},[15,43734],{"className":43735,"style":461},[302],[15,43737],{"className":43738,"style":481},[480],[15,43740,43741,43744],{"style":484},[15,43742],{"className":43743,"style":461},[302],[15,43745,43747],{"className":43746},[59],[15,43748,117],{"className":43749},[59],[15,43751,318],{"className":43752},[317],[15,43754,43756],{"className":43755},[290],[15,43757,43759],{"className":43758,"style":3778},[294],[15,43760],{},[15,43762],{"className":43763},[153,441],[15,43765],{"className":43766,"style":2587},[157],[15,43768,4813],{"className":43769},[2591],[15,43771],{"className":43772,"style":2587},[157],[15,43774,43776,43779,43873],{"className":43775},[59],[15,43777],{"className":43778},[146,441],[15,43780,43782],{"className":43781},[238],[15,43783,43785,43865],{"className":43784},[285,286],[15,43786,43788,43862],{"className":43787},[290],[15,43789,43791,43843,43851],{"className":43790,"style":22889},[294],[15,43792,43793,43796],{"style":43547},[15,43794],{"className":43795,"style":461},[302],[15,43797,43799],{"className":43798},[59],[15,43800,43802],{"className":43801},[59,34367],[15,43803,43805,43835],{"className":43804},[285,286],[15,43806,43808,43832],{"className":43807},[290],[15,43809,43811,43820],{"className":43810,"style":42683},[294],[15,43812,43814,43817],{"className":43813,"style":11863},[6307],[15,43815],{"className":43816,"style":461},[302],[15,43818,769],{"className":43819,"style":34387},[59,60],[15,43821,43822,43825],{"style":42695},[15,43823],{"className":43824,"style":461},[302],[15,43826,43828],{"className":43827,"style":34444},[34443],[6323,43829,43830],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,43831],{"d":34451},[15,43833,318],{"className":43834},[317],[15,43836,43838],{"className":43837},[290],[15,43839,43841],{"className":43840,"style":42715},[294],[15,43842],{},[15,43844,43845,43848],{"style":473},[15,43846],{"className":43847,"style":461},[302],[15,43849],{"className":43850,"style":481},[480],[15,43852,43853,43856],{"style":484},[15,43854],{"className":43855,"style":461},[302],[15,43857,43859],{"className":43858},[59],[15,43860,2463],{"className":43861},[59],[15,43863,318],{"className":43864},[317],[15,43866,43868],{"className":43867},[290],[15,43869,43871],{"className":43870,"style":43626},[294],[15,43872],{},[15,43874],{"className":43875},[153,441],[15,43877],{"className":43878,"style":2587},[157],[15,43880,2470],{"className":43881},[2591],[15,43883],{"className":43884,"style":2587},[157],[15,43886,117],{"className":43887},[59],[15,43889,43891],{"className":43890},[59],[15,43892,120],{"className":43893},[419,3720],[15,43895,43896,43899],{"style":43458},[15,43897],{"className":43898,"style":43422},[302],[15,43900,43902,43905,43908,43911,43914,43917,43920,43923,43926,43929,43973,43976,43979,43982,43985,43988,43991,43994,43997,44041,44044,44047,44050,44053,44082,44085,44088,44091,44094,44097,44100,44103],{"className":43901},[59],[15,43903],{"className":43904},[59],[15,43906],{"className":43907,"style":158},[157],[15,43909,123],{"className":43910},[162],[15,43912],{"className":43913,"style":158},[157],[15,43915,117],{"className":43916},[59],[15,43918],{"className":43919,"style":2587},[157],[15,43921,4813],{"className":43922},[2591],[15,43924],{"className":43925,"style":2587},[157],[15,43927,2463],{"className":43928},[59],[15,43930,43932],{"className":43931},[59,34367],[15,43933,43935,43965],{"className":43934},[285,286],[15,43936,43938,43962],{"className":43937},[290],[15,43939,43941,43950],{"className":43940,"style":40537},[294],[15,43942,43944,43947],{"className":43943,"style":11863},[6307],[15,43945],{"className":43946,"style":461},[302],[15,43948,769],{"className":43949,"style":34387},[59,60],[15,43951,43952,43955],{"style":40552},[15,43953],{"className":43954,"style":461},[302],[15,43956,43958],{"className":43957,"style":34444},[34443],[6323,43959,43960],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,43961],{"d":34451},[15,43963,318],{"className":43964},[317],[15,43966,43968],{"className":43967},[290],[15,43969,43971],{"className":43970,"style":40572},[294],[15,43972],{},[15,43974],{"className":43975,"style":2587},[157],[15,43977,2470],{"className":43978},[2591],[15,43980],{"className":43981,"style":2587},[157],[15,43983,769],{"className":43984},[59,60],[15,43986],{"className":43987,"style":158},[157],[15,43989,123],{"className":43990},[162],[15,43992],{"className":43993,"style":158},[157],[15,43995,113],{"className":43996},[146],[15,43998,44000],{"className":43999},[59,34367],[15,44001,44003,44033],{"className":44002},[285,286],[15,44004,44006,44030],{"className":44005},[290],[15,44007,44009,44018],{"className":44008,"style":40537},[294],[15,44010,44012,44015],{"className":44011,"style":11863},[6307],[15,44013],{"className":44014,"style":461},[302],[15,44016,769],{"className":44017,"style":34387},[59,60],[15,44019,44020,44023],{"style":40552},[15,44021],{"className":44022,"style":461},[302],[15,44024,44026],{"className":44025,"style":34444},[34443],[6323,44027,44028],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,44029],{"d":34451},[15,44031,318],{"className":44032},[317],[15,44034,44036],{"className":44035},[290],[15,44037,44039],{"className":44038,"style":40572},[294],[15,44040],{},[15,44042],{"className":44043,"style":2587},[157],[15,44045,4813],{"className":44046},[2591],[15,44048],{"className":44049,"style":2587},[157],[15,44051,117],{"className":44052},[59],[15,44054,44056,44059],{"className":44055},[153],[15,44057,120],{"className":44058},[153],[15,44060,44062],{"className":44061},[281],[15,44063,44065],{"className":44064},[285],[15,44066,44068],{"className":44067},[290],[15,44069,44071],{"className":44070,"style":19735},[294],[15,44072,44073,44076],{"style":8277},[15,44074],{"className":44075,"style":303},[302],[15,44077,44079],{"className":44078},[307,308,309,310],[15,44080,2463],{"className":44081},[59,310],[15,44083],{"className":44084,"style":158},[157],[15,44086,123],{"className":44087},[162],[15,44089],{"className":44090,"style":158},[157],[15,44092,37],{"className":44093,"style":61},[59,60],[15,44095,113],{"className":44096},[146],[15,44098,769],{"className":44099},[59,60],[15,44101,120],{"className":44102},[153],[15,44104,551],{"className":44105},[573],[15,44107,318],{"className":44108},[317],[15,44110,44112],{"className":44111},[290],[15,44113,44115],{"className":44114,"style":43474},[294],[15,44116],{},[11,44118,21280,44119,44248,44249,44307],{},[15,44120,44122,44154],{"className":44121,"translate":19},[18],[15,44123,44125],{"className":44124},[23],[25,44126,44127],{"xmlns":27},[29,44128,44129,44151],{},[32,44130,44131,44147,44149],{},[7553,44132,44133,44135,44145],{},[35,44134,37],{},[32,44136,44137,44139,44141,44143],{},[35,44138,7561],{},[35,44140,7564],{},[35,44142,7567],{},[35,44144,7570],{},[110,44146,7573],{"lspace":1247,"rspace":1247},[110,44148,123],{},[35,44150,37],{},[39,44152,44153],{"encoding":41},"f^{*}_{skew}=f",[15,44155,44157,44239],{"className":44156,"ariaHidden":46},[45],[15,44158,44160,44164,44230,44233,44236],{"className":44159},[50],[15,44161],{"className":44162,"style":44163},[54],"height:0.9775em;vertical-align:-0.2831em;",[15,44165,44167,44170],{"className":44166},[59],[15,44168,37],{"className":44169,"style":61},[59,60],[15,44171,44173],{"className":44172},[281],[15,44174,44176,44222],{"className":44175},[285,286],[15,44177,44179,44219],{"className":44178},[290],[15,44180,44182,44205],{"className":44181,"style":8499},[294],[15,44183,44184,44187],{"style":8502},[15,44185],{"className":44186,"style":303},[302],[15,44188,44190],{"className":44189},[307,308,309,310],[15,44191,44193,44196,44199,44202],{"className":44192},[59,310],[15,44194,7561],{"className":44195},[59,60,310],[15,44197,7564],{"className":44198,"style":8267},[59,60,310],[15,44200,7567],{"className":44201},[59,60,310],[15,44203,7570],{"className":44204,"style":8274},[59,60,310],[15,44206,44207,44210],{"style":6865},[15,44208],{"className":44209,"style":303},[302],[15,44211,44213],{"className":44212},[307,308,309,310],[15,44214,44216],{"className":44215},[59,310],[15,44217,7573],{"className":44218},[59,310],[15,44220,318],{"className":44221},[317],[15,44223,44225],{"className":44224},[290],[15,44226,44228],{"className":44227,"style":8547},[294],[15,44229],{},[15,44231],{"className":44232,"style":158},[157],[15,44234,123],{"className":44235},[162],[15,44237],{"className":44238,"style":158},[157],[15,44240,44242,44245],{"className":44241},[50],[15,44243],{"className":44244,"style":55},[54],[15,44246,37],{"className":44247,"style":61},[59,60],"，所以 Hellinger",[15,44250,44252,44270],{"className":44251,"translate":19},[18],[15,44253,44255],{"className":44254},[23],[25,44256,44257],{"xmlns":27},[29,44258,44259,44267],{},[32,44260,44261],{},[6814,44262,44263,44265],{},[32,44264],{},[115,44266,2463],{},[39,44268,44269],{"encoding":41},"^2",[15,44271,44273],{"className":44272,"ariaHidden":46},[45],[15,44274,44276,44279],{"className":44275},[50],[15,44277],{"className":44278,"style":20028},[54],[15,44280,44282,44284],{"className":44281},[59],[15,44283],{},[15,44285,44287],{"className":44286},[281],[15,44288,44290],{"className":44289},[285],[15,44291,44293],{"className":44292},[290],[15,44294,44296],{"className":44295,"style":20028},[294],[15,44297,44298,44301],{"style":6865},[15,44299],{"className":44300,"style":303},[302],[15,44302,44304],{"className":44303},[307,308,309,310],[15,44305,2463],{"className":44306},[59,310]," 也满足对称判别准则（4.3 节）。",[11,44309,44310,44312,44313,44427,44428,44431,44432,44488,44489,44545,44546,44704,44705,44733],{},[1225,44311,24193],{}," Hellinger 与 Bhattacharyya 系数 ",[15,44314,44316,44344],{"className":44315,"translate":19},[18],[15,44317,44319],{"className":44318},[23],[25,44320,44321],{"xmlns":27},[29,44322,44323,44341],{},[32,44324,44325,44327,44329,44331,44333],{},[35,44326,39291],{},[35,44328,39294],{},[110,44330,123],{},[110,44332,1287],{},[34339,44334,44335],{},[32,44336,44337,44339],{},[35,44338,11],{},[35,44340,944],{},[39,44342,44343],{"encoding":41},"BC=\\int\\sqrt{pq}",[15,44345,44347,44368],{"className":44346,"ariaHidden":46},[45],[15,44348,44350,44353,44356,44359,44362,44365],{"className":44349},[50],[15,44351],{"className":44352,"style":664},[54],[15,44354,39291],{"className":44355,"style":39387},[59,60],[15,44357,39294],{"className":44358,"style":10782},[59,60],[15,44360],{"className":44361,"style":158},[157],[15,44363,123],{"className":44364},[162],[15,44366],{"className":44367,"style":158},[157],[15,44369,44371,44374,44377,44380],{"className":44370},[50],[15,44372],{"className":44373,"style":39008},[54],[15,44375,1287],{"className":44376,"style":5617},[1484,1485,5616],[15,44378],{"className":44379,"style":406},[157],[15,44381,44383],{"className":44382},[59,34367],[15,44384,44386,44419],{"className":44385},[285,286],[15,44387,44389,44416],{"className":44388},[290],[15,44390,44392,44404],{"className":44391,"style":39027},[294],[15,44393,44395,44398],{"className":44394,"style":11863},[6307],[15,44396],{"className":44397,"style":461},[302],[15,44399,44401],{"className":44400,"style":34387},[59],[15,44402,41605],{"className":44403,"style":981},[59,60],[15,44405,44406,44409],{"style":39039},[15,44407],{"className":44408,"style":461},[302],[15,44410,44412],{"className":44411,"style":34444},[34443],[6323,44413,44414],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,44415],{"d":34451},[15,44417,318],{"className":44418},[317],[15,44420,44422],{"className":44421},[290],[15,44423,44425],{"className":44424,"style":39059},[294],[15,44426],{}," 把「两个分布的",[1225,44429,44430],{},"重叠程度","」量化：",[15,44433,44435,44455],{"className":44434,"translate":19},[18],[15,44436,44438],{"className":44437},[23],[25,44439,44440],{"xmlns":27},[29,44441,44442,44452],{},[32,44443,44444,44446,44448,44450],{},[35,44445,39291],{},[35,44447,39294],{},[110,44449,123],{},[115,44451,117],{},[39,44453,44454],{"encoding":41},"BC=1",[15,44456,44458,44479],{"className":44457,"ariaHidden":46},[45],[15,44459,44461,44464,44467,44470,44473,44476],{"className":44460},[50],[15,44462],{"className":44463,"style":664},[54],[15,44465,39291],{"className":44466,"style":39387},[59,60],[15,44468,39294],{"className":44469,"style":10782},[59,60],[15,44471],{"className":44472,"style":158},[157],[15,44474,123],{"className":44475},[162],[15,44477],{"className":44478,"style":158},[157],[15,44480,44482,44485],{"className":44481},[50],[15,44483],{"className":44484,"style":172},[54],[15,44486,117],{"className":44487},[59]," 表示完全重合，",[15,44490,44492,44512],{"className":44491,"translate":19},[18],[15,44493,44495],{"className":44494},[23],[25,44496,44497],{"xmlns":27},[29,44498,44499,44509],{},[32,44500,44501,44503,44505,44507],{},[35,44502,39291],{},[35,44504,39294],{},[110,44506,123],{},[115,44508,126],{},[39,44510,44511],{"encoding":41},"BC=0",[15,44513,44515,44536],{"className":44514,"ariaHidden":46},[45],[15,44516,44518,44521,44524,44527,44530,44533],{"className":44517},[50],[15,44519],{"className":44520,"style":664},[54],[15,44522,39291],{"className":44523,"style":39387},[59,60],[15,44525,39294],{"className":44526,"style":10782},[59,60],[15,44528],{"className":44529,"style":158},[157],[15,44531,123],{"className":44532},[162],[15,44534],{"className":44535,"style":158},[157],[15,44537,44539,44542],{"className":44538},[50],[15,44540],{"className":44541,"style":172},[54],[15,44543,126],{"className":44544},[59]," 表示支撑分离。由它可造出真正的距离 ",[15,44547,44549,44590],{"className":44548,"translate":19},[18],[15,44550,44552],{"className":44551},[23],[25,44553,44554],{"xmlns":27},[29,44555,44556,44587],{},[32,44557,44558,44561,44563,44565,44567,44569,44571,44573],{},[35,44559,44560],{},"ρ",[110,44562,113],{"stretchy":112},[35,44564,206],{},[110,44566,551],{"separator":46},[35,44568,213],{},[110,44570,120],{"stretchy":112},[110,44572,123],{},[34339,44574,44575],{},[32,44576,44577,44579,44581,44583,44585],{},[115,44578,2463],{},[110,44580,4813],{},[115,44582,2463],{},[35,44584,39291],{},[35,44586,39294],{},[39,44588,44589],{"encoding":41},"\\rho(P,Q)=\\sqrt{2-2BC}",[15,44591,44593,44629],{"className":44592,"ariaHidden":46},[45],[15,44594,44596,44599,44602,44605,44608,44611,44614,44617,44620,44623,44626],{"className":44595},[50],[15,44597],{"className":44598,"style":139},[54],[15,44600,44560],{"className":44601},[59,60],[15,44603,113],{"className":44604},[146],[15,44606,206],{"className":44607,"style":334},[59,60],[15,44609,551],{"className":44610},[573],[15,44612],{"className":44613,"style":406},[157],[15,44615,213],{"className":44616},[59,60],[15,44618,120],{"className":44619},[153],[15,44621],{"className":44622,"style":158},[157],[15,44624,123],{"className":44625},[162],[15,44627],{"className":44628,"style":158},[157],[15,44630,44632,44636],{"className":44631},[50],[15,44633],{"className":44634,"style":44635},[54],"height:1.04em;vertical-align:-0.155em;",[15,44637,44639],{"className":44638},[59,34367],[15,44640,44642,44695],{"className":44641},[285,286],[15,44643,44645,44692],{"className":44644},[290],[15,44646,44649,44679],{"className":44647,"style":44648},[294],"height:0.885em;",[15,44650,44652,44655],{"className":44651,"style":11863},[6307],[15,44653],{"className":44654,"style":461},[302],[15,44656,44658,44661,44664,44667,44670,44673,44676],{"className":44657,"style":34387},[59],[15,44659,2463],{"className":44660},[59],[15,44662],{"className":44663,"style":2587},[157],[15,44665,4813],{"className":44666},[2591],[15,44668],{"className":44669,"style":2587},[157],[15,44671,2463],{"className":44672},[59],[15,44674,39291],{"className":44675,"style":39387},[59,60],[15,44677,39294],{"className":44678,"style":10782},[59,60],[15,44680,44682,44685],{"style":44681},"top:-2.845em;",[15,44683],{"className":44684,"style":461},[302],[15,44686,44688],{"className":44687,"style":34444},[34443],[6323,44689,44690],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,44691],{"d":34451},[15,44693,318],{"className":44694},[317],[15,44696,44698],{"className":44697},[290],[15,44699,44702],{"className":44700,"style":44701},[294],"height:0.155em;",[15,44703],{},"，而且它对绝对连续性不作要求，支撑分离时也只取到有限的最大值 ",[15,44706,44708,44721],{"className":44707,"translate":19},[18],[15,44709,44711],{"className":44710},[23],[25,44712,44713],{"xmlns":27},[29,44714,44715,44719],{},[32,44716,44717],{},[115,44718,2463],{},[39,44720,2463],{"encoding":41},[15,44722,44724],{"className":44723,"ariaHidden":46},[45],[15,44725,44727,44730],{"className":44726},[50],[15,44728],{"className":44729,"style":172},[54],[15,44731,2463],{"className":44732},[59],"，不会像 KL 那样发散——这让它在数值与统计上格外稳健。Hellinger 距离与 Fisher 信息度量在无穷小尺度上相容（4.6 节），并在非参数估计的 Le Cam 三点法、量子信息中的保真度（fidelity）、以及 Hellinger–Fisher–Rao 几何里扮演中心角色。",[2311,44735,44737],{"id":44736},"_36-α-散度","3.6 α-散度",[11,44739,14261,44740,44821],{},[15,44741,44743,44772],{"className":44742,"translate":19},[18],[15,44744,44746],{"className":44745},[23],[25,44747,44748],{"xmlns":27},[29,44749,44750,44769],{},[32,44751,44752,44755,44757,44759,44761,44763,44765,44767],{},[35,44753,44754],{},"α",[110,44756,5909],{},[110,44758,113],{"stretchy":112},[110,44760,4813],{},[115,44762,117],{},[110,44764,551],{"separator":46},[115,44766,117],{},[110,44768,120],{"stretchy":112},[39,44770,44771],{"encoding":41},"\\alpha\\in(-1,1)",[15,44773,44775,44794],{"className":44774,"ariaHidden":46},[45],[15,44776,44778,44781,44785,44788,44791],{"className":44777},[50],[15,44779],{"className":44780,"style":5924},[54],[15,44782,44754],{"className":44783,"style":44784},[59,60],"margin-right:0.0037em;",[15,44786],{"className":44787,"style":158},[157],[15,44789,5909],{"className":44790},[162],[15,44792],{"className":44793,"style":158},[157],[15,44795,44797,44800,44803,44806,44809,44812,44815,44818],{"className":44796},[50],[15,44798],{"className":44799,"style":139},[54],[15,44801,113],{"className":44802},[146],[15,44804,4813],{"className":44805},[59],[15,44807,117],{"className":44808},[59],[15,44810,551],{"className":44811},[573],[15,44813],{"className":44814,"style":406},[157],[15,44816,117],{"className":44817},[59],[15,44819,120],{"className":44820},[153],"，取",[15,44823,44825],{"className":44824,"translate":19},[180],[15,44826,44828,44902],{"className":44827,"translate":19},[18],[15,44829,44831],{"className":44830},[23],[25,44832,44833],{"xmlns":27,"display":189},[29,44834,44835,44899],{},[32,44836,44837,44843,44845,44847,44849,44851,44867,44897],{},[195,44838,44839,44841],{},[35,44840,37],{},[35,44842,44754],{},[110,44844,113],{"stretchy":112},[35,44846,769],{},[110,44848,120],{"stretchy":112},[110,44850,123],{},[238,44852,44853,44855],{},[115,44854,38989],{},[32,44856,44857,44859,44861],{},[115,44858,117],{},[110,44860,4813],{},[6814,44862,44863,44865],{},[35,44864,44754],{},[115,44866,2463],{},[32,44868,44869,44871,44873,44875,44895],{},[110,44870,113],{"fence":46},[115,44872,117],{},[110,44874,4813],{},[6814,44876,44877,44879],{},[35,44878,769],{},[32,44880,44881,44883,44885,44887,44889,44891,44893],{},[110,44882,113],{"stretchy":112},[115,44884,117],{},[110,44886,2470],{},[35,44888,44754],{},[110,44890,120],{"stretchy":112},[35,44892,941],{"mathvariant":209},[115,44894,2463],{},[110,44896,120],{"fence":46},[35,44898,4375],{"mathvariant":209},[39,44900,44901],{"encoding":41},"f_\\alpha(t)=\\frac{4}{1-\\alpha^2}\n\\left(1-t^{(1+\\alpha)\u002F2}\\right).",[15,44903,44905,44970],{"className":44904,"ariaHidden":46},[45],[15,44906,44908,44911,44952,44955,44958,44961,44964,44967],{"className":44907},[50],[15,44909],{"className":44910,"style":139},[54],[15,44912,44914,44917],{"className":44913},[59],[15,44915,37],{"className":44916,"style":61},[59,60],[15,44918,44920],{"className":44919},[281],[15,44921,44923,44944],{"className":44922},[285,286],[15,44924,44926,44941],{"className":44925},[290],[15,44927,44930],{"className":44928,"style":44929},[294],"height:0.1514em;",[15,44931,44932,44935],{"style":27509},[15,44933],{"className":44934,"style":303},[302],[15,44936,44938],{"className":44937},[307,308,309,310],[15,44939,44754],{"className":44940,"style":44784},[59,60,310],[15,44942,318],{"className":44943},[317],[15,44945,44947],{"className":44946},[290],[15,44948,44950],{"className":44949,"style":7968},[294],[15,44951],{},[15,44953,113],{"className":44954},[146],[15,44956,769],{"className":44957},[59,60],[15,44959,120],{"className":44960},[153],[15,44962],{"className":44963,"style":158},[157],[15,44965,123],{"className":44966},[162],[15,44968],{"className":44969,"style":158},[157],[15,44971,44973,44976,45078,45081,45157,45160],{"className":44972},[50],[15,44974],{"className":44975,"style":26616},[54],[15,44977,44979,44982,45075],{"className":44978},[59],[15,44980],{"className":44981},[146,441],[15,44983,44985],{"className":44984},[238],[15,44986,44988,45067],{"className":44987},[285,286],[15,44989,44991,45064],{"className":44990},[290],[15,44992,44994,45045,45053],{"className":44993,"style":22889},[294],[15,44995,44996,44999],{"style":457},[15,44997],{"className":44998,"style":461},[302],[15,45000,45002,45005,45008,45011,45014],{"className":45001},[59],[15,45003,117],{"className":45004},[59],[15,45006],{"className":45007,"style":2587},[157],[15,45009,4813],{"className":45010},[2591],[15,45012],{"className":45013,"style":2587},[157],[15,45015,45017,45020],{"className":45016},[59],[15,45018,44754],{"className":45019,"style":44784},[59,60],[15,45021,45023],{"className":45022},[281],[15,45024,45026],{"className":45025},[285],[15,45027,45029],{"className":45028},[290],[15,45030,45033],{"className":45031,"style":45032},[294],"height:0.7401em;",[15,45034,45036,45039],{"style":45035},"top:-2.989em;margin-right:0.05em;",[15,45037],{"className":45038,"style":303},[302],[15,45040,45042],{"className":45041},[307,308,309,310],[15,45043,2463],{"className":45044},[59,310],[15,45046,45047,45050],{"style":473},[15,45048],{"className":45049,"style":461},[302],[15,45051],{"className":45052,"style":481},[480],[15,45054,45055,45058],{"style":484},[15,45056],{"className":45057,"style":461},[302],[15,45059,45061],{"className":45060},[59],[15,45062,38989],{"className":45063},[59],[15,45065,318],{"className":45066},[317],[15,45068,45070],{"className":45069},[290],[15,45071,45073],{"className":45072,"style":17015},[294],[15,45074],{},[15,45076],{"className":45077},[153,441],[15,45079],{"className":45080,"style":406},[157],[15,45082,45084,45090,45093,45096,45099,45102,45151],{"className":45083},[410],[15,45085,45087],{"className":45086,"style":415},[146,414],[15,45088,113],{"className":45089},[419,3720],[15,45091,117],{"className":45092},[59],[15,45094],{"className":45095,"style":2587},[157],[15,45097,4813],{"className":45098},[2591],[15,45100],{"className":45101,"style":2587},[157],[15,45103,45105,45108],{"className":45104},[59],[15,45106,769],{"className":45107},[59,60],[15,45109,45111],{"className":45110},[281],[15,45112,45114],{"className":45113},[285],[15,45115,45117],{"className":45116},[290],[15,45118,45121],{"className":45119,"style":45120},[294],"height:0.938em;",[15,45122,45123,45126],{"style":8277},[15,45124],{"className":45125,"style":303},[302],[15,45127,45129],{"className":45128},[307,308,309,310],[15,45130,45132,45135,45138,45141,45144,45147],{"className":45131},[59,310],[15,45133,113],{"className":45134},[146,310],[15,45136,117],{"className":45137},[59,310],[15,45139,2470],{"className":45140},[2591,310],[15,45142,44754],{"className":45143,"style":44784},[59,60,310],[15,45145,120],{"className":45146},[153,310],[15,45148,45150],{"className":45149},[59,310],"\u002F2",[15,45152,45154],{"className":45153,"style":415},[153,414],[15,45155,120],{"className":45156},[419,3720],[15,45158],{"className":45159,"style":406},[157],[15,45161,4375],{"className":45162},[59],[11,45164,45165,45166,45344,45345,45608],{},"代入模板，记 ",[15,45167,45169,45210],{"className":45168,"translate":19},[18],[15,45170,45172],{"className":45171},[23],[25,45173,45174],{"xmlns":27},[29,45175,45176,45207],{},[32,45177,45178,45181,45183,45195,45197,45199,45201,45203,45205],{},[35,45179,45180],{},"a",[110,45182,123],{},[238,45184,45185,45193],{},[32,45186,45187,45189,45191],{},[115,45188,117],{},[110,45190,2470],{},[35,45192,44754],{},[115,45194,2463],{},[110,45196,5909],{},[110,45198,113],{"stretchy":112},[115,45200,126],{},[110,45202,551],{"separator":46},[115,45204,117],{},[110,45206,120],{"stretchy":112},[39,45208,45209],{"encoding":41},"a=\\frac{1+\\alpha}{2}\\in(0,1)",[15,45211,45213,45231,45320],{"className":45212,"ariaHidden":46},[45],[15,45214,45216,45219,45222,45225,45228],{"className":45215},[50],[15,45217],{"className":45218,"style":2345},[54],[15,45220,45180],{"className":45221},[59,60],[15,45223],{"className":45224,"style":158},[157],[15,45226,123],{"className":45227},[162],[15,45229],{"className":45230,"style":158},[157],[15,45232,45234,45237,45311,45314,45317],{"className":45233},[50],[15,45235],{"className":45236,"style":2505},[54],[15,45238,45240,45243,45308],{"className":45239},[59],[15,45241],{"className":45242},[146,441],[15,45244,45246],{"className":45245},[238],[15,45247,45249,45300],{"className":45248},[285,286],[15,45250,45252,45297],{"className":45251},[290],[15,45253,45255,45269,45277],{"className":45254,"style":2524},[294],[15,45256,45257,45260],{"style":2527},[15,45258],{"className":45259,"style":461},[302],[15,45261,45263],{"className":45262},[307,308,309,310],[15,45264,45266],{"className":45265},[59,310],[15,45267,2463],{"className":45268},[59,310],[15,45270,45271,45274],{"style":473},[15,45272],{"className":45273,"style":461},[302],[15,45275],{"className":45276,"style":481},[480],[15,45278,45279,45282],{"style":2550},[15,45280],{"className":45281,"style":461},[302],[15,45283,45285],{"className":45284},[307,308,309,310],[15,45286,45288,45291,45294],{"className":45287},[59,310],[15,45289,117],{"className":45290},[59,310],[15,45292,2470],{"className":45293},[2591,310],[15,45295,44754],{"className":45296,"style":44784},[59,60,310],[15,45298,318],{"className":45299},[317],[15,45301,45303],{"className":45302},[290],[15,45304,45306],{"className":45305,"style":2572},[294],[15,45307],{},[15,45309],{"className":45310},[153,441],[15,45312],{"className":45313,"style":158},[157],[15,45315,5909],{"className":45316},[162],[15,45318],{"className":45319,"style":158},[157],[15,45321,45323,45326,45329,45332,45335,45338,45341],{"className":45322},[50],[15,45324],{"className":45325,"style":139},[54],[15,45327,113],{"className":45328},[146],[15,45330,126],{"className":45331},[59],[15,45333,551],{"className":45334},[573],[15,45336],{"className":45337,"style":406},[157],[15,45339,117],{"className":45340},[59],[15,45342,120],{"className":45343},[153],"（于是 ",[15,45346,45348,45396],{"className":45347,"translate":19},[18],[15,45349,45351],{"className":45350},[23],[25,45352,45353],{"xmlns":27},[29,45354,45355,45393],{},[32,45356,45357,45373,45375],{},[238,45358,45359,45361],{},[115,45360,38989],{},[32,45362,45363,45365,45367],{},[115,45364,117],{},[110,45366,4813],{},[6814,45368,45369,45371],{},[35,45370,44754],{},[115,45372,2463],{},[110,45374,123],{},[238,45376,45377,45379],{},[115,45378,117],{},[32,45380,45381,45383,45385,45387,45389,45391],{},[35,45382,45180],{},[110,45384,113],{"stretchy":112},[115,45386,117],{},[110,45388,4813],{},[35,45390,45180],{},[110,45392,120],{"stretchy":112},[39,45394,45395],{"encoding":41},"\\frac{4}{1-\\alpha^2}=\\frac{1}{a(1-a)}",[15,45397,45399,45517],{"className":45398,"ariaHidden":46},[45],[15,45400,45402,45406,45508,45511,45514],{"className":45401},[50],[15,45403],{"className":45404,"style":45405},[54],"height:1.2484em;vertical-align:-0.4033em;",[15,45407,45409,45412,45505],{"className":45408},[59],[15,45410],{"className":45411},[146,441],[15,45413,45415],{"className":45414},[238],[15,45416,45418,45497],{"className":45417},[285,286],[15,45419,45421,45494],{"className":45420},[290],[15,45422,45424,45472,45480],{"className":45423,"style":2524},[294],[15,45425,45426,45429],{"style":2527},[15,45427],{"className":45428,"style":461},[302],[15,45430,45432],{"className":45431},[307,308,309,310],[15,45433,45435,45438,45441],{"className":45434},[59,310],[15,45436,117],{"className":45437},[59,310],[15,45439,4813],{"className":45440},[2591,310],[15,45442,45444,45447],{"className":45443},[59,310],[15,45445,44754],{"className":45446,"style":44784},[59,60,310],[15,45448,45450],{"className":45449},[281],[15,45451,45453],{"className":45452},[285],[15,45454,45456],{"className":45455},[290],[15,45457,45460],{"className":45458,"style":45459},[294],"height:0.7463em;",[15,45461,45463,45466],{"style":45462},"top:-2.786em;margin-right:0.0714em;",[15,45464],{"className":45465,"style":30206},[302],[15,45467,45469],{"className":45468},[307,30210,9674,310],[15,45470,2463],{"className":45471},[59,310],[15,45473,45474,45477],{"style":473},[15,45475],{"className":45476,"style":461},[302],[15,45478],{"className":45479,"style":481},[480],[15,45481,45482,45485],{"style":2550},[15,45483],{"className":45484,"style":461},[302],[15,45486,45488],{"className":45487},[307,308,309,310],[15,45489,45491],{"className":45490},[59,310],[15,45492,38989],{"className":45493},[59,310],[15,45495,318],{"className":45496},[317],[15,45498,45500],{"className":45499},[290],[15,45501,45503],{"className":45502,"style":16429},[294],[15,45504],{},[15,45506],{"className":45507},[153,441],[15,45509],{"className":45510,"style":158},[157],[15,45512,123],{"className":45513},[162],[15,45515],{"className":45516,"style":158},[157],[15,45518,45520,45524],{"className":45519},[50],[15,45521],{"className":45522,"style":45523},[54],"height:1.3651em;vertical-align:-0.52em;",[15,45525,45527,45530,45605],{"className":45526},[59],[15,45528],{"className":45529},[146,441],[15,45531,45533],{"className":45532},[238],[15,45534,45536,45596],{"className":45535},[285,286],[15,45537,45539,45593],{"className":45538},[290],[15,45540,45542,45571,45579],{"className":45541,"style":2524},[294],[15,45543,45544,45547],{"style":2527},[15,45545],{"className":45546,"style":461},[302],[15,45548,45550],{"className":45549},[307,308,309,310],[15,45551,45553,45556,45559,45562,45565,45568],{"className":45552},[59,310],[15,45554,45180],{"className":45555},[59,60,310],[15,45557,113],{"className":45558},[146,310],[15,45560,117],{"className":45561},[59,310],[15,45563,4813],{"className":45564},[2591,310],[15,45566,45180],{"className":45567},[59,60,310],[15,45569,120],{"className":45570},[153,310],[15,45572,45573,45576],{"style":473},[15,45574],{"className":45575,"style":461},[302],[15,45577],{"className":45578,"style":481},[480],[15,45580,45581,45584],{"style":2550},[15,45582],{"className":45583,"style":461},[302],[15,45585,45587],{"className":45586},[307,308,309,310],[15,45588,45590],{"className":45589},[59,310],[15,45591,117],{"className":45592},[59,310],[15,45594,318],{"className":45595},[317],[15,45597,45599],{"className":45598},[290],[15,45600,45603],{"className":45601,"style":45602},[294],"height:0.52em;",[15,45604],{},[15,45606],{"className":45607},[153,441],"）：",[15,45610,45612],{"className":45611,"translate":19},[180],[15,45613,45615,45701],{"className":45614,"translate":19},[18],[15,45616,45618],{"className":45617},[23],[25,45619,45620],{"xmlns":27,"display":189},[29,45621,45622,45698],{},[32,45623,45624,45630,45632,45634,45636,45638,45640,45642,45660,45696],{},[195,45625,45626,45628],{},[35,45627,199],{},[35,45629,44754],{},[110,45631,113],{"stretchy":112},[35,45633,206],{},[35,45635,210],{"mathvariant":209},[35,45637,213],{},[110,45639,120],{"stretchy":112},[110,45641,123],{},[238,45643,45644,45646],{},[115,45645,117],{},[32,45647,45648,45650,45652,45654,45656,45658],{},[35,45649,45180],{},[110,45651,113],{"stretchy":112},[115,45653,117],{},[110,45655,4813],{},[35,45657,45180],{},[110,45659,120],{"stretchy":112},[32,45661,45662,45664,45666,45668,45670,45676,45688,45690,45692,45694],{},[110,45663,113],{"fence":46},[115,45665,117],{},[110,45667,4813],{},[110,45669,1287],{},[6814,45671,45672,45674],{},[35,45673,11],{},[35,45675,45180],{},[6814,45677,45678,45680],{},[35,45679,944],{},[32,45681,45682,45684,45686],{},[115,45683,117],{},[110,45685,4813],{},[35,45687,45180],{},[1297,45689,1299],{},[35,45691,244],{},[35,45693,774],{},[110,45695,120],{"fence":46},[35,45697,4375],{"mathvariant":209},[39,45699,45700],{"encoding":41},"D_\\alpha(P\\|Q)=\\frac{1}{a(1-a)}\n\\left(1-\\int p^{a}q^{1-a}\\,dx\\right).",[15,45702,45704,45774],{"className":45703,"ariaHidden":46},[45],[15,45705,45707,45710,45750,45753,45756,45759,45762,45765,45768,45771],{"className":45706},[50],[15,45708],{"className":45709,"style":139},[54],[15,45711,45713,45716],{"className":45712},[59],[15,45714,199],{"className":45715,"style":277},[59,60],[15,45717,45719],{"className":45718},[281],[15,45720,45722,45742],{"className":45721},[285,286],[15,45723,45725,45739],{"className":45724},[290],[15,45726,45728],{"className":45727,"style":44929},[294],[15,45729,45730,45733],{"style":298},[15,45731],{"className":45732,"style":303},[302],[15,45734,45736],{"className":45735},[307,308,309,310],[15,45737,44754],{"className":45738,"style":44784},[59,60,310],[15,45740,318],{"className":45741},[317],[15,45743,45745],{"className":45744},[290],[15,45746,45748],{"className":45747,"style":7968},[294],[15,45749],{},[15,45751,113],{"className":45752},[146],[15,45754,206],{"className":45755,"style":334},[59,60],[15,45757,210],{"className":45758},[59],[15,45760,213],{"className":45761},[59,60],[15,45763,120],{"className":45764},[153],[15,45766],{"className":45767,"style":158},[157],[15,45769,123],{"className":45770},[162],[15,45772],{"className":45773,"style":158},[157],[15,45775,45777,45780,45863,45866,45979,45982],{"className":45776},[50],[15,45778],{"className":45779,"style":359},[54],[15,45781,45783,45786,45860],{"className":45782},[59],[15,45784],{"className":45785},[146,441],[15,45787,45789],{"className":45788},[238],[15,45790,45792,45852],{"className":45791},[285,286],[15,45793,45795,45849],{"className":45794},[290],[15,45796,45798,45830,45838],{"className":45797,"style":22889},[294],[15,45799,45800,45803],{"style":457},[15,45801],{"className":45802,"style":461},[302],[15,45804,45806,45809,45812,45815,45818,45821,45824,45827],{"className":45805},[59],[15,45807,45180],{"className":45808},[59,60],[15,45810,113],{"className":45811},[146],[15,45813,117],{"className":45814},[59],[15,45816],{"className":45817,"style":2587},[157],[15,45819,4813],{"className":45820},[2591],[15,45822],{"className":45823,"style":2587},[157],[15,45825,45180],{"className":45826},[59,60],[15,45828,120],{"className":45829},[153],[15,45831,45832,45835],{"style":473},[15,45833],{"className":45834,"style":461},[302],[15,45836],{"className":45837,"style":481},[480],[15,45839,45840,45843],{"style":484},[15,45841],{"className":45842,"style":461},[302],[15,45844,45846],{"className":45845},[59],[15,45847,117],{"className":45848},[59],[15,45850,318],{"className":45851},[317],[15,45853,45855],{"className":45854},[290],[15,45856,45858],{"className":45857,"style":1601},[294],[15,45859],{},[15,45861],{"className":45862},[153,441],[15,45864],{"className":45865,"style":406},[157],[15,45867,45869,45875,45878,45881,45884,45887,45890,45893,45926,45964,45967,45970,45973],{"className":45868},[410],[15,45870,45872],{"className":45871,"style":415},[146,414],[15,45873,113],{"className":45874},[419,309],[15,45876,117],{"className":45877},[59],[15,45879],{"className":45880,"style":2587},[157],[15,45882,4813],{"className":45883},[2591],[15,45885],{"className":45886,"style":2587},[157],[15,45888,1287],{"className":45889,"style":1487},[1484,1485,1486],[15,45891],{"className":45892,"style":406},[157],[15,45894,45896,45899],{"className":45895},[59],[15,45897,11],{"className":45898},[59,60],[15,45900,45902],{"className":45901},[281],[15,45903,45905],{"className":45904},[285],[15,45906,45908],{"className":45907},[290],[15,45909,45912],{"className":45910,"style":45911},[294],"height:0.7144em;",[15,45913,45914,45917],{"style":8277},[15,45915],{"className":45916,"style":303},[302],[15,45918,45920],{"className":45919},[307,308,309,310],[15,45921,45923],{"className":45922},[59,310],[15,45924,45180],{"className":45925},[59,60,310],[15,45927,45929,45932],{"className":45928},[59],[15,45930,944],{"className":45931,"style":981},[59,60],[15,45933,45935],{"className":45934},[281],[15,45936,45938],{"className":45937},[285],[15,45939,45941],{"className":45940},[290],[15,45942,45944],{"className":45943,"style":19735},[294],[15,45945,45946,45949],{"style":8277},[15,45947],{"className":45948,"style":303},[302],[15,45950,45952],{"className":45951},[307,308,309,310],[15,45953,45955,45958,45961],{"className":45954},[59,310],[15,45956,117],{"className":45957},[59,310],[15,45959,4813],{"className":45960},[2591,310],[15,45962,45180],{"className":45963},[59,60,310],[15,45965],{"className":45966,"style":406},[157],[15,45968,244],{"className":45969},[59,60],[15,45971,774],{"className":45972},[59,60],[15,45974,45976],{"className":45975,"style":415},[153,414],[15,45977,120],{"className":45978},[419,309],[15,45980],{"className":45981,"style":406},[157],[15,45983,4375],{"className":45984},[59],[11,45986,45987,45988,45991,45992,32224,46047,9400],{},"这正是 Csiszár \u002F Amari 的 ",[1225,45989,45990],{},"α-散度","（差一个参数重命名）。",[15,45993,45995,46017],{"className":45994,"translate":19},[18],[15,45996,45998],{"className":45997},[23],[25,45999,46000],{"xmlns":27},[29,46001,46002,46014],{},[32,46003,46004,46006,46008,46010,46012],{},[35,46005,45180],{},[110,46007,123],{},[115,46009,117],{},[35,46011,941],{"mathvariant":209},[115,46013,2463],{},[39,46015,46016],{"encoding":41},"a=1\u002F2",[15,46018,46020,46038],{"className":46019,"ariaHidden":46},[45],[15,46021,46023,46026,46029,46032,46035],{"className":46022},[50],[15,46024],{"className":46025,"style":2345},[54],[15,46027,45180],{"className":46028},[59,60],[15,46030],{"className":46031,"style":158},[157],[15,46033,123],{"className":46034},[162],[15,46036],{"className":46037,"style":158},[157],[15,46039,46041,46044],{"className":46040},[50],[15,46042],{"className":46043,"style":139},[54],[15,46045,33639],{"className":46046},[59],[15,46048,46050,46084],{"className":46049,"translate":19},[18],[15,46051,46053],{"className":46052},[23],[25,46054,46055],{"xmlns":27},[29,46056,46057,46081],{},[32,46058,46059,46077,46079],{},[238,46060,46061,46063],{},[115,46062,117],{},[32,46064,46065,46067,46069,46071,46073,46075],{},[35,46066,45180],{},[110,46068,113],{"stretchy":112},[115,46070,117],{},[110,46072,4813],{},[35,46074,45180],{},[110,46076,120],{"stretchy":112},[110,46078,123],{},[115,46080,38989],{},[39,46082,46083],{"encoding":41},"\\frac{1}{a(1-a)}=4",[15,46085,46087,46185],{"className":46086,"ariaHidden":46},[45],[15,46088,46090,46093,46176,46179,46182],{"className":46089},[50],[15,46091],{"className":46092,"style":45523},[54],[15,46094,46096,46099,46173],{"className":46095},[59],[15,46097],{"className":46098},[146,441],[15,46100,46102],{"className":46101},[238],[15,46103,46105,46165],{"className":46104},[285,286],[15,46106,46108,46162],{"className":46107},[290],[15,46109,46111,46140,46148],{"className":46110,"style":2524},[294],[15,46112,46113,46116],{"style":2527},[15,46114],{"className":46115,"style":461},[302],[15,46117,46119],{"className":46118},[307,308,309,310],[15,46120,46122,46125,46128,46131,46134,46137],{"className":46121},[59,310],[15,46123,45180],{"className":46124},[59,60,310],[15,46126,113],{"className":46127},[146,310],[15,46129,117],{"className":46130},[59,310],[15,46132,4813],{"className":46133},[2591,310],[15,46135,45180],{"className":46136},[59,60,310],[15,46138,120],{"className":46139},[153,310],[15,46141,46142,46145],{"style":473},[15,46143],{"className":46144,"style":461},[302],[15,46146],{"className":46147,"style":481},[480],[15,46149,46150,46153],{"style":2550},[15,46151],{"className":46152,"style":461},[302],[15,46154,46156],{"className":46155},[307,308,309,310],[15,46157,46159],{"className":46158},[59,310],[15,46160,117],{"className":46161},[59,310],[15,46163,318],{"className":46164},[317],[15,46166,46168],{"className":46167},[290],[15,46169,46171],{"className":46170,"style":45602},[294],[15,46172],{},[15,46174],{"className":46175},[153,441],[15,46177],{"className":46178,"style":158},[157],[15,46180,123],{"className":46181},[162],[15,46183],{"className":46184,"style":158},[157],[15,46186,46188,46191],{"className":46187},[50],[15,46189],{"className":46190,"style":172},[54],[15,46192,38989],{"className":46193},[59],[15,46195,46197],{"className":46196,"translate":19},[180],[15,46198,46200,46266],{"className":46199,"translate":19},[18],[15,46201,46203],{"className":46202},[23],[25,46204,46205],{"xmlns":27,"display":189},[29,46206,46207,46263],{},[32,46208,46209,46221,46223,46225,46227,46229,46231,46233,46235,46249,46251,46253,46261],{},[195,46210,46211,46213],{},[35,46212,199],{},[32,46214,46215,46217,46219],{},[35,46216,44754],{},[110,46218,123],{},[115,46220,126],{},[110,46222,113],{"stretchy":112},[35,46224,206],{},[35,46226,210],{"mathvariant":209},[35,46228,213],{},[110,46230,120],{"stretchy":112},[110,46232,123],{},[115,46234,38989],{},[32,46236,46237,46239,46241,46243,46245,46247],{},[110,46238,113],{"fence":46},[115,46240,117],{},[110,46242,4813],{},[35,46244,39291],{},[35,46246,39294],{},[110,46248,120],{"fence":46},[110,46250,123],{},[115,46252,38989],{},[7553,46254,46255,46257,46259],{},[35,46256,33884],{},[1297,46258,42137],{},[115,46260,2463],{},[110,46262,551],{"separator":46},[39,46264,46265],{"encoding":41},"D_{\\alpha=0}(P\\|Q)=4\\left(1-BC\\right)\n=4H^2_{\\text{Bhattacharyya}},",[15,46267,46269,46348,46396],{"className":46268,"ariaHidden":46},[45],[15,46270,46272,46275,46324,46327,46330,46333,46336,46339,46342,46345],{"className":46271},[50],[15,46273],{"className":46274,"style":139},[54],[15,46276,46278,46281],{"className":46277},[59],[15,46279,199],{"className":46280,"style":277},[59,60],[15,46282,46284],{"className":46283},[281],[15,46285,46287,46316],{"className":46286},[285,286],[15,46288,46290,46313],{"className":46289},[290],[15,46291,46293],{"className":46292,"style":11133},[294],[15,46294,46295,46298],{"style":298},[15,46296],{"className":46297,"style":303},[302],[15,46299,46301],{"className":46300},[307,308,309,310],[15,46302,46304,46307,46310],{"className":46303},[59,310],[15,46305,44754],{"className":46306,"style":44784},[59,60,310],[15,46308,123],{"className":46309},[162,310],[15,46311,126],{"className":46312},[59,310],[15,46314,318],{"className":46315},[317],[15,46317,46319],{"className":46318},[290],[15,46320,46322],{"className":46321,"style":7968},[294],[15,46323],{},[15,46325,113],{"className":46326},[146],[15,46328,206],{"className":46329,"style":334},[59,60],[15,46331,210],{"className":46332},[59],[15,46334,213],{"className":46335},[59,60],[15,46337,120],{"className":46338},[153],[15,46340],{"className":46341,"style":158},[157],[15,46343,123],{"className":46344},[162],[15,46346],{"className":46347,"style":158},[157],[15,46349,46351,46354,46357,46360,46387,46390,46393],{"className":46350},[50],[15,46352],{"className":46353,"style":139},[54],[15,46355,38989],{"className":46356},[59],[15,46358],{"className":46359,"style":406},[157],[15,46361,46363,46366,46369,46372,46375,46378,46381,46384],{"className":46362},[410],[15,46364,113],{"className":46365,"style":415},[146,414],[15,46367,117],{"className":46368},[59],[15,46370],{"className":46371,"style":2587},[157],[15,46373,4813],{"className":46374},[2591],[15,46376],{"className":46377,"style":2587},[157],[15,46379,39291],{"className":46380,"style":39387},[59,60],[15,46382,39294],{"className":46383,"style":10782},[59,60],[15,46385,120],{"className":46386,"style":415},[153,414],[15,46388],{"className":46389,"style":158},[157],[15,46391,123],{"className":46392},[162],[15,46394],{"className":46395,"style":158},[157],[15,46397,46399,46403,46406,46463],{"className":46398},[50],[15,46400],{"className":46401,"style":46402},[54],"height:1.2472em;vertical-align:-0.3831em;",[15,46404,38989],{"className":46405},[59],[15,46407,46409,46412],{"className":46408},[59],[15,46410,33884],{"className":46411,"style":34038},[59,60],[15,46413,46415],{"className":46414},[281],[15,46416,46418,46455],{"className":46417},[285,286],[15,46419,46421,46452],{"className":46420},[290],[15,46422,46424,46441],{"className":46423,"style":19735},[294],[15,46425,46426,46429],{"style":42280},[15,46427],{"className":46428,"style":303},[302],[15,46430,46432],{"className":46431},[307,308,309,310],[15,46433,46435],{"className":46434},[59,310],[15,46436,46438],{"className":46437},[59,4598,310],[15,46439,42137],{"className":46440},[59,310],[15,46442,46443,46446],{"style":8277},[15,46444],{"className":46445,"style":303},[302],[15,46447,46449],{"className":46448},[307,308,309,310],[15,46450,2463],{"className":46451},[59,310],[15,46453,318],{"className":46454},[317],[15,46456,46458],{"className":46457},[290],[15,46459,46461],{"className":46460,"style":42316},[294],[15,46462],{},[15,46464,551],{"className":46465},[573],[11,46467,21280,46468,46519,46520,3853,46590,46647,46648,46651],{},[15,46469,46471,46489],{"className":46470,"translate":19},[18],[15,46472,46474],{"className":46473},[23],[25,46475,46476],{"xmlns":27},[29,46477,46478,46486],{},[32,46479,46480,46482,46484],{},[35,46481,44754],{},[110,46483,123],{},[115,46485,126],{},[39,46487,46488],{"encoding":41},"\\alpha=0",[15,46490,46492,46510],{"className":46491,"ariaHidden":46},[45],[15,46493,46495,46498,46501,46504,46507],{"className":46494},[50],[15,46496],{"className":46497,"style":2345},[54],[15,46499,44754],{"className":46500,"style":44784},[59,60],[15,46502],{"className":46503,"style":158},[157],[15,46505,123],{"className":46506},[162],[15,46508],{"className":46509,"style":158},[157],[15,46511,46513,46516],{"className":46512},[50],[15,46514],{"className":46515,"style":172},[54],[15,46517,126],{"className":46518},[59]," 是 Hellinger 型散度。两个端点极限要小心：",[15,46521,46523,46541],{"className":46522,"translate":19},[18],[15,46524,46526],{"className":46525},[23],[25,46527,46528],{"xmlns":27},[29,46529,46530,46538],{},[32,46531,46532],{},[195,46533,46534,46536],{},[35,46535,37],{},[35,46537,44754],{},[39,46539,46540],{"encoding":41},"f_\\alpha",[15,46542,46544],{"className":46543,"ariaHidden":46},[45],[15,46545,46547,46550],{"className":46546},[50],[15,46548],{"className":46549,"style":55},[54],[15,46551,46553,46556],{"className":46552},[59],[15,46554,37],{"className":46555,"style":61},[59,60],[15,46557,46559],{"className":46558},[281],[15,46560,46562,46582],{"className":46561},[285,286],[15,46563,46565,46579],{"className":46564},[290],[15,46566,46568],{"className":46567,"style":44929},[294],[15,46569,46570,46573],{"style":27509},[15,46571],{"className":46572,"style":303},[302],[15,46574,46576],{"className":46575},[307,308,309,310],[15,46577,44754],{"className":46578,"style":44784},[59,60,310],[15,46580,318],{"className":46581},[317],[15,46583,46585],{"className":46584},[290],[15,46586,46588],{"className":46587,"style":7968},[294],[15,46589],{},[15,46591,46593,46614],{"className":46592,"translate":19},[18],[15,46594,46596],{"className":46595},[23],[25,46597,46598],{"xmlns":27},[29,46599,46600,46611],{},[32,46601,46602,46604,46606,46609],{},[35,46603,44754],{},[110,46605,1029],{},[110,46607,46608],{},"±",[115,46610,117],{},[39,46612,46613],{"encoding":41},"\\alpha\\to\\pm1",[15,46615,46617,46635],{"className":46616,"ariaHidden":46},[45],[15,46618,46620,46623,46626,46629,46632],{"className":46619},[50],[15,46621],{"className":46622,"style":2345},[54],[15,46624,44754],{"className":46625,"style":44784},[59,60],[15,46627],{"className":46628,"style":158},[157],[15,46630,1029],{"className":46631},[162],[15,46633],{"className":46634,"style":158},[157],[15,46636,46638,46641,46644],{"className":46637},[50],[15,46639],{"className":46640,"style":12578},[54],[15,46642,46608],{"className":46643},[59],[15,46645,117],{"className":46646},[59]," 时逐点发散，但",[1225,46649,46650],{},"散度值","收敛到 KL：",[15,46653,46655],{"className":46654,"translate":19},[180],[15,46656,46658,46787],{"className":46657,"translate":19},[18],[15,46659,46661],{"className":46660},[23],[25,46662,46663],{"xmlns":27,"display":189},[29,46664,46665,46784],{},[32,46666,46667,46684,46690,46692,46694,46696,46698,46700,46702,46712,46714,46716,46718,46720,46722,46724,46726,46744,46750,46752,46754,46756,46758,46760,46762,46772,46774,46776,46778,46780,46782],{},[6016,46668,46669,46676],{},[32,46670,46671,46674],{},[35,46672,46673],{},"lim",[110,46675,4103],{},[32,46677,46678,46680,46682],{},[35,46679,44754],{},[110,46681,1029],{},[115,46683,117],{},[195,46685,46686,46688],{},[35,46687,199],{},[35,46689,44754],{},[110,46691,113],{"stretchy":112},[35,46693,206],{},[35,46695,210],{"mathvariant":209},[35,46697,213],{},[110,46699,120],{"stretchy":112},[110,46701,123],{},[195,46703,46704,46706],{},[35,46705,199],{},[32,46707,46708,46710],{},[35,46709,10694],{},[35,46711,21893],{},[110,46713,113],{"stretchy":112},[35,46715,206],{},[35,46717,210],{"mathvariant":209},[35,46719,213],{},[110,46721,120],{"stretchy":112},[110,46723,551],{"separator":46},[157,46725],{"width":3262},[6016,46727,46728,46734],{},[32,46729,46730,46732],{},[35,46731,46673],{},[110,46733,4103],{},[32,46735,46736,46738,46740,46742],{},[35,46737,44754],{},[110,46739,1029],{},[110,46741,4813],{},[115,46743,117],{},[195,46745,46746,46748],{},[35,46747,199],{},[35,46749,44754],{},[110,46751,113],{"stretchy":112},[35,46753,206],{},[35,46755,210],{"mathvariant":209},[35,46757,213],{},[110,46759,120],{"stretchy":112},[110,46761,123],{},[195,46763,46764,46766],{},[35,46765,199],{},[32,46767,46768,46770],{},[35,46769,10694],{},[35,46771,21893],{},[110,46773,113],{"stretchy":112},[35,46775,213],{},[35,46777,210],{"mathvariant":209},[35,46779,206],{},[110,46781,120],{"stretchy":112},[35,46783,4375],{"mathvariant":209},[39,46785,46786],{"encoding":41},"\\lim_{\\alpha\\to1}D_\\alpha(P\\|Q)=D_{KL}(P\\|Q),\n\\qquad\n\\lim_{\\alpha\\to-1}D_\\alpha(P\\|Q)=D_{KL}(Q\\|P).",[15,46788,46790,46919,47120],{"className":46789,"ariaHidden":46},[45],[15,46791,46793,46797,46852,46855,46895,46898,46901,46904,46907,46910,46913,46916],{"className":46792},[50],[15,46794],{"className":46795,"style":46796},[54],"height:1.4671em;vertical-align:-0.7171em;",[15,46798,46800],{"className":46799},[1484,13716],[15,46801,46803,46843],{"className":46802},[285,286],[15,46804,46806,46840],{"className":46805},[290],[15,46807,46809,46830],{"className":46808,"style":12597},[294],[15,46810,46812,46815],{"style":46811},"top:-2.3829em;margin-left:0em;",[15,46813],{"className":46814,"style":461},[302],[15,46816,46818],{"className":46817},[307,308,309,310],[15,46819,46821,46824,46827],{"className":46820},[59,310],[15,46822,44754],{"className":46823,"style":44784},[59,60,310],[15,46825,1029],{"className":46826},[162,310],[15,46828,117],{"className":46829},[59,310],[15,46831,46832,46835],{"style":11863},[15,46833],{"className":46834,"style":461},[302],[15,46836,46837],{},[15,46838,46673],{"className":46839},[1484],[15,46841,318],{"className":46842},[317],[15,46844,46846],{"className":46845},[290],[15,46847,46850],{"className":46848,"style":46849},[294],"height:0.7171em;",[15,46851],{},[15,46853],{"className":46854,"style":406},[157],[15,46856,46858,46861],{"className":46857},[59],[15,46859,199],{"className":46860,"style":277},[59,60],[15,46862,46864],{"className":46863},[281],[15,46865,46867,46887],{"className":46866},[285,286],[15,46868,46870,46884],{"className":46869},[290],[15,46871,46873],{"className":46872,"style":44929},[294],[15,46874,46875,46878],{"style":298},[15,46876],{"className":46877,"style":303},[302],[15,46879,46881],{"className":46880},[307,308,309,310],[15,46882,44754],{"className":46883,"style":44784},[59,60,310],[15,46885,318],{"className":46886},[317],[15,46888,46890],{"className":46889},[290],[15,46891,46893],{"className":46892,"style":7968},[294],[15,46894],{},[15,46896,113],{"className":46897},[146],[15,46899,206],{"className":46900,"style":334},[59,60],[15,46902,210],{"className":46903},[59],[15,46905,213],{"className":46906},[59,60],[15,46908,120],{"className":46909},[153],[15,46911],{"className":46912,"style":158},[157],[15,46914,123],{"className":46915},[162],[15,46917],{"className":46918,"style":158},[157],[15,46920,46922,46926,46972,46975,46978,46981,46984,46987,46990,46993,46996,47053,47056,47096,47099,47102,47105,47108,47111,47114,47117],{"className":46921},[50],[15,46923],{"className":46924,"style":46925},[54],"height:1.5254em;vertical-align:-0.7754em;",[15,46927,46929,46932],{"className":46928},[59],[15,46930,199],{"className":46931,"style":277},[59,60],[15,46933,46935],{"className":46934},[281],[15,46936,46938,46964],{"className":46937},[285,286],[15,46939,46941,46961],{"className":46940},[290],[15,46942,46944],{"className":46943,"style":379},[294],[15,46945,46946,46949],{"style":298},[15,46947],{"className":46948,"style":303},[302],[15,46950,46952],{"className":46951},[307,308,309,310],[15,46953,46955,46958],{"className":46954},[59,310],[15,46956,10694],{"className":46957,"style":10782},[59,60,310],[15,46959,21893],{"className":46960},[59,60,310],[15,46962,318],{"className":46963},[317],[15,46965,46967],{"className":46966},[290],[15,46968,46970],{"className":46969,"style":7968},[294],[15,46971],{},[15,46973,113],{"className":46974},[146],[15,46976,206],{"className":46977,"style":334},[59,60],[15,46979,210],{"className":46980},[59],[15,46982,213],{"className":46983},[59,60],[15,46985,120],{"className":46986},[153],[15,46988,551],{"className":46989},[573],[15,46991],{"className":46992,"style":3634},[157],[15,46994],{"className":46995,"style":406},[157],[15,46997,46999],{"className":46998},[1484,13716],[15,47000,47002,47044],{"className":47001},[285,286],[15,47003,47005,47041],{"className":47004},[290],[15,47006,47008,47031],{"className":47007,"style":12597},[294],[15,47009,47010,47013],{"style":46811},[15,47011],{"className":47012,"style":461},[302],[15,47014,47016],{"className":47015},[307,308,309,310],[15,47017,47019,47022,47025,47028],{"className":47018},[59,310],[15,47020,44754],{"className":47021,"style":44784},[59,60,310],[15,47023,1029],{"className":47024},[162,310],[15,47026,4813],{"className":47027},[59,310],[15,47029,117],{"className":47030},[59,310],[15,47032,47033,47036],{"style":11863},[15,47034],{"className":47035,"style":461},[302],[15,47037,47038],{},[15,47039,46673],{"className":47040},[1484],[15,47042,318],{"className":47043},[317],[15,47045,47047],{"className":47046},[290],[15,47048,47051],{"className":47049,"style":47050},[294],"height:0.7754em;",[15,47052],{},[15,47054],{"className":47055,"style":406},[157],[15,47057,47059,47062],{"className":47058},[59],[15,47060,199],{"className":47061,"style":277},[59,60],[15,47063,47065],{"className":47064},[281],[15,47066,47068,47088],{"className":47067},[285,286],[15,47069,47071,47085],{"className":47070},[290],[15,47072,47074],{"className":47073,"style":44929},[294],[15,47075,47076,47079],{"style":298},[15,47077],{"className":47078,"style":303},[302],[15,47080,47082],{"className":47081},[307,308,309,310],[15,47083,44754],{"className":47084,"style":44784},[59,60,310],[15,47086,318],{"className":47087},[317],[15,47089,47091],{"className":47090},[290],[15,47092,47094],{"className":47093,"style":7968},[294],[15,47095],{},[15,47097,113],{"className":47098},[146],[15,47100,206],{"className":47101,"style":334},[59,60],[15,47103,210],{"className":47104},[59],[15,47106,213],{"className":47107},[59,60],[15,47109,120],{"className":47110},[153],[15,47112],{"className":47113,"style":158},[157],[15,47115,123],{"className":47116},[162],[15,47118],{"className":47119,"style":158},[157],[15,47121,47123,47126,47172,47175,47178,47181,47184,47187],{"className":47122},[50],[15,47124],{"className":47125,"style":139},[54],[15,47127,47129,47132],{"className":47128},[59],[15,47130,199],{"className":47131,"style":277},[59,60],[15,47133,47135],{"className":47134},[281],[15,47136,47138,47164],{"className":47137},[285,286],[15,47139,47141,47161],{"className":47140},[290],[15,47142,47144],{"className":47143,"style":379},[294],[15,47145,47146,47149],{"style":298},[15,47147],{"className":47148,"style":303},[302],[15,47150,47152],{"className":47151},[307,308,309,310],[15,47153,47155,47158],{"className":47154},[59,310],[15,47156,10694],{"className":47157,"style":10782},[59,60,310],[15,47159,21893],{"className":47160},[59,60,310],[15,47162,318],{"className":47163},[317],[15,47165,47167],{"className":47166},[290],[15,47168,47170],{"className":47169,"style":7968},[294],[15,47171],{},[15,47173,113],{"className":47174},[146],[15,47176,213],{"className":47177},[59,60],[15,47179,210],{"className":47180},[59],[15,47182,206],{"className":47183,"style":334},[59,60],[15,47185,120],{"className":47186},[153],[15,47188,4375],{"className":47189},[59],[11,47191,47192,47247,47248,2745,47321,47475,47476,9400],{},[1225,47193,47194,47195,47246],{},"推导 ",[15,47196,47198,47216],{"className":47197,"translate":19},[18],[15,47199,47201],{"className":47200},[23],[25,47202,47203],{"xmlns":27},[29,47204,47205,47213],{},[32,47206,47207,47209,47211],{},[35,47208,44754],{},[110,47210,1029],{},[115,47212,117],{},[39,47214,47215],{"encoding":41},"\\alpha\\to1",[15,47217,47219,47237],{"className":47218,"ariaHidden":46},[45],[15,47220,47222,47225,47228,47231,47234],{"className":47221},[50],[15,47223],{"className":47224,"style":2345},[54],[15,47226,44754],{"className":47227,"style":44784},[59,60],[15,47229],{"className":47230,"style":158},[157],[15,47232,1029],{"className":47233},[162],[15,47235],{"className":47236,"style":158},[157],[15,47238,47240,47243],{"className":47239},[50],[15,47241],{"className":47242,"style":172},[54],[15,47244,117],{"className":47245},[59]," 的极限。"," 令 ",[15,47249,47251,47273],{"className":47250,"translate":19},[18],[15,47252,47254],{"className":47253},[23],[25,47255,47256],{"xmlns":27},[29,47257,47258,47270],{},[32,47259,47260,47262,47264,47266,47268],{},[35,47261,45180],{},[110,47263,123],{},[115,47265,117],{},[110,47267,4813],{},[35,47269,15712],{},[39,47271,47272],{"encoding":41},"a=1-\\delta",[15,47274,47276,47294,47312],{"className":47275,"ariaHidden":46},[45],[15,47277,47279,47282,47285,47288,47291],{"className":47278},[50],[15,47280],{"className":47281,"style":2345},[54],[15,47283,45180],{"className":47284},[59,60],[15,47286],{"className":47287,"style":158},[157],[15,47289,123],{"className":47290},[162],[15,47292],{"className":47293,"style":158},[157],[15,47295,47297,47300,47303,47306,47309],{"className":47296},[50],[15,47298],{"className":47299,"style":12578},[54],[15,47301,117],{"className":47302},[59],[15,47304],{"className":47305,"style":2587},[157],[15,47307,4813],{"className":47308},[2591],[15,47310],{"className":47311,"style":2587},[157],[15,47313,47315,47318],{"className":47314},[50],[15,47316],{"className":47317,"style":12597},[54],[15,47319,15712],{"className":47320,"style":15761},[59,60],[15,47322,47324,47356],{"className":47323,"translate":19},[18],[15,47325,47327],{"className":47326},[23],[25,47328,47329],{"xmlns":27},[29,47330,47331,47353],{},[32,47332,47333,47335,47337,47349,47351],{},[35,47334,15712],{},[110,47336,123],{},[238,47338,47339,47347],{},[32,47340,47341,47343,47345],{},[115,47342,117],{},[110,47344,4813],{},[35,47346,44754],{},[115,47348,2463],{},[110,47350,1029],{},[115,47352,126],{},[39,47354,47355],{"encoding":41},"\\delta=\\frac{1-\\alpha}{2}\\to0",[15,47357,47359,47377,47466],{"className":47358,"ariaHidden":46},[45],[15,47360,47362,47365,47368,47371,47374],{"className":47361},[50],[15,47363],{"className":47364,"style":12597},[54],[15,47366,15712],{"className":47367,"style":15761},[59,60],[15,47369],{"className":47370,"style":158},[157],[15,47372,123],{"className":47373},[162],[15,47375],{"className":47376,"style":158},[157],[15,47378,47380,47383,47457,47460,47463],{"className":47379},[50],[15,47381],{"className":47382,"style":2505},[54],[15,47384,47386,47389,47454],{"className":47385},[59],[15,47387],{"className":47388},[146,441],[15,47390,47392],{"className":47391},[238],[15,47393,47395,47446],{"className":47394},[285,286],[15,47396,47398,47443],{"className":47397},[290],[15,47399,47401,47415,47423],{"className":47400,"style":2524},[294],[15,47402,47403,47406],{"style":2527},[15,47404],{"className":47405,"style":461},[302],[15,47407,47409],{"className":47408},[307,308,309,310],[15,47410,47412],{"className":47411},[59,310],[15,47413,2463],{"className":47414},[59,310],[15,47416,47417,47420],{"style":473},[15,47418],{"className":47419,"style":461},[302],[15,47421],{"className":47422,"style":481},[480],[15,47424,47425,47428],{"style":2550},[15,47426],{"className":47427,"style":461},[302],[15,47429,47431],{"className":47430},[307,308,309,310],[15,47432,47434,47437,47440],{"className":47433},[59,310],[15,47435,117],{"className":47436},[59,310],[15,47438,4813],{"className":47439},[2591,310],[15,47441,44754],{"className":47442,"style":44784},[59,60,310],[15,47444,318],{"className":47445},[317],[15,47447,47449],{"className":47448},[290],[15,47450,47452],{"className":47451,"style":2572},[294],[15,47453],{},[15,47455],{"className":47456},[153,441],[15,47458],{"className":47459,"style":158},[157],[15,47461,1029],{"className":47462},[162],[15,47464],{"className":47465,"style":158},[157],[15,47467,47469,47472],{"className":47468},[50],[15,47470],{"className":47471,"style":172},[54],[15,47473,126],{"className":47474},[59],"。用 ",[15,47477,47479,47545],{"className":47478,"translate":19},[18],[15,47480,47482],{"className":47481},[23],[25,47483,47484],{"xmlns":27},[29,47485,47486,47542],{},[32,47487,47488,47500,47502,47504,47506,47522,47524,47526,47528,47530,47532,47534,47536,47538,47540],{},[6814,47489,47490,47492],{},[35,47491,774],{},[32,47493,47494,47496,47498],{},[115,47495,117],{},[110,47497,4813],{},[35,47499,15712],{},[110,47501,123],{},[35,47503,774],{},[1297,47505,1299],{},[6814,47507,47508,47510],{},[35,47509,7567],{},[32,47511,47512,47514,47516,47518,47520],{},[110,47513,4813],{},[35,47515,15712],{},[35,47517,4100],{},[110,47519,4103],{},[35,47521,774],{},[110,47523,32959],{},[35,47525,774],{},[110,47527,113],{"stretchy":112},[115,47529,117],{},[110,47531,4813],{},[35,47533,15712],{},[35,47535,4100],{},[110,47537,4103],{},[35,47539,774],{},[110,47541,120],{"stretchy":112},[39,47543,47544],{"encoding":41},"x^{1-\\delta}=x\\,e^{-\\delta\\log x}\\approx x(1-\\delta\\log x)",[15,47546,47548,47602,47681,47705],{"className":47547,"ariaHidden":46},[45],[15,47549,47551,47555,47593,47596,47599],{"className":47550},[50],[15,47552],{"className":47553,"style":47554},[54],"height:0.8491em;",[15,47556,47558,47561],{"className":47557},[59],[15,47559,774],{"className":47560},[59,60],[15,47562,47564],{"className":47563},[281],[15,47565,47567],{"className":47566},[285],[15,47568,47570],{"className":47569},[290],[15,47571,47573],{"className":47572,"style":47554},[294],[15,47574,47575,47578],{"style":6865},[15,47576],{"className":47577,"style":303},[302],[15,47579,47581],{"className":47580},[307,308,309,310],[15,47582,47584,47587,47590],{"className":47583},[59,310],[15,47585,117],{"className":47586},[59,310],[15,47588,4813],{"className":47589},[2591,310],[15,47591,15712],{"className":47592,"style":15761},[59,60,310],[15,47594],{"className":47595,"style":158},[157],[15,47597,123],{"className":47598},[162],[15,47600],{"className":47601,"style":158},[157],[15,47603,47605,47608,47611,47614,47672,47675,47678],{"className":47604},[50],[15,47606],{"className":47607,"style":47554},[54],[15,47609,774],{"className":47610},[59,60],[15,47612],{"className":47613,"style":406},[157],[15,47615,47617,47620],{"className":47616},[59],[15,47618,7567],{"className":47619},[59,60],[15,47621,47623],{"className":47622},[281],[15,47624,47626],{"className":47625},[285],[15,47627,47629],{"className":47628},[290],[15,47630,47632],{"className":47631,"style":47554},[294],[15,47633,47634,47637],{"style":6865},[15,47635],{"className":47636,"style":303},[302],[15,47638,47640],{"className":47639},[307,308,309,310],[15,47641,47643,47646,47649,47652,47666,47669],{"className":47642},[59,310],[15,47644,4813],{"className":47645},[59,310],[15,47647,15712],{"className":47648,"style":15761},[59,60,310],[15,47650],{"className":47651,"style":42366},[157,310],[15,47653,47655,47659,47663],{"className":47654},[1484,310],[15,47656,47658],{"className":47657},[310],"l",[15,47660,47662],{"className":47661},[310],"o",[15,47664,4158],{"className":47665,"style":4157},[310],[15,47667],{"className":47668,"style":42366},[157,310],[15,47670,774],{"className":47671},[59,60,310],[15,47673],{"className":47674,"style":158},[157],[15,47676,32959],{"className":47677},[162],[15,47679],{"className":47680,"style":158},[157],[15,47682,47684,47687,47690,47693,47696,47699,47702],{"className":47683},[50],[15,47685],{"className":47686,"style":139},[54],[15,47688,774],{"className":47689},[59,60],[15,47691,113],{"className":47692},[146],[15,47694,117],{"className":47695},[59],[15,47697],{"className":47698,"style":2587},[157],[15,47700,4813],{"className":47701},[2591],[15,47703],{"className":47704,"style":2587},[157],[15,47706,47708,47711,47714,47717,47722,47725,47728],{"className":47707},[50],[15,47709],{"className":47710,"style":139},[54],[15,47712,15712],{"className":47713,"style":15761},[59,60],[15,47715],{"className":47716,"style":406},[157],[15,47718,4154,47720],{"className":47719},[1484],[15,47721,4158],{"style":4157},[15,47723],{"className":47724,"style":406},[157],[15,47726,774],{"className":47727},[59,60],[15,47729,120],{"className":47730},[153],[15,47732,47734],{"className":47733,"translate":19},[180],[15,47735,47737,47831],{"className":47736,"translate":19},[18],[15,47738,47740],{"className":47739},[23],[25,47741,47742],{"xmlns":27,"display":189},[29,47743,47744,47828],{},[32,47745,47746,47748,47760,47766,47768,47770,47772,47774,47776,47778,47780,47782,47784,47790,47792,47794,47796,47798,47800,47802,47804,47806,47816,47818,47820,47822,47824,47826],{},[110,47747,1287],{},[6814,47749,47750,47752],{},[35,47751,11],{},[32,47753,47754,47756,47758],{},[115,47755,117],{},[110,47757,4813],{},[35,47759,15712],{},[6814,47761,47762,47764],{},[35,47763,944],{},[35,47765,15712],{},[110,47767,32959],{},[110,47769,1287],{},[35,47771,11],{},[110,47773,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[115,47775,117],{},[110,47777,4813],{},[35,47779,15712],{},[35,47781,4100],{},[110,47783,4103],{},[238,47785,47786,47788],{},[35,47787,11],{},[35,47789,944],{},[110,47791,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,47793,244],{},[35,47795,774],{},[110,47797,123],{},[115,47799,117],{},[110,47801,4813],{},[35,47803,15712],{},[1297,47805,1299],{},[195,47807,47808,47810],{},[35,47809,199],{},[32,47811,47812,47814],{},[35,47813,10694],{},[35,47815,21893],{},[110,47817,113],{"stretchy":112},[35,47819,206],{},[35,47821,210],{"mathvariant":209},[35,47823,213],{},[110,47825,120],{"stretchy":112},[110,47827,551],{"separator":46},[39,47829,47830],{"encoding":41},"\\int p^{1-\\delta}q^{\\delta}\n\\approx\\int p\\Big(1-\\delta\\log\\frac{p}{q}\\Big)dx\n=1-\\delta\\,D_{KL}(P\\|Q),",[15,47832,47834,47926,47959,48063,48081],{"className":47833,"ariaHidden":46},[45],[15,47835,47837,47840,47843,47846,47885,47917,47920,47923],{"className":47836},[50],[15,47838],{"className":47839,"style":5777},[54],[15,47841,1287],{"className":47842,"style":1487},[1484,1485,1486],[15,47844],{"className":47845,"style":406},[157],[15,47847,47849,47852],{"className":47848},[59],[15,47850,11],{"className":47851},[59,60],[15,47853,47855],{"className":47854},[281],[15,47856,47858],{"className":47857},[285],[15,47859,47861],{"className":47860},[290],[15,47862,47865],{"className":47863,"style":47864},[294],"height:0.8991em;",[15,47866,47867,47870],{"style":8277},[15,47868],{"className":47869,"style":303},[302],[15,47871,47873],{"className":47872},[307,308,309,310],[15,47874,47876,47879,47882],{"className":47875},[59,310],[15,47877,117],{"className":47878},[59,310],[15,47880,4813],{"className":47881},[2591,310],[15,47883,15712],{"className":47884,"style":15761},[59,60,310],[15,47886,47888,47891],{"className":47887},[59],[15,47889,944],{"className":47890,"style":981},[59,60],[15,47892,47894],{"className":47893},[281],[15,47895,47897],{"className":47896},[285],[15,47898,47900],{"className":47899},[290],[15,47901,47903],{"className":47902,"style":47864},[294],[15,47904,47905,47908],{"style":8277},[15,47906],{"className":47907,"style":303},[302],[15,47909,47911],{"className":47910},[307,308,309,310],[15,47912,47914],{"className":47913},[59,310],[15,47915,15712],{"className":47916,"style":15761},[59,60,310],[15,47918],{"className":47919,"style":158},[157],[15,47921,32959],{"className":47922},[162],[15,47924],{"className":47925,"style":158},[157],[15,47927,47929,47932,47935,47938,47941,47947,47950,47953,47956],{"className":47928},[50],[15,47930],{"className":47931,"style":5777},[54],[15,47933,1287],{"className":47934,"style":1487},[1484,1485,1486],[15,47936],{"className":47937,"style":406},[157],[15,47939,11],{"className":47940},[59,60],[15,47942,47944],{"className":47943},[59],[15,47945,113],{"className":47946},[419,3720],[15,47948,117],{"className":47949},[59],[15,47951],{"className":47952,"style":2587},[157],[15,47954,4813],{"className":47955},[2591],[15,47957],{"className":47958,"style":2587},[157],[15,47960,47962,47966,47969,47972,47977,47980,48042,48048,48051,48054,48057,48060],{"className":47961},[50],[15,47963],{"className":47964,"style":47965},[54],"height:2.0304em;vertical-align:-0.8804em;",[15,47967,15712],{"className":47968,"style":15761},[59,60],[15,47970],{"className":47971,"style":406},[157],[15,47973,4154,47975],{"className":47974},[1484],[15,47976,4158],{"style":4157},[15,47978],{"className":47979,"style":406},[157],[15,47981,47983,47986,48039],{"className":47982},[59],[15,47984],{"className":47985},[146,441],[15,47987,47989],{"className":47988},[238],[15,47990,47992,48031],{"className":47991},[285,286],[15,47993,47995,48028],{"className":47994},[290],[15,47996,47998,48009,48017],{"className":47997,"style":3554},[294],[15,47999,48000,48003],{"style":457},[15,48001],{"className":48002,"style":461},[302],[15,48004,48006],{"className":48005},[59],[15,48007,944],{"className":48008,"style":981},[59,60],[15,48010,48011,48014],{"style":473},[15,48012],{"className":48013,"style":461},[302],[15,48015],{"className":48016,"style":481},[480],[15,48018,48019,48022],{"style":484},[15,48020],{"className":48021,"style":461},[302],[15,48023,48025],{"className":48024},[59],[15,48026,11],{"className":48027},[59,60],[15,48029,318],{"className":48030},[317],[15,48032,48034],{"className":48033},[290],[15,48035,48037],{"className":48036,"style":506},[294],[15,48038],{},[15,48040],{"className":48041},[153,441],[15,48043,48045],{"className":48044},[59],[15,48046,120],{"className":48047},[419,3720],[15,48049,244],{"className":48050},[59,60],[15,48052,774],{"className":48053},[59,60],[15,48055],{"className":48056,"style":158},[157],[15,48058,123],{"className":48059},[162],[15,48061],{"className":48062,"style":158},[157],[15,48064,48066,48069,48072,48075,48078],{"className":48065},[50],[15,48067],{"className":48068,"style":12578},[54],[15,48070,117],{"className":48071},[59],[15,48073],{"className":48074,"style":2587},[157],[15,48076,4813],{"className":48077},[2591],[15,48079],{"className":48080,"style":2587},[157],[15,48082,48084,48087,48090,48093,48139,48142,48145,48148,48151,48154],{"className":48083},[50],[15,48085],{"className":48086,"style":139},[54],[15,48088,15712],{"className":48089,"style":15761},[59,60],[15,48091],{"className":48092,"style":406},[157],[15,48094,48096,48099],{"className":48095},[59],[15,48097,199],{"className":48098,"style":277},[59,60],[15,48100,48102],{"className":48101},[281],[15,48103,48105,48131],{"className":48104},[285,286],[15,48106,48108,48128],{"className":48107},[290],[15,48109,48111],{"className":48110,"style":379},[294],[15,48112,48113,48116],{"style":298},[15,48114],{"className":48115,"style":303},[302],[15,48117,48119],{"className":48118},[307,308,309,310],[15,48120,48122,48125],{"className":48121},[59,310],[15,48123,10694],{"className":48124,"style":10782},[59,60,310],[15,48126,21893],{"className":48127},[59,60,310],[15,48129,318],{"className":48130},[317],[15,48132,48134],{"className":48133},[290],[15,48135,48137],{"className":48136,"style":7968},[294],[15,48138],{},[15,48140,113],{"className":48141},[146],[15,48143,206],{"className":48144,"style":334},[59,60],[15,48146,210],{"className":48147},[59],[15,48149,213],{"className":48150},[59,60],[15,48152,120],{"className":48153},[153],[15,48155,551],{"className":48156},[573],[11,48158,48159],{},"于是",[15,48161,48163],{"className":48162,"translate":19},[180],[15,48164,48166,48367],{"className":48165,"translate":19},[18],[15,48167,48169],{"className":48168},[23],[25,48170,48171],{"xmlns":27,"display":189},[29,48172,48173,48364],{},[1243,48174,48175,48241,48301],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,48176,48177,48187],{},[1252,48178,48179],{},[1255,48180,48181],{"scriptlevel":126,"displaystyle":46},[195,48182,48183,48185],{},[35,48184,199],{},[35,48186,44754],{},[1252,48188,48189],{},[1255,48190,48191],{"scriptlevel":126,"displaystyle":46},[32,48192,48193,48195,48197,48215,48217,48219,48229,48231,48233,48235,48237,48239],{},[32,48194],{},[110,48196,123],{},[238,48198,48199,48201],{},[115,48200,117],{},[32,48202,48203,48205,48207,48209,48211,48213],{},[35,48204,45180],{},[110,48206,113],{"stretchy":112},[115,48208,117],{},[110,48210,4813],{},[35,48212,45180],{},[110,48214,120],{"stretchy":112},[110,48216,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,48218,15712],{},[195,48220,48221,48223],{},[35,48222,199],{},[32,48224,48225,48227],{},[35,48226,10694],{},[35,48228,21893],{},[110,48230,113],{"stretchy":112},[35,48232,206],{},[35,48234,210],{"mathvariant":209},[35,48236,213],{},[110,48238,120],{"stretchy":112},[110,48240,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,48242,48243,48249],{},[1252,48244,48245],{},[1255,48246,48247],{"scriptlevel":126,"displaystyle":46},[32,48248],{},[1252,48250,48251],{},[1255,48252,48253],{"scriptlevel":126,"displaystyle":46},[32,48254,48255,48257,48259,48277,48279,48281,48291,48293,48295,48297,48299],{},[32,48256],{},[110,48258,123],{},[238,48260,48261,48263],{},[115,48262,117],{},[32,48264,48265,48267,48269,48271,48273,48275],{},[110,48266,113],{"stretchy":112},[115,48268,117],{},[110,48270,4813],{},[35,48272,15712],{},[110,48274,120],{"stretchy":112},[35,48276,15712],{},[110,48278,3299],{},[35,48280,15712],{},[195,48282,48283,48285],{},[35,48284,199],{},[32,48286,48287,48289],{},[35,48288,10694],{},[35,48290,21893],{},[110,48292,113],{"stretchy":112},[35,48294,206],{},[35,48296,210],{"mathvariant":209},[35,48298,213],{},[110,48300,120],{"stretchy":112},[1249,48302,48303,48309],{},[1252,48304,48305],{},[1255,48306,48307],{"scriptlevel":126,"displaystyle":46},[32,48308],{},[1252,48310,48311],{},[1255,48312,48313],{"scriptlevel":126,"displaystyle":46},[32,48314,48315,48317,48319,48342,48352,48354,48356,48358,48360,48362],{},[32,48316],{},[157,48318],{"width":3262},[48320,48321,48322,48325,48338],"munderover",{},[110,48323,1029],{"stretchy":46,"minsize":48324},"3.0em",[48326,48327,48330],"mpadded",{"width":48328,"lspace":48329},"+0.6em","0.3em",[32,48331,48332,48334,48336],{},[35,48333,15712],{},[110,48335,1029],{},[115,48337,126],{},[48326,48339,48340],{"width":48328,"lspace":48329},[32,48341],{},[195,48343,48344,48346],{},[35,48345,199],{},[32,48347,48348,48350],{},[35,48349,10694],{},[35,48351,21893],{},[110,48353,113],{"stretchy":112},[35,48355,206],{},[35,48357,210],{"mathvariant":209},[35,48359,213],{},[110,48361,120],{"stretchy":112},[35,48363,4375],{"mathvariant":209},[39,48365,48366],{"encoding":41},"\\begin{aligned}\nD_\\alpha\n&=\\frac{1}{a(1-a)}\n\\big(\\delta D_{KL}(P\\|Q)\\big)\\\\[2pt]\n&=\\frac{1}{(1-\\delta)\\delta}\n\\cdot\\delta D_{KL}(P\\|Q)\\\\\n&\\qquad\\xrightarrow[\\delta\\to0]{}D_{KL}(P\\|Q).\n\\end{aligned}",[15,48368,48370],{"className":48369,"ariaHidden":46},[45],[15,48371,48373,48377],{"className":48372},[50],[15,48374],{"className":48375,"style":48376},[54],"height:6.563em;vertical-align:-3.0315em;",[15,48378,48380],{"className":48379},[59],[15,48381,48383,48475],{"className":48382},[1243],[15,48384,48386],{"className":48385},[1360],[15,48387,48389,48466],{"className":48388},[285,286],[15,48390,48392,48463],{"className":48391},[290],[15,48393,48396,48445,48454],{"className":48394,"style":48395},[294],"height:3.5315em;",[15,48397,48399,48402],{"style":48398},"top:-5.5315em;",[15,48400],{"className":48401,"style":22666},[302],[15,48403,48405],{"className":48404},[59],[15,48406,48408,48411],{"className":48407},[59],[15,48409,199],{"className":48410,"style":277},[59,60],[15,48412,48414],{"className":48413},[281],[15,48415,48417,48437],{"className":48416},[285,286],[15,48418,48420,48434],{"className":48419},[290],[15,48421,48423],{"className":48422,"style":44929},[294],[15,48424,48425,48428],{"style":298},[15,48426],{"className":48427,"style":303},[302],[15,48429,48431],{"className":48430},[307,308,309,310],[15,48432,44754],{"className":48433,"style":44784},[59,60,310],[15,48435,318],{"className":48436},[317],[15,48438,48440],{"className":48439},[290],[15,48441,48443],{"className":48442,"style":7968},[294],[15,48444],{},[15,48446,48448,48451],{"style":48447},"top:-2.9741em;",[15,48449],{"className":48450,"style":22666},[302],[15,48452],{"className":48453},[59],[15,48455,48457,48460],{"style":48456},"top:-0.8981em;",[15,48458],{"className":48459,"style":22666},[302],[15,48461],{"className":48462},[59],[15,48464,318],{"className":48465},[317],[15,48467,48469],{"className":48468},[290],[15,48470,48473],{"className":48471,"style":48472},[294],"height:3.0315em;",[15,48474],{},[15,48476,48478],{"className":48477},[1451],[15,48479,48481,49007],{"className":48480},[285,286],[15,48482,48484,49004],{"className":48483},[290],[15,48485,48487,48666,48842],{"className":48486,"style":48395},[294],[15,48488,48489,48492],{"style":48398},[15,48490],{"className":48491,"style":22666},[302],[15,48493,48495,48498,48501,48504,48507,48590,48596,48599,48645,48648,48651,48654,48657,48660],{"className":48494},[59],[15,48496],{"className":48497},[59],[15,48499],{"className":48500,"style":158},[157],[15,48502,123],{"className":48503},[162],[15,48505],{"className":48506,"style":158},[157],[15,48508,48510,48513,48587],{"className":48509},[59],[15,48511],{"className":48512},[146,441],[15,48514,48516],{"className":48515},[238],[15,48517,48519,48579],{"className":48518},[285,286],[15,48520,48522,48576],{"className":48521},[290],[15,48523,48525,48557,48565],{"className":48524,"style":22889},[294],[15,48526,48527,48530],{"style":457},[15,48528],{"className":48529,"style":461},[302],[15,48531,48533,48536,48539,48542,48545,48548,48551,48554],{"className":48532},[59],[15,48534,45180],{"className":48535},[59,60],[15,48537,113],{"className":48538},[146],[15,48540,117],{"className":48541},[59],[15,48543],{"className":48544,"style":2587},[157],[15,48546,4813],{"className":48547},[2591],[15,48549],{"className":48550,"style":2587},[157],[15,48552,45180],{"className":48553},[59,60],[15,48555,120],{"className":48556},[153],[15,48558,48559,48562],{"style":473},[15,48560],{"className":48561,"style":461},[302],[15,48563],{"className":48564,"style":481},[480],[15,48566,48567,48570],{"style":484},[15,48568],{"className":48569,"style":461},[302],[15,48571,48573],{"className":48572},[59],[15,48574,117],{"className":48575},[59],[15,48577,318],{"className":48578},[317],[15,48580,48582],{"className":48581},[290],[15,48583,48585],{"className":48584,"style":1601},[294],[15,48586],{},[15,48588],{"className":48589},[153,441],[15,48591,48593],{"className":48592},[59],[15,48594,113],{"className":48595},[419,9674],[15,48597,15712],{"className":48598,"style":15761},[59,60],[15,48600,48602,48605],{"className":48601},[59],[15,48603,199],{"className":48604,"style":277},[59,60],[15,48606,48608],{"className":48607},[281],[15,48609,48611,48637],{"className":48610},[285,286],[15,48612,48614,48634],{"className":48613},[290],[15,48615,48617],{"className":48616,"style":379},[294],[15,48618,48619,48622],{"style":298},[15,48620],{"className":48621,"style":303},[302],[15,48623,48625],{"className":48624},[307,308,309,310],[15,48626,48628,48631],{"className":48627},[59,310],[15,48629,10694],{"className":48630,"style":10782},[59,60,310],[15,48632,21893],{"className":48633},[59,60,310],[15,48635,318],{"className":48636},[317],[15,48638,48640],{"className":48639},[290],[15,48641,48643],{"className":48642,"style":7968},[294],[15,48644],{},[15,48646,113],{"className":48647},[146],[15,48649,206],{"className":48650,"style":334},[59,60],[15,48652,210],{"className":48653},[59],[15,48655,213],{"className":48656},[59,60],[15,48658,120],{"className":48659},[153],[15,48661,48663],{"className":48662},[59],[15,48664,120],{"className":48665},[419,9674],[15,48667,48668,48671],{"style":48447},[15,48669],{"className":48670,"style":22666},[302],[15,48672,48674,48677,48680,48683,48686,48769,48772,48775,48778,48781,48827,48830,48833,48836,48839],{"className":48673},[59],[15,48675],{"className":48676},[59],[15,48678],{"className":48679,"style":158},[157],[15,48681,123],{"className":48682},[162],[15,48684],{"className":48685,"style":158},[157],[15,48687,48689,48692,48766],{"className":48688},[59],[15,48690],{"className":48691},[146,441],[15,48693,48695],{"className":48694},[238],[15,48696,48698,48758],{"className":48697},[285,286],[15,48699,48701,48755],{"className":48700},[290],[15,48702,48704,48736,48744],{"className":48703,"style":22889},[294],[15,48705,48706,48709],{"style":457},[15,48707],{"className":48708,"style":461},[302],[15,48710,48712,48715,48718,48721,48724,48727,48730,48733],{"className":48711},[59],[15,48713,113],{"className":48714},[146],[15,48716,117],{"className":48717},[59],[15,48719],{"className":48720,"style":2587},[157],[15,48722,4813],{"className":48723},[2591],[15,48725],{"className":48726,"style":2587},[157],[15,48728,15712],{"className":48729,"style":15761},[59,60],[15,48731,120],{"className":48732},[153],[15,48734,15712],{"className":48735,"style":15761},[59,60],[15,48737,48738,48741],{"style":473},[15,48739],{"className":48740,"style":461},[302],[15,48742],{"className":48743,"style":481},[480],[15,48745,48746,48749],{"style":484},[15,48747],{"className":48748,"style":461},[302],[15,48750,48752],{"className":48751},[59],[15,48753,117],{"className":48754},[59],[15,48756,318],{"className":48757},[317],[15,48759,48761],{"className":48760},[290],[15,48762,48764],{"className":48763,"style":1601},[294],[15,48765],{},[15,48767],{"className":48768},[153,441],[15,48770],{"className":48771,"style":2587},[157],[15,48773,3299],{"className":48774},[2591],[15,48776],{"className":48777,"style":2587},[157],[15,48779,15712],{"className":48780,"style":15761},[59,60],[15,48782,48784,48787],{"className":48783},[59],[15,48785,199],{"className":48786,"style":277},[59,60],[15,48788,48790],{"className":48789},[281],[15,48791,48793,48819],{"className":48792},[285,286],[15,48794,48796,48816],{"className":48795},[290],[15,48797,48799],{"className":48798,"style":379},[294],[15,48800,48801,48804],{"style":298},[15,48802],{"className":48803,"style":303},[302],[15,48805,48807],{"className":48806},[307,308,309,310],[15,48808,48810,48813],{"className":48809},[59,310],[15,48811,10694],{"className":48812,"style":10782},[59,60,310],[15,48814,21893],{"className":48815},[59,60,310],[15,48817,318],{"className":48818},[317],[15,48820,48822],{"className":48821},[290],[15,48823,48825],{"className":48824,"style":7968},[294],[15,48826],{},[15,48828,113],{"className":48829},[146],[15,48831,206],{"className":48832,"style":334},[59,60],[15,48834,210],{"className":48835},[59],[15,48837,213],{"className":48838},[59,60],[15,48840,120],{"className":48841},[153],[15,48843,48844,48847],{"style":48456},[15,48845],{"className":48846,"style":22666},[302],[15,48848,48850,48853,48856,48859,48937,48940,48986,48989,48992,48995,48998,49001],{"className":48849},[59],[15,48851],{"className":48852},[59],[15,48854],{"className":48855,"style":3634},[157],[15,48857],{"className":48858,"style":158},[157],[15,48860,48863],{"className":48861},[162,48862],"x-arrow",[15,48864,48866,48928],{"className":48865},[285,286],[15,48867,48869,48925],{"className":48868},[290],[15,48870,48873,48886,48904],{"className":48871,"style":48872},[294],"height:0.622em;",[15,48874,48876,48879],{"style":48875},"top:-3.322em;",[15,48877],{"className":48878,"style":303},[302],[15,48880,48883],{"className":48881},[307,308,309,310,48882],"x-arrow-pad",[15,48884],{"className":48885},[59,310],[15,48887,48890,48893],{"className":48888,"style":48889},[6307],"top:-2.689em;",[15,48891],{"className":48892,"style":303},[302],[15,48894,48897],{"className":48895,"style":48896},[34443],"height:0.522em;min-width:1.469em;",[6323,48898,48901],{"xmlns":6325,"width":6326,"height":48899,"viewBox":48900,"preserveAspectRatio":6350},"0.522em","0 0 400000 522",[6331,48902],{"d":48903},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[15,48905,48907,48910],{"style":48906},"top:-2.0919em;",[15,48908],{"className":48909,"style":303},[302],[15,48911,48913],{"className":48912},[307,308,309,310,48882],[15,48914,48916,48919,48922],{"className":48915},[59,310],[15,48917,15712],{"className":48918,"style":15761},[59,60,310],[15,48920,1029],{"className":48921},[162,310],[15,48923,126],{"className":48924},[59,310],[15,48926,318],{"className":48927},[317],[15,48929,48931],{"className":48930},[290],[15,48932,48935],{"className":48933,"style":48934},[294],"height:0.6081em;",[15,48936],{},[15,48938],{"className":48939,"style":158},[157],[15,48941,48943,48946],{"className":48942},[59],[15,48944,199],{"className":48945,"style":277},[59,60],[15,48947,48949],{"className":48948},[281],[15,48950,48952,48978],{"className":48951},[285,286],[15,48953,48955,48975],{"className":48954},[290],[15,48956,48958],{"className":48957,"style":379},[294],[15,48959,48960,48963],{"style":298},[15,48961],{"className":48962,"style":303},[302],[15,48964,48966],{"className":48965},[307,308,309,310],[15,48967,48969,48972],{"className":48968},[59,310],[15,48970,10694],{"className":48971,"style":10782},[59,60,310],[15,48973,21893],{"className":48974},[59,60,310],[15,48976,318],{"className":48977},[317],[15,48979,48981],{"className":48980},[290],[15,48982,48984],{"className":48983,"style":7968},[294],[15,48985],{},[15,48987,113],{"className":48988},[146],[15,48990,206],{"className":48991,"style":334},[59,60],[15,48993,210],{"className":48994},[59],[15,48996,213],{"className":48997},[59,60],[15,48999,120],{"className":49000},[153],[15,49002,4375],{"className":49003},[59],[15,49005,318],{"className":49006},[317],[15,49008,49010],{"className":49009},[290],[15,49011,49013],{"className":49012,"style":48472},[294],[15,49014],{},[11,49016,49017,49073,49074,49103],{},[15,49018,49020,49040],{"className":49019,"translate":19},[18],[15,49021,49023],{"className":49022},[23],[25,49024,49025],{"xmlns":27},[29,49026,49027,49037],{},[32,49028,49029,49031,49033,49035],{},[35,49030,44754],{},[110,49032,1029],{},[110,49034,4813],{},[115,49036,117],{},[39,49038,49039],{"encoding":41},"\\alpha\\to-1",[15,49041,49043,49061],{"className":49042,"ariaHidden":46},[45],[15,49044,49046,49049,49052,49055,49058],{"className":49045},[50],[15,49047],{"className":49048,"style":2345},[54],[15,49050,44754],{"className":49051,"style":44784},[59,60],[15,49053],{"className":49054,"style":158},[157],[15,49056,1029],{"className":49057},[162],[15,49059],{"className":49060,"style":158},[157],[15,49062,49064,49067,49070],{"className":49063},[50],[15,49065],{"className":49066,"style":12578},[54],[15,49068,4813],{"className":49069},[59],[15,49071,117],{"className":49072},[59]," 对称地给出反向 KL。所以 α-散度把 KL（两个方向）与 Hellinger 连成一条曲线，",[15,49075,49077,49091],{"className":49076,"translate":19},[18],[15,49078,49080],{"className":49079},[23],[25,49081,49082],{"xmlns":27},[29,49083,49084,49088],{},[32,49085,49086],{},[35,49087,44754],{},[39,49089,49090],{"encoding":41},"\\alpha",[15,49092,49094],{"className":49093,"ariaHidden":46},[45],[15,49095,49097,49100],{"className":49096},[50],[15,49098],{"className":49099,"style":2345},[54],[15,49101,44754],{"className":49102,"style":44784},[59,60]," 是「在对称与不对称之间连续插值」的旋钮。",[11,49105,49106,49108,49109,49137,49138,49172,49173,49201,49202,49252,49253,49256,49257,49285,49286,49314,49315,49343,49344,49372],{},[1225,49107,24193],{}," α-散度的价值在于它把「方向」与「强度」一并参数化：",[15,49110,49112,49125],{"className":49111,"translate":19},[18],[15,49113,49115],{"className":49114},[23],[25,49116,49117],{"xmlns":27},[29,49118,49119,49123],{},[32,49120,49121],{},[35,49122,44754],{},[39,49124,49090],{"encoding":41},[15,49126,49128],{"className":49127,"ariaHidden":46},[45],[15,49129,49131,49134],{"className":49130},[50],[15,49132],{"className":49133,"style":2345},[54],[15,49135,44754],{"className":49136,"style":44784},[59,60]," 从 ",[15,49139,49141,49157],{"className":49140,"translate":19},[18],[15,49142,49144],{"className":49143},[23],[25,49145,49146],{"xmlns":27},[29,49147,49148,49154],{},[32,49149,49150,49152],{},[110,49151,4813],{},[115,49153,117],{},[39,49155,49156],{"encoding":41},"-1",[15,49158,49160],{"className":49159,"ariaHidden":46},[45],[15,49161,49163,49166,49169],{"className":49162},[50],[15,49164],{"className":49165,"style":12578},[54],[15,49167,4813],{"className":49168},[59],[15,49170,117],{"className":49171},[59]," 扫到 ",[15,49174,49176,49189],{"className":49175,"translate":19},[18],[15,49177,49179],{"className":49178},[23],[25,49180,49181],{"xmlns":27},[29,49182,49183,49187],{},[32,49184,49185],{},[115,49186,117],{},[39,49188,117],{"encoding":41},[15,49190,49192],{"className":49191,"ariaHidden":46},[45],[15,49193,49195,49198],{"className":49194},[50],[15,49196],{"className":49197,"style":172},[54],[15,49199,117],{"className":49200},[59]," 时，散度由反向 KL（mode-seeking）连续过渡到正向 KL（mass-covering），中间在 ",[15,49203,49205,49222],{"className":49204,"translate":19},[18],[15,49206,49208],{"className":49207},[23],[25,49209,49210],{"xmlns":27},[29,49211,49212,49220],{},[32,49213,49214,49216,49218],{},[35,49215,44754],{},[110,49217,123],{},[115,49219,126],{},[39,49221,46488],{"encoding":41},[15,49223,49225,49243],{"className":49224,"ariaHidden":46},[45],[15,49226,49228,49231,49234,49237,49240],{"className":49227},[50],[15,49229],{"className":49230,"style":2345},[54],[15,49232,44754],{"className":49233,"style":44784},[59,60],[15,49235],{"className":49236,"style":158},[157],[15,49238,123],{"className":49239},[162],[15,49241],{"className":49242,"style":158},[157],[15,49244,49246,49249],{"className":49245},[50],[15,49247],{"className":49248,"style":172},[54],[15,49250,126],{"className":49251},[59]," 处恰好经过 Hellinger 这个对称点。在 Amari 的",[1225,49254,49255],{},"信息几何","里，α-族是唯一同时拥有 ",[15,49258,49260,49273],{"className":49259,"translate":19},[18],[15,49261,49263],{"className":49262},[23],[25,49264,49265],{"xmlns":27},[29,49266,49267,49271],{},[32,49268,49269],{},[35,49270,44754],{},[39,49272,49090],{"encoding":41},[15,49274,49276],{"className":49275,"ariaHidden":46},[45],[15,49277,49279,49282],{"className":49278},[50],[15,49280],{"className":49281,"style":2345},[54],[15,49283,44754],{"className":49284,"style":44784},[59,60],"-对偶平坦结构的单参数散度族：它诱导的度量是 Fisher 度量，诱导的仿射联络是 ",[15,49287,49289,49302],{"className":49288,"translate":19},[18],[15,49290,49292],{"className":49291},[23],[25,49293,49294],{"xmlns":27},[29,49295,49296,49300],{},[32,49297,49298],{},[35,49299,44754],{},[39,49301,49090],{"encoding":41},[15,49303,49305],{"className":49304,"ariaHidden":46},[45],[15,49306,49308,49311],{"className":49307},[50],[15,49309],{"className":49310,"style":2345},[54],[15,49312,44754],{"className":49313,"style":44784},[59,60],"-联络，这正是它被称为「散度范本」的原因。在机器学习中，",[15,49316,49318,49331],{"className":49317,"translate":19},[18],[15,49319,49321],{"className":49320},[23],[25,49322,49323],{"xmlns":27},[29,49324,49325,49329],{},[32,49326,49327],{},[35,49328,44754],{},[39,49330,49090],{"encoding":41},[15,49332,49334],{"className":49333,"ariaHidden":46},[45],[15,49335,49337,49340],{"className":49336},[50],[15,49338],{"className":49339,"style":2345},[54],[15,49341,44754],{"className":49342,"style":44784},[59,60],"-GAN 与 ",[15,49345,49347,49360],{"className":49346,"translate":19},[18],[15,49348,49350],{"className":49349},[23],[25,49351,49352],{"xmlns":27},[29,49353,49354,49358],{},[32,49355,49356],{},[35,49357,44754],{},[39,49359,49090],{"encoding":41},[15,49361,49363],{"className":49362,"ariaHidden":46},[45],[15,49364,49366,49369],{"className":49365},[50],[15,49367],{"className":49368,"style":2345},[54],[15,49370,44754],{"className":49371,"style":44784},[59,60],"-VI 用一个参数调节「对异常值的鲁棒性」与「模式覆盖」之间的取舍；在信号处理中它用于独立成分分析（ICA）与鲁棒估计。",[2311,49374,49376],{"id":49375},"_37-与-rényi-散度的关系","3.7 与 Rényi 散度的关系",[11,49378,49379],{},"Rényi 散度定义为",[15,49381,49383],{"className":49382,"translate":19},[180],[15,49384,49386,49514],{"className":49385,"translate":19},[18],[15,49387,49389],{"className":49388},[23],[25,49390,49391],{"xmlns":27,"display":189},[29,49392,49393,49511],{},[1243,49394,49395,49475],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,49396,49397,49421],{},[1252,49398,49399],{},[1255,49400,49401],{"scriptlevel":126,"displaystyle":46},[32,49402,49403,49411,49413,49415,49417,49419],{},[7553,49404,49405,49407,49409],{},[35,49406,199],{},[35,49408,44754],{},[35,49410,1032],{},[110,49412,113],{"stretchy":112},[35,49414,206],{},[35,49416,210],{"mathvariant":209},[35,49418,213],{},[110,49420,120],{"stretchy":112},[1252,49422,49423],{},[1255,49424,49425],{"scriptlevel":126,"displaystyle":46},[32,49426,49427,49429,49431,49443,49445,49447,49449,49455,49467,49469,49471,49473],{},[32,49428],{},[110,49430,123],{},[238,49432,49433,49435],{},[115,49434,117],{},[32,49436,49437,49439,49441],{},[35,49438,44754],{},[110,49440,4813],{},[115,49442,117],{},[35,49444,4100],{},[110,49446,4103],{},[110,49448,1287],{},[6814,49450,49451,49453],{},[35,49452,11],{},[35,49454,44754],{},[6814,49456,49457,49459],{},[35,49458,944],{},[32,49460,49461,49463,49465],{},[115,49462,117],{},[110,49464,4813],{},[35,49466,44754],{},[1297,49468,1299],{},[35,49470,244],{},[35,49472,774],{},[110,49474,551],{"separator":46},[1249,49476,49477,49483],{},[1252,49478,49479],{},[1255,49480,49481],{"scriptlevel":126,"displaystyle":46},[32,49482],{},[1252,49484,49485],{},[1255,49486,49487],{"scriptlevel":126,"displaystyle":46},[32,49488,49489,49491,49493,49495,49497,49499,49501,49503,49505,49508],{},[32,49490],{},[157,49492],{"width":3262},[35,49494,44754],{},[110,49496,2903],{},[115,49498,126],{},[110,49500,551],{"separator":46},[1297,49502,4283],{},[35,49504,44754],{},[110,49506,49507],{"mathvariant":209},"≠",[115,49509,49510],{},"1.",[39,49512,49513],{"encoding":41},"\\begin{aligned}\nD^{R}_{\\alpha}(P\\|Q)\n&=\\frac{1}{\\alpha-1}\n\\log\\int p^{\\alpha}q^{1-\\alpha}\\,dx,\\\\[2pt]\n&\\qquad \\alpha>0,\\ \\alpha\\ne1 .\n\\end{aligned}",[15,49515,49517],{"className":49516,"ariaHidden":46},[45],[15,49518,49520,49524],{"className":49519},[50],[15,49521],{"className":49522,"style":49523},[54],"height:3.7223em;vertical-align:-1.6111em;",[15,49525,49527],{"className":49526},[59],[15,49528,49530,49647],{"className":49529},[1243],[15,49531,49533],{"className":49532},[1360],[15,49534,49536,49638],{"className":49535},[285,286],[15,49537,49539,49635],{"className":49538},[290],[15,49540,49543,49626],{"className":49541,"style":49542},[294],"height:2.1111em;",[15,49544,49546,49549],{"style":49545},"top:-4.1111em;",[15,49547],{"className":49548,"style":6273},[302],[15,49550,49552,49611,49614,49617,49620,49623],{"className":49551},[59],[15,49553,49555,49558],{"className":49554},[59],[15,49556,199],{"className":49557,"style":277},[59,60],[15,49559,49561],{"className":49560},[281],[15,49562,49564,49603],{"className":49563},[285,286],[15,49565,49567,49600],{"className":49566},[290],[15,49568,49570,49585],{"className":49569,"style":38512},[294],[15,49571,49573,49576],{"style":49572},"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;",[15,49574],{"className":49575,"style":303},[302],[15,49577,49579],{"className":49578},[307,308,309,310],[15,49580,49582],{"className":49581},[59,310],[15,49583,44754],{"className":49584,"style":44784},[59,60,310],[15,49586,49587,49590],{"style":8277},[15,49588],{"className":49589,"style":303},[302],[15,49591,49593],{"className":49592},[307,308,309,310],[15,49594,49596],{"className":49595},[59,310],[15,49597,1032],{"className":49598,"style":49599},[59,60,310],"margin-right:0.0077em;",[15,49601,318],{"className":49602},[317],[15,49604,49606],{"className":49605},[290],[15,49607,49609],{"className":49608,"style":8299},[294],[15,49610],{},[15,49612,113],{"className":49613},[146],[15,49615,206],{"className":49616,"style":334},[59,60],[15,49618,210],{"className":49619},[59],[15,49621,213],{"className":49622},[59,60],[15,49624,120],{"className":49625},[153],[15,49627,49629,49632],{"style":49628},"top:-2.1089em;",[15,49630],{"className":49631,"style":6273},[302],[15,49633],{"className":49634},[59],[15,49636,318],{"className":49637},[317],[15,49639,49641],{"className":49640},[290],[15,49642,49645],{"className":49643,"style":49644},[294],"height:1.6111em;",[15,49646],{},[15,49648,49650],{"className":49649},[1451],[15,49651,49653,49941],{"className":49652},[285,286],[15,49654,49656,49938],{"className":49655},[290],[15,49657,49659,49852],{"className":49658,"style":49542},[294],[15,49660,49661,49664],{"style":49545},[15,49662],{"className":49663,"style":6273},[302],[15,49665,49667,49670,49673,49676,49679,49753,49756,49761,49764,49767,49770,49802,49840,49843,49846,49849],{"className":49666},[59],[15,49668],{"className":49669},[59],[15,49671],{"className":49672,"style":158},[157],[15,49674,123],{"className":49675},[162],[15,49677],{"className":49678,"style":158},[157],[15,49680,49682,49685,49750],{"className":49681},[59],[15,49683],{"className":49684},[146,441],[15,49686,49688],{"className":49687},[238],[15,49689,49691,49742],{"className":49690},[285,286],[15,49692,49694,49739],{"className":49693},[290],[15,49695,49697,49720,49728],{"className":49696,"style":22889},[294],[15,49698,49699,49702],{"style":457},[15,49700],{"className":49701,"style":461},[302],[15,49703,49705,49708,49711,49714,49717],{"className":49704},[59],[15,49706,44754],{"className":49707,"style":44784},[59,60],[15,49709],{"className":49710,"style":2587},[157],[15,49712,4813],{"className":49713},[2591],[15,49715],{"className":49716,"style":2587},[157],[15,49718,117],{"className":49719},[59],[15,49721,49722,49725],{"style":473},[15,49723],{"className":49724,"style":461},[302],[15,49726],{"className":49727,"style":481},[480],[15,49729,49730,49733],{"style":484},[15,49731],{"className":49732,"style":461},[302],[15,49734,49736],{"className":49735},[59],[15,49737,117],{"className":49738},[59],[15,49740,318],{"className":49741},[317],[15,49743,49745],{"className":49744},[290],[15,49746,49748],{"className":49747,"style":17015},[294],[15,49749],{},[15,49751],{"className":49752},[153,441],[15,49754],{"className":49755,"style":406},[157],[15,49757,4154,49759],{"className":49758},[1484],[15,49760,4158],{"style":4157},[15,49762],{"className":49763,"style":406},[157],[15,49765,1287],{"className":49766,"style":1487},[1484,1485,1486],[15,49768],{"className":49769,"style":406},[157],[15,49771,49773,49776],{"className":49772},[59],[15,49774,11],{"className":49775},[59,60],[15,49777,49779],{"className":49778},[281],[15,49780,49782],{"className":49781},[285],[15,49783,49785],{"className":49784},[290],[15,49786,49788],{"className":49787,"style":45911},[294],[15,49789,49790,49793],{"style":8277},[15,49791],{"className":49792,"style":303},[302],[15,49794,49796],{"className":49795},[307,308,309,310],[15,49797,49799],{"className":49798},[59,310],[15,49800,44754],{"className":49801,"style":44784},[59,60,310],[15,49803,49805,49808],{"className":49804},[59],[15,49806,944],{"className":49807,"style":981},[59,60],[15,49809,49811],{"className":49810},[281],[15,49812,49814],{"className":49813},[285],[15,49815,49817],{"className":49816},[290],[15,49818,49820],{"className":49819,"style":19735},[294],[15,49821,49822,49825],{"style":8277},[15,49823],{"className":49824,"style":303},[302],[15,49826,49828],{"className":49827},[307,308,309,310],[15,49829,49831,49834,49837],{"className":49830},[59,310],[15,49832,117],{"className":49833},[59,310],[15,49835,4813],{"className":49836},[2591,310],[15,49838,44754],{"className":49839,"style":44784},[59,60,310],[15,49841],{"className":49842,"style":406},[157],[15,49844,244],{"className":49845},[59,60],[15,49847,774],{"className":49848},[59,60],[15,49850,551],{"className":49851},[573],[15,49853,49854,49857],{"style":49628},[15,49855],{"className":49856,"style":6273},[302],[15,49858,49860,49863,49866,49869,49872,49875,49878,49881,49884,49887,49890,49893,49896,49932,49935],{"className":49859},[59],[15,49861],{"className":49862},[59],[15,49864],{"className":49865,"style":3634},[157],[15,49867,44754],{"className":49868,"style":44784},[59,60],[15,49870],{"className":49871,"style":158},[157],[15,49873,2903],{"className":49874},[162],[15,49876],{"className":49877,"style":158},[157],[15,49879,126],{"className":49880},[59],[15,49882,551],{"className":49883},[573],[15,49885,4283],{"className":49886},[157],[15,49888],{"className":49889,"style":406},[157],[15,49891,44754],{"className":49892,"style":44784},[59,60],[15,49894],{"className":49895,"style":158},[157],[15,49897,49899,49926,49929],{"className":49898},[162],[15,49900,49902],{"className":49901},[162],[15,49903,49905],{"className":49904},[59,4400],[15,49906,49908],{"className":49907},[4404],[15,49909,49911,49914,49923],{"className":49910},[4408],[15,49912],{"className":49913,"style":55},[54],[15,49915,49917],{"className":49916},[4415],[15,49918,49920],{"className":49919},[59],[15,49921,4422],{"className":49922},[162],[15,49924],{"className":49925},[4426],[15,49927],{"className":49928},[157,4430],[15,49930,123],{"className":49931},[162],[15,49933],{"className":49934,"style":158},[157],[15,49936,49510],{"className":49937},[59],[15,49939,318],{"className":49940},[317],[15,49942,49944],{"className":49943},[290],[15,49945,49947],{"className":49946,"style":49644},[294],[15,49948],{},[11,49950,49951,49952,49984,49985,50036,50037,50213,50214,50415],{},"它不是（直接的）f-散度，因为 ",[15,49953,49955,49970],{"className":49954,"translate":19},[18],[15,49956,49958],{"className":49957},[23],[25,49959,49960],{"xmlns":27},[29,49961,49962,49968],{},[32,49963,49964,49966],{},[35,49965,4100],{},[110,49967,4103],{},[39,49969,21583],{"encoding":41},[15,49971,49973],{"className":49972,"ariaHidden":46},[45],[15,49974,49976,49979],{"className":49975},[50],[15,49977],{"className":49978,"style":55},[54],[15,49980,4154,49982],{"className":49981},[1484],[15,49983,4158],{"style":4157}," 包在积分外面（这正是它满足可乘可加性、但一般不满足数据处理不等式的根源：",[15,49986,49988,50006],{"className":49987,"translate":19},[18],[15,49989,49991],{"className":49990},[23],[25,49992,49993],{"xmlns":27},[29,49994,49995,50003],{},[32,49996,49997,49999,50001],{},[35,49998,44754],{},[110,50000,2903],{},[115,50002,117],{},[39,50004,50005],{"encoding":41},"\\alpha>1",[15,50007,50009,50027],{"className":50008,"ariaHidden":46},[45],[15,50010,50012,50015,50018,50021,50024],{"className":50011},[50],[15,50013],{"className":50014,"style":5924},[54],[15,50016,44754],{"className":50017,"style":44784},[59,60],[15,50019],{"className":50020,"style":158},[157],[15,50022,2903],{"className":50023},[162],[15,50025],{"className":50026,"style":158},[157],[15,50028,50030,50033],{"className":50029},[50],[15,50031],{"className":50032,"style":172},[54],[15,50034,117],{"className":50035},[59]," 的 Rényi 散度可以在随机变换下增大）。它与 α-散度是\"同一积分的两种包装\"：沿用 3.6 节的指数记号 ",[15,50038,50040,50079],{"className":50039,"translate":19},[18],[15,50041,50043],{"className":50042},[23],[25,50044,50045],{"xmlns":27},[29,50046,50047,50077],{},[32,50048,50049,50051,50053,50065,50067,50069,50071,50073,50075],{},[35,50050,45180],{},[110,50052,123],{},[238,50054,50055,50063],{},[32,50056,50057,50059,50061],{},[115,50058,117],{},[110,50060,2470],{},[35,50062,44754],{},[115,50064,2463],{},[110,50066,5909],{},[110,50068,113],{"stretchy":112},[115,50070,126],{},[110,50072,551],{"separator":46},[115,50074,117],{},[110,50076,120],{"stretchy":112},[39,50078,45209],{"encoding":41},[15,50080,50082,50100,50189],{"className":50081,"ariaHidden":46},[45],[15,50083,50085,50088,50091,50094,50097],{"className":50084},[50],[15,50086],{"className":50087,"style":2345},[54],[15,50089,45180],{"className":50090},[59,60],[15,50092],{"className":50093,"style":158},[157],[15,50095,123],{"className":50096},[162],[15,50098],{"className":50099,"style":158},[157],[15,50101,50103,50106,50180,50183,50186],{"className":50102},[50],[15,50104],{"className":50105,"style":2505},[54],[15,50107,50109,50112,50177],{"className":50108},[59],[15,50110],{"className":50111},[146,441],[15,50113,50115],{"className":50114},[238],[15,50116,50118,50169],{"className":50117},[285,286],[15,50119,50121,50166],{"className":50120},[290],[15,50122,50124,50138,50146],{"className":50123,"style":2524},[294],[15,50125,50126,50129],{"style":2527},[15,50127],{"className":50128,"style":461},[302],[15,50130,50132],{"className":50131},[307,308,309,310],[15,50133,50135],{"className":50134},[59,310],[15,50136,2463],{"className":50137},[59,310],[15,50139,50140,50143],{"style":473},[15,50141],{"className":50142,"style":461},[302],[15,50144],{"className":50145,"style":481},[480],[15,50147,50148,50151],{"style":2550},[15,50149],{"className":50150,"style":461},[302],[15,50152,50154],{"className":50153},[307,308,309,310],[15,50155,50157,50160,50163],{"className":50156},[59,310],[15,50158,117],{"className":50159},[59,310],[15,50161,2470],{"className":50162},[2591,310],[15,50164,44754],{"className":50165,"style":44784},[59,60,310],[15,50167,318],{"className":50168},[317],[15,50170,50172],{"className":50171},[290],[15,50173,50175],{"className":50174,"style":2572},[294],[15,50176],{},[15,50178],{"className":50179},[153,441],[15,50181],{"className":50182,"style":158},[157],[15,50184,5909],{"className":50185},[162],[15,50187],{"className":50188,"style":158},[157],[15,50190,50192,50195,50198,50201,50204,50207,50210],{"className":50191},[50],[15,50193],{"className":50194,"style":139},[54],[15,50196,113],{"className":50197},[146],[15,50199,126],{"className":50200},[59],[15,50202,551],{"className":50203},[573],[15,50205],{"className":50206,"style":406},[157],[15,50208,117],{"className":50209},[59],[15,50211,120],{"className":50212},[153],"， ",[15,50215,50217,50263],{"className":50216,"translate":19},[18],[15,50218,50220],{"className":50219},[23],[25,50221,50222],{"xmlns":27},[29,50223,50224,50260],{},[32,50225,50226,50232,50234,50236,50242,50254,50256,50258],{},[195,50227,50228,50230],{},[35,50229,33603],{},[35,50231,45180],{},[110,50233,123],{},[110,50235,1287],{},[6814,50237,50238,50240],{},[35,50239,11],{},[35,50241,45180],{},[6814,50243,50244,50246],{},[35,50245,944],{},[32,50247,50248,50250,50252],{},[115,50249,117],{},[110,50251,4813],{},[35,50253,45180],{},[1297,50255,1299],{},[35,50257,244],{},[35,50259,774],{},[39,50261,50262],{"encoding":41},"Z_a=\\int p^{a}q^{1-a}\\,dx",[15,50264,50266,50322],{"className":50265,"ariaHidden":46},[45],[15,50267,50269,50272,50313,50316,50319],{"className":50268},[50],[15,50270],{"className":50271,"style":15961},[54],[15,50273,50275,50278],{"className":50274},[59],[15,50276,33603],{"className":50277,"style":10782},[59,60],[15,50279,50281],{"className":50280},[281],[15,50282,50284,50305],{"className":50283},[285,286],[15,50285,50287,50302],{"className":50286},[290],[15,50288,50290],{"className":50289,"style":44929},[294],[15,50291,50293,50296],{"style":50292},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[15,50294],{"className":50295,"style":303},[302],[15,50297,50299],{"className":50298},[307,308,309,310],[15,50300,45180],{"className":50301},[59,60,310],[15,50303,318],{"className":50304},[317],[15,50306,50308],{"className":50307},[290],[15,50309,50311],{"className":50310,"style":7968},[294],[15,50312],{},[15,50314],{"className":50315,"style":158},[157],[15,50317,123],{"className":50318},[162],[15,50320],{"className":50321,"style":158},[157],[15,50323,50325,50329,50332,50335,50368,50406,50409,50412],{"className":50324},[50],[15,50326],{"className":50327,"style":50328},[54],"height:1.1202em;vertical-align:-0.3061em;",[15,50330,1287],{"className":50331,"style":5617},[1484,1485,5616],[15,50333],{"className":50334,"style":406},[157],[15,50336,50338,50341],{"className":50337},[59],[15,50339,11],{"className":50340},[59,60],[15,50342,50344],{"className":50343},[281],[15,50345,50347],{"className":50346},[285],[15,50348,50350],{"className":50349},[290],[15,50351,50354],{"className":50352,"style":50353},[294],"height:0.6644em;",[15,50355,50356,50359],{"style":6865},[15,50357],{"className":50358,"style":303},[302],[15,50360,50362],{"className":50361},[307,308,309,310],[15,50363,50365],{"className":50364},[59,310],[15,50366,45180],{"className":50367},[59,60,310],[15,50369,50371,50374],{"className":50370},[59],[15,50372,944],{"className":50373,"style":981},[59,60],[15,50375,50377],{"className":50376},[281],[15,50378,50380],{"className":50379},[285],[15,50381,50383],{"className":50382},[290],[15,50384,50386],{"className":50385,"style":20028},[294],[15,50387,50388,50391],{"style":6865},[15,50389],{"className":50390,"style":303},[302],[15,50392,50394],{"className":50393},[307,308,309,310],[15,50395,50397,50400,50403],{"className":50396},[59,310],[15,50398,117],{"className":50399},[59,310],[15,50401,4813],{"className":50402},[2591,310],[15,50404,45180],{"className":50405},[59,60,310],[15,50407],{"className":50408,"style":406},[157],[15,50410,244],{"className":50411},[59,60],[15,50413,774],{"className":50414},[59,60],"，则 3.6 节给出",[15,50417,50419],{"className":50418,"translate":19},[180],[15,50420,50422,50468],{"className":50421,"translate":19},[18],[15,50423,50425],{"className":50424},[23],[25,50426,50427],{"xmlns":27,"display":189},[29,50428,50429,50465],{},[32,50430,50431,50437,50439,50441,50443,50445,50447,50449,50451,50453,50455,50457,50463],{},[195,50432,50433,50435],{},[35,50434,33603],{},[35,50436,45180],{},[110,50438,123],{},[115,50440,117],{},[110,50442,4813],{},[35,50444,45180],{},[110,50446,113],{"stretchy":112},[115,50448,117],{},[110,50450,4813],{},[35,50452,45180],{},[110,50454,120],{"stretchy":112},[1297,50456,1299],{},[195,50458,50459,50461],{},[35,50460,199],{},[35,50462,44754],{},[110,50464,551],{"separator":46},[39,50466,50467],{"encoding":41},"Z_a=1-a(1-a)\\,D_\\alpha ,",[15,50469,50471,50526,50544,50568],{"className":50470,"ariaHidden":46},[45],[15,50472,50474,50477,50517,50520,50523],{"className":50473},[50],[15,50475],{"className":50476,"style":15961},[54],[15,50478,50480,50483],{"className":50479},[59],[15,50481,33603],{"className":50482,"style":10782},[59,60],[15,50484,50486],{"className":50485},[281],[15,50487,50489,50509],{"className":50488},[285,286],[15,50490,50492,50506],{"className":50491},[290],[15,50493,50495],{"className":50494,"style":44929},[294],[15,50496,50497,50500],{"style":50292},[15,50498],{"className":50499,"style":303},[302],[15,50501,50503],{"className":50502},[307,308,309,310],[15,50504,45180],{"className":50505},[59,60,310],[15,50507,318],{"className":50508},[317],[15,50510,50512],{"className":50511},[290],[15,50513,50515],{"className":50514,"style":7968},[294],[15,50516],{},[15,50518],{"className":50519,"style":158},[157],[15,50521,123],{"className":50522},[162],[15,50524],{"className":50525,"style":158},[157],[15,50527,50529,50532,50535,50538,50541],{"className":50528},[50],[15,50530],{"className":50531,"style":12578},[54],[15,50533,117],{"className":50534},[59],[15,50536],{"className":50537,"style":2587},[157],[15,50539,4813],{"className":50540},[2591],[15,50542],{"className":50543,"style":2587},[157],[15,50545,50547,50550,50553,50556,50559,50562,50565],{"className":50546},[50],[15,50548],{"className":50549,"style":139},[54],[15,50551,45180],{"className":50552},[59,60],[15,50554,113],{"className":50555},[146],[15,50557,117],{"className":50558},[59],[15,50560],{"className":50561,"style":2587},[157],[15,50563,4813],{"className":50564},[2591],[15,50566],{"className":50567,"style":2587},[157],[15,50569,50571,50574,50577,50580,50583,50623],{"className":50570},[50],[15,50572],{"className":50573,"style":139},[54],[15,50575,45180],{"className":50576},[59,60],[15,50578,120],{"className":50579},[153],[15,50581],{"className":50582,"style":406},[157],[15,50584,50586,50589],{"className":50585},[59],[15,50587,199],{"className":50588,"style":277},[59,60],[15,50590,50592],{"className":50591},[281],[15,50593,50595,50615],{"className":50594},[285,286],[15,50596,50598,50612],{"className":50597},[290],[15,50599,50601],{"className":50600,"style":44929},[294],[15,50602,50603,50606],{"style":298},[15,50604],{"className":50605,"style":303},[302],[15,50607,50609],{"className":50608},[307,308,309,310],[15,50610,44754],{"className":50611,"style":44784},[59,60,310],[15,50613,318],{"className":50614},[317],[15,50616,50618],{"className":50617},[290],[15,50619,50621],{"className":50620,"style":7968},[294],[15,50622],{},[15,50624,551],{"className":50625},[573],[11,50627,50628,50629,50632,50633,50661,50662,50724,50725,50753],{},"而把 Rényi 的",[1225,50630,50631],{},"阶数","取为 ",[15,50634,50636,50649],{"className":50635,"translate":19},[18],[15,50637,50639],{"className":50638},[23],[25,50640,50641],{"xmlns":27},[29,50642,50643,50647],{},[32,50644,50645],{},[35,50646,45180],{},[39,50648,45180],{"encoding":41},[15,50650,50652],{"className":50651,"ariaHidden":46},[45],[15,50653,50655,50658],{"className":50654},[50],[15,50656],{"className":50657,"style":2345},[54],[15,50659,45180],{"className":50660},[59,60],"（注意 order ",[15,50663,50665,50679],{"className":50664,"translate":19},[18],[15,50666,50668],{"className":50667},[23],[25,50669,50670],{"xmlns":27},[29,50671,50672,50676],{},[32,50673,50674],{},[110,50675,49507],{"mathvariant":209},[39,50677,50678],{"encoding":41},"\\neq",[15,50680,50682],{"className":50681,"ariaHidden":46},[45],[15,50683,50685,50688],{"className":50684},[50],[15,50686],{"className":50687,"style":55},[54],[15,50689,50691,50718,50721],{"className":50690},[162],[15,50692,50694],{"className":50693},[162],[15,50695,50697],{"className":50696},[59,4400],[15,50698,50700],{"className":50699},[4404],[15,50701,50703,50706,50715],{"className":50702},[4408],[15,50704],{"className":50705,"style":55},[54],[15,50707,50709],{"className":50708},[4415],[15,50710,50712],{"className":50711},[59],[15,50713,4422],{"className":50714},[162],[15,50716],{"className":50717},[4426],[15,50719],{"className":50720},[157,4430],[15,50722,123],{"className":50723},[162]," 3.6 的参数 ",[15,50726,50728,50741],{"className":50727,"translate":19},[18],[15,50729,50731],{"className":50730},[23],[25,50732,50733],{"xmlns":27},[29,50734,50735,50739],{},[32,50736,50737],{},[35,50738,44754],{},[39,50740,49090],{"encoding":41},[15,50742,50744],{"className":50743,"ariaHidden":46},[45],[15,50745,50747,50750],{"className":50746},[50],[15,50748],{"className":50749,"style":2345},[54],[15,50751,44754],{"className":50752,"style":44784},[59,60],"，只是经过线性换算）：",[15,50755,50757],{"className":50756,"translate":19},[180],[15,50758,50760,50864],{"className":50759,"translate":19},[18],[15,50761,50763],{"className":50762},[23],[25,50764,50765],{"xmlns":27,"display":189},[29,50766,50767,50861],{},[32,50768,50769,50777,50779,50781,50783,50785,50787,50789,50801,50803,50805,50811,50813,50815,50827,50829,50831,50833,50835,50837,50839,50841,50843,50845,50847,50849,50851,50857,50859],{},[7553,50770,50771,50773,50775],{},[35,50772,199],{},[35,50774,45180],{},[35,50776,1032],{},[110,50778,113],{"stretchy":112},[35,50780,206],{},[35,50782,210],{"mathvariant":209},[35,50784,213],{},[110,50786,120],{"stretchy":112},[110,50788,123],{},[238,50790,50791,50793],{},[115,50792,117],{},[32,50794,50795,50797,50799],{},[35,50796,45180],{},[110,50798,4813],{},[115,50800,117],{},[35,50802,4100],{},[110,50804,4103],{},[195,50806,50807,50809],{},[35,50808,33603],{},[35,50810,45180],{},[110,50812,123],{},[110,50814,4813],{},[238,50816,50817,50819],{},[115,50818,117],{},[32,50820,50821,50823,50825],{},[115,50822,117],{},[110,50824,4813],{},[35,50826,45180],{},[1297,50828,1299],{},[35,50830,4100],{},[110,50832,4103],{},[110,50834,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,50836,117],{},[110,50838,4813],{},[35,50840,45180],{},[110,50842,113],{"stretchy":112},[115,50844,117],{},[110,50846,4813],{},[35,50848,45180],{},[110,50850,120],{"stretchy":112},[195,50852,50853,50855],{},[35,50854,199],{},[35,50856,44754],{},[110,50858,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,50860,4375],{"mathvariant":209},[39,50862,50863],{"encoding":41},"D^{R}_{a}(P\\|Q)=\\frac{1}{a-1}\\log Z_a\n=-\\frac{1}{1-a}\\,\\log\\big(1-a(1-a)D_\\alpha\\big).",[15,50865,50867,50955,51095,51210,51234],{"className":50866,"ariaHidden":46},[45],[15,50868,50870,50874,50931,50934,50937,50940,50943,50946,50949,50952],{"className":50869},[50],[15,50871],{"className":50872,"style":50873},[54],"height:1.1413em;vertical-align:-0.25em;",[15,50875,50877,50880],{"className":50876},[59],[15,50878,199],{"className":50879,"style":277},[59,60],[15,50881,50883],{"className":50882},[281],[15,50884,50886,50923],{"className":50885},[285,286],[15,50887,50889,50920],{"className":50888},[290],[15,50890,50892,50906],{"className":50891,"style":38512},[294],[15,50893,50894,50897],{"style":49572},[15,50895],{"className":50896,"style":303},[302],[15,50898,50900],{"className":50899},[307,308,309,310],[15,50901,50903],{"className":50902},[59,310],[15,50904,45180],{"className":50905},[59,60,310],[15,50907,50908,50911],{"style":8277},[15,50909],{"className":50910,"style":303},[302],[15,50912,50914],{"className":50913},[307,308,309,310],[15,50915,50917],{"className":50916},[59,310],[15,50918,1032],{"className":50919,"style":49599},[59,60,310],[15,50921,318],{"className":50922},[317],[15,50924,50926],{"className":50925},[290],[15,50927,50929],{"className":50928,"style":8299},[294],[15,50930],{},[15,50932,113],{"className":50933},[146],[15,50935,206],{"className":50936,"style":334},[59,60],[15,50938,210],{"className":50939},[59],[15,50941,213],{"className":50942},[59,60],[15,50944,120],{"className":50945},[153],[15,50947],{"className":50948,"style":158},[157],[15,50950,123],{"className":50951},[162],[15,50953],{"className":50954,"style":158},[157],[15,50956,50958,50961,51035,51038,51043,51046,51086,51089,51092],{"className":50957},[50],[15,50959],{"className":50960,"style":26616},[54],[15,50962,50964,50967,51032],{"className":50963},[59],[15,50965],{"className":50966},[146,441],[15,50968,50970],{"className":50969},[238],[15,50971,50973,51024],{"className":50972},[285,286],[15,50974,50976,51021],{"className":50975},[290],[15,50977,50979,51002,51010],{"className":50978,"style":22889},[294],[15,50980,50981,50984],{"style":457},[15,50982],{"className":50983,"style":461},[302],[15,50985,50987,50990,50993,50996,50999],{"className":50986},[59],[15,50988,45180],{"className":50989},[59,60],[15,50991],{"className":50992,"style":2587},[157],[15,50994,4813],{"className":50995},[2591],[15,50997],{"className":50998,"style":2587},[157],[15,51000,117],{"className":51001},[59],[15,51003,51004,51007],{"style":473},[15,51005],{"className":51006,"style":461},[302],[15,51008],{"className":51009,"style":481},[480],[15,51011,51012,51015],{"style":484},[15,51013],{"className":51014,"style":461},[302],[15,51016,51018],{"className":51017},[59],[15,51019,117],{"className":51020},[59],[15,51022,318],{"className":51023},[317],[15,51025,51027],{"className":51026},[290],[15,51028,51030],{"className":51029,"style":17015},[294],[15,51031],{},[15,51033],{"className":51034},[153,441],[15,51036],{"className":51037,"style":406},[157],[15,51039,4154,51041],{"className":51040},[1484],[15,51042,4158],{"style":4157},[15,51044],{"className":51045,"style":406},[157],[15,51047,51049,51052],{"className":51048},[59],[15,51050,33603],{"className":51051,"style":10782},[59,60],[15,51053,51055],{"className":51054},[281],[15,51056,51058,51078],{"className":51057},[285,286],[15,51059,51061,51075],{"className":51060},[290],[15,51062,51064],{"className":51063,"style":44929},[294],[15,51065,51066,51069],{"style":50292},[15,51067],{"className":51068,"style":303},[302],[15,51070,51072],{"className":51071},[307,308,309,310],[15,51073,45180],{"className":51074},[59,60,310],[15,51076,318],{"className":51077},[317],[15,51079,51081],{"className":51080},[290],[15,51082,51084],{"className":51083,"style":7968},[294],[15,51085],{},[15,51087],{"className":51088,"style":158},[157],[15,51090,123],{"className":51091},[162],[15,51093],{"className":51094,"style":158},[157],[15,51096,51098,51101,51104,51178,51181,51184,51189,51192,51198,51201,51204,51207],{"className":51097},[50],[15,51099],{"className":51100,"style":26616},[54],[15,51102,4813],{"className":51103},[59],[15,51105,51107,51110,51175],{"className":51106},[59],[15,51108],{"className":51109},[146,441],[15,51111,51113],{"className":51112},[238],[15,51114,51116,51167],{"className":51115},[285,286],[15,51117,51119,51164],{"className":51118},[290],[15,51120,51122,51145,51153],{"className":51121,"style":22889},[294],[15,51123,51124,51127],{"style":457},[15,51125],{"className":51126,"style":461},[302],[15,51128,51130,51133,51136,51139,51142],{"className":51129},[59],[15,51131,117],{"className":51132},[59],[15,51134],{"className":51135,"style":2587},[157],[15,51137,4813],{"className":51138},[2591],[15,51140],{"className":51141,"style":2587},[157],[15,51143,45180],{"className":51144},[59,60],[15,51146,51147,51150],{"style":473},[15,51148],{"className":51149,"style":461},[302],[15,51151],{"className":51152,"style":481},[480],[15,51154,51155,51158],{"style":484},[15,51156],{"className":51157,"style":461},[302],[15,51159,51161],{"className":51160},[59],[15,51162,117],{"className":51163},[59],[15,51165,318],{"className":51166},[317],[15,51168,51170],{"className":51169},[290],[15,51171,51173],{"className":51172,"style":17015},[294],[15,51174],{},[15,51176],{"className":51177},[153,441],[15,51179],{"className":51180,"style":406},[157],[15,51182],{"className":51183,"style":406},[157],[15,51185,4154,51187],{"className":51186},[1484],[15,51188,4158],{"style":4157},[15,51190],{"className":51191,"style":406},[157],[15,51193,51195],{"className":51194},[59],[15,51196,113],{"className":51197},[419,9674],[15,51199,117],{"className":51200},[59],[15,51202],{"className":51203,"style":2587},[157],[15,51205,4813],{"className":51206},[2591],[15,51208],{"className":51209,"style":2587},[157],[15,51211,51213,51216,51219,51222,51225,51228,51231],{"className":51212},[50],[15,51214],{"className":51215,"style":139},[54],[15,51217,45180],{"className":51218},[59,60],[15,51220,113],{"className":51221},[146],[15,51223,117],{"className":51224},[59],[15,51226],{"className":51227,"style":2587},[157],[15,51229,4813],{"className":51230},[2591],[15,51232],{"className":51233,"style":2587},[157],[15,51235,51237,51240,51243,51246,51286,51292],{"className":51236},[50],[15,51238],{"className":51239,"style":20563},[54],[15,51241,45180],{"className":51242},[59,60],[15,51244,120],{"className":51245},[153],[15,51247,51249,51252],{"className":51248},[59],[15,51250,199],{"className":51251,"style":277},[59,60],[15,51253,51255],{"className":51254},[281],[15,51256,51258,51278],{"className":51257},[285,286],[15,51259,51261,51275],{"className":51260},[290],[15,51262,51264],{"className":51263,"style":44929},[294],[15,51265,51266,51269],{"style":298},[15,51267],{"className":51268,"style":303},[302],[15,51270,51272],{"className":51271},[307,308,309,310],[15,51273,44754],{"className":51274,"style":44784},[59,60,310],[15,51276,318],{"className":51277},[317],[15,51279,51281],{"className":51280},[290],[15,51282,51284],{"className":51283,"style":7968},[294],[15,51285],{},[15,51287,51289],{"className":51288},[59],[15,51290,120],{"className":51291},[419,9674],[15,51293,4375],{"className":51294},[59],[11,51296,51297,51298,51445,51446,51474,51475,51507],{},"这说明两者是一条\"幂—对数\"的两级包装链：f-散度是对似然比幂 ",[15,51299,51301,51327],{"className":51300,"translate":19},[18],[15,51302,51304],{"className":51303},[23],[25,51305,51306],{"xmlns":27},[29,51307,51308,51324],{},[32,51309,51310,51312,51318],{},[110,51311,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[238,51313,51314,51316],{},[35,51315,11],{},[35,51317,944],{},[6814,51319,51320,51322],{},[110,51321,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,51323,45180],{},[39,51325,51326],{"encoding":41},"\\big(\\frac pq\\big)^a",[15,51328,51330],{"className":51329,"ariaHidden":46},[45],[15,51331,51333,51337,51343,51411],{"className":51332},[50],[15,51334],{"className":51335,"style":51336},[54],"height:1.3854em;vertical-align:-0.4811em;",[15,51338,51340],{"className":51339},[59],[15,51341,113],{"className":51342},[419,9674],[15,51344,51346,51349,51408],{"className":51345},[59],[15,51347],{"className":51348},[146,441],[15,51350,51352],{"className":51351},[238],[15,51353,51355,51400],{"className":51354},[285,286],[15,51356,51358,51397],{"className":51357},[290],[15,51359,51361,51375,51383],{"className":51360,"style":3103},[294],[15,51362,51363,51366],{"style":2527},[15,51364],{"className":51365,"style":461},[302],[15,51367,51369],{"className":51368},[307,308,309,310],[15,51370,51372],{"className":51371},[59,310],[15,51373,944],{"className":51374,"style":981},[59,60,310],[15,51376,51377,51380],{"style":473},[15,51378],{"className":51379,"style":461},[302],[15,51381],{"className":51382,"style":481},[480],[15,51384,51385,51388],{"style":2853},[15,51386],{"className":51387,"style":461},[302],[15,51389,51391],{"className":51390},[307,308,309,310],[15,51392,51394],{"className":51393},[59,310],[15,51395,11],{"className":51396},[59,60,310],[15,51398,318],{"className":51399},[317],[15,51401,51403],{"className":51402},[290],[15,51404,51406],{"className":51405,"style":2739},[294],[15,51407],{},[15,51409],{"className":51410},[153,441],[15,51412,51414,51420],{"className":51413},[59],[15,51415,51417],{"className":51416},[59],[15,51418,120],{"className":51419},[419,9674],[15,51421,51423],{"className":51422},[281],[15,51424,51426],{"className":51425},[285],[15,51427,51429],{"className":51428},[290],[15,51430,51433],{"className":51431,"style":51432},[294],"height:0.9043em;",[15,51434,51436,51439],{"style":51435},"top:-3.3029em;margin-right:0.05em;",[15,51437],{"className":51438,"style":303},[302],[15,51440,51442],{"className":51441},[307,308,309,310],[15,51443,45180],{"className":51444},[59,60,310]," 做 ",[15,51447,51449,51462],{"className":51448,"translate":19},[18],[15,51450,51452],{"className":51451},[23],[25,51453,51454],{"xmlns":27},[29,51455,51456,51460],{},[32,51457,51458],{},[35,51459,213],{},[39,51461,213],{"encoding":41},[15,51463,51465],{"className":51464,"ariaHidden":46},[45],[15,51466,51468,51471],{"className":51467},[50],[15,51469],{"className":51470,"style":566},[54],[15,51472,213],{"className":51473},[59,60]," 下的线性平均，Rényi 在外面再套一层对数。所以 f-散度族与 Rényi 族\"同源\"：后者是前者经 ",[15,51476,51478,51493],{"className":51477,"translate":19},[18],[15,51479,51481],{"className":51480},[23],[25,51482,51483],{"xmlns":27},[29,51484,51485,51491],{},[32,51486,51487,51489],{},[35,51488,4100],{},[110,51490,4103],{},[39,51492,21583],{"encoding":41},[15,51494,51496],{"className":51495,"ariaHidden":46},[45],[15,51497,51499,51502],{"className":51498},[50],[15,51500],{"className":51501,"style":55},[54],[15,51503,4154,51505],{"className":51504},[1484],[15,51506,4158],{"style":4157}," 变换后的\"信息量\"版本。",[11,51509,51510,51512,51513,51516],{},[1225,51511,24193],{}," Rényi 散度在",[1225,51514,51515],{},"假设检验","中直接就是误差指数：Chernoff 信息",[15,51518,51520],{"className":51519,"translate":19},[180],[15,51521,51523,51646],{"className":51522,"translate":19},[18],[15,51524,51526],{"className":51525},[23],[25,51527,51528],{"xmlns":27,"display":189},[29,51529,51530,51643],{},[32,51531,51532,51534,51536,51538,51540,51542,51544,51546,51566,51568,51570,51572,51574,51576,51584,51586,51588,51590,51592,51594,51596,51598,51600,51602,51623,51625,51631],{},[35,51533,39294],{},[110,51535,113],{"stretchy":112},[35,51537,206],{},[110,51539,551],{"separator":46},[35,51541,213],{},[110,51543,120],{"stretchy":112},[110,51545,123],{},[6016,51547,51548,51554],{},[32,51549,51550,51552],{},[35,51551,35432],{},[110,51553,4103],{},[32,51555,51556,51558,51560,51562,51564],{},[115,51557,126],{},[110,51559,7251],{},[35,51561,11339],{},[110,51563,7251],{},[115,51565,117],{},[110,51567,113],{"stretchy":112},[115,51569,117],{},[110,51571,4813],{},[35,51573,11339],{},[110,51575,120],{"stretchy":112},[7553,51577,51578,51580,51582],{},[35,51579,199],{},[35,51581,11339],{},[35,51583,1032],{},[110,51585,113],{"stretchy":112},[35,51587,206],{},[35,51589,210],{"mathvariant":209},[35,51591,213],{},[110,51593,120],{"stretchy":112},[110,51595,123],{},[110,51597,4813],{},[35,51599,4100],{},[110,51601,4103],{},[6016,51603,51604,51611],{},[32,51605,51606,51609],{},[35,51607,51608],{},"min",[110,51610,4103],{},[32,51612,51613,51615,51617,51619,51621],{},[115,51614,126],{},[110,51616,9952],{},[35,51618,11339],{},[110,51620,9952],{},[115,51622,117],{},[110,51624,1287],{},[6814,51626,51627,51629],{},[35,51628,11],{},[35,51630,11339],{},[6814,51632,51633,51635],{},[35,51634,944],{},[32,51636,51637,51639,51641],{},[115,51638,117],{},[110,51640,4813],{},[35,51642,11339],{},[39,51644,51645],{"encoding":41},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}\n(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)\n=-\\log\\min_{0\\le\\lambda\\le1}\n\\int p^\\lambda q^{1-\\lambda}",[15,51647,51649,51685,51768,51861],{"className":51648,"ariaHidden":46},[45],[15,51650,51652,51655,51658,51661,51664,51667,51670,51673,51676,51679,51682],{"className":51651},[50],[15,51653],{"className":51654,"style":139},[54],[15,51656,39294],{"className":51657,"style":10782},[59,60],[15,51659,113],{"className":51660},[146],[15,51662,206],{"className":51663,"style":334},[59,60],[15,51665,551],{"className":51666},[573],[15,51668],{"className":51669,"style":406},[157],[15,51671,213],{"className":51672},[59,60],[15,51674,120],{"className":51675},[153],[15,51677],{"className":51678,"style":158},[157],[15,51680,123],{"className":51681},[162],[15,51683],{"className":51684,"style":158},[157],[15,51686,51688,51692,51753,51756,51759,51762,51765],{"className":51687},[50],[15,51689],{"className":51690,"style":51691},[54],"height:1.7239em;vertical-align:-0.9739em;",[15,51693,51695],{"className":51694},[1484,13716],[15,51696,51698,51744],{"className":51697},[285,286],[15,51699,51701,51741],{"className":51700},[290],[15,51702,51704,51731],{"className":51703,"style":2345},[294],[15,51705,51707,51710],{"style":51706},"top:-2.1535em;margin-left:0em;",[15,51708],{"className":51709,"style":461},[302],[15,51711,51713],{"className":51712},[307,308,309,310],[15,51714,51716,51719,51722,51725,51728],{"className":51715},[59,310],[15,51717,126],{"className":51718},[59,310],[15,51720,7251],{"className":51721},[162,310],[15,51723,11339],{"className":51724},[59,60,310],[15,51726,7251],{"className":51727},[162,310],[15,51729,117],{"className":51730},[59,310],[15,51732,51733,51736],{"style":11863},[15,51734],{"className":51735,"style":461},[302],[15,51737,51738],{},[15,51739,35432],{"className":51740},[1484],[15,51742,318],{"className":51743},[317],[15,51745,51747],{"className":51746},[290],[15,51748,51751],{"className":51749,"style":51750},[294],"height:0.9739em;",[15,51752],{},[15,51754,113],{"className":51755},[146],[15,51757,117],{"className":51758},[59],[15,51760],{"className":51761,"style":2587},[157],[15,51763,4813],{"className":51764},[2591],[15,51766],{"className":51767,"style":2587},[157],[15,51769,51771,51774,51777,51780,51837,51840,51843,51846,51849,51852,51855,51858],{"className":51770},[50],[15,51772],{"className":51773,"style":50873},[54],[15,51775,11339],{"className":51776},[59,60],[15,51778,120],{"className":51779},[153],[15,51781,51783,51786],{"className":51782},[59],[15,51784,199],{"className":51785,"style":277},[59,60],[15,51787,51789],{"className":51788},[281],[15,51790,51792,51829],{"className":51791},[285,286],[15,51793,51795,51826],{"className":51794},[290],[15,51796,51798,51812],{"className":51797,"style":38512},[294],[15,51799,51800,51803],{"style":49572},[15,51801],{"className":51802,"style":303},[302],[15,51804,51806],{"className":51805},[307,308,309,310],[15,51807,51809],{"className":51808},[59,310],[15,51810,11339],{"className":51811},[59,60,310],[15,51813,51814,51817],{"style":8277},[15,51815],{"className":51816,"style":303},[302],[15,51818,51820],{"className":51819},[307,308,309,310],[15,51821,51823],{"className":51822},[59,310],[15,51824,1032],{"className":51825,"style":49599},[59,60,310],[15,51827,318],{"className":51828},[317],[15,51830,51832],{"className":51831},[290],[15,51833,51835],{"className":51834,"style":8299},[294],[15,51836],{},[15,51838,113],{"className":51839},[146],[15,51841,206],{"className":51842,"style":334},[59,60],[15,51844,210],{"className":51845},[59],[15,51847,213],{"className":51848},[59,60],[15,51850,120],{"className":51851},[153],[15,51853],{"className":51854,"style":158},[157],[15,51856,123],{"className":51857},[162],[15,51859],{"className":51860,"style":158},[157],[15,51862,51864,51867,51870,51873,51878,51881,51943,51946,51949,51952,51981],{"className":51863},[50],[15,51865],{"className":51866,"style":5777},[54],[15,51868,4813],{"className":51869},[59],[15,51871],{"className":51872,"style":406},[157],[15,51874,4154,51876],{"className":51875},[1484],[15,51877,4158],{"style":4157},[15,51879],{"className":51880,"style":406},[157],[15,51882,51884],{"className":51883},[1484,13716],[15,51885,51887,51934],{"className":51886},[285,286],[15,51888,51890,51931],{"className":51889},[290],[15,51891,51894,51921],{"className":51892,"style":51893},[294],"height:0.6679em;",[15,51895,51897,51900],{"style":51896},"top:-2.3479em;margin-left:0em;",[15,51898],{"className":51899,"style":461},[302],[15,51901,51903],{"className":51902},[307,308,309,310],[15,51904,51906,51909,51912,51915,51918],{"className":51905},[59,310],[15,51907,126],{"className":51908},[59,310],[15,51910,9952],{"className":51911},[162,310],[15,51913,11339],{"className":51914},[59,60,310],[15,51916,9952],{"className":51917},[162,310],[15,51919,117],{"className":51920},[59,310],[15,51922,51923,51926],{"style":11863},[15,51924],{"className":51925,"style":461},[302],[15,51927,51928],{},[15,51929,51608],{"className":51930},[1484],[15,51932,318],{"className":51933},[317],[15,51935,51937],{"className":51936},[290],[15,51938,51941],{"className":51939,"style":51940},[294],"height:0.8473em;",[15,51942],{},[15,51944],{"className":51945,"style":406},[157],[15,51947,1287],{"className":51948,"style":1487},[1484,1485,1486],[15,51950],{"className":51951,"style":406},[157],[15,51953,51955,51958],{"className":51954},[59],[15,51956,11],{"className":51957},[59,60],[15,51959,51961],{"className":51960},[281],[15,51962,51964],{"className":51963},[285],[15,51965,51967],{"className":51966},[290],[15,51968,51970],{"className":51969,"style":47864},[294],[15,51971,51972,51975],{"style":8277},[15,51973],{"className":51974,"style":303},[302],[15,51976,51978],{"className":51977},[307,308,309,310],[15,51979,11339],{"className":51980},[59,60,310],[15,51982,51984,51987],{"className":51983},[59],[15,51985,944],{"className":51986,"style":981},[59,60],[15,51988,51990],{"className":51989},[281],[15,51991,51993],{"className":51992},[285],[15,51994,51996],{"className":51995},[290],[15,51997,51999],{"className":51998,"style":47864},[294],[15,52000,52001,52004],{"style":8277},[15,52002],{"className":52003,"style":303},[302],[15,52005,52007],{"className":52006},[307,308,309,310],[15,52008,52010,52013,52016],{"className":52009},[59,310],[15,52011,117],{"className":52012},[59,310],[15,52014,4813],{"className":52015},[2591,310],[15,52017,11339],{"className":52018},[59,60,310],[11,52020,52021,52022,52188,52189,3853,52260,52310,52311,52362,52363,52482,52483,52486],{},"决定对称检验错误概率的衰减速率，Stein 引理给出的单侧指数则是 ",[15,52023,52025,52057],{"className":52024,"translate":19},[18],[15,52026,52028],{"className":52027},[23],[25,52029,52030],{"xmlns":27},[29,52031,52032,52054],{},[32,52033,52034,52042,52044],{},[7553,52035,52036,52038,52040],{},[35,52037,199],{},[115,52039,117],{},[35,52041,1032],{},[110,52043,123],{},[195,52045,52046,52048],{},[35,52047,199],{},[32,52049,52050,52052],{},[35,52051,10694],{},[35,52053,21893],{},[39,52055,52056],{"encoding":41},"D^{R}_{1}=D_{KL}",[15,52058,52060,52136],{"className":52059,"ariaHidden":46},[45],[15,52061,52063,52067,52127,52130,52133],{"className":52062},[50],[15,52064],{"className":52065,"style":52066},[54],"height:1.0894em;vertical-align:-0.2481em;",[15,52068,52070,52073],{"className":52069},[59],[15,52071,199],{"className":52072,"style":277},[59,60],[15,52074,52076],{"className":52075},[281],[15,52077,52079,52118],{"className":52078},[285,286],[15,52080,52082,52115],{"className":52081},[290],[15,52083,52086,52101],{"className":52084,"style":52085},[294],"height:0.8413em;",[15,52087,52089,52092],{"style":52088},"top:-2.4519em;margin-left:-0.0278em;margin-right:0.05em;",[15,52090],{"className":52091,"style":303},[302],[15,52093,52095],{"className":52094},[307,308,309,310],[15,52096,52098],{"className":52097},[59,310],[15,52099,117],{"className":52100},[59,310],[15,52102,52103,52106],{"style":6865},[15,52104],{"className":52105,"style":303},[302],[15,52107,52109],{"className":52108},[307,308,309,310],[15,52110,52112],{"className":52111},[59,310],[15,52113,1032],{"className":52114,"style":49599},[59,60,310],[15,52116,318],{"className":52117},[317],[15,52119,52121],{"className":52120},[290],[15,52122,52125],{"className":52123,"style":52124},[294],"height:0.2481em;",[15,52126],{},[15,52128],{"className":52129,"style":158},[157],[15,52131,123],{"className":52132},[162],[15,52134],{"className":52135,"style":158},[157],[15,52137,52139,52142],{"className":52138},[50],[15,52140],{"className":52141,"style":15961},[54],[15,52143,52145,52148],{"className":52144},[59],[15,52146,199],{"className":52147,"style":277},[59,60],[15,52149,52151],{"className":52150},[281],[15,52152,52154,52180],{"className":52153},[285,286],[15,52155,52157,52177],{"className":52156},[290],[15,52158,52160],{"className":52159,"style":379},[294],[15,52161,52162,52165],{"style":298},[15,52163],{"className":52164,"style":303},[302],[15,52166,52168],{"className":52167},[307,308,309,310],[15,52169,52171,52174],{"className":52170},[59,310],[15,52172,10694],{"className":52173,"style":10782},[59,60,310],[15,52175,21893],{"className":52176},[59,60,310],[15,52178,318],{"className":52179},[317],[15,52181,52183],{"className":52182},[290],[15,52184,52186],{"className":52185,"style":7968},[294],[15,52187],{},"。对应的 Rényi 熵 ",[15,52190,52192,52210],{"className":52191,"translate":19},[18],[15,52193,52195],{"className":52194},[23],[25,52196,52197],{"xmlns":27},[29,52198,52199,52207],{},[32,52200,52201],{},[195,52202,52203,52205],{},[35,52204,33884],{},[35,52206,44754],{},[39,52208,52209],{"encoding":41},"H_\\alpha",[15,52211,52213],{"className":52212,"ariaHidden":46},[45],[15,52214,52216,52219],{"className":52215},[50],[15,52217],{"className":52218,"style":15961},[54],[15,52220,52222,52225],{"className":52221},[59],[15,52223,33884],{"className":52224,"style":34038},[59,60],[15,52226,52228],{"className":52227},[281],[15,52229,52231,52252],{"className":52230},[285,286],[15,52232,52234,52249],{"className":52233},[290],[15,52235,52237],{"className":52236,"style":44929},[294],[15,52238,52240,52243],{"style":52239},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[15,52241],{"className":52242,"style":303},[302],[15,52244,52246],{"className":52245},[307,308,309,310],[15,52247,44754],{"className":52248,"style":44784},[59,60,310],[15,52250,318],{"className":52251},[317],[15,52253,52255],{"className":52254},[290],[15,52256,52258],{"className":52257,"style":7968},[294],[15,52259],{},[15,52261,52263,52280],{"className":52262,"translate":19},[18],[15,52264,52266],{"className":52265},[23],[25,52267,52268],{"xmlns":27},[29,52269,52270,52278],{},[32,52271,52272,52274,52276],{},[35,52273,44754],{},[110,52275,1029],{},[115,52277,117],{},[39,52279,47215],{"encoding":41},[15,52281,52283,52301],{"className":52282,"ariaHidden":46},[45],[15,52284,52286,52289,52292,52295,52298],{"className":52285},[50],[15,52287],{"className":52288,"style":2345},[54],[15,52290,44754],{"className":52291,"style":44784},[59,60],[15,52293],{"className":52294,"style":158},[157],[15,52296,1029],{"className":52297},[162],[15,52299],{"className":52300,"style":158},[157],[15,52302,52304,52307],{"className":52303},[50],[15,52305],{"className":52306,"style":172},[54],[15,52308,117],{"className":52309},[59]," 时退化为 Shannon 熵、在 ",[15,52312,52314,52332],{"className":52313,"translate":19},[18],[15,52315,52317],{"className":52316},[23],[25,52318,52319],{"xmlns":27},[29,52320,52321,52329],{},[32,52322,52323,52325,52327],{},[35,52324,44754],{},[110,52326,1029],{},[35,52328,1024],{"mathvariant":209},[39,52330,52331],{"encoding":41},"\\alpha\\to\\infty",[15,52333,52335,52353],{"className":52334,"ariaHidden":46},[45],[15,52336,52338,52341,52344,52347,52350],{"className":52337},[50],[15,52339],{"className":52340,"style":2345},[54],[15,52342,44754],{"className":52343,"style":44784},[59,60],[15,52345],{"className":52346,"style":158},[157],[15,52348,1029],{"className":52349},[162],[15,52351],{"className":52352,"style":158},[157],[15,52354,52356,52359],{"className":52355},[50],[15,52357],{"className":52358,"style":2345},[54],[15,52360,1024],{"className":52361},[59]," 时退化为 min-entropy ",[15,52364,52366,52403],{"className":52365,"translate":19},[18],[15,52367,52369],{"className":52368},[23],[25,52370,52371],{"xmlns":27},[29,52372,52373,52400],{},[32,52374,52375,52377,52379,52381,52392,52394,52396,52398],{},[110,52376,4813],{},[35,52378,4100],{},[110,52380,4103],{},[195,52382,52383,52390],{},[32,52384,52385,52388],{},[35,52386,52387],{},"max",[110,52389,4103],{},[35,52391,774],{},[35,52393,11],{},[110,52395,113],{"stretchy":112},[35,52397,774],{},[110,52399,120],{"stretchy":112},[39,52401,52402],{"encoding":41},"-\\log\\max_x p(x)",[15,52404,52406],{"className":52405,"ariaHidden":46},[45],[15,52407,52409,52412,52415,52418,52423,52426,52467,52470,52473,52476,52479],{"className":52408},[50],[15,52410],{"className":52411,"style":139},[54],[15,52413,4813],{"className":52414},[59],[15,52416],{"className":52417,"style":406},[157],[15,52419,4154,52421],{"className":52420},[1484],[15,52422,4158],{"style":4157},[15,52424],{"className":52425,"style":406},[157],[15,52427,52429,52432],{"className":52428},[1484],[15,52430,52387],{"className":52431},[1484],[15,52433,52435],{"className":52434},[281],[15,52436,52438,52459],{"className":52437},[285,286],[15,52439,52441,52456],{"className":52440},[290],[15,52442,52444],{"className":52443,"style":44929},[294],[15,52445,52447,52450],{"style":52446},"top:-2.55em;margin-right:0.05em;",[15,52448],{"className":52449,"style":303},[302],[15,52451,52453],{"className":52452},[307,308,309,310],[15,52454,774],{"className":52455},[59,60,310],[15,52457,318],{"className":52458},[317],[15,52460,52462],{"className":52461},[290],[15,52463,52465],{"className":52464,"style":7968},[294],[15,52466],{},[15,52468],{"className":52469,"style":406},[157],[15,52471,11],{"className":52472},[59,60],[15,52474,113],{"className":52475},[146],[15,52477,774],{"className":52478},[59,60],[15,52480,120],{"className":52481},[153],"，因此在密码学、随机性提取与 ",[1225,52484,52485],{},"Rényi 差分隐私（RDP）"," 中被用来对隐私预算做更紧致的记账。它与 f-散度族的\"同源\"关系也给出一条实用经验：讨论可加性、信息几何与变分表示时用 f-散度更顺手，讨论误差指数与熵时用它的对数版本更自然。",[2311,52488,52490],{"id":52489},"_38-汇总表","3.8 汇总表",[52492,52493,52494,52589],"table",{},[52495,52496,52497],"thead",{},[52498,52499,52500,52504,52550,52552,52555],"tr",{},[52501,52502,52503],"th",{},"散度",[52501,52505,52506],{},[15,52507,52509,52529],{"className":52508,"translate":19},[18],[15,52510,52512],{"className":52511},[23],[25,52513,52514],{"xmlns":27},[29,52515,52516,52526],{},[32,52517,52518,52520,52522,52524],{},[35,52519,37],{},[110,52521,113],{"stretchy":112},[35,52523,769],{},[110,52525,120],{"stretchy":112},[39,52527,52528],{"encoding":41},"f(t)",[15,52530,52532],{"className":52531,"ariaHidden":46},[45],[15,52533,52535,52538,52541,52544,52547],{"className":52534},[50],[15,52536],{"className":52537,"style":139},[54],[15,52539,37],{"className":52540,"style":61},[59,60],[15,52542,113],{"className":52543},[146],[15,52545,769],{"className":52546},[59,60],[15,52548,120],{"className":52549},[153],[52501,52551,29686],{},[52501,52553,52554],{},"有界",[52501,52556,52557,52588],{},[15,52558,52560,52576],{"className":52559,"translate":19},[18],[15,52561,52563],{"className":52562},[23],[25,52564,52565],{"xmlns":27},[29,52566,52567,52573],{},[32,52568,52569,52571],{},[35,52570,46673],{},[110,52572,4103],{},[39,52574,52575],{"encoding":41},"\\lim",[15,52577,52579],{"className":52578,"ariaHidden":46},[45],[15,52580,52582,52585],{"className":52581},[50],[15,52583],{"className":52584,"style":12597},[54],[15,52586,46673],{"className":52587},[1484]," 行为（不重叠支撑）",[52590,52591,52592,52793,52992,53120,53518,53737,53932,54212,54488],"tbody",{},[52498,52593,52594,52702,52753,52756,52758],{},[52595,52596,52597,52598],"td",{},"KL ",[15,52599,52601,52632],{"className":52600,"translate":19},[18],[15,52602,52604],{"className":52603},[23],[25,52605,52606],{"xmlns":27},[29,52607,52608,52630],{},[32,52609,52610,52620,52622,52624,52626,52628],{},[195,52611,52612,52614],{},[35,52613,199],{},[32,52615,52616,52618],{},[35,52617,10694],{},[35,52619,21893],{},[110,52621,113],{"stretchy":112},[35,52623,206],{},[35,52625,210],{"mathvariant":209},[35,52627,213],{},[110,52629,120],{"stretchy":112},[39,52631,24353],{"encoding":41},[15,52633,52635],{"className":52634,"ariaHidden":46},[45],[15,52636,52638,52641,52687,52690,52693,52696,52699],{"className":52637},[50],[15,52639],{"className":52640,"style":139},[54],[15,52642,52644,52647],{"className":52643},[59],[15,52645,199],{"className":52646,"style":277},[59,60],[15,52648,52650],{"className":52649},[281],[15,52651,52653,52679],{"className":52652},[285,286],[15,52654,52656,52676],{"className":52655},[290],[15,52657,52659],{"className":52658,"style":379},[294],[15,52660,52661,52664],{"style":298},[15,52662],{"className":52663,"style":303},[302],[15,52665,52667],{"className":52666},[307,308,309,310],[15,52668,52670,52673],{"className":52669},[59,310],[15,52671,10694],{"className":52672,"style":10782},[59,60,310],[15,52674,21893],{"className":52675},[59,60,310],[15,52677,318],{"className":52678},[317],[15,52680,52682],{"className":52681},[290],[15,52683,52685],{"className":52684,"style":7968},[294],[15,52686],{},[15,52688,113],{"className":52689},[146],[15,52691,206],{"className":52692,"style":334},[59,60],[15,52694,210],{"className":52695},[59],[15,52697,213],{"className":52698},[59,60],[15,52700,120],{"className":52701},[153],[52595,52703,52704],{},[15,52705,52707,52727],{"className":52706,"translate":19},[18],[15,52708,52710],{"className":52709},[23],[25,52711,52712],{"xmlns":27},[29,52713,52714,52724],{},[32,52715,52716,52718,52720,52722],{},[35,52717,769],{},[35,52719,4100],{},[110,52721,4103],{},[35,52723,769],{},[39,52725,52726],{"encoding":41},"t\\log t",[15,52728,52730],{"className":52729,"ariaHidden":46},[45],[15,52731,52733,52736,52739,52742,52747,52750],{"className":52732},[50],[15,52734],{"className":52735,"style":55},[54],[15,52737,769],{"className":52738},[59,60],[15,52740],{"className":52741,"style":406},[157],[15,52743,4154,52745],{"className":52744},[1484],[15,52746,4158],{"style":4157},[15,52748],{"className":52749,"style":406},[157],[15,52751,769],{"className":52752},[59,60],[52595,52754,52755],{},"否",[52595,52757,52755],{},[52595,52759,52760],{},[15,52761,52763,52778],{"className":52762,"translate":19},[18],[15,52764,52766],{"className":52765},[23],[25,52767,52768],{"xmlns":27},[29,52769,52770,52776],{},[32,52771,52772,52774],{},[110,52773,2470],{},[35,52775,1024],{"mathvariant":209},[39,52777,4241],{"encoding":41},[15,52779,52781],{"className":52780,"ariaHidden":46},[45],[15,52782,52784,52787,52790],{"className":52783},[50],[15,52785],{"className":52786,"style":4251},[54],[15,52788,2470],{"className":52789},[59],[15,52791,1024],{"className":52792},[59],[52498,52794,52795,52902,52953,52955,52957],{},[52595,52796,52797,52798],{},"反向 KL ",[15,52799,52801,52832],{"className":52800,"translate":19},[18],[15,52802,52804],{"className":52803},[23],[25,52805,52806],{"xmlns":27},[29,52807,52808,52830],{},[32,52809,52810,52820,52822,52824,52826,52828],{},[195,52811,52812,52814],{},[35,52813,199],{},[32,52815,52816,52818],{},[35,52817,10694],{},[35,52819,21893],{},[110,52821,113],{"stretchy":112},[35,52823,213],{},[35,52825,210],{"mathvariant":209},[35,52827,206],{},[110,52829,120],{"stretchy":112},[39,52831,22375],{"encoding":41},[15,52833,52835],{"className":52834,"ariaHidden":46},[45],[15,52836,52838,52841,52887,52890,52893,52896,52899],{"className":52837},[50],[15,52839],{"className":52840,"style":139},[54],[15,52842,52844,52847],{"className":52843},[59],[15,52845,199],{"className":52846,"style":277},[59,60],[15,52848,52850],{"className":52849},[281],[15,52851,52853,52879],{"className":52852},[285,286],[15,52854,52856,52876],{"className":52855},[290],[15,52857,52859],{"className":52858,"style":379},[294],[15,52860,52861,52864],{"style":298},[15,52862],{"className":52863,"style":303},[302],[15,52865,52867],{"className":52866},[307,308,309,310],[15,52868,52870,52873],{"className":52869},[59,310],[15,52871,10694],{"className":52872,"style":10782},[59,60,310],[15,52874,21893],{"className":52875},[59,60,310],[15,52877,318],{"className":52878},[317],[15,52880,52882],{"className":52881},[290],[15,52883,52885],{"className":52884,"style":7968},[294],[15,52886],{},[15,52888,113],{"className":52889},[146],[15,52891,213],{"className":52892},[59,60],[15,52894,210],{"className":52895},[59],[15,52897,206],{"className":52898,"style":334},[59,60],[15,52900,120],{"className":52901},[153],[52595,52903,52904],{},[15,52905,52907,52927],{"className":52906,"translate":19},[18],[15,52908,52910],{"className":52909},[23],[25,52911,52912],{"xmlns":27},[29,52913,52914,52924],{},[32,52915,52916,52918,52920,52922],{},[110,52917,4813],{},[35,52919,4100],{},[110,52921,4103],{},[35,52923,769],{},[39,52925,52926],{"encoding":41},"-\\log t",[15,52928,52930],{"className":52929,"ariaHidden":46},[45],[15,52931,52933,52936,52939,52942,52947,52950],{"className":52932},[50],[15,52934],{"className":52935,"style":55},[54],[15,52937,4813],{"className":52938},[59],[15,52940],{"className":52941,"style":406},[157],[15,52943,4154,52945],{"className":52944},[1484],[15,52946,4158],{"style":4157},[15,52948],{"className":52949,"style":406},[157],[15,52951,769],{"className":52952},[59,60],[52595,52954,52755],{},[52595,52956,52755],{},[52595,52958,52959],{},[15,52960,52962,52977],{"className":52961,"translate":19},[18],[15,52963,52965],{"className":52964},[23],[25,52966,52967],{"xmlns":27},[29,52968,52969,52975],{},[32,52970,52971,52973],{},[110,52972,2470],{},[35,52974,1024],{"mathvariant":209},[39,52976,4241],{"encoding":41},[15,52978,52980],{"className":52979,"ariaHidden":46},[45],[15,52981,52983,52986,52989],{"className":52982},[50],[15,52984],{"className":52985,"style":4251},[54],[15,52987,2470],{"className":52988},[59],[15,52990,1024],{"className":52991},[59],[52498,52993,52994,52997,53080,53083,53085],{},[52595,52995,52996],{},"Jeffreys（对称 KL）",[52595,52998,52999],{},[15,53000,53002,53030],{"className":53001,"translate":19},[18],[15,53003,53005],{"className":53004},[23],[25,53006,53007],{"xmlns":27},[29,53008,53009,53027],{},[32,53010,53011,53013,53015,53017,53019,53021,53023,53025],{},[110,53012,113],{"stretchy":112},[35,53014,769],{},[110,53016,4813],{},[115,53018,117],{},[110,53020,120],{"stretchy":112},[35,53022,4100],{},[110,53024,4103],{},[35,53026,769],{},[39,53028,53029],{"encoding":41},"(t-1)\\log t",[15,53031,53033,53054],{"className":53032,"ariaHidden":46},[45],[15,53034,53036,53039,53042,53045,53048,53051],{"className":53035},[50],[15,53037],{"className":53038,"style":139},[54],[15,53040,113],{"className":53041},[146],[15,53043,769],{"className":53044},[59,60],[15,53046],{"className":53047,"style":2587},[157],[15,53049,4813],{"className":53050},[2591],[15,53052],{"className":53053,"style":2587},[157],[15,53055,53057,53060,53063,53066,53069,53074,53077],{"className":53056},[50],[15,53058],{"className":53059,"style":139},[54],[15,53061,117],{"className":53062},[59],[15,53064,120],{"className":53065},[153],[15,53067],{"className":53068,"style":406},[157],[15,53070,4154,53072],{"className":53071},[1484],[15,53073,4158],{"style":4157},[15,53075],{"className":53076,"style":406},[157],[15,53078,769],{"className":53079},[59,60],[52595,53081,53082],{},"是",[52595,53084,52755],{},[52595,53086,53087],{},[15,53088,53090,53105],{"className":53089,"translate":19},[18],[15,53091,53093],{"className":53092},[23],[25,53094,53095],{"xmlns":27},[29,53096,53097,53103],{},[32,53098,53099,53101],{},[110,53100,2470],{},[35,53102,1024],{"mathvariant":209},[39,53104,4241],{"encoding":41},[15,53106,53108],{"className":53107,"ariaHidden":46},[45],[15,53109,53111,53114,53117],{"className":53110},[50],[15,53112],{"className":53113,"style":4251},[54],[15,53115,2470],{"className":53116},[59],[15,53118,1024],{"className":53119},[59],[52498,53121,53122,53125,53415,53417,53476],{},[52595,53123,53124],{},"JS",[52595,53126,53127],{},[15,53128,53130,53188],{"className":53129,"translate":19},[18],[15,53131,53133],{"className":53132},[23],[25,53134,53135],{"xmlns":27},[29,53136,53137,53185],{},[32,53138,53139,53145,53147,53149,53151,53153,53155,53157,53159,53161,53163,53165,53167,53169,53171,53183],{},[238,53140,53141,53143],{},[115,53142,117],{},[115,53144,2463],{},[110,53146,230],{"stretchy":112},[35,53148,769],{},[35,53150,4100],{},[110,53152,4103],{},[35,53154,769],{},[110,53156,4813],{},[110,53158,113],{"stretchy":112},[35,53160,769],{},[110,53162,2470],{},[115,53164,117],{},[110,53166,120],{"stretchy":112},[35,53168,4100],{},[110,53170,4103],{},[238,53172,53173,53181],{},[32,53174,53175,53177,53179],{},[35,53176,769],{},[110,53178,2470],{},[115,53180,117],{},[115,53182,2463],{},[110,53184,257],{"stretchy":112},[39,53186,53187],{"encoding":41},"\\frac12[t\\log t-(t+1)\\log\\frac{t+1}{2}]",[15,53189,53191,53294,53315],{"className":53190,"ariaHidden":46},[45],[15,53192,53194,53197,53265,53268,53271,53274,53279,53282,53285,53288,53291],{"className":53193},[50],[15,53195],{"className":53196,"style":2505},[54],[15,53198,53200,53203,53262],{"className":53199},[59],[15,53201],{"className":53202},[146,441],[15,53204,53206],{"className":53205},[238],[15,53207,53209,53254],{"className":53208},[285,286],[15,53210,53212,53251],{"className":53211},[290],[15,53213,53215,53229,53237],{"className":53214,"style":2524},[294],[15,53216,53217,53220],{"style":2527},[15,53218],{"className":53219,"style":461},[302],[15,53221,53223],{"className":53222},[307,308,309,310],[15,53224,53226],{"className":53225},[59,310],[15,53227,2463],{"className":53228},[59,310],[15,53230,53231,53234],{"style":473},[15,53232],{"className":53233,"style":461},[302],[15,53235],{"className":53236,"style":481},[480],[15,53238,53239,53242],{"style":2550},[15,53240],{"className":53241,"style":461},[302],[15,53243,53245],{"className":53244},[307,308,309,310],[15,53246,53248],{"className":53247},[59,310],[15,53249,117],{"className":53250},[59,310],[15,53252,318],{"className":53253},[317],[15,53255,53257],{"className":53256},[290],[15,53258,53260],{"className":53259,"style":2572},[294],[15,53261],{},[15,53263],{"className":53264},[153,441],[15,53266,230],{"className":53267},[146],[15,53269,769],{"className":53270},[59,60],[15,53272],{"className":53273,"style":406},[157],[15,53275,4154,53277],{"className":53276},[1484],[15,53278,4158],{"style":4157},[15,53280],{"className":53281,"style":406},[157],[15,53283,769],{"className":53284},[59,60],[15,53286],{"className":53287,"style":2587},[157],[15,53289,4813],{"className":53290},[2591],[15,53292],{"className":53293,"style":2587},[157],[15,53295,53297,53300,53303,53306,53309,53312],{"className":53296},[50],[15,53298],{"className":53299,"style":139},[54],[15,53301,113],{"className":53302},[146],[15,53304,769],{"className":53305},[59,60],[15,53307],{"className":53308,"style":2587},[157],[15,53310,2470],{"className":53311},[2591],[15,53313],{"className":53314,"style":2587},[157],[15,53316,53318,53321,53324,53327,53330,53335,53338,53412],{"className":53317},[50],[15,53319],{"className":53320,"style":2505},[54],[15,53322,117],{"className":53323},[59],[15,53325,120],{"className":53326},[153],[15,53328],{"className":53329,"style":406},[157],[15,53331,4154,53333],{"className":53332},[1484],[15,53334,4158],{"style":4157},[15,53336],{"className":53337,"style":406},[157],[15,53339,53341,53344,53409],{"className":53340},[59],[15,53342],{"className":53343},[146,441],[15,53345,53347],{"className":53346},[238],[15,53348,53350,53401],{"className":53349},[285,286],[15,53351,53353,53398],{"className":53352},[290],[15,53354,53356,53370,53378],{"className":53355,"style":2524},[294],[15,53357,53358,53361],{"style":2527},[15,53359],{"className":53360,"style":461},[302],[15,53362,53364],{"className":53363},[307,308,309,310],[15,53365,53367],{"className":53366},[59,310],[15,53368,2463],{"className":53369},[59,310],[15,53371,53372,53375],{"style":473},[15,53373],{"className":53374,"style":461},[302],[15,53376],{"className":53377,"style":481},[480],[15,53379,53380,53383],{"style":2550},[15,53381],{"className":53382,"style":461},[302],[15,53384,53386],{"className":53385},[307,308,309,310],[15,53387,53389,53392,53395],{"className":53388},[59,310],[15,53390,769],{"className":53391},[59,60,310],[15,53393,2470],{"className":53394},[2591,310],[15,53396,117],{"className":53397},[59,310],[15,53399,318],{"className":53400},[317],[15,53402,53404],{"className":53403},[290],[15,53405,53407],{"className":53406,"style":2572},[294],[15,53408],{},[15,53410],{"className":53411},[153,441],[15,53413,257],{"className":53414},[153],[52595,53416,53082],{},[52595,53418,53419,53420,53475],{},"是（",[15,53421,53423,53443],{"className":53422,"translate":19},[18],[15,53424,53426],{"className":53425},[23],[25,53427,53428],{"xmlns":27},[29,53429,53430,53440],{},[32,53431,53432,53434,53436,53438],{},[110,53433,9952],{},[35,53435,4100],{},[110,53437,4103],{},[115,53439,2463],{},[39,53441,53442],{"encoding":41},"\\le\\log2",[15,53444,53446,53458],{"className":53445,"ariaHidden":46},[45],[15,53447,53449,53452,53455],{"className":53448},[50],[15,53450],{"className":53451,"style":43188},[54],[15,53453,9952],{"className":53454},[162],[15,53456],{"className":53457,"style":158},[157],[15,53459,53461,53464,53469,53472],{"className":53460},[50],[15,53462],{"className":53463,"style":55},[54],[15,53465,4154,53467],{"className":53466},[1484],[15,53468,4158],{"style":4157},[15,53470],{"className":53471,"style":406},[157],[15,53473,2463],{"className":53474},[59],"）",[52595,53477,53478],{},[15,53479,53481,53498],{"className":53480,"translate":19},[18],[15,53482,53484],{"className":53483},[23],[25,53485,53486],{"xmlns":27},[29,53487,53488,53496],{},[32,53489,53490,53492,53494],{},[35,53491,4100],{},[110,53493,4103],{},[115,53495,2463],{},[39,53497,34304],{"encoding":41},[15,53499,53501],{"className":53500,"ariaHidden":46},[45],[15,53502,53504,53507,53512,53515],{"className":53503},[50],[15,53505],{"className":53506,"style":55},[54],[15,53508,4154,53510],{"className":53509},[1484],[15,53511,4158],{"style":4157},[15,53513],{"className":53514,"style":406},[157],[15,53516,2463],{"className":53517},[59],[52498,53519,53520,53523,53660,53662,53707],{},[52595,53521,53522],{},"全变差 TV",[52595,53524,53525],{},[15,53526,53528,53556],{"className":53527,"translate":19},[18],[15,53529,53531],{"className":53530},[23],[25,53532,53533],{"xmlns":27},[29,53534,53535,53553],{},[32,53536,53537,53543,53545,53547,53549,53551],{},[238,53538,53539,53541],{},[115,53540,117],{},[115,53542,2463],{},[110,53544,4808],{"stretchy":112},[35,53546,769],{},[110,53548,4813],{},[115,53550,117],{},[110,53552,4808],{"stretchy":112},[39,53554,53555],{"encoding":41},"\\frac12\\lvert t-1\\rvert",[15,53557,53559,53648],{"className":53558,"ariaHidden":46},[45],[15,53560,53562,53565,53633,53636,53639,53642,53645],{"className":53561},[50],[15,53563],{"className":53564,"style":2505},[54],[15,53566,53568,53571,53630],{"className":53567},[59],[15,53569],{"className":53570},[146,441],[15,53572,53574],{"className":53573},[238],[15,53575,53577,53622],{"className":53576},[285,286],[15,53578,53580,53619],{"className":53579},[290],[15,53581,53583,53597,53605],{"className":53582,"style":2524},[294],[15,53584,53585,53588],{"style":2527},[15,53586],{"className":53587,"style":461},[302],[15,53589,53591],{"className":53590},[307,308,309,310],[15,53592,53594],{"className":53593},[59,310],[15,53595,2463],{"className":53596},[59,310],[15,53598,53599,53602],{"style":473},[15,53600],{"className":53601,"style":461},[302],[15,53603],{"className":53604,"style":481},[480],[15,53606,53607,53610],{"style":2550},[15,53608],{"className":53609,"style":461},[302],[15,53611,53613],{"className":53612},[307,308,309,310],[15,53614,53616],{"className":53615},[59,310],[15,53617,117],{"className":53618},[59,310],[15,53620,318],{"className":53621},[317],[15,53623,53625],{"className":53624},[290],[15,53626,53628],{"className":53627,"style":2572},[294],[15,53629],{},[15,53631],{"className":53632},[153,441],[15,53634,4808],{"className":53635},[146],[15,53637,769],{"className":53638},[59,60],[15,53640],{"className":53641,"style":2587},[157],[15,53643,4813],{"className":53644},[2591],[15,53646],{"className":53647,"style":2587},[157],[15,53649,53651,53654,53657],{"className":53650},[50],[15,53652],{"className":53653,"style":139},[54],[15,53655,117],{"className":53656},[59],[15,53658,4808],{"className":53659},[153],[52595,53661,53082],{},[52595,53663,53419,53664,53475],{},[15,53665,53667,53683],{"className":53666,"translate":19},[18],[15,53668,53670],{"className":53669},[23],[25,53671,53672],{"xmlns":27},[29,53673,53674,53680],{},[32,53675,53676,53678],{},[110,53677,9952],{},[115,53679,117],{},[39,53681,53682],{"encoding":41},"\\le1",[15,53684,53686,53698],{"className":53685,"ariaHidden":46},[45],[15,53687,53689,53692,53695],{"className":53688},[50],[15,53690],{"className":53691,"style":43188},[54],[15,53693,9952],{"className":53694},[162],[15,53696],{"className":53697,"style":158},[157],[15,53699,53701,53704],{"className":53700},[50],[15,53702],{"className":53703,"style":172},[54],[15,53705,117],{"className":53706},[59],[52595,53708,53709],{},[15,53710,53712,53725],{"className":53711,"translate":19},[18],[15,53713,53715],{"className":53714},[23],[25,53716,53717],{"xmlns":27},[29,53718,53719,53723],{},[32,53720,53721],{},[115,53722,117],{},[39,53724,117],{"encoding":41},[15,53726,53728],{"className":53727,"ariaHidden":46},[45],[15,53729,53731,53734],{"className":53730},[50],[15,53732],{"className":53733,"style":172},[54],[15,53735,117],{"className":53736},[59],[52498,53738,53739,53800,53893,53895,53897],{},[52595,53740,53741,53742],{},"Pearson ",[15,53743,53745,53762],{"className":53744,"translate":19},[18],[15,53746,53748],{"className":53747},[23],[25,53749,53750],{"xmlns":27},[29,53751,53752,53760],{},[32,53753,53754],{},[6814,53755,53756,53758],{},[35,53757,37449],{},[115,53759,2463],{},[39,53761,40394],{"encoding":41},[15,53763,53765],{"className":53764,"ariaHidden":46},[45],[15,53766,53768,53771],{"className":53767},[50],[15,53769],{"className":53770,"style":40404},[54],[15,53772,53774,53777],{"className":53773},[59],[15,53775,37449],{"className":53776},[59,60],[15,53778,53780],{"className":53779},[281],[15,53781,53783],{"className":53782},[285],[15,53784,53786],{"className":53785},[290],[15,53787,53789],{"className":53788,"style":20028},[294],[15,53790,53791,53794],{"style":6865},[15,53792],{"className":53793,"style":303},[302],[15,53795,53797],{"className":53796},[307,308,309,310],[15,53798,2463],{"className":53799},[59,310],[52595,53801,53802],{},[15,53803,53805,53831],{"className":53804,"translate":19},[18],[15,53806,53808],{"className":53807},[23],[25,53809,53810],{"xmlns":27},[29,53811,53812,53828],{},[32,53813,53814,53816,53818,53820,53822],{},[110,53815,113],{"stretchy":112},[35,53817,769],{},[110,53819,4813],{},[115,53821,117],{},[6814,53823,53824,53826],{},[110,53825,120],{"stretchy":112},[115,53827,2463],{},[39,53829,53830],{"encoding":41},"(t-1)^2",[15,53832,53834,53855],{"className":53833,"ariaHidden":46},[45],[15,53835,53837,53840,53843,53846,53849,53852],{"className":53836},[50],[15,53838],{"className":53839,"style":139},[54],[15,53841,113],{"className":53842},[146],[15,53844,769],{"className":53845},[59,60],[15,53847],{"className":53848,"style":2587},[157],[15,53850,4813],{"className":53851},[2591],[15,53853],{"className":53854,"style":2587},[157],[15,53856,53858,53861,53864],{"className":53857},[50],[15,53859],{"className":53860,"style":20003},[54],[15,53862,117],{"className":53863},[59],[15,53865,53867,53870],{"className":53866},[153],[15,53868,120],{"className":53869},[153],[15,53871,53873],{"className":53872},[281],[15,53874,53876],{"className":53875},[285],[15,53877,53879],{"className":53878},[290],[15,53880,53882],{"className":53881,"style":20028},[294],[15,53883,53884,53887],{"style":6865},[15,53885],{"className":53886,"style":303},[302],[15,53888,53890],{"className":53889},[307,308,309,310],[15,53891,2463],{"className":53892},[59,310],[52595,53894,52755],{},[52595,53896,52755],{},[52595,53898,53899],{},[15,53900,53902,53917],{"className":53901,"translate":19},[18],[15,53903,53905],{"className":53904},[23],[25,53906,53907],{"xmlns":27},[29,53908,53909,53915],{},[32,53910,53911,53913],{},[110,53912,2470],{},[35,53914,1024],{"mathvariant":209},[39,53916,4241],{"encoding":41},[15,53918,53920],{"className":53919,"ariaHidden":46},[45],[15,53921,53923,53926,53929],{"className":53922},[50],[15,53924],{"className":53925,"style":4251},[54],[15,53927,2470],{"className":53928},[59],[15,53930,1024],{"className":53931},[59],[52498,53933,53934,54020,54173,54175,54177],{},[52595,53935,53936,53937],{},"Neyman ",[15,53938,53940,53960],{"className":53939,"translate":19},[18],[15,53941,53943],{"className":53942},[23],[25,53944,53945],{"xmlns":27},[29,53946,53947,53957],{},[32,53948,53949],{},[7553,53950,53951,53953,53955],{},[35,53952,37449],{},[35,53954,38284],{},[115,53956,2463],{},[39,53958,53959],{"encoding":41},"\\chi^2_N",[15,53961,53963],{"className":53962,"ariaHidden":46},[45],[15,53964,53966,53969],{"className":53965},[50],[15,53967],{"className":53968,"style":38339},[54],[15,53970,53972,53975],{"className":53971},[59],[15,53973,37449],{"className":53974},[59,60],[15,53976,53978],{"className":53977},[281],[15,53979,53981,54012],{"className":53980},[285,286],[15,53982,53984,54009],{"className":53983},[290],[15,53985,53987,53998],{"className":53986,"style":20028},[294],[15,53988,53989,53992],{"style":38360},[15,53990],{"className":53991,"style":303},[302],[15,53993,53995],{"className":53994},[307,308,309,310],[15,53996,38284],{"className":53997,"style":25601},[59,60,310],[15,53999,54000,54003],{"style":6865},[15,54001],{"className":54002,"style":303},[302],[15,54004,54006],{"className":54005},[307,308,309,310],[15,54007,2463],{"className":54008},[59,310],[15,54010,318],{"className":54011},[317],[15,54013,54015],{"className":54014},[290],[15,54016,54018],{"className":54017,"style":38390},[294],[15,54019],{},[52595,54021,54022],{},[15,54023,54025,54057],{"className":54024,"translate":19},[18],[15,54026,54028],{"className":54027},[23],[25,54029,54030],{"xmlns":27},[29,54031,54032,54054],{},[32,54033,54034],{},[238,54035,54036,54052],{},[32,54037,54038,54040,54042,54044,54046],{},[110,54039,113],{"stretchy":112},[35,54041,769],{},[110,54043,4813],{},[115,54045,117],{},[6814,54047,54048,54050],{},[110,54049,120],{"stretchy":112},[115,54051,2463],{},[35,54053,769],{},[39,54055,54056],{"encoding":41},"\\frac{(t-1)^2}{t}",[15,54058,54060],{"className":54059,"ariaHidden":46},[45],[15,54061,54063,54067],{"className":54062},[50],[15,54064],{"className":54065,"style":54066},[54],"height:1.4539em;vertical-align:-0.345em;",[15,54068,54070,54073,54170],{"className":54069},[59],[15,54071],{"className":54072},[146,441],[15,54074,54076],{"className":54075},[238],[15,54077,54079,54162],{"className":54078},[285,286],[15,54080,54082,54159],{"className":54081},[290],[15,54083,54085,54099,54107],{"className":54084,"style":38448},[294],[15,54086,54087,54090],{"style":2527},[15,54088],{"className":54089,"style":461},[302],[15,54091,54093],{"className":54092},[307,308,309,310],[15,54094,54096],{"className":54095},[59,310],[15,54097,769],{"className":54098},[59,60,310],[15,54100,54101,54104],{"style":473},[15,54102],{"className":54103,"style":461},[302],[15,54105],{"className":54106,"style":481},[480],[15,54108,54109,54112],{"style":26418},[15,54110],{"className":54111,"style":461},[302],[15,54113,54115],{"className":54114},[307,308,309,310],[15,54116,54118,54121,54124,54127,54130],{"className":54117},[59,310],[15,54119,113],{"className":54120},[146,310],[15,54122,769],{"className":54123},[59,60,310],[15,54125,4813],{"className":54126},[2591,310],[15,54128,117],{"className":54129},[59,310],[15,54131,54133,54136],{"className":54132},[153,310],[15,54134,120],{"className":54135},[153,310],[15,54137,54139],{"className":54138},[281],[15,54140,54142],{"className":54141},[285],[15,54143,54145],{"className":54144},[290],[15,54146,54148],{"className":54147,"style":38512},[294],[15,54149,54150,54153],{"style":38515},[15,54151],{"className":54152,"style":30206},[302],[15,54154,54156],{"className":54155},[307,30210,9674,310],[15,54157,2463],{"className":54158},[59,310],[15,54160,318],{"className":54161},[317],[15,54163,54165],{"className":54164},[290],[15,54166,54168],{"className":54167,"style":2572},[294],[15,54169],{},[15,54171],{"className":54172},[153,441],[52595,54174,52755],{},[52595,54176,52755],{},[52595,54178,54179],{},[15,54180,54182,54197],{"className":54181,"translate":19},[18],[15,54183,54185],{"className":54184},[23],[25,54186,54187],{"xmlns":27},[29,54188,54189,54195],{},[32,54190,54191,54193],{},[110,54192,2470],{},[35,54194,1024],{"mathvariant":209},[39,54196,4241],{"encoding":41},[15,54198,54200],{"className":54199,"ariaHidden":46},[45],[15,54201,54203,54206,54209],{"className":54202},[50],[15,54204],{"className":54205,"style":4251},[54],[15,54207,2470],{"className":54208},[59],[15,54210,1024],{"className":54211},[59],[52498,54213,54214,54275,54411,54413,54458],{},[52595,54215,54216,54217,54274],{},"Hellinger",[15,54218,54220,54237],{"className":54219,"translate":19},[18],[15,54221,54223],{"className":54222},[23],[25,54224,54225],{"xmlns":27},[29,54226,54227,54235],{},[32,54228,54229],{},[6814,54230,54231,54233],{},[32,54232],{},[115,54234,2463],{},[39,54236,44269],{"encoding":41},[15,54238,54240],{"className":54239,"ariaHidden":46},[45],[15,54241,54243,54246],{"className":54242},[50],[15,54244],{"className":54245,"style":20028},[54],[15,54247,54249,54251],{"className":54248},[59],[15,54250],{},[15,54252,54254],{"className":54253},[281],[15,54255,54257],{"className":54256},[285],[15,54258,54260],{"className":54259},[290],[15,54261,54263],{"className":54262,"style":20028},[294],[15,54264,54265,54268],{"style":6865},[15,54266],{"className":54267,"style":303},[302],[15,54269,54271],{"className":54270},[307,308,309,310],[15,54272,2463],{"className":54273},[59,310],"（本文约定）",[52595,54276,54277],{},[15,54278,54280,54308],{"className":54279,"translate":19},[18],[15,54281,54283],{"className":54282},[23],[25,54284,54285],{"xmlns":27},[29,54286,54287,54305],{},[32,54288,54289,54291,54295,54297,54299],{},[110,54290,113],{"stretchy":112},[34339,54292,54293],{},[35,54294,769],{},[110,54296,4813],{},[115,54298,117],{},[6814,54300,54301,54303],{},[110,54302,120],{"stretchy":112},[115,54304,2463],{},[39,54306,54307],{"encoding":41},"(\\sqrt t-1)^2",[15,54309,54311,54373],{"className":54310,"ariaHidden":46},[45],[15,54312,54314,54317,54320,54364,54367,54370],{"className":54313},[50],[15,54315],{"className":54316,"style":42667},[54],[15,54318,113],{"className":54319},[146],[15,54321,54323],{"className":54322},[59,34367],[15,54324,54326,54356],{"className":54325},[285,286],[15,54327,54329,54353],{"className":54328},[290],[15,54330,54332,54341],{"className":54331,"style":42683},[294],[15,54333,54335,54338],{"className":54334,"style":11863},[6307],[15,54336],{"className":54337,"style":461},[302],[15,54339,769],{"className":54340,"style":34387},[59,60],[15,54342,54343,54346],{"style":42695},[15,54344],{"className":54345,"style":461},[302],[15,54347,54349],{"className":54348,"style":34444},[34443],[6323,54350,54351],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,54352],{"d":34451},[15,54354,318],{"className":54355},[317],[15,54357,54359],{"className":54358},[290],[15,54360,54362],{"className":54361,"style":42715},[294],[15,54363],{},[15,54365],{"className":54366,"style":2587},[157],[15,54368,4813],{"className":54369},[2591],[15,54371],{"className":54372,"style":2587},[157],[15,54374,54376,54379,54382],{"className":54375},[50],[15,54377],{"className":54378,"style":20003},[54],[15,54380,117],{"className":54381},[59],[15,54383,54385,54388],{"className":54384},[153],[15,54386,120],{"className":54387},[153],[15,54389,54391],{"className":54390},[281],[15,54392,54394],{"className":54393},[285],[15,54395,54397],{"className":54396},[290],[15,54398,54400],{"className":54399,"style":20028},[294],[15,54401,54402,54405],{"style":6865},[15,54403],{"className":54404,"style":303},[302],[15,54406,54408],{"className":54407},[307,308,309,310],[15,54409,2463],{"className":54410},[59,310],[52595,54412,53082],{},[52595,54414,53419,54415,53475],{},[15,54416,54418,54434],{"className":54417,"translate":19},[18],[15,54419,54421],{"className":54420},[23],[25,54422,54423],{"xmlns":27},[29,54424,54425,54431],{},[32,54426,54427,54429],{},[110,54428,9952],{},[115,54430,2463],{},[39,54432,54433],{"encoding":41},"\\le2",[15,54435,54437,54449],{"className":54436,"ariaHidden":46},[45],[15,54438,54440,54443,54446],{"className":54439},[50],[15,54441],{"className":54442,"style":43188},[54],[15,54444,9952],{"className":54445},[162],[15,54447],{"className":54448,"style":158},[157],[15,54450,54452,54455],{"className":54451},[50],[15,54453],{"className":54454,"style":172},[54],[15,54456,2463],{"className":54457},[59],[52595,54459,54460],{},[15,54461,54463,54476],{"className":54462,"translate":19},[18],[15,54464,54466],{"className":54465},[23],[25,54467,54468],{"xmlns":27},[29,54469,54470,54474],{},[32,54471,54472],{},[115,54473,2463],{},[39,54475,2463],{"encoding":41},[15,54477,54479],{"className":54478,"ariaHidden":46},[45],[15,54480,54482,54485],{"className":54481},[50],[15,54483],{"className":54484,"style":172},[54],[15,54486,2463],{"className":54487},[59],[52498,54489,54490,54571,54814,54816,54818],{},[52595,54491,54492,54493],{},"α-散度 ",[15,54494,54496,54523],{"className":54495,"translate":19},[18],[15,54497,54499],{"className":54498},[23],[25,54500,54501],{"xmlns":27},[29,54502,54503,54521],{},[32,54504,54505,54507,54509,54511,54513,54515,54517,54519],{},[35,54506,44754],{},[110,54508,5909],{},[110,54510,113],{"stretchy":112},[110,54512,4813],{},[115,54514,117],{},[110,54516,551],{"separator":46},[115,54518,117],{},[110,54520,120],{"stretchy":112},[39,54522,44771],{"encoding":41},[15,54524,54526,54544],{"className":54525,"ariaHidden":46},[45],[15,54527,54529,54532,54535,54538,54541],{"className":54528},[50],[15,54530],{"className":54531,"style":5924},[54],[15,54533,44754],{"className":54534,"style":44784},[59,60],[15,54536],{"className":54537,"style":158},[157],[15,54539,5909],{"className":54540},[162],[15,54542],{"className":54543,"style":158},[157],[15,54545,54547,54550,54553,54556,54559,54562,54565,54568],{"className":54546},[50],[15,54548],{"className":54549,"style":139},[54],[15,54551,113],{"className":54552},[146],[15,54554,4813],{"className":54555},[59],[15,54557,117],{"className":54558},[59],[15,54560,551],{"className":54561},[573],[15,54563],{"className":54564,"style":406},[157],[15,54566,117],{"className":54567},[59],[15,54569,120],{"className":54570},[153],[52595,54572,54573],{},[15,54574,54576,54632],{"className":54575,"translate":19},[18],[15,54577,54579],{"className":54578},[23],[25,54580,54581],{"xmlns":27},[29,54582,54583,54629],{},[32,54584,54585,54601,54603,54605,54607,54627],{},[238,54586,54587,54589],{},[115,54588,38989],{},[32,54590,54591,54593,54595],{},[115,54592,117],{},[110,54594,4813],{},[6814,54596,54597,54599],{},[35,54598,44754],{},[115,54600,2463],{},[110,54602,113],{"stretchy":112},[115,54604,117],{},[110,54606,4813],{},[6814,54608,54609,54611],{},[35,54610,769],{},[32,54612,54613,54615,54617,54619,54621,54623,54625],{},[110,54614,113],{"stretchy":112},[115,54616,117],{},[110,54618,2470],{},[35,54620,44754],{},[110,54622,120],{"stretchy":112},[35,54624,941],{"mathvariant":209},[115,54626,2463],{},[110,54628,120],{"stretchy":112},[39,54630,54631],{"encoding":41},"\\frac{4}{1-\\alpha^2}(1-t^{(1+\\alpha)\u002F2})",[15,54633,54635,54756],{"className":54634,"ariaHidden":46},[45],[15,54636,54638,54641,54741,54744,54747,54750,54753],{"className":54637},[50],[15,54639],{"className":54640,"style":45405},[54],[15,54642,54644,54647,54738],{"className":54643},[59],[15,54645],{"className":54646},[146,441],[15,54648,54650],{"className":54649},[238],[15,54651,54653,54730],{"className":54652},[285,286],[15,54654,54656,54727],{"className":54655},[290],[15,54657,54659,54705,54713],{"className":54658,"style":2524},[294],[15,54660,54661,54664],{"style":2527},[15,54662],{"className":54663,"style":461},[302],[15,54665,54667],{"className":54666},[307,308,309,310],[15,54668,54670,54673,54676],{"className":54669},[59,310],[15,54671,117],{"className":54672},[59,310],[15,54674,4813],{"className":54675},[2591,310],[15,54677,54679,54682],{"className":54678},[59,310],[15,54680,44754],{"className":54681,"style":44784},[59,60,310],[15,54683,54685],{"className":54684},[281],[15,54686,54688],{"className":54687},[285],[15,54689,54691],{"className":54690},[290],[15,54692,54694],{"className":54693,"style":45459},[294],[15,54695,54696,54699],{"style":45462},[15,54697],{"className":54698,"style":30206},[302],[15,54700,54702],{"className":54701},[307,30210,9674,310],[15,54703,2463],{"className":54704},[59,310],[15,54706,54707,54710],{"style":473},[15,54708],{"className":54709,"style":461},[302],[15,54711],{"className":54712,"style":481},[480],[15,54714,54715,54718],{"style":2550},[15,54716],{"className":54717,"style":461},[302],[15,54719,54721],{"className":54720},[307,308,309,310],[15,54722,54724],{"className":54723},[59,310],[15,54725,38989],{"className":54726},[59,310],[15,54728,318],{"className":54729},[317],[15,54731,54733],{"className":54732},[290],[15,54734,54736],{"className":54735,"style":16429},[294],[15,54737],{},[15,54739],{"className":54740},[153,441],[15,54742,113],{"className":54743},[146],[15,54745,117],{"className":54746},[59],[15,54748],{"className":54749,"style":2587},[157],[15,54751,4813],{"className":54752},[2591],[15,54754],{"className":54755,"style":2587},[157],[15,54757,54759,54763,54811],{"className":54758},[50],[15,54760],{"className":54761,"style":54762},[54],"height:1.138em;vertical-align:-0.25em;",[15,54764,54766,54769],{"className":54765},[59],[15,54767,769],{"className":54768},[59,60],[15,54770,54772],{"className":54771},[281],[15,54773,54775],{"className":54774},[285],[15,54776,54778],{"className":54777},[290],[15,54779,54782],{"className":54780,"style":54781},[294],"height:0.888em;",[15,54783,54784,54787],{"style":6865},[15,54785],{"className":54786,"style":303},[302],[15,54788,54790],{"className":54789},[307,308,309,310],[15,54791,54793,54796,54799,54802,54805,54808],{"className":54792},[59,310],[15,54794,113],{"className":54795},[146,310],[15,54797,117],{"className":54798},[59,310],[15,54800,2470],{"className":54801},[2591,310],[15,54803,44754],{"className":54804,"style":44784},[59,60,310],[15,54806,120],{"className":54807},[153,310],[15,54809,45150],{"className":54810},[59,310],[15,54812,120],{"className":54813},[153],[52595,54815,52755],{},[52595,54817,52755],{},[52595,54819,54820,54821,53475],{},"有限（",[15,54822,54824,54844],{"className":54823,"translate":19},[18],[15,54825,54827],{"className":54826},[23],[25,54828,54829],{"xmlns":27},[29,54830,54831,54841],{},[32,54832,54833,54835,54837,54839],{},[35,54834,44754],{},[110,54836,49507],{"mathvariant":209},[110,54838,46608],{},[115,54840,117],{},[39,54842,54843],{"encoding":41},"\\alpha\\ne\\pm1",[15,54845,54847,54898],{"className":54846,"ariaHidden":46},[45],[15,54848,54850,54853,54856,54859,54895],{"className":54849},[50],[15,54851],{"className":54852,"style":55},[54],[15,54854,44754],{"className":54855,"style":44784},[59,60],[15,54857],{"className":54858,"style":158},[157],[15,54860,54862,54889,54892],{"className":54861},[162],[15,54863,54865],{"className":54864},[162],[15,54866,54868],{"className":54867},[59,4400],[15,54869,54871],{"className":54870},[4404],[15,54872,54874,54877,54886],{"className":54873},[4408],[15,54875],{"className":54876,"style":55},[54],[15,54878,54880],{"className":54879},[4415],[15,54881,54883],{"className":54882},[59],[15,54884,4422],{"className":54885},[162],[15,54887],{"className":54888},[4426],[15,54890],{"className":54891},[157,4430],[15,54893,123],{"className":54894},[162],[15,54896],{"className":54897,"style":158},[157],[15,54899,54901,54904,54907],{"className":54900},[50],[15,54902],{"className":54903,"style":12578},[54],[15,54905,46608],{"className":54906},[59],[15,54908,117],{"className":54909},[59],[528,54911,54913],{"id":54912},"_4-基本性质","4. 基本性质",[11,54915,54916,54917,15795,54981,55138,55139,10180],{},"下列性质逐个给出推导。约定 ",[15,54918,54920,54942],{"className":54919,"translate":19},[18],[15,54921,54923],{"className":54922},[23],[25,54924,54925],{"xmlns":27},[29,54926,54927,54939],{},[32,54928,54929,54931,54933,54935,54937],{},[35,54930,206],{},[110,54932,551],{"separator":46},[35,54934,213],{},[110,54936,714],{},[35,54938,2364],{},[39,54940,54941],{"encoding":41},"P,Q\\ll\\mu",[15,54943,54945,54972],{"className":54944,"ariaHidden":46},[45],[15,54946,54948,54951,54954,54957,54960,54963,54966,54969],{"className":54947},[50],[15,54949],{"className":54950,"style":566},[54],[15,54952,206],{"className":54953,"style":334},[59,60],[15,54955,551],{"className":54956},[573],[15,54958],{"className":54959,"style":406},[157],[15,54961,213],{"className":54962},[59,60],[15,54964],{"className":54965,"style":158},[157],[15,54967,714],{"className":54968},[162],[15,54970],{"className":54971,"style":158},[157],[15,54973,54975,54978],{"className":54974},[50],[15,54976],{"className":54977,"style":2276},[54],[15,54979,2364],{"className":54980},[59,60],[15,54982,54984,55016],{"className":54983,"translate":19},[18],[15,54985,54987],{"className":54986},[23],[25,54988,54989],{"xmlns":27},[29,54990,54991,55013],{},[32,54992,54993,54995,54997,55003,55005,55007,55009,55011],{},[35,54994,2364],{},[110,54996,123],{},[238,54998,54999,55001],{},[115,55000,117],{},[115,55002,2463],{},[110,55004,113],{"stretchy":112},[35,55006,206],{},[110,55008,2470],{},[35,55010,213],{},[110,55012,120],{"stretchy":112},[39,55014,55015],{"encoding":41},"\\mu=\\frac12(P+Q)",[15,55017,55019,55037,55126],{"className":55018,"ariaHidden":46},[45],[15,55020,55022,55025,55028,55031,55034],{"className":55021},[50],[15,55023],{"className":55024,"style":2276},[54],[15,55026,2364],{"className":55027},[59,60],[15,55029],{"className":55030,"style":158},[157],[15,55032,123],{"className":55033},[162],[15,55035],{"className":55036,"style":158},[157],[15,55038,55040,55043,55111,55114,55117,55120,55123],{"className":55039},[50],[15,55041],{"className":55042,"style":2505},[54],[15,55044,55046,55049,55108],{"className":55045},[59],[15,55047],{"className":55048},[146,441],[15,55050,55052],{"className":55051},[238],[15,55053,55055,55100],{"className":55054},[285,286],[15,55056,55058,55097],{"className":55057},[290],[15,55059,55061,55075,55083],{"className":55060,"style":2524},[294],[15,55062,55063,55066],{"style":2527},[15,55064],{"className":55065,"style":461},[302],[15,55067,55069],{"className":55068},[307,308,309,310],[15,55070,55072],{"className":55071},[59,310],[15,55073,2463],{"className":55074},[59,310],[15,55076,55077,55080],{"style":473},[15,55078],{"className":55079,"style":461},[302],[15,55081],{"className":55082,"style":481},[480],[15,55084,55085,55088],{"style":2550},[15,55086],{"className":55087,"style":461},[302],[15,55089,55091],{"className":55090},[307,308,309,310],[15,55092,55094],{"className":55093},[59,310],[15,55095,117],{"className":55096},[59,310],[15,55098,318],{"className":55099},[317],[15,55101,55103],{"className":55102},[290],[15,55104,55106],{"className":55105,"style":2572},[294],[15,55107],{},[15,55109],{"className":55110},[153,441],[15,55112,113],{"className":55113},[146],[15,55115,206],{"className":55116,"style":334},[59,60],[15,55118],{"className":55119,"style":2587},[157],[15,55121,2470],{"className":55122},[2591],[15,55124],{"className":55125,"style":2587},[157],[15,55127,55129,55132,55135],{"className":55128},[50],[15,55130],{"className":55131,"style":139},[54],[15,55133,213],{"className":55134},[59,60],[15,55136,120],{"className":55137},[153]," 或任一控制测度），",[15,55140,55142,55167],{"className":55141,"translate":19},[18],[15,55143,55145],{"className":55144},[23],[25,55146,55147],{"xmlns":27},[29,55148,55149,55165],{},[32,55150,55151,55153,55155,55157,55159,55161,55163],{},[35,55152,769],{},[110,55154,123],{},[35,55156,244],{},[35,55158,206],{},[35,55160,941],{"mathvariant":209},[35,55162,244],{},[35,55164,213],{},[39,55166,5333],{"encoding":41},[15,55168,55170,55188],{"className":55169,"ariaHidden":46},[45],[15,55171,55173,55176,55179,55182,55185],{"className":55172},[50],[15,55174],{"className":55175,"style":5343},[54],[15,55177,769],{"className":55178},[59,60],[15,55180],{"className":55181,"style":158},[157],[15,55183,123],{"className":55184},[162],[15,55186],{"className":55187,"style":158},[157],[15,55189,55191,55194,55197,55200,55203,55206],{"className":55190},[50],[15,55192],{"className":55193,"style":139},[54],[15,55195,244],{"className":55196},[59,60],[15,55198,206],{"className":55199,"style":334},[59,60],[15,55201,941],{"className":55202},[59],[15,55204,244],{"className":55205},[59,60],[15,55207,213],{"className":55208},[59,60],[2311,55210,55212],{"id":55211},"_41-非负性","4.1 非负性",[993,55214,55216,55260,55385],{"title":55215},"命题 4.1（非负性）",[11,55217,55218,55219,2745],{},"对一切概率分布 ",[15,55220,55222,55239],{"className":55221,"translate":19},[18],[15,55223,55225],{"className":55224},[23],[25,55226,55227],{"xmlns":27},[29,55228,55229,55237],{},[32,55230,55231,55233,55235],{},[35,55232,206],{},[110,55234,551],{"separator":46},[35,55236,213],{},[39,55238,556],{"encoding":41},[15,55240,55242],{"className":55241,"ariaHidden":46},[45],[15,55243,55245,55248,55251,55254,55257],{"className":55244},[50],[15,55246],{"className":55247,"style":566},[54],[15,55249,206],{"className":55250,"style":334},[59,60],[15,55252,551],{"className":55253},[573],[15,55255],{"className":55256,"style":406},[157],[15,55258,213],{"className":55259},[59,60],[15,55261,55263],{"className":55262,"translate":19},[180],[15,55264,55266,55300],{"className":55265,"translate":19},[18],[15,55267,55269],{"className":55268},[23],[25,55270,55271],{"xmlns":27,"display":189},[29,55272,55273,55297],{},[32,55274,55275,55281,55283,55285,55287,55289,55291,55293,55295],{},[195,55276,55277,55279],{},[35,55278,199],{},[35,55280,37],{},[110,55282,113],{"stretchy":112},[35,55284,206],{},[35,55286,210],{"mathvariant":209},[35,55288,213],{},[110,55290,120],{"stretchy":112},[110,55292,6928],{},[115,55294,126],{},[110,55296,551],{"separator":46},[39,55298,55299],{"encoding":41},"D_f(P\\|Q)\\ge 0,",[15,55301,55303,55373],{"className":55302,"ariaHidden":46},[45],[15,55304,55306,55309,55349,55352,55355,55358,55361,55364,55367,55370],{"className":55305},[50],[15,55307],{"className":55308,"style":270},[54],[15,55310,55312,55315],{"className":55311},[59],[15,55313,199],{"className":55314,"style":277},[59,60],[15,55316,55318],{"className":55317},[281],[15,55319,55321,55341],{"className":55320},[285,286],[15,55322,55324,55338],{"className":55323},[290],[15,55325,55327],{"className":55326,"style":295},[294],[15,55328,55329,55332],{"style":298},[15,55330],{"className":55331,"style":303},[302],[15,55333,55335],{"className":55334},[307,308,309,310],[15,55336,37],{"className":55337,"style":61},[59,60,310],[15,55339,318],{"className":55340},[317],[15,55342,55344],{"className":55343},[290],[15,55345,55347],{"className":55346,"style":325},[294],[15,55348],{},[15,55350,113],{"className":55351},[146],[15,55353,206],{"className":55354,"style":334},[59,60],[15,55356,210],{"className":55357},[59],[15,55359,213],{"className":55360},[59,60],[15,55362,120],{"className":55363},[153],[15,55365],{"className":55366,"style":158},[157],[15,55368,6928],{"className":55369},[162],[15,55371],{"className":55372,"style":158},[157],[15,55374,55376,55379,55382],{"className":55375},[50],[15,55377],{"className":55378,"style":9358},[54],[15,55380,126],{"className":55381},[59],[15,55383,551],{"className":55384},[573],[11,55386,55387,55388,55416,55417,10180],{},"且当 ",[15,55389,55391,55404],{"className":55390,"translate":19},[18],[15,55392,55394],{"className":55393},[23],[25,55395,55396],{"xmlns":27},[29,55397,55398,55402],{},[32,55399,55400],{},[35,55401,37],{},[39,55403,37],{"encoding":41},[15,55405,55407],{"className":55406,"ariaHidden":46},[45],[15,55408,55410,55413],{"className":55409},[50],[15,55411],{"className":55412,"style":55},[54],[15,55414,37],{"className":55415,"style":61},[59,60]," 严格凸时，等号成立当且仅当 ",[15,55418,55420,55437],{"className":55419,"translate":19},[18],[15,55421,55423],{"className":55422},[23],[25,55424,55425],{"xmlns":27},[29,55426,55427,55435],{},[32,55428,55429,55431,55433],{},[35,55430,206],{},[110,55432,123],{},[35,55434,213],{},[39,55436,10271],{"encoding":41},[15,55438,55440,55458],{"className":55439,"ariaHidden":46},[45],[15,55441,55443,55446,55449,55452,55455],{"className":55442},[50],[15,55444],{"className":55445,"style":664},[54],[15,55447,206],{"className":55448,"style":334},[59,60],[15,55450],{"className":55451,"style":158},[157],[15,55453,123],{"className":55454},[162],[15,55456],{"className":55457,"style":158},[157],[15,55459,55461,55464],{"className":55460},[50],[15,55462],{"className":55463,"style":566},[54],[15,55465,213],{"className":55466},[59,60],[11,55468,55469,55472,55473,55502,55503,55531,55532,3853,55661,55689,55690,55740,55741,55769,55770,55938,55939,56031,56032,56082,56083,56133],{},[1225,55470,55471],{},"证明。"," Jensen 已给出 ",[15,55474,55476,55490],{"className":55475,"translate":19},[18],[15,55477,55479],{"className":55478},[23],[25,55480,55481],{"xmlns":27},[29,55482,55483,55487],{},[32,55484,55485],{},[110,55486,6928],{},[39,55488,55489],{"encoding":41},"\\ge",[15,55491,55493],{"className":55492,"ariaHidden":46},[45],[15,55494,55496,55499],{"className":55495},[50],[15,55497],{"className":55498,"style":43188},[54],[15,55500,6928],{"className":55501},[162],"（见 2.1）。等号条件：若 ",[15,55504,55506,55519],{"className":55505,"translate":19},[18],[15,55507,55509],{"className":55508},[23],[25,55510,55511],{"xmlns":27},[29,55512,55513,55517],{},[32,55514,55515],{},[35,55516,37],{},[39,55518,37],{"encoding":41},[15,55520,55522],{"className":55521,"ariaHidden":46},[45],[15,55523,55525,55528],{"className":55524},[50],[15,55526],{"className":55527,"style":55},[54],[15,55529,37],{"className":55530,"style":61},[59,60]," 严格凸，Jensen 取等号当且仅当 ",[15,55533,55535,55567],{"className":55534,"translate":19},[18],[15,55536,55538],{"className":55537},[23],[25,55539,55540],{"xmlns":27},[29,55541,55542,55564],{},[32,55543,55544,55546,55548,55554,55556,55558,55560,55562],{},[35,55545,769],{},[110,55547,123],{},[195,55549,55550,55552],{},[35,55551,223],{"mathvariant":222},[35,55553,213],{},[110,55555,230],{"stretchy":112},[35,55557,769],{},[110,55559,257],{"stretchy":112},[110,55561,123],{},[115,55563,117],{},[39,55565,55566],{"encoding":41},"t=\\mathbb E_Q[t]=1",[15,55568,55570,55588,55652],{"className":55569,"ariaHidden":46},[45],[15,55571,55573,55576,55579,55582,55585],{"className":55572},[50],[15,55574],{"className":55575,"style":5343},[54],[15,55577,769],{"className":55578},[59,60],[15,55580],{"className":55581,"style":158},[157],[15,55583,123],{"className":55584},[162],[15,55586],{"className":55587,"style":158},[157],[15,55589,55591,55594,55634,55637,55640,55643,55646,55649],{"className":55590},[50],[15,55592],{"className":55593,"style":270},[54],[15,55595,55597,55600],{"className":55596},[59],[15,55598,223],{"className":55599},[59,366],[15,55601,55603],{"className":55602},[281],[15,55604,55606,55626],{"className":55605},[285,286],[15,55607,55609,55623],{"className":55608},[290],[15,55610,55612],{"className":55611,"style":379},[294],[15,55613,55614,55617],{"style":382},[15,55615],{"className":55616,"style":303},[302],[15,55618,55620],{"className":55619},[307,308,309,310],[15,55621,213],{"className":55622},[59,60,310],[15,55624,318],{"className":55625},[317],[15,55627,55629],{"className":55628},[290],[15,55630,55632],{"className":55631,"style":325},[294],[15,55633],{},[15,55635,230],{"className":55636},[146],[15,55638,769],{"className":55639},[59,60],[15,55641,257],{"className":55642},[153],[15,55644],{"className":55645,"style":158},[157],[15,55647,123],{"className":55648},[162],[15,55650],{"className":55651,"style":158},[157],[15,55653,55655,55658],{"className":55654},[50],[15,55656],{"className":55657,"style":172},[54],[15,55659,117],{"className":55660},[59],[15,55662,55664,55677],{"className":55663,"translate":19},[18],[15,55665,55667],{"className":55666},[23],[25,55668,55669],{"xmlns":27},[29,55670,55671,55675],{},[32,55672,55673],{},[35,55674,213],{},[39,55676,213],{"encoding":41},[15,55678,55680],{"className":55679,"ariaHidden":46},[45],[15,55681,55683,55686],{"className":55682},[50],[15,55684],{"className":55685,"style":566},[54],[15,55687,213],{"className":55688},[59,60]," 下几乎必然成立，即 ",[15,55691,55693,55710],{"className":55692,"translate":19},[18],[15,55694,55696],{"className":55695},[23],[25,55697,55698],{"xmlns":27},[29,55699,55700,55708],{},[32,55701,55702,55704,55706],{},[35,55703,206],{},[110,55705,123],{},[35,55707,213],{},[39,55709,10271],{"encoding":41},[15,55711,55713,55731],{"className":55712,"ariaHidden":46},[45],[15,55714,55716,55719,55722,55725,55728],{"className":55715},[50],[15,55717],{"className":55718,"style":664},[54],[15,55720,206],{"className":55721,"style":334},[59,60],[15,55723],{"className":55724,"style":158},[157],[15,55726,123],{"className":55727},[162],[15,55729],{"className":55730,"style":158},[157],[15,55732,55734,55737],{"className":55733},[50],[15,55735],{"className":55736,"style":566},[54],[15,55738,213],{"className":55739},[59,60],"。若 ",[15,55742,55744,55757],{"className":55743,"translate":19},[18],[15,55745,55747],{"className":55746},[23],[25,55748,55749],{"xmlns":27},[29,55750,55751,55755],{},[32,55752,55753],{},[35,55754,37],{},[39,55756,37],{"encoding":41},[15,55758,55760],{"className":55759,"ariaHidden":46},[45],[15,55761,55763,55766],{"className":55762},[50],[15,55764],{"className":55765,"style":55},[54],[15,55767,37],{"className":55768,"style":61},[59,60]," 只是凸而非严格凸（如 ",[15,55771,55773,55810],{"className":55772,"translate":19},[18],[15,55774,55776],{"className":55775},[23],[25,55777,55778],{"xmlns":27},[29,55779,55780,55808],{},[32,55781,55782,55784,55786,55788,55790,55792,55798,55800,55802,55804,55806],{},[35,55783,37],{},[110,55785,113],{"stretchy":112},[35,55787,769],{},[110,55789,120],{"stretchy":112},[110,55791,123],{},[238,55793,55794,55796],{},[115,55795,117],{},[115,55797,2463],{},[35,55799,4808],{"mathvariant":209},[35,55801,769],{},[110,55803,4813],{},[115,55805,117],{},[35,55807,4808],{"mathvariant":209},[39,55809,34556],{"encoding":41},[15,55811,55813,55840,55929],{"className":55812,"ariaHidden":46},[45],[15,55814,55816,55819,55822,55825,55828,55831,55834,55837],{"className":55815},[50],[15,55817],{"className":55818,"style":139},[54],[15,55820,37],{"className":55821,"style":61},[59,60],[15,55823,113],{"className":55824},[146],[15,55826,769],{"className":55827},[59,60],[15,55829,120],{"className":55830},[153],[15,55832],{"className":55833,"style":158},[157],[15,55835,123],{"className":55836},[162],[15,55838],{"className":55839,"style":158},[157],[15,55841,55843,55846,55914,55917,55920,55923,55926],{"className":55842},[50],[15,55844],{"className":55845,"style":2505},[54],[15,55847,55849,55852,55911],{"className":55848},[59],[15,55850],{"className":55851},[146,441],[15,55853,55855],{"className":55854},[238],[15,55856,55858,55903],{"className":55857},[285,286],[15,55859,55861,55900],{"className":55860},[290],[15,55862,55864,55878,55886],{"className":55863,"style":2524},[294],[15,55865,55866,55869],{"style":2527},[15,55867],{"className":55868,"style":461},[302],[15,55870,55872],{"className":55871},[307,308,309,310],[15,55873,55875],{"className":55874},[59,310],[15,55876,2463],{"className":55877},[59,310],[15,55879,55880,55883],{"style":473},[15,55881],{"className":55882,"style":461},[302],[15,55884],{"className":55885,"style":481},[480],[15,55887,55888,55891],{"style":2550},[15,55889],{"className":55890,"style":461},[302],[15,55892,55894],{"className":55893},[307,308,309,310],[15,55895,55897],{"className":55896},[59,310],[15,55898,117],{"className":55899},[59,310],[15,55901,318],{"className":55902},[317],[15,55904,55906],{"className":55905},[290],[15,55907,55909],{"className":55908,"style":2572},[294],[15,55910],{},[15,55912],{"className":55913},[153,441],[15,55915,4808],{"className":55916},[59],[15,55918,769],{"className":55919},[59,60],[15,55921],{"className":55922,"style":2587},[157],[15,55924,4813],{"className":55925},[2591],[15,55927],{"className":55928,"style":2587},[157],[15,55930,55932,55935],{"className":55931},[50],[15,55933],{"className":55934,"style":139},[54],[15,55936,34679],{"className":55937},[59],"），则只能保证 ",[15,55940,55942,55964],{"className":55941,"translate":19},[18],[15,55943,55945],{"className":55944},[23],[25,55946,55947],{"xmlns":27},[29,55948,55949,55961],{},[32,55950,55951,55957,55959],{},[195,55952,55953,55955],{},[35,55954,199],{},[35,55956,37],{},[110,55958,123],{},[115,55960,126],{},[39,55962,55963],{"encoding":41},"D_f=0",[15,55965,55967,56022],{"className":55966,"ariaHidden":46},[45],[15,55968,55970,55973,56013,56016,56019],{"className":55969},[50],[15,55971],{"className":55972,"style":4032},[54],[15,55974,55976,55979],{"className":55975},[59],[15,55977,199],{"className":55978,"style":277},[59,60],[15,55980,55982],{"className":55981},[281],[15,55983,55985,56005],{"className":55984},[285,286],[15,55986,55988,56002],{"className":55987},[290],[15,55989,55991],{"className":55990,"style":295},[294],[15,55992,55993,55996],{"style":298},[15,55994],{"className":55995,"style":303},[302],[15,55997,55999],{"className":55998},[307,308,309,310],[15,56000,37],{"className":56001,"style":61},[59,60,310],[15,56003,318],{"className":56004},[317],[15,56006,56008],{"className":56007},[290],[15,56009,56011],{"className":56010,"style":325},[294],[15,56012],{},[15,56014],{"className":56015,"style":158},[157],[15,56017,123],{"className":56018},[162],[15,56020],{"className":56021,"style":158},[157],[15,56023,56025,56028],{"className":56024},[50],[15,56026],{"className":56027,"style":172},[54],[15,56029,126],{"className":56030},[59]," 时不必然 ",[15,56033,56035,56052],{"className":56034,"translate":19},[18],[15,56036,56038],{"className":56037},[23],[25,56039,56040],{"xmlns":27},[29,56041,56042,56050],{},[32,56043,56044,56046,56048],{},[35,56045,206],{},[110,56047,123],{},[35,56049,213],{},[39,56051,10271],{"encoding":41},[15,56053,56055,56073],{"className":56054,"ariaHidden":46},[45],[15,56056,56058,56061,56064,56067,56070],{"className":56057},[50],[15,56059],{"className":56060,"style":664},[54],[15,56062,206],{"className":56063,"style":334},[59,60],[15,56065],{"className":56066,"style":158},[157],[15,56068,123],{"className":56069},[162],[15,56071],{"className":56072,"style":158},[157],[15,56074,56076,56079],{"className":56075},[50],[15,56077],{"className":56078,"style":566},[54],[15,56080,213],{"className":56081},[59,60],"：TV 是反例，",[15,56084,56086,56103],{"className":56085,"translate":19},[18],[15,56087,56089],{"className":56088},[23],[25,56090,56091],{"xmlns":27},[29,56092,56093,56101],{},[32,56094,56095,56097,56099],{},[35,56096,206],{},[110,56098,123],{},[35,56100,213],{},[39,56102,10271],{"encoding":41},[15,56104,56106,56124],{"className":56105,"ariaHidden":46},[45],[15,56107,56109,56112,56115,56118,56121],{"className":56108},[50],[15,56110],{"className":56111,"style":664},[54],[15,56113,206],{"className":56114,"style":334},[59,60],[15,56116],{"className":56117,"style":158},[157],[15,56119,123],{"className":56120},[162],[15,56122],{"className":56123,"style":158},[157],[15,56125,56127,56130],{"className":56126},[50],[15,56128],{"className":56129,"style":566},[54],[15,56131,213],{"className":56132},[59,60]," 时才是唯一使 TV 为 0 的一对（TV 也对）。",[2311,56135,56137],{"id":56136},"_42-联合凸性","4.2 联合凸性",[993,56139,56141,56610],{"title":56140},"命题 4.2（联合凸性）",[11,56142,56143,56144,2745,56340,2745,56536,41638],{},"若 ",[15,56145,56147,56188],{"className":56146,"translate":19},[18],[15,56148,56150],{"className":56149},[23],[25,56151,56152],{"xmlns":27},[29,56153,56154,56186],{},[32,56155,56156,56158,56160,56162,56168,56170,56172,56174,56176,56178,56180],{},[35,56157,206],{},[110,56159,123],{},[35,56161,11339],{},[195,56163,56164,56166],{},[35,56165,206],{},[115,56167,117],{},[110,56169,2470],{},[110,56171,113],{"stretchy":112},[115,56173,117],{},[110,56175,4813],{},[35,56177,11339],{},[110,56179,120],{"stretchy":112},[195,56181,56182,56184],{},[35,56183,206],{},[115,56185,2463],{},[39,56187,11446],{"encoding":41},[15,56189,56191,56209,56267,56288],{"className":56190,"ariaHidden":46},[45],[15,56192,56194,56197,56200,56203,56206],{"className":56193},[50],[15,56195],{"className":56196,"style":664},[54],[15,56198,206],{"className":56199,"style":334},[59,60],[15,56201],{"className":56202,"style":158},[157],[15,56204,123],{"className":56205},[162],[15,56207],{"className":56208,"style":158},[157],[15,56210,56212,56215,56218,56258,56261,56264],{"className":56211},[50],[15,56213],{"className":56214,"style":11474},[54],[15,56216,11339],{"className":56217},[59,60],[15,56219,56221,56224],{"className":56220},[59],[15,56222,206],{"className":56223,"style":334},[59,60],[15,56225,56227],{"className":56226},[281],[15,56228,56230,56250],{"className":56229},[285,286],[15,56231,56233,56247],{"className":56232},[290],[15,56234,56236],{"className":56235,"style":11133},[294],[15,56237,56238,56241],{"style":11136},[15,56239],{"className":56240,"style":303},[302],[15,56242,56244],{"className":56243},[307,308,309,310],[15,56245,117],{"className":56246},[59,310],[15,56248,318],{"className":56249},[317],[15,56251,56253],{"className":56252},[290],[15,56254,56256],{"className":56255,"style":7968},[294],[15,56257],{},[15,56259],{"className":56260,"style":2587},[157],[15,56262,2470],{"className":56263},[2591],[15,56265],{"className":56266,"style":2587},[157],[15,56268,56270,56273,56276,56279,56282,56285],{"className":56269},[50],[15,56271],{"className":56272,"style":139},[54],[15,56274,113],{"className":56275},[146],[15,56277,117],{"className":56278},[59],[15,56280],{"className":56281,"style":2587},[157],[15,56283,4813],{"className":56284},[2591],[15,56286],{"className":56287,"style":2587},[157],[15,56289,56291,56294,56297,56300],{"className":56290},[50],[15,56292],{"className":56293,"style":139},[54],[15,56295,11339],{"className":56296},[59,60],[15,56298,120],{"className":56299},[153],[15,56301,56303,56306],{"className":56302},[59],[15,56304,206],{"className":56305,"style":334},[59,60],[15,56307,56309],{"className":56308},[281],[15,56310,56312,56332],{"className":56311},[285,286],[15,56313,56315,56329],{"className":56314},[290],[15,56316,56318],{"className":56317,"style":11133},[294],[15,56319,56320,56323],{"style":11136},[15,56321],{"className":56322,"style":303},[302],[15,56324,56326],{"className":56325},[307,308,309,310],[15,56327,2463],{"className":56328},[59,310],[15,56330,318],{"className":56331},[317],[15,56333,56335],{"className":56334},[290],[15,56336,56338],{"className":56337,"style":7968},[294],[15,56339],{},[15,56341,56343,56384],{"className":56342,"translate":19},[18],[15,56344,56346],{"className":56345},[23],[25,56347,56348],{"xmlns":27},[29,56349,56350,56382],{},[32,56351,56352,56354,56356,56358,56364,56366,56368,56370,56372,56374,56376],{},[35,56353,213],{},[110,56355,123],{},[35,56357,11339],{},[195,56359,56360,56362],{},[35,56361,213],{},[115,56363,117],{},[110,56365,2470],{},[110,56367,113],{"stretchy":112},[115,56369,117],{},[110,56371,4813],{},[35,56373,11339],{},[110,56375,120],{"stretchy":112},[195,56377,56378,56380],{},[35,56379,213],{},[115,56381,2463],{},[39,56383,11644],{"encoding":41},[15,56385,56387,56405,56463,56484],{"className":56386,"ariaHidden":46},[45],[15,56388,56390,56393,56396,56399,56402],{"className":56389},[50],[15,56391],{"className":56392,"style":566},[54],[15,56394,213],{"className":56395},[59,60],[15,56397],{"className":56398,"style":158},[157],[15,56400,123],{"className":56401},[162],[15,56403],{"className":56404,"style":158},[157],[15,56406,56408,56411,56414,56454,56457,56460],{"className":56407},[50],[15,56409],{"className":56410,"style":55},[54],[15,56412,11339],{"className":56413},[59,60],[15,56415,56417,56420],{"className":56416},[59],[15,56418,213],{"className":56419},[59,60],[15,56421,56423],{"className":56422},[281],[15,56424,56426,56446],{"className":56425},[285,286],[15,56427,56429,56443],{"className":56428},[290],[15,56430,56432],{"className":56431,"style":11133},[294],[15,56433,56434,56437],{"style":382},[15,56435],{"className":56436,"style":303},[302],[15,56438,56440],{"className":56439},[307,308,309,310],[15,56441,117],{"className":56442},[59,310],[15,56444,318],{"className":56445},[317],[15,56447,56449],{"className":56448},[290],[15,56450,56452],{"className":56451,"style":7968},[294],[15,56453],{},[15,56455],{"className":56456,"style":2587},[157],[15,56458,2470],{"className":56459},[2591],[15,56461],{"className":56462,"style":2587},[157],[15,56464,56466,56469,56472,56475,56478,56481],{"className":56465},[50],[15,56467],{"className":56468,"style":139},[54],[15,56470,113],{"className":56471},[146],[15,56473,117],{"className":56474},[59],[15,56476],{"className":56477,"style":2587},[157],[15,56479,4813],{"className":56480},[2591],[15,56482],{"className":56483,"style":2587},[157],[15,56485,56487,56490,56493,56496],{"className":56486},[50],[15,56488],{"className":56489,"style":139},[54],[15,56491,11339],{"className":56492},[59,60],[15,56494,120],{"className":56495},[153],[15,56497,56499,56502],{"className":56498},[59],[15,56500,213],{"className":56501},[59,60],[15,56503,56505],{"className":56504},[281],[15,56506,56508,56528],{"className":56507},[285,286],[15,56509,56511,56525],{"className":56510},[290],[15,56512,56514],{"className":56513,"style":11133},[294],[15,56515,56516,56519],{"style":382},[15,56517],{"className":56518,"style":303},[302],[15,56520,56522],{"className":56521},[307,308,309,310],[15,56523,2463],{"className":56524},[59,310],[15,56526,318],{"className":56527},[317],[15,56529,56531],{"className":56530},[290],[15,56532,56534],{"className":56533,"style":7968},[294],[15,56535],{},[15,56537,56539,56565],{"className":56538,"translate":19},[18],[15,56540,56542],{"className":56541},[23],[25,56543,56544],{"xmlns":27},[29,56545,56546,56562],{},[32,56547,56548,56550,56552,56554,56556,56558,56560],{},[35,56549,11339],{},[110,56551,5909],{},[110,56553,230],{"stretchy":112},[115,56555,126],{},[110,56557,551],{"separator":46},[115,56559,117],{},[110,56561,257],{"stretchy":112},[39,56563,56564],{"encoding":41},"\\lambda\\in[0,1]",[15,56566,56568,56586],{"className":56567,"ariaHidden":46},[45],[15,56569,56571,56574,56577,56580,56583],{"className":56570},[50],[15,56572],{"className":56573,"style":11364},[54],[15,56575,11339],{"className":56576},[59,60],[15,56578],{"className":56579,"style":158},[157],[15,56581,5909],{"className":56582},[162],[15,56584],{"className":56585,"style":158},[157],[15,56587,56589,56592,56595,56598,56601,56604,56607],{"className":56588},[50],[15,56590],{"className":56591,"style":139},[54],[15,56593,230],{"className":56594},[146],[15,56596,126],{"className":56597},[59],[15,56599,551],{"className":56600},[573],[15,56602],{"className":56603,"style":406},[157],[15,56605,117],{"className":56606},[59],[15,56608,257],{"className":56609},[153],[15,56611,56613],{"className":56612,"translate":19},[180],[15,56614,56616,56710],{"className":56615,"translate":19},[18],[15,56617,56619],{"className":56618},[23],[25,56620,56621],{"xmlns":27,"display":189},[29,56622,56623,56707],{},[32,56624,56625,56631,56633,56635,56637,56639,56641,56643,56645,56651,56653,56659,56661,56667,56669,56671,56673,56675,56677,56679,56681,56687,56689,56695,56697,56703,56705],{},[195,56626,56627,56629],{},[35,56628,199],{},[35,56630,37],{},[110,56632,113],{"stretchy":112},[35,56634,206],{},[35,56636,210],{"mathvariant":209},[35,56638,213],{},[110,56640,120],{"stretchy":112},[110,56642,9952],{},[35,56644,11339],{},[195,56646,56647,56649],{},[35,56648,199],{},[35,56650,37],{},[110,56652,113],{"stretchy":112},[195,56654,56655,56657],{},[35,56656,206],{},[115,56658,117],{},[35,56660,210],{"mathvariant":209},[195,56662,56663,56665],{},[35,56664,213],{},[115,56666,117],{},[110,56668,120],{"stretchy":112},[110,56670,2470],{},[110,56672,113],{"stretchy":112},[115,56674,117],{},[110,56676,4813],{},[35,56678,11339],{},[110,56680,120],{"stretchy":112},[195,56682,56683,56685],{},[35,56684,199],{},[35,56686,37],{},[110,56688,113],{"stretchy":112},[195,56690,56691,56693],{},[35,56692,206],{},[115,56694,2463],{},[35,56696,210],{"mathvariant":209},[195,56698,56699,56701],{},[35,56700,213],{},[115,56702,2463],{},[110,56704,120],{"stretchy":112},[35,56706,4375],{"mathvariant":209},[39,56708,56709],{"encoding":41},"D_f(P\\|Q)\n\\le \\lambda D_f(P_1\\|Q_1)\n+(1-\\lambda)D_f(P_2\\|Q_2).",[15,56711,56713,56783,56930,56951],{"className":56712,"ariaHidden":46},[45],[15,56714,56716,56719,56759,56762,56765,56768,56771,56774,56777,56780],{"className":56715},[50],[15,56717],{"className":56718,"style":270},[54],[15,56720,56722,56725],{"className":56721},[59],[15,56723,199],{"className":56724,"style":277},[59,60],[15,56726,56728],{"className":56727},[281],[15,56729,56731,56751],{"className":56730},[285,286],[15,56732,56734,56748],{"className":56733},[290],[15,56735,56737],{"className":56736,"style":295},[294],[15,56738,56739,56742],{"style":298},[15,56740],{"className":56741,"style":303},[302],[15,56743,56745],{"className":56744},[307,308,309,310],[15,56746,37],{"className":56747,"style":61},[59,60,310],[15,56749,318],{"className":56750},[317],[15,56752,56754],{"className":56753},[290],[15,56755,56757],{"className":56756,"style":325},[294],[15,56758],{},[15,56760,113],{"className":56761},[146],[15,56763,206],{"className":56764,"style":334},[59,60],[15,56766,210],{"className":56767},[59],[15,56769,213],{"className":56770},[59,60],[15,56772,120],{"className":56773},[153],[15,56775],{"className":56776,"style":158},[157],[15,56778,9952],{"className":56779},[162],[15,56781],{"className":56782,"style":158},[157],[15,56784,56786,56789,56792,56832,56835,56875,56878,56918,56921,56924,56927],{"className":56785},[50],[15,56787],{"className":56788,"style":270},[54],[15,56790,11339],{"className":56791},[59,60],[15,56793,56795,56798],{"className":56794},[59],[15,56796,199],{"className":56797,"style":277},[59,60],[15,56799,56801],{"className":56800},[281],[15,56802,56804,56824],{"className":56803},[285,286],[15,56805,56807,56821],{"className":56806},[290],[15,56808,56810],{"className":56809,"style":295},[294],[15,56811,56812,56815],{"style":298},[15,56813],{"className":56814,"style":303},[302],[15,56816,56818],{"className":56817},[307,308,309,310],[15,56819,37],{"className":56820,"style":61},[59,60,310],[15,56822,318],{"className":56823},[317],[15,56825,56827],{"className":56826},[290],[15,56828,56830],{"className":56829,"style":325},[294],[15,56831],{},[15,56833,113],{"className":56834},[146],[15,56836,56838,56841],{"className":56837},[59],[15,56839,206],{"className":56840,"style":334},[59,60],[15,56842,56844],{"className":56843},[281],[15,56845,56847,56867],{"className":56846},[285,286],[15,56848,56850,56864],{"className":56849},[290],[15,56851,56853],{"className":56852,"style":11133},[294],[15,56854,56855,56858],{"style":11136},[15,56856],{"className":56857,"style":303},[302],[15,56859,56861],{"className":56860},[307,308,309,310],[15,56862,117],{"className":56863},[59,310],[15,56865,318],{"className":56866},[317],[15,56868,56870],{"className":56869},[290],[15,56871,56873],{"className":56872,"style":7968},[294],[15,56874],{},[15,56876,210],{"className":56877},[59],[15,56879,56881,56884],{"className":56880},[59],[15,56882,213],{"className":56883},[59,60],[15,56885,56887],{"className":56886},[281],[15,56888,56890,56910],{"className":56889},[285,286],[15,56891,56893,56907],{"className":56892},[290],[15,56894,56896],{"className":56895,"style":11133},[294],[15,56897,56898,56901],{"style":382},[15,56899],{"className":56900,"style":303},[302],[15,56902,56904],{"className":56903},[307,308,309,310],[15,56905,117],{"className":56906},[59,310],[15,56908,318],{"className":56909},[317],[15,56911,56913],{"className":56912},[290],[15,56914,56916],{"className":56915,"style":7968},[294],[15,56917],{},[15,56919,120],{"className":56920},[153],[15,56922],{"className":56923,"style":2587},[157],[15,56925,2470],{"className":56926},[2591],[15,56928],{"className":56929,"style":2587},[157],[15,56931,56933,56936,56939,56942,56945,56948],{"className":56932},[50],[15,56934],{"className":56935,"style":139},[54],[15,56937,113],{"className":56938},[146],[15,56940,117],{"className":56941},[59],[15,56943],{"className":56944,"style":2587},[157],[15,56946,4813],{"className":56947},[2591],[15,56949],{"className":56950,"style":2587},[157],[15,56952,56954,56957,56960,56963,57003,57006,57046,57049,57089,57092],{"className":56953},[50],[15,56955],{"className":56956,"style":270},[54],[15,56958,11339],{"className":56959},[59,60],[15,56961,120],{"className":56962},[153],[15,56964,56966,56969],{"className":56965},[59],[15,56967,199],{"className":56968,"style":277},[59,60],[15,56970,56972],{"className":56971},[281],[15,56973,56975,56995],{"className":56974},[285,286],[15,56976,56978,56992],{"className":56977},[290],[15,56979,56981],{"className":56980,"style":295},[294],[15,56982,56983,56986],{"style":298},[15,56984],{"className":56985,"style":303},[302],[15,56987,56989],{"className":56988},[307,308,309,310],[15,56990,37],{"className":56991,"style":61},[59,60,310],[15,56993,318],{"className":56994},[317],[15,56996,56998],{"className":56997},[290],[15,56999,57001],{"className":57000,"style":325},[294],[15,57002],{},[15,57004,113],{"className":57005},[146],[15,57007,57009,57012],{"className":57008},[59],[15,57010,206],{"className":57011,"style":334},[59,60],[15,57013,57015],{"className":57014},[281],[15,57016,57018,57038],{"className":57017},[285,286],[15,57019,57021,57035],{"className":57020},[290],[15,57022,57024],{"className":57023,"style":11133},[294],[15,57025,57026,57029],{"style":11136},[15,57027],{"className":57028,"style":303},[302],[15,57030,57032],{"className":57031},[307,308,309,310],[15,57033,2463],{"className":57034},[59,310],[15,57036,318],{"className":57037},[317],[15,57039,57041],{"className":57040},[290],[15,57042,57044],{"className":57043,"style":7968},[294],[15,57045],{},[15,57047,210],{"className":57048},[59],[15,57050,57052,57055],{"className":57051},[59],[15,57053,213],{"className":57054},[59,60],[15,57056,57058],{"className":57057},[281],[15,57059,57061,57081],{"className":57060},[285,286],[15,57062,57064,57078],{"className":57063},[290],[15,57065,57067],{"className":57066,"style":11133},[294],[15,57068,57069,57072],{"style":382},[15,57070],{"className":57071,"style":303},[302],[15,57073,57075],{"className":57074},[307,308,309,310],[15,57076,2463],{"className":57077},[59,310],[15,57079,318],{"className":57080},[317],[15,57082,57084],{"className":57083},[290],[15,57085,57087],{"className":57086,"style":7968},[294],[15,57088],{},[15,57090,120],{"className":57091},[153],[15,57093,4375],{"className":57094},[59],[11,57096,57097,57099,57100,57128,57129,57160,57161,57514,57515,57566,57567,57652,57653,57785],{},[1225,57098,55471],{}," 这是 ",[15,57101,57103,57116],{"className":57102,"translate":19},[18],[15,57104,57106],{"className":57105},[23],[25,57107,57108],{"xmlns":27},[29,57109,57110,57114],{},[32,57111,57112],{},[35,57113,37],{},[39,57115,37],{"encoding":41},[15,57117,57119],{"className":57118,"ariaHidden":46},[45],[15,57120,57122,57125],{"className":57121},[50],[15,57123],{"className":57124,"style":55},[54],[15,57126,37],{"className":57127,"style":61},[59,60]," 凸性加上「",[15,57130,57132,57148],{"className":57131,"translate":19},[18],[15,57133,57135],{"className":57134},[23],[25,57136,57137],{"xmlns":27},[29,57138,57139,57145],{},[32,57140,57141,57143],{},[35,57142,35432],{},[110,57144,4103],{},[39,57146,57147],{"encoding":41},"\\sup",[15,57149,57151],{"className":57150,"ariaHidden":46},[45],[15,57152,57154,57157],{"className":57153},[50],[15,57155],{"className":57156,"style":2276},[54],[15,57158,35432],{"className":57159},[1484]," 与线性运算」的标准结果，也可用 f-散度的变分表示（4.4 节）直接看：",[15,57162,57164,57244],{"className":57163,"translate":19},[18],[15,57165,57167],{"className":57166},[23],[25,57168,57169],{"xmlns":27},[29,57170,57171,57241],{},[32,57172,57173,57179,57181,57183,57185,57187,57189,57191,57201,57203,57209,57211,57213,57215,57217,57223,57225,57231,57233,57235,57237,57239],{},[195,57174,57175,57177],{},[35,57176,199],{},[35,57178,37],{},[110,57180,113],{"stretchy":112},[35,57182,206],{},[35,57184,210],{"mathvariant":209},[35,57186,213],{},[110,57188,120],{"stretchy":112},[110,57190,123],{},[195,57192,57193,57199],{},[32,57194,57195,57197],{},[35,57196,35432],{},[110,57198,4103],{},[35,57200,4158],{},[110,57202,2898],{"stretchy":112},[195,57204,57205,57207],{},[35,57206,223],{"mathvariant":222},[35,57208,206],{},[110,57210,230],{"stretchy":112},[35,57212,4158],{},[110,57214,257],{"stretchy":112},[110,57216,4813],{},[195,57218,57219,57221],{},[35,57220,223],{"mathvariant":222},[35,57222,213],{},[110,57224,230],{"stretchy":112},[6814,57226,57227,57229],{},[35,57228,37],{},[110,57230,7573],{},[110,57232,113],{"stretchy":112},[35,57234,4158],{},[110,57236,120],{"stretchy":112},[110,57238,257],{"stretchy":112},[110,57240,2908],{"stretchy":112},[39,57242,57243],{"encoding":41},"D_f(P\\|Q)=\\sup_g\\{\\mathbb E_P[g]-\\mathbb E_Q[f^*(g)]\\}",[15,57245,57247,57317,57426],{"className":57246,"ariaHidden":46},[45],[15,57248,57250,57253,57293,57296,57299,57302,57305,57308,57311,57314],{"className":57249},[50],[15,57251],{"className":57252,"style":270},[54],[15,57254,57256,57259],{"className":57255},[59],[15,57257,199],{"className":57258,"style":277},[59,60],[15,57260,57262],{"className":57261},[281],[15,57263,57265,57285],{"className":57264},[285,286],[15,57266,57268,57282],{"className":57267},[290],[15,57269,57271],{"className":57270,"style":295},[294],[15,57272,57273,57276],{"style":298},[15,57274],{"className":57275,"style":303},[302],[15,57277,57279],{"className":57278},[307,308,309,310],[15,57280,37],{"className":57281,"style":61},[59,60,310],[15,57283,318],{"className":57284},[317],[15,57286,57288],{"className":57287},[290],[15,57289,57291],{"className":57290,"style":325},[294],[15,57292],{},[15,57294,113],{"className":57295},[146],[15,57297,206],{"className":57298,"style":334},[59,60],[15,57300,210],{"className":57301},[59],[15,57303,213],{"className":57304},[59,60],[15,57306,120],{"className":57307},[153],[15,57309],{"className":57310,"style":158},[157],[15,57312,123],{"className":57313},[162],[15,57315],{"className":57316,"style":158},[157],[15,57318,57320,57324,57365,57368,57408,57411,57414,57417,57420,57423],{"className":57319},[50],[15,57321],{"className":57322,"style":57323},[54],"height:1.1302em;vertical-align:-0.3802em;",[15,57325,57327,57330],{"className":57326},[1484],[15,57328,35432],{"className":57329},[1484],[15,57331,57333],{"className":57332},[281],[15,57334,57336,57356],{"className":57335},[285,286],[15,57337,57339,57353],{"className":57338},[290],[15,57340,57342],{"className":57341,"style":36999},[294],[15,57343,57344,57347],{"style":35578},[15,57345],{"className":57346,"style":303},[302],[15,57348,57350],{"className":57349},[307,308,309,310],[15,57351,4158],{"className":57352,"style":981},[59,60,310],[15,57354,318],{"className":57355},[317],[15,57357,57359],{"className":57358},[290],[15,57360,57363],{"className":57361,"style":57362},[294],"height:0.3802em;",[15,57364],{},[15,57366,2898],{"className":57367},[146],[15,57369,57371,57374],{"className":57370},[59],[15,57372,223],{"className":57373},[59,366],[15,57375,57377],{"className":57376},[281],[15,57378,57380,57400],{"className":57379},[285,286],[15,57381,57383,57397],{"className":57382},[290],[15,57384,57386],{"className":57385,"style":379},[294],[15,57387,57388,57391],{"style":382},[15,57389],{"className":57390,"style":303},[302],[15,57392,57394],{"className":57393},[307,308,309,310],[15,57395,206],{"className":57396,"style":334},[59,60,310],[15,57398,318],{"className":57399},[317],[15,57401,57403],{"className":57402},[290],[15,57404,57406],{"className":57405,"style":7968},[294],[15,57407],{},[15,57409,230],{"className":57410},[146],[15,57412,4158],{"className":57413,"style":981},[59,60],[15,57415,257],{"className":57416},[153],[15,57418],{"className":57419,"style":2587},[157],[15,57421,4813],{"className":57422},[2591],[15,57424],{"className":57425,"style":2587},[157],[15,57427,57429,57432,57472,57475,57504,57507,57510],{"className":57428},[50],[15,57430],{"className":57431,"style":270},[54],[15,57433,57435,57438],{"className":57434},[59],[15,57436,223],{"className":57437},[59,366],[15,57439,57441],{"className":57440},[281],[15,57442,57444,57464],{"className":57443},[285,286],[15,57445,57447,57461],{"className":57446},[290],[15,57448,57450],{"className":57449,"style":379},[294],[15,57451,57452,57455],{"style":382},[15,57453],{"className":57454,"style":303},[302],[15,57456,57458],{"className":57457},[307,308,309,310],[15,57459,213],{"className":57460},[59,60,310],[15,57462,318],{"className":57463},[317],[15,57465,57467],{"className":57466},[290],[15,57468,57470],{"className":57469,"style":325},[294],[15,57471],{},[15,57473,230],{"className":57474},[146],[15,57476,57478,57481],{"className":57477},[59],[15,57479,37],{"className":57480,"style":61},[59,60],[15,57482,57484],{"className":57483},[281],[15,57485,57487],{"className":57486},[285],[15,57488,57490],{"className":57489},[290],[15,57491,57493],{"className":57492,"style":8499},[294],[15,57494,57495,57498],{"style":6865},[15,57496],{"className":57497,"style":303},[302],[15,57499,57501],{"className":57500},[307,308,309,310],[15,57502,7573],{"className":57503},[2591,310],[15,57505,113],{"className":57506},[146],[15,57508,4158],{"className":57509,"style":981},[59,60],[15,57511,57513],{"className":57512},[153],")]}","，右端关于 ",[15,57516,57518,57539],{"className":57517,"translate":19},[18],[15,57519,57521],{"className":57520},[23],[25,57522,57523],{"xmlns":27},[29,57524,57525,57537],{},[32,57526,57527,57529,57531,57533,57535],{},[110,57528,113],{"stretchy":112},[35,57530,206],{},[110,57532,551],{"separator":46},[35,57534,213],{},[110,57536,120],{"stretchy":112},[39,57538,11031],{"encoding":41},[15,57540,57542],{"className":57541,"ariaHidden":46},[45],[15,57543,57545,57548,57551,57554,57557,57560,57563],{"className":57544},[50],[15,57546],{"className":57547,"style":139},[54],[15,57549,113],{"className":57550},[146],[15,57552,206],{"className":57553,"style":334},[59,60],[15,57555,551],{"className":57556},[573],[15,57558],{"className":57559,"style":406},[157],[15,57561,213],{"className":57562},[59,60],[15,57564,120],{"className":57565},[153]," 是凸的（",[15,57568,57570,57594],{"className":57569,"translate":19},[18],[15,57571,57573],{"className":57572},[23],[25,57574,57575],{"xmlns":27},[29,57576,57577,57591],{},[32,57578,57579,57585,57587,57589],{},[195,57580,57581,57583],{},[35,57582,223],{"mathvariant":222},[35,57584,206],{},[110,57586,230],{"stretchy":112},[35,57588,4158],{},[110,57590,257],{"stretchy":112},[39,57592,57593],{"encoding":41},"\\mathbb E_P[g]",[15,57595,57597],{"className":57596,"ariaHidden":46},[45],[15,57598,57600,57603,57643,57646,57649],{"className":57599},[50],[15,57601],{"className":57602,"style":139},[54],[15,57604,57606,57609],{"className":57605},[59],[15,57607,223],{"className":57608},[59,366],[15,57610,57612],{"className":57611},[281],[15,57613,57615,57635],{"className":57614},[285,286],[15,57616,57618,57632],{"className":57617},[290],[15,57619,57621],{"className":57620,"style":379},[294],[15,57622,57623,57626],{"style":382},[15,57624],{"className":57625,"style":303},[302],[15,57627,57629],{"className":57628},[307,308,309,310],[15,57630,206],{"className":57631,"style":334},[59,60,310],[15,57633,318],{"className":57634},[317],[15,57636,57638],{"className":57637},[290],[15,57639,57641],{"className":57640,"style":7968},[294],[15,57642],{},[15,57644,230],{"className":57645},[146],[15,57647,4158],{"className":57648,"style":981},[59,60],[15,57650,257],{"className":57651},[153]," 线性、",[15,57654,57656,57692],{"className":57655,"translate":19},[18],[15,57657,57659],{"className":57658},[23],[25,57660,57661],{"xmlns":27},[29,57662,57663,57689],{},[32,57664,57665,57667,57673,57675,57681,57683,57685,57687],{},[110,57666,4813],{},[195,57668,57669,57671],{},[35,57670,223],{"mathvariant":222},[35,57672,213],{},[110,57674,230],{"stretchy":112},[6814,57676,57677,57679],{},[35,57678,37],{},[110,57680,7573],{},[110,57682,113],{"stretchy":112},[35,57684,4158],{},[110,57686,120],{"stretchy":112},[110,57688,257],{"stretchy":112},[39,57690,57691],{"encoding":41},"-\\mathbb E_Q[f^*(g)]",[15,57693,57695],{"className":57694,"ariaHidden":46},[45],[15,57696,57698,57701,57704,57744,57747,57776,57779,57782],{"className":57697},[50],[15,57699],{"className":57700,"style":270},[54],[15,57702,4813],{"className":57703},[59],[15,57705,57707,57710],{"className":57706},[59],[15,57708,223],{"className":57709},[59,366],[15,57711,57713],{"className":57712},[281],[15,57714,57716,57736],{"className":57715},[285,286],[15,57717,57719,57733],{"className":57718},[290],[15,57720,57722],{"className":57721,"style":379},[294],[15,57723,57724,57727],{"style":382},[15,57725],{"className":57726,"style":303},[302],[15,57728,57730],{"className":57729},[307,308,309,310],[15,57731,213],{"className":57732},[59,60,310],[15,57734,318],{"className":57735},[317],[15,57737,57739],{"className":57738},[290],[15,57740,57742],{"className":57741,"style":325},[294],[15,57743],{},[15,57745,230],{"className":57746},[146],[15,57748,57750,57753],{"className":57749},[59],[15,57751,37],{"className":57752,"style":61},[59,60],[15,57754,57756],{"className":57755},[281],[15,57757,57759],{"className":57758},[285],[15,57760,57762],{"className":57761},[290],[15,57763,57765],{"className":57764,"style":8499},[294],[15,57766,57767,57770],{"style":6865},[15,57768],{"className":57769,"style":303},[302],[15,57771,57773],{"className":57772},[307,308,309,310],[15,57774,7573],{"className":57775},[2591,310],[15,57777,113],{"className":57778},[146],[15,57780,4158],{"className":57781,"style":981},[59,60],[15,57783,20390],{"className":57784},[153]," 线性），取上确界后仍凸。",[11,57787,57788,57789,2745,57817,57935,57936,2745,57964,10965,58081,9400,58084,58200,58201,58229,58230,58258,58259,58287],{},"等价地，固定 ",[15,57790,57792,57805],{"className":57791,"translate":19},[18],[15,57793,57795],{"className":57794},[23],[25,57796,57797],{"xmlns":27},[29,57798,57799,57803],{},[32,57800,57801],{},[35,57802,213],{},[39,57804,213],{"encoding":41},[15,57806,57808],{"className":57807,"ariaHidden":46},[45],[15,57809,57811,57814],{"className":57810},[50],[15,57812],{"className":57813,"style":566},[54],[15,57815,213],{"className":57816},[59,60],[15,57818,57820,57852],{"className":57819,"translate":19},[18],[15,57821,57823],{"className":57822},[23],[25,57824,57825],{"xmlns":27},[29,57826,57827,57849],{},[32,57828,57829,57831,57833,57839,57841,57843,57845,57847],{},[35,57830,206],{},[110,57832,8684],{},[195,57834,57835,57837],{},[35,57836,199],{},[35,57838,37],{},[110,57840,113],{"stretchy":112},[35,57842,206],{},[35,57844,210],{"mathvariant":209},[35,57846,213],{},[110,57848,120],{"stretchy":112},[39,57850,57851],{"encoding":41},"P\\mapsto D_f(P\\|Q)",[15,57853,57855,57874],{"className":57854,"ariaHidden":46},[45],[15,57856,57858,57862,57865,57868,57871],{"className":57857},[50],[15,57859],{"className":57860,"style":57861},[54],"height:0.6943em;vertical-align:-0.011em;",[15,57863,206],{"className":57864,"style":334},[59,60],[15,57866],{"className":57867,"style":158},[157],[15,57869,8684],{"className":57870},[162],[15,57872],{"className":57873,"style":158},[157],[15,57875,57877,57880,57920,57923,57926,57929,57932],{"className":57876},[50],[15,57878],{"className":57879,"style":270},[54],[15,57881,57883,57886],{"className":57882},[59],[15,57884,199],{"className":57885,"style":277},[59,60],[15,57887,57889],{"className":57888},[281],[15,57890,57892,57912],{"className":57891},[285,286],[15,57893,57895,57909],{"className":57894},[290],[15,57896,57898],{"className":57897,"style":295},[294],[15,57899,57900,57903],{"style":298},[15,57901],{"className":57902,"style":303},[302],[15,57904,57906],{"className":57905},[307,308,309,310],[15,57907,37],{"className":57908,"style":61},[59,60,310],[15,57910,318],{"className":57911},[317],[15,57913,57915],{"className":57914},[290],[15,57916,57918],{"className":57917,"style":325},[294],[15,57919],{},[15,57921,113],{"className":57922},[146],[15,57924,206],{"className":57925,"style":334},[59,60],[15,57927,210],{"className":57928},[59],[15,57930,213],{"className":57931},[59,60],[15,57933,120],{"className":57934},[153]," 凸；固定 ",[15,57937,57939,57952],{"className":57938,"translate":19},[18],[15,57940,57942],{"className":57941},[23],[25,57943,57944],{"xmlns":27},[29,57945,57946,57950],{},[32,57947,57948],{},[35,57949,206],{},[39,57951,206],{"encoding":41},[15,57953,57955],{"className":57954,"ariaHidden":46},[45],[15,57956,57958,57961],{"className":57957},[50],[15,57959],{"className":57960,"style":664},[54],[15,57962,206],{"className":57963,"style":334},[59,60],[15,57965,57967,57999],{"className":57966,"translate":19},[18],[15,57968,57970],{"className":57969},[23],[25,57971,57972],{"xmlns":27},[29,57973,57974,57996],{},[32,57975,57976,57978,57980,57986,57988,57990,57992,57994],{},[35,57977,213],{},[110,57979,8684],{},[195,57981,57982,57984],{},[35,57983,199],{},[35,57985,37],{},[110,57987,113],{"stretchy":112},[35,57989,206],{},[35,57991,210],{"mathvariant":209},[35,57993,213],{},[110,57995,120],{"stretchy":112},[39,57997,57998],{"encoding":41},"Q\\mapsto D_f(P\\|Q)",[15,58000,58002,58020],{"className":58001,"ariaHidden":46},[45],[15,58003,58005,58008,58011,58014,58017],{"className":58004},[50],[15,58006],{"className":58007,"style":566},[54],[15,58009,213],{"className":58010},[59,60],[15,58012],{"className":58013,"style":158},[157],[15,58015,8684],{"className":58016},[162],[15,58018],{"className":58019,"style":158},[157],[15,58021,58023,58026,58066,58069,58072,58075,58078],{"className":58022},[50],[15,58024],{"className":58025,"style":270},[54],[15,58027,58029,58032],{"className":58028},[59],[15,58030,199],{"className":58031,"style":277},[59,60],[15,58033,58035],{"className":58034},[281],[15,58036,58038,58058],{"className":58037},[285,286],[15,58039,58041,58055],{"className":58040},[290],[15,58042,58044],{"className":58043,"style":295},[294],[15,58045,58046,58049],{"style":298},[15,58047],{"className":58048,"style":303},[302],[15,58050,58052],{"className":58051},[307,308,309,310],[15,58053,37],{"className":58054,"style":61},[59,60,310],[15,58056,318],{"className":58057},[317],[15,58059,58061],{"className":58060},[290],[15,58062,58064],{"className":58063,"style":325},[294],[15,58065],{},[15,58067,113],{"className":58068},[146],[15,58070,206],{"className":58071,"style":334},[59,60],[15,58073,210],{"className":58074},[59],[15,58076,213],{"className":58077},[59,60],[15,58079,120],{"className":58080},[153],[1225,58082,58083],{},"注意",[15,58085,58087,58118],{"className":58086,"translate":19},[18],[15,58088,58090],{"className":58089},[23],[25,58091,58092],{"xmlns":27},[29,58093,58094,58116],{},[32,58095,58096,58098,58100,58106,58108,58110,58112,58114],{},[35,58097,213],{},[110,58099,8684],{},[195,58101,58102,58104],{},[35,58103,199],{},[35,58105,37],{},[110,58107,113],{"stretchy":112},[35,58109,206],{},[35,58111,210],{"mathvariant":209},[35,58113,213],{},[110,58115,120],{"stretchy":112},[39,58117,57998],{"encoding":41},[15,58119,58121,58139],{"className":58120,"ariaHidden":46},[45],[15,58122,58124,58127,58130,58133,58136],{"className":58123},[50],[15,58125],{"className":58126,"style":566},[54],[15,58128,213],{"className":58129},[59,60],[15,58131],{"className":58132,"style":158},[157],[15,58134,8684],{"className":58135},[162],[15,58137],{"className":58138,"style":158},[157],[15,58140,58142,58145,58185,58188,58191,58194,58197],{"className":58141},[50],[15,58143],{"className":58144,"style":270},[54],[15,58146,58148,58151],{"className":58147},[59],[15,58149,199],{"className":58150,"style":277},[59,60],[15,58152,58154],{"className":58153},[281],[15,58155,58157,58177],{"className":58156},[285,286],[15,58158,58160,58174],{"className":58159},[290],[15,58161,58163],{"className":58162,"style":295},[294],[15,58164,58165,58168],{"style":298},[15,58166],{"className":58167,"style":303},[302],[15,58169,58171],{"className":58170},[307,308,309,310],[15,58172,37],{"className":58173,"style":61},[59,60,310],[15,58175,318],{"className":58176},[317],[15,58178,58180],{"className":58179},[290],[15,58181,58183],{"className":58182,"style":325},[294],[15,58184],{},[15,58186,113],{"className":58187},[146],[15,58189,206],{"className":58190,"style":334},[59,60],[15,58192,210],{"className":58193},[59],[15,58195,213],{"className":58196},[59,60],[15,58198,120],{"className":58199},[153]," 凸是「以 ",[15,58202,58204,58217],{"className":58203,"translate":19},[18],[15,58205,58207],{"className":58206},[23],[25,58208,58209],{"xmlns":27},[29,58210,58211,58215],{},[32,58212,58213],{},[35,58214,213],{},[39,58216,213],{"encoding":41},[15,58218,58220],{"className":58219,"ariaHidden":46},[45],[15,58221,58223,58226],{"className":58222},[50],[15,58224],{"className":58225,"style":566},[54],[15,58227,213],{"className":58228},[59,60]," 为参照」的凸性，它与「",[15,58231,58233,58246],{"className":58232,"translate":19},[18],[15,58234,58236],{"className":58235},[23],[25,58237,58238],{"xmlns":27},[29,58239,58240,58244],{},[32,58241,58242],{},[35,58243,213],{},[39,58245,213],{"encoding":41},[15,58247,58249],{"className":58248,"ariaHidden":46},[45],[15,58250,58252,58255],{"className":58251},[50],[15,58253],{"className":58254,"style":566},[54],[15,58256,213],{"className":58257},[59,60]," 出现在分母上」的直觉相反，这个凸性正是变分推断里「对 ",[15,58260,58262,58275],{"className":58261,"translate":19},[18],[15,58263,58265],{"className":58264},[23],[25,58266,58267],{"xmlns":27},[29,58268,58269,58273],{},[32,58270,58271],{},[35,58272,944],{},[39,58274,944],{"encoding":41},[15,58276,58278],{"className":58277,"ariaHidden":46},[45],[15,58279,58281,58284],{"className":58280},[50],[15,58282],{"className":58283,"style":2276},[54],[15,58285,944],{"className":58286,"style":981},[59,60]," 做平均场优化收敛到全局最优」的根据之一。",[2311,58289,58291],{"id":58290},"_43-斜对称关系","4.3 斜对称关系",[993,58293,58295,58393,58611],{"title":58294},"定义 4.1（斜共轭）",[11,58296,14261,58297,58392],{},[15,58298,58300,58329],{"className":58299,"translate":19},[18],[15,58301,58303],{"className":58302},[23],[25,58304,58305],{"xmlns":27},[29,58306,58307,58327],{},[32,58308,58309,58311,58313,58315,58317,58319,58321,58323,58325],{},[35,58310,37],{},[110,58312,1015],{},[110,58314,230],{"stretchy":112},[115,58316,126],{},[110,58318,551],{"separator":46},[35,58320,1024],{"mathvariant":209},[110,58322,120],{"stretchy":112},[110,58324,1029],{},[35,58326,1032],{"mathvariant":222},[39,58328,1035],{"encoding":41},[15,58330,58332,58350,58383],{"className":58331,"ariaHidden":46},[45],[15,58333,58335,58338,58341,58344,58347],{"className":58334},[50],[15,58336],{"className":58337,"style":55},[54],[15,58339,37],{"className":58340,"style":61},[59,60],[15,58342],{"className":58343,"style":158},[157],[15,58345,1015],{"className":58346},[162],[15,58348],{"className":58349,"style":158},[157],[15,58351,58353,58356,58359,58362,58365,58368,58371,58374,58377,58380],{"className":58352},[50],[15,58354],{"className":58355,"style":139},[54],[15,58357,230],{"className":58358},[146],[15,58360,126],{"className":58361},[59],[15,58363,551],{"className":58364},[573],[15,58366],{"className":58367,"style":406},[157],[15,58369,1024],{"className":58370},[59],[15,58372,120],{"className":58373},[153],[15,58375],{"className":58376,"style":158},[157],[15,58378,1029],{"className":58379},[162],[15,58381],{"className":58382,"style":158},[157],[15,58384,58386,58389],{"className":58385},[50],[15,58387],{"className":58388,"style":1096},[54],[15,58390,1032],{"className":58391},[59,366],"，称",[15,58394,58396],{"className":58395,"translate":19},[180],[15,58397,58399,58461],{"className":58398,"translate":19},[18],[15,58400,58402],{"className":58401},[23],[25,58403,58404],{"xmlns":27,"display":189},[29,58405,58406,58458],{},[32,58407,58408,58424,58426,58428,58430,58432,58434,58436,58438,58440,58442,58444,58446,58448,58450,58452,58454,58456],{},[7553,58409,58410,58412,58422],{},[35,58411,37],{},[32,58413,58414,58416,58418,58420],{},[35,58415,7561],{},[35,58417,7564],{},[35,58419,7567],{},[35,58421,7570],{},[110,58423,7573],{"lspace":1247,"rspace":1247},[110,58425,113],{"stretchy":112},[35,58427,769],{},[110,58429,120],{"stretchy":112},[110,58431,123],{},[35,58433,769],{},[1297,58435,1299],{},[35,58437,37],{},[110,58439,113],{"stretchy":112},[115,58441,117],{},[35,58443,941],{"mathvariant":209},[35,58445,769],{},[110,58447,120],{"stretchy":112},[110,58449,551],{"separator":46},[157,58451],{"width":3262},[35,58453,769],{},[110,58455,2903],{},[115,58457,126],{},[39,58459,58460],{"encoding":41},"f^{*}_{skew}(t)=t\\,f(1\u002Ft),\\qquad t>0",[15,58462,58464,58554,58602],{"className":58463,"ariaHidden":46},[45],[15,58465,58467,58470,58536,58539,58542,58545,58548,58551],{"className":58466},[50],[15,58468],{"className":58469,"style":139},[54],[15,58471,58473,58476],{"className":58472},[59],[15,58474,37],{"className":58475,"style":61},[59,60],[15,58477,58479],{"className":58478},[281],[15,58480,58482,58528],{"className":58481},[285,286],[15,58483,58485,58525],{"className":58484},[290],[15,58486,58488,58511],{"className":58487,"style":8248},[294],[15,58489,58490,58493],{"style":8251},[15,58491],{"className":58492,"style":303},[302],[15,58494,58496],{"className":58495},[307,308,309,310],[15,58497,58499,58502,58505,58508],{"className":58498},[59,310],[15,58500,7561],{"className":58501},[59,60,310],[15,58503,7564],{"className":58504,"style":8267},[59,60,310],[15,58506,7567],{"className":58507},[59,60,310],[15,58509,7570],{"className":58510,"style":8274},[59,60,310],[15,58512,58513,58516],{"style":8277},[15,58514],{"className":58515,"style":303},[302],[15,58517,58519],{"className":58518},[307,308,309,310],[15,58520,58522],{"className":58521},[59,310],[15,58523,7573],{"className":58524},[59,310],[15,58526,318],{"className":58527},[317],[15,58529,58531],{"className":58530},[290],[15,58532,58534],{"className":58533,"style":8299},[294],[15,58535],{},[15,58537,113],{"className":58538},[146],[15,58540,769],{"className":58541},[59,60],[15,58543,120],{"className":58544},[153],[15,58546],{"className":58547,"style":158},[157],[15,58549,123],{"className":58550},[162],[15,58552],{"className":58553,"style":158},[157],[15,58555,58557,58560,58563,58566,58569,58572,58575,58578,58581,58584,58587,58590,58593,58596,58599],{"className":58556},[50],[15,58558],{"className":58559,"style":139},[54],[15,58561,769],{"className":58562},[59,60],[15,58564],{"className":58565,"style":406},[157],[15,58567,37],{"className":58568,"style":61},[59,60],[15,58570,113],{"className":58571},[146],[15,58573,8589],{"className":58574},[59],[15,58576,769],{"className":58577},[59,60],[15,58579,120],{"className":58580},[153],[15,58582,551],{"className":58583},[573],[15,58585],{"className":58586,"style":3634},[157],[15,58588],{"className":58589,"style":406},[157],[15,58591,769],{"className":58592},[59,60],[15,58594],{"className":58595,"style":158},[157],[15,58597,2903],{"className":58598},[162],[15,58600],{"className":58601,"style":158},[157],[15,58603,58605,58608],{"className":58604},[50],[15,58606],{"className":58607,"style":172},[54],[15,58609,126],{"className":58610},[59],[11,58612,58613,58614,33825,58642,10180],{},"为 ",[15,58615,58617,58630],{"className":58616,"translate":19},[18],[15,58618,58620],{"className":58619},[23],[25,58621,58622],{"xmlns":27},[29,58623,58624,58628],{},[32,58625,58626],{},[35,58627,37],{},[39,58629,37],{"encoding":41},[15,58631,58633],{"className":58632,"ariaHidden":46},[45],[15,58634,58636,58639],{"className":58635},[50],[15,58637],{"className":58638,"style":55},[54],[15,58640,37],{"className":58641,"style":61},[59,60],[1225,58643,35788],{},[993,58645,58647,58691],{"title":58646},"命题 4.3（斜对称）",[11,58648,58649,58650,2745],{},"对任意概率分布 ",[15,58651,58653,58670],{"className":58652,"translate":19},[18],[15,58654,58656],{"className":58655},[23],[25,58657,58658],{"xmlns":27},[29,58659,58660,58668],{},[32,58661,58662,58664,58666],{},[35,58663,206],{},[110,58665,551],{"separator":46},[35,58667,213],{},[39,58669,556],{"encoding":41},[15,58671,58673],{"className":58672,"ariaHidden":46},[45],[15,58674,58676,58679,58682,58685,58688],{"className":58675},[50],[15,58677],{"className":58678,"style":566},[54],[15,58680,206],{"className":58681,"style":334},[59,60],[15,58683,551],{"className":58684},[573],[15,58686],{"className":58687,"style":406},[157],[15,58689,213],{"className":58690},[59,60],[15,58692,58694],{"className":58693,"translate":19},[180],[15,58695,58697,58759],{"className":58696,"translate":19},[18],[15,58698,58700],{"className":58699},[23],[25,58701,58702],{"xmlns":27,"display":189},[29,58703,58704,58756],{},[32,58705,58706,58712,58714,58716,58718,58720,58722,58724,58744,58746,58748,58750,58752,58754],{},[195,58707,58708,58710],{},[35,58709,199],{},[35,58711,37],{},[110,58713,113],{"stretchy":112},[35,58715,206],{},[35,58717,210],{"mathvariant":209},[35,58719,213],{},[110,58721,120],{"stretchy":112},[110,58723,123],{},[195,58725,58726,58728],{},[35,58727,199],{},[7553,58729,58730,58732,58742],{},[35,58731,37],{},[32,58733,58734,58736,58738,58740],{},[35,58735,7561],{},[35,58737,7564],{},[35,58739,7567],{},[35,58741,7570],{},[110,58743,7573],{"lspace":1247,"rspace":1247},[110,58745,113],{"stretchy":112},[35,58747,213],{},[35,58749,210],{"mathvariant":209},[35,58751,206],{},[110,58753,120],{"stretchy":112},[35,58755,4375],{"mathvariant":209},[39,58757,58758],{"encoding":41},"D_f(P\\|Q)=D_{f^{*}_{skew}}(Q\\|P).",[15,58760,58762,58832],{"className":58761,"ariaHidden":46},[45],[15,58763,58765,58768,58808,58811,58814,58817,58820,58823,58826,58829],{"className":58764},[50],[15,58766],{"className":58767,"style":270},[54],[15,58769,58771,58774],{"className":58770},[59],[15,58772,199],{"className":58773,"style":277},[59,60],[15,58775,58777],{"className":58776},[281],[15,58778,58780,58800],{"className":58779},[285,286],[15,58781,58783,58797],{"className":58782},[290],[15,58784,58786],{"className":58785,"style":295},[294],[15,58787,58788,58791],{"style":298},[15,58789],{"className":58790,"style":303},[302],[15,58792,58794],{"className":58793},[307,308,309,310],[15,58795,37],{"className":58796,"style":61},[59,60,310],[15,58798,318],{"className":58799},[317],[15,58801,58803],{"className":58802},[290],[15,58804,58806],{"className":58805,"style":325},[294],[15,58807],{},[15,58809,113],{"className":58810},[146],[15,58812,206],{"className":58813,"style":334},[59,60],[15,58815,210],{"className":58816},[59],[15,58818,213],{"className":58819},[59,60],[15,58821,120],{"className":58822},[153],[15,58824],{"className":58825,"style":158},[157],[15,58827,123],{"className":58828},[162],[15,58830],{"className":58831,"style":158},[157],[15,58833,58835,58839,58950,58953,58956,58959,58962,58965],{"className":58834},[50],[15,58836],{"className":58837,"style":58838},[54],"height:1.1431em;vertical-align:-0.3931em;",[15,58840,58842,58845],{"className":58841},[59],[15,58843,199],{"className":58844,"style":277},[59,60],[15,58846,58848],{"className":58847},[281],[15,58849,58851,58941],{"className":58850},[285,286],[15,58852,58854,58938],{"className":58853},[290],[15,58855,58857],{"className":58856,"style":295},[294],[15,58858,58859,58862],{"style":298},[15,58860],{"className":58861,"style":303},[302],[15,58863,58865],{"className":58864},[307,308,309,310],[15,58866,58868],{"className":58867},[59,310],[15,58869,58871,58874],{"className":58870},[59,310],[15,58872,37],{"className":58873,"style":61},[59,60,310],[15,58875,58877],{"className":58876},[281],[15,58878,58880,58929],{"className":58879},[285,286],[15,58881,58883,58926],{"className":58882},[290],[15,58884,58887,58911],{"className":58885,"style":58886},[294],"height:0.6771em;",[15,58888,58890,58893],{"style":58889},"top:-2.1528em;margin-left:-0.1076em;margin-right:0.0714em;",[15,58891],{"className":58892,"style":30206},[302],[15,58894,58896],{"className":58895},[307,30210,9674,310],[15,58897,58899,58902,58905,58908],{"className":58898},[59,310],[15,58900,7561],{"className":58901},[59,60,310],[15,58903,7564],{"className":58904,"style":8267},[59,60,310],[15,58906,7567],{"className":58907},[59,60,310],[15,58909,7570],{"className":58910,"style":8274},[59,60,310],[15,58912,58914,58917],{"style":58913},"top:-2.8448em;margin-right:0.0714em;",[15,58915],{"className":58916,"style":30206},[302],[15,58918,58920],{"className":58919},[307,30210,9674,310],[15,58921,58923],{"className":58922},[59,310],[15,58924,7573],{"className":58925},[59,310],[15,58927,318],{"className":58928},[317],[15,58930,58932],{"className":58931},[290],[15,58933,58936],{"className":58934,"style":58935},[294],"height:0.3472em;",[15,58937],{},[15,58939,318],{"className":58940},[317],[15,58942,58944],{"className":58943},[290],[15,58945,58948],{"className":58946,"style":58947},[294],"height:0.3931em;",[15,58949],{},[15,58951,113],{"className":58952},[146],[15,58954,213],{"className":58955},[59,60],[15,58957,210],{"className":58958},[59],[15,58960,206],{"className":58961,"style":334},[59,60],[15,58963,120],{"className":58964},[153],[15,58966,4375],{"className":58967},[59],[11,58969,58970,11060,58972,59072],{},[1225,58971,55471],{},[15,58973,58975,59009],{"className":58974,"translate":19},[18],[15,58976,58978],{"className":58977},[23],[25,58979,58980],{"xmlns":27},[29,58981,58982,59006],{},[32,58983,58984,58986,58988,58990,58992,58994,58996,58998,59000,59002,59004],{},[35,58985,7561],{},[110,58987,123],{},[35,58989,244],{},[35,58991,213],{},[35,58993,941],{"mathvariant":209},[35,58995,244],{},[35,58997,206],{},[110,58999,123],{},[115,59001,117],{},[35,59003,941],{"mathvariant":209},[35,59005,769],{},[39,59007,59008],{"encoding":41},"s=dQ\u002FdP=1\u002Ft",[15,59010,59012,59030,59060],{"className":59011,"ariaHidden":46},[45],[15,59013,59015,59018,59021,59024,59027],{"className":59014},[50],[15,59016],{"className":59017,"style":2345},[54],[15,59019,7561],{"className":59020},[59,60],[15,59022],{"className":59023,"style":158},[157],[15,59025,123],{"className":59026},[162],[15,59028],{"className":59029,"style":158},[157],[15,59031,59033,59036,59039,59042,59045,59048,59051,59054,59057],{"className":59032},[50],[15,59034],{"className":59035,"style":139},[54],[15,59037,244],{"className":59038},[59,60],[15,59040,213],{"className":59041},[59,60],[15,59043,941],{"className":59044},[59],[15,59046,244],{"className":59047},[59,60],[15,59049,206],{"className":59050,"style":334},[59,60],[15,59052],{"className":59053,"style":158},[157],[15,59055,123],{"className":59056},[162],[15,59058],{"className":59059,"style":158},[157],[15,59061,59063,59066,59069],{"className":59062},[50],[15,59064],{"className":59065,"style":139},[54],[15,59067,8589],{"className":59068},[59],[15,59070,769],{"className":59071},[59,60],"。则",[15,59074,59076],{"className":59075,"translate":19},[180],[15,59077,59079,59256],{"className":59078,"translate":19},[18],[15,59080,59082],{"className":59081},[23],[25,59083,59084],{"xmlns":27,"display":189},[29,59085,59086,59253],{},[1243,59087,59088,59166],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,59089,59090,59112],{},[1252,59091,59092],{},[1255,59093,59094],{"scriptlevel":126,"displaystyle":46},[32,59095,59096,59102,59104,59106,59108,59110],{},[195,59097,59098,59100],{},[35,59099,199],{},[35,59101,37],{},[110,59103,113],{"stretchy":112},[35,59105,206],{},[35,59107,210],{"mathvariant":209},[35,59109,213],{},[110,59111,120],{"stretchy":112},[1252,59113,59114],{},[1255,59115,59116],{"scriptlevel":126,"displaystyle":46},[32,59117,59118,59120,59122,59124,59126,59128,59130,59132,59134,59136,59138,59140,59142,59144,59146,59158,59160,59162,59164],{},[32,59119],{},[110,59121,123],{},[110,59123,1287],{},[35,59125,37],{},[110,59127,113],{"stretchy":112},[35,59129,769],{},[110,59131,120],{"stretchy":112},[1297,59133,1299],{},[35,59135,244],{},[35,59137,213],{},[110,59139,123],{},[110,59141,1287],{},[35,59143,37],{},[1297,59145,1304],{},[32,59147,59148,59150,59156],{},[110,59149,113],{"fence":46},[238,59151,59152,59154],{},[115,59153,117],{},[35,59155,7561],{},[110,59157,120],{"fence":46},[35,59159,7561],{},[1297,59161,1299],{},[35,59163,244],{},[35,59165,206],{},[1249,59167,59168,59174],{},[1252,59169,59170],{},[1255,59171,59172],{"scriptlevel":126,"displaystyle":46},[32,59173],{},[1252,59175,59176],{},[1255,59177,59178],{"scriptlevel":126,"displaystyle":46},[32,59179,59180,59182,59184,59186,59202,59204,59206,59208,59210,59212,59214,59216,59236,59238,59240,59242,59244,59246,59248,59250],{},[32,59181],{},[110,59183,123],{},[110,59185,1287],{},[7553,59187,59188,59190,59200],{},[35,59189,37],{},[32,59191,59192,59194,59196,59198],{},[35,59193,7561],{},[35,59195,7564],{},[35,59197,7567],{},[35,59199,7570],{},[110,59201,7573],{"lspace":1247,"rspace":1247},[110,59203,113],{"stretchy":112},[35,59205,7561],{},[110,59207,120],{"stretchy":112},[1297,59209,1299],{},[35,59211,244],{},[35,59213,206],{},[110,59215,123],{},[195,59217,59218,59220],{},[35,59219,199],{},[7553,59221,59222,59224,59234],{},[35,59223,37],{},[32,59225,59226,59228,59230,59232],{},[35,59227,7561],{},[35,59229,7564],{},[35,59231,7567],{},[35,59233,7570],{},[110,59235,7573],{"lspace":1247,"rspace":1247},[110,59237,113],{"stretchy":112},[35,59239,213],{},[35,59241,210],{"mathvariant":209},[35,59243,206],{},[110,59245,120],{"stretchy":112},[35,59247,4375],{"mathvariant":209},[157,59249],{"width":3262},[35,59251,59252],{"mathvariant":209},"□",[39,59254,59255],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)&=\\int f(t)\\,dQ\n=\\int f\\!\\left(\\frac1s\\right) s\\,dP\\\\\n&=\\int f^{*}_{skew}(s)\\,dP\n=D_{f^{*}_{skew}}(Q\\|P).\\qquad\\square\n\\end{aligned}",[15,59257,59259],{"className":59258,"ariaHidden":46},[45],[15,59260,59262,59266],{"className":59261},[50],[15,59263],{"className":59264,"style":59265},[54],"height:4.9223em;vertical-align:-2.2111em;",[15,59267,59269],{"className":59268},[59],[15,59270,59272,59370],{"className":59271},[1243],[15,59273,59275],{"className":59274},[1360],[15,59276,59278,59361],{"className":59277},[285,286],[15,59279,59281,59358],{"className":59280},[290],[15,59282,59285,59349],{"className":59283,"style":59284},[294],"height:2.7111em;",[15,59286,59288,59291],{"style":59287},"top:-4.7111em;",[15,59289],{"className":59290,"style":1377},[302],[15,59292,59294,59334,59337,59340,59343,59346],{"className":59293},[59],[15,59295,59297,59300],{"className":59296},[59],[15,59298,199],{"className":59299,"style":277},[59,60],[15,59301,59303],{"className":59302},[281],[15,59304,59306,59326],{"className":59305},[285,286],[15,59307,59309,59323],{"className":59308},[290],[15,59310,59312],{"className":59311,"style":295},[294],[15,59313,59314,59317],{"style":298},[15,59315],{"className":59316,"style":303},[302],[15,59318,59320],{"className":59319},[307,308,309,310],[15,59321,37],{"className":59322,"style":61},[59,60,310],[15,59324,318],{"className":59325},[317],[15,59327,59329],{"className":59328},[290],[15,59330,59332],{"className":59331,"style":325},[294],[15,59333],{},[15,59335,113],{"className":59336},[146],[15,59338,206],{"className":59339,"style":334},[59,60],[15,59341,210],{"className":59342},[59],[15,59344,213],{"className":59345},[59,60],[15,59347,120],{"className":59348},[153],[15,59350,59352,59355],{"style":59351},"top:-2.1011em;",[15,59353],{"className":59354,"style":1377},[302],[15,59356],{"className":59357},[59],[15,59359,318],{"className":59360},[317],[15,59362,59364],{"className":59363},[290],[15,59365,59368],{"className":59366,"style":59367},[294],"height:2.2111em;",[15,59369],{},[15,59371,59373],{"className":59372},[1451],[15,59374,59376,59798],{"className":59375},[285,286],[15,59377,59379,59795],{"className":59378},[290],[15,59380,59382,59545],{"className":59381,"style":59284},[294],[15,59383,59384,59387],{"style":59287},[15,59385],{"className":59386,"style":1377},[302],[15,59388,59390,59393,59396,59399,59402,59405,59408,59411,59414,59417,59420,59423,59426,59429,59432,59435,59438,59441,59444,59447,59450,59453,59530,59533,59536,59539,59542],{"className":59389},[59],[15,59391],{"className":59392},[59],[15,59394],{"className":59395,"style":158},[157],[15,59397,123],{"className":59398},[162],[15,59400],{"className":59401,"style":158},[157],[15,59403,1287],{"className":59404,"style":1487},[1484,1485,1486],[15,59406],{"className":59407,"style":406},[157],[15,59409,37],{"className":59410,"style":61},[59,60],[15,59412,113],{"className":59413},[146],[15,59415,769],{"className":59416},[59,60],[15,59418,120],{"className":59419},[153],[15,59421],{"className":59422,"style":406},[157],[15,59424,244],{"className":59425},[59,60],[15,59427,213],{"className":59428},[59,60],[15,59430],{"className":59431,"style":158},[157],[15,59433,123],{"className":59434},[162],[15,59436],{"className":59437,"style":158},[157],[15,59439,1287],{"className":59440,"style":1487},[1484,1485,1486],[15,59442],{"className":59443,"style":406},[157],[15,59445,37],{"className":59446,"style":61},[59,60],[15,59448],{"className":59449,"style":1512},[157],[15,59451],{"className":59452,"style":406},[157],[15,59454,59456,59462,59524],{"className":59455},[410],[15,59457,59459],{"className":59458,"style":415},[146,414],[15,59460,113],{"className":59461},[419,309],[15,59463,59465,59468,59521],{"className":59464},[59],[15,59466],{"className":59467},[146,441],[15,59469,59471],{"className":59470},[238],[15,59472,59474,59513],{"className":59473},[285,286],[15,59475,59477,59510],{"className":59476},[290],[15,59478,59480,59491,59499],{"className":59479,"style":22889},[294],[15,59481,59482,59485],{"style":457},[15,59483],{"className":59484,"style":461},[302],[15,59486,59488],{"className":59487},[59],[15,59489,7561],{"className":59490},[59,60],[15,59492,59493,59496],{"style":473},[15,59494],{"className":59495,"style":461},[302],[15,59497],{"className":59498,"style":481},[480],[15,59500,59501,59504],{"style":484},[15,59502],{"className":59503,"style":461},[302],[15,59505,59507],{"className":59506},[59],[15,59508,117],{"className":59509},[59],[15,59511,318],{"className":59512},[317],[15,59514,59516],{"className":59515},[290],[15,59517,59519],{"className":59518,"style":3778},[294],[15,59520],{},[15,59522],{"className":59523},[153,441],[15,59525,59527],{"className":59526,"style":415},[153,414],[15,59528,120],{"className":59529},[419,309],[15,59531],{"className":59532,"style":406},[157],[15,59534,7561],{"className":59535},[59,60],[15,59537],{"className":59538,"style":406},[157],[15,59540,244],{"className":59541},[59,60],[15,59543,206],{"className":59544,"style":334},[59,60],[15,59546,59547,59550],{"style":59351},[15,59548],{"className":59549,"style":1377},[302],[15,59551,59553,59556,59559,59562,59565,59568,59571,59637,59640,59643,59646,59649,59652,59655,59658,59661,59664,59770,59773,59776,59779,59782,59785,59788,59791],{"className":59552},[59],[15,59554],{"className":59555},[59],[15,59557],{"className":59558,"style":158},[157],[15,59560,123],{"className":59561},[162],[15,59563],{"className":59564,"style":158},[157],[15,59566,1287],{"className":59567,"style":1487},[1484,1485,1486],[15,59569],{"className":59570,"style":406},[157],[15,59572,59574,59577],{"className":59573},[59],[15,59575,37],{"className":59576,"style":61},[59,60],[15,59578,59580],{"className":59579},[281],[15,59581,59583,59629],{"className":59582},[285,286],[15,59584,59586,59626],{"className":59585},[290],[15,59587,59589,59612],{"className":59588,"style":8248},[294],[15,59590,59591,59594],{"style":8251},[15,59592],{"className":59593,"style":303},[302],[15,59595,59597],{"className":59596},[307,308,309,310],[15,59598,59600,59603,59606,59609],{"className":59599},[59,310],[15,59601,7561],{"className":59602},[59,60,310],[15,59604,7564],{"className":59605,"style":8267},[59,60,310],[15,59607,7567],{"className":59608},[59,60,310],[15,59610,7570],{"className":59611,"style":8274},[59,60,310],[15,59613,59614,59617],{"style":8277},[15,59615],{"className":59616,"style":303},[302],[15,59618,59620],{"className":59619},[307,308,309,310],[15,59621,59623],{"className":59622},[59,310],[15,59624,7573],{"className":59625},[59,310],[15,59627,318],{"className":59628},[317],[15,59630,59632],{"className":59631},[290],[15,59633,59635],{"className":59634,"style":8299},[294],[15,59636],{},[15,59638,113],{"className":59639},[146],[15,59641,7561],{"className":59642},[59,60],[15,59644,120],{"className":59645},[153],[15,59647],{"className":59648,"style":406},[157],[15,59650,244],{"className":59651},[59,60],[15,59653,206],{"className":59654,"style":334},[59,60],[15,59656],{"className":59657,"style":158},[157],[15,59659,123],{"className":59660},[162],[15,59662],{"className":59663,"style":158},[157],[15,59665,59667,59670],{"className":59666},[59],[15,59668,199],{"className":59669,"style":277},[59,60],[15,59671,59673],{"className":59672},[281],[15,59674,59676,59762],{"className":59675},[285,286],[15,59677,59679,59759],{"className":59678},[290],[15,59680,59682],{"className":59681,"style":295},[294],[15,59683,59684,59687],{"style":298},[15,59685],{"className":59686,"style":303},[302],[15,59688,59690],{"className":59689},[307,308,309,310],[15,59691,59693],{"className":59692},[59,310],[15,59694,59696,59699],{"className":59695},[59,310],[15,59697,37],{"className":59698,"style":61},[59,60,310],[15,59700,59702],{"className":59701},[281],[15,59703,59705,59751],{"className":59704},[285,286],[15,59706,59708,59748],{"className":59707},[290],[15,59709,59711,59734],{"className":59710,"style":58886},[294],[15,59712,59713,59716],{"style":58889},[15,59714],{"className":59715,"style":30206},[302],[15,59717,59719],{"className":59718},[307,30210,9674,310],[15,59720,59722,59725,59728,59731],{"className":59721},[59,310],[15,59723,7561],{"className":59724},[59,60,310],[15,59726,7564],{"className":59727,"style":8267},[59,60,310],[15,59729,7567],{"className":59730},[59,60,310],[15,59732,7570],{"className":59733,"style":8274},[59,60,310],[15,59735,59736,59739],{"style":58913},[15,59737],{"className":59738,"style":30206},[302],[15,59740,59742],{"className":59741},[307,30210,9674,310],[15,59743,59745],{"className":59744},[59,310],[15,59746,7573],{"className":59747},[59,310],[15,59749,318],{"className":59750},[317],[15,59752,59754],{"className":59753},[290],[15,59755,59757],{"className":59756,"style":58935},[294],[15,59758],{},[15,59760,318],{"className":59761},[317],[15,59763,59765],{"className":59764},[290],[15,59766,59768],{"className":59767,"style":58947},[294],[15,59769],{},[15,59771,113],{"className":59772},[146],[15,59774,213],{"className":59775},[59,60],[15,59777,210],{"className":59778},[59],[15,59780,206],{"className":59781,"style":334},[59,60],[15,59783,120],{"className":59784},[153],[15,59786,4375],{"className":59787},[59],[15,59789],{"className":59790,"style":3634},[157],[15,59792,59252],{"className":59793},[59,59794],"amsrm",[15,59796,318],{"className":59797},[317],[15,59799,59801],{"className":59800},[290],[15,59802,59804],{"className":59803,"style":59367},[294],[15,59805],{},[11,59807,59808,6494,59811,59880,59881,60064,60065,60106,60107,60234,60235,60300,60301,60585,60586,60678],{},[1225,59809,59810],{},"推论（对称判别准则）。",[15,59812,59814,59831],{"className":59813,"translate":19},[18],[15,59815,59817],{"className":59816},[23],[25,59818,59819],{"xmlns":27},[29,59820,59821,59829],{},[32,59822,59823],{},[195,59824,59825,59827],{},[35,59826,199],{},[35,59828,37],{},[39,59830,4022],{"encoding":41},[15,59832,59834],{"className":59833,"ariaHidden":46},[45],[15,59835,59837,59840],{"className":59836},[50],[15,59838],{"className":59839,"style":4032},[54],[15,59841,59843,59846],{"className":59842},[59],[15,59844,199],{"className":59845,"style":277},[59,60],[15,59847,59849],{"className":59848},[281],[15,59850,59852,59872],{"className":59851},[285,286],[15,59853,59855,59869],{"className":59854},[290],[15,59856,59858],{"className":59857,"style":295},[294],[15,59859,59860,59863],{"style":298},[15,59861],{"className":59862,"style":303},[302],[15,59864,59866],{"className":59865},[307,308,309,310],[15,59867,37],{"className":59868,"style":61},[59,60,310],[15,59870,318],{"className":59871},[317],[15,59873,59875],{"className":59874},[290],[15,59876,59878],{"className":59877,"style":325},[294],[15,59879],{}," 对称（",[15,59882,59884,59930],{"className":59883,"translate":19},[18],[15,59885,59887],{"className":59886},[23],[25,59888,59889],{"xmlns":27},[29,59890,59891,59927],{},[32,59892,59893,59899,59901,59903,59905,59907,59909,59911,59917,59919,59921,59923,59925],{},[195,59894,59895,59897],{},[35,59896,199],{},[35,59898,37],{},[110,59900,113],{"stretchy":112},[35,59902,206],{},[35,59904,210],{"mathvariant":209},[35,59906,213],{},[110,59908,120],{"stretchy":112},[110,59910,123],{},[195,59912,59913,59915],{},[35,59914,199],{},[35,59916,37],{},[110,59918,113],{"stretchy":112},[35,59920,213],{},[35,59922,210],{"mathvariant":209},[35,59924,206],{},[110,59926,120],{"stretchy":112},[39,59928,59929],{"encoding":41},"D_f(P\\|Q)=D_f(Q\\|P)",[15,59931,59933,60003],{"className":59932,"ariaHidden":46},[45],[15,59934,59936,59939,59979,59982,59985,59988,59991,59994,59997,60000],{"className":59935},[50],[15,59937],{"className":59938,"style":270},[54],[15,59940,59942,59945],{"className":59941},[59],[15,59943,199],{"className":59944,"style":277},[59,60],[15,59946,59948],{"className":59947},[281],[15,59949,59951,59971],{"className":59950},[285,286],[15,59952,59954,59968],{"className":59953},[290],[15,59955,59957],{"className":59956,"style":295},[294],[15,59958,59959,59962],{"style":298},[15,59960],{"className":59961,"style":303},[302],[15,59963,59965],{"className":59964},[307,308,309,310],[15,59966,37],{"className":59967,"style":61},[59,60,310],[15,59969,318],{"className":59970},[317],[15,59972,59974],{"className":59973},[290],[15,59975,59977],{"className":59976,"style":325},[294],[15,59978],{},[15,59980,113],{"className":59981},[146],[15,59983,206],{"className":59984,"style":334},[59,60],[15,59986,210],{"className":59987},[59],[15,59989,213],{"className":59990},[59,60],[15,59992,120],{"className":59993},[153],[15,59995],{"className":59996,"style":158},[157],[15,59998,123],{"className":59999},[162],[15,60001],{"className":60002,"style":158},[157],[15,60004,60006,60009,60049,60052,60055,60058,60061],{"className":60005},[50],[15,60007],{"className":60008,"style":270},[54],[15,60010,60012,60015],{"className":60011},[59],[15,60013,199],{"className":60014,"style":277},[59,60],[15,60016,60018],{"className":60017},[281],[15,60019,60021,60041],{"className":60020},[285,286],[15,60022,60024,60038],{"className":60023},[290],[15,60025,60027],{"className":60026,"style":295},[294],[15,60028,60029,60032],{"style":298},[15,60030],{"className":60031,"style":303},[302],[15,60033,60035],{"className":60034},[307,308,309,310],[15,60036,37],{"className":60037,"style":61},[59,60,310],[15,60039,318],{"className":60040},[317],[15,60042,60044],{"className":60043},[290],[15,60045,60047],{"className":60046,"style":325},[294],[15,60048],{},[15,60050,113],{"className":60051},[146],[15,60053,213],{"className":60054},[59,60],[15,60056,210],{"className":60057},[59],[15,60059,206],{"className":60060,"style":334},[59,60],[15,60062,120],{"className":60063},[153]," 对所有 ",[15,60066,60068,60085],{"className":60067,"translate":19},[18],[15,60069,60071],{"className":60070},[23],[25,60072,60073],{"xmlns":27},[29,60074,60075,60083],{},[32,60076,60077,60079,60081],{},[35,60078,206],{},[110,60080,551],{"separator":46},[35,60082,213],{},[39,60084,556],{"encoding":41},[15,60086,60088],{"className":60087,"ariaHidden":46},[45],[15,60089,60091,60094,60097,60100,60103],{"className":60090},[50],[15,60092],{"className":60093,"style":566},[54],[15,60095,206],{"className":60096,"style":334},[59,60],[15,60098,551],{"className":60099},[573],[15,60101],{"className":60102,"style":406},[157],[15,60104,213],{"className":60105},[59,60],"）当且仅当 ",[15,60108,60110,60141],{"className":60109,"translate":19},[18],[15,60111,60113],{"className":60112},[23],[25,60114,60115],{"xmlns":27},[29,60116,60117,60139],{},[32,60118,60119,60135,60137],{},[7553,60120,60121,60123,60133],{},[35,60122,37],{},[32,60124,60125,60127,60129,60131],{},[35,60126,7561],{},[35,60128,7564],{},[35,60130,7567],{},[35,60132,7570],{},[110,60134,7573],{"lspace":1247,"rspace":1247},[110,60136,123],{},[35,60138,37],{},[39,60140,44153],{"encoding":41},[15,60142,60144,60225],{"className":60143,"ariaHidden":46},[45],[15,60145,60147,60150,60216,60219,60222],{"className":60146},[50],[15,60148],{"className":60149,"style":44163},[54],[15,60151,60153,60156],{"className":60152},[59],[15,60154,37],{"className":60155,"style":61},[59,60],[15,60157,60159],{"className":60158},[281],[15,60160,60162,60208],{"className":60161},[285,286],[15,60163,60165,60205],{"className":60164},[290],[15,60166,60168,60191],{"className":60167,"style":8499},[294],[15,60169,60170,60173],{"style":8502},[15,60171],{"className":60172,"style":303},[302],[15,60174,60176],{"className":60175},[307,308,309,310],[15,60177,60179,60182,60185,60188],{"className":60178},[59,310],[15,60180,7561],{"className":60181},[59,60,310],[15,60183,7564],{"className":60184,"style":8267},[59,60,310],[15,60186,7567],{"className":60187},[59,60,310],[15,60189,7570],{"className":60190,"style":8274},[59,60,310],[15,60192,60193,60196],{"style":6865},[15,60194],{"className":60195,"style":303},[302],[15,60197,60199],{"className":60198},[307,308,309,310],[15,60200,60202],{"className":60201},[59,310],[15,60203,7573],{"className":60204},[59,310],[15,60206,318],{"className":60207},[317],[15,60209,60211],{"className":60210},[290],[15,60212,60214],{"className":60213,"style":8547},[294],[15,60215],{},[15,60217],{"className":60218,"style":158},[157],[15,60220,123],{"className":60221},[162],[15,60223],{"className":60224,"style":158},[157],[15,60226,60228,60231],{"className":60227},[50],[15,60229],{"className":60230,"style":55},[54],[15,60232,37],{"className":60233,"style":61},[59,60],"（模去 ",[15,60236,60238,60261],{"className":60237,"translate":19},[18],[15,60239,60241],{"className":60240},[23],[25,60242,60243],{"xmlns":27},[29,60244,60245,60259],{},[32,60246,60247,60249,60251,60253,60255,60257],{},[35,60248,5906],{},[110,60250,113],{"stretchy":112},[35,60252,769],{},[110,60254,4813],{},[115,60256,117],{},[110,60258,120],{"stretchy":112},[39,60260,6620],{"encoding":41},[15,60262,60264,60288],{"className":60263,"ariaHidden":46},[45],[15,60265,60267,60270,60273,60276,60279,60282,60285],{"className":60266},[50],[15,60268],{"className":60269,"style":139},[54],[15,60271,5906],{"className":60272},[59,60],[15,60274,113],{"className":60275},[146],[15,60277,769],{"className":60278},[59,60],[15,60280],{"className":60281,"style":2587},[157],[15,60283,4813],{"className":60284},[2591],[15,60286],{"className":60287,"style":2587},[157],[15,60289,60291,60294,60297],{"className":60290},[50],[15,60292],{"className":60293,"style":139},[54],[15,60295,117],{"className":60296},[59],[15,60298,120],{"className":60299},[153],"）。验证 TV：",[15,60302,60304,60358],{"className":60303,"translate":19},[18],[15,60305,60307],{"className":60306},[23],[25,60308,60309],{"xmlns":27},[29,60310,60311,60355],{},[32,60312,60313,60315,60317,60323,60325,60327,60329,60331,60333,60335,60337,60339,60345,60347,60349,60351,60353],{},[35,60314,769],{},[110,60316,3299],{},[238,60318,60319,60321],{},[115,60320,117],{},[115,60322,2463],{},[35,60324,4808],{"mathvariant":209},[115,60326,117],{},[35,60328,941],{"mathvariant":209},[35,60330,769],{},[110,60332,4813],{},[115,60334,117],{},[35,60336,4808],{"mathvariant":209},[110,60338,123],{},[238,60340,60341,60343],{},[115,60342,117],{},[115,60344,2463],{},[35,60346,4808],{"mathvariant":209},[35,60348,769],{},[110,60350,4813],{},[115,60352,117],{},[35,60354,4808],{"mathvariant":209},[39,60356,60357],{"encoding":41},"t\\cdot\\frac12|1\u002Ft-1|=\\frac12|t-1|",[15,60359,60361,60379,60469,60487,60576],{"className":60360,"ariaHidden":46},[45],[15,60362,60364,60367,60370,60373,60376],{"className":60363},[50],[15,60365],{"className":60366,"style":5343},[54],[15,60368,769],{"className":60369},[59,60],[15,60371],{"className":60372,"style":2587},[157],[15,60374,3299],{"className":60375},[2591],[15,60377],{"className":60378,"style":2587},[157],[15,60380,60382,60385,60453,60457,60460,60463,60466],{"className":60381},[50],[15,60383],{"className":60384,"style":2505},[54],[15,60386,60388,60391,60450],{"className":60387},[59],[15,60389],{"className":60390},[146,441],[15,60392,60394],{"className":60393},[238],[15,60395,60397,60442],{"className":60396},[285,286],[15,60398,60400,60439],{"className":60399},[290],[15,60401,60403,60417,60425],{"className":60402,"style":2524},[294],[15,60404,60405,60408],{"style":2527},[15,60406],{"className":60407,"style":461},[302],[15,60409,60411],{"className":60410},[307,308,309,310],[15,60412,60414],{"className":60413},[59,310],[15,60415,2463],{"className":60416},[59,310],[15,60418,60419,60422],{"style":473},[15,60420],{"className":60421,"style":461},[302],[15,60423],{"className":60424,"style":481},[480],[15,60426,60427,60430],{"style":2550},[15,60428],{"className":60429,"style":461},[302],[15,60431,60433],{"className":60432},[307,308,309,310],[15,60434,60436],{"className":60435},[59,310],[15,60437,117],{"className":60438},[59,310],[15,60440,318],{"className":60441},[317],[15,60443,60445],{"className":60444},[290],[15,60446,60448],{"className":60447,"style":2572},[294],[15,60449],{},[15,60451],{"className":60452},[153,441],[15,60454,60456],{"className":60455},[59],"∣1\u002F",[15,60458,769],{"className":60459},[59,60],[15,60461],{"className":60462,"style":2587},[157],[15,60464,4813],{"className":60465},[2591],[15,60467],{"className":60468,"style":2587},[157],[15,60470,60472,60475,60478,60481,60484],{"className":60471},[50],[15,60473],{"className":60474,"style":139},[54],[15,60476,34679],{"className":60477},[59],[15,60479],{"className":60480,"style":158},[157],[15,60482,123],{"className":60483},[162],[15,60485],{"className":60486,"style":158},[157],[15,60488,60490,60493,60561,60564,60567,60570,60573],{"className":60489},[50],[15,60491],{"className":60492,"style":2505},[54],[15,60494,60496,60499,60558],{"className":60495},[59],[15,60497],{"className":60498},[146,441],[15,60500,60502],{"className":60501},[238],[15,60503,60505,60550],{"className":60504},[285,286],[15,60506,60508,60547],{"className":60507},[290],[15,60509,60511,60525,60533],{"className":60510,"style":2524},[294],[15,60512,60513,60516],{"style":2527},[15,60514],{"className":60515,"style":461},[302],[15,60517,60519],{"className":60518},[307,308,309,310],[15,60520,60522],{"className":60521},[59,310],[15,60523,2463],{"className":60524},[59,310],[15,60526,60527,60530],{"style":473},[15,60528],{"className":60529,"style":461},[302],[15,60531],{"className":60532,"style":481},[480],[15,60534,60535,60538],{"style":2550},[15,60536],{"className":60537,"style":461},[302],[15,60539,60541],{"className":60540},[307,308,309,310],[15,60542,60544],{"className":60543},[59,310],[15,60545,117],{"className":60546},[59,310],[15,60548,318],{"className":60549},[317],[15,60551,60553],{"className":60552},[290],[15,60554,60556],{"className":60555,"style":2572},[294],[15,60557],{},[15,60559],{"className":60560},[153,441],[15,60562,4808],{"className":60563},[59],[15,60565,769],{"className":60566},[59,60],[15,60568],{"className":60569,"style":2587},[157],[15,60571,4813],{"className":60572},[2591],[15,60574],{"className":60575,"style":2587},[157],[15,60577,60579,60582],{"className":60578},[50],[15,60580],{"className":60581,"style":139},[54],[15,60583,34679],{"className":60584},[59],"；JS 的 ",[15,60587,60589,60624],{"className":60588,"translate":19},[18],[15,60590,60592],{"className":60591},[23],[25,60593,60594],{"xmlns":27},[29,60595,60596,60622],{},[32,60597,60598,60600,60602,60604,60606,60608,60610,60612,60614,60616,60618,60620],{},[35,60599,769],{},[35,60601,37],{},[110,60603,113],{"stretchy":112},[115,60605,117],{},[35,60607,941],{"mathvariant":209},[35,60609,769],{},[110,60611,120],{"stretchy":112},[110,60613,123],{},[35,60615,37],{},[110,60617,113],{"stretchy":112},[35,60619,769],{},[110,60621,120],{"stretchy":112},[39,60623,23569],{"encoding":41},[15,60625,60627,60660],{"className":60626,"ariaHidden":46},[45],[15,60628,60630,60633,60636,60639,60642,60645,60648,60651,60654,60657],{"className":60629},[50],[15,60631],{"className":60632,"style":139},[54],[15,60634,769],{"className":60635},[59,60],[15,60637,37],{"className":60638,"style":61},[59,60],[15,60640,113],{"className":60641},[146],[15,60643,8589],{"className":60644},[59],[15,60646,769],{"className":60647},[59,60],[15,60649,120],{"className":60650},[153],[15,60652],{"className":60653,"style":158},[157],[15,60655,123],{"className":60656},[162],[15,60658],{"className":60659,"style":158},[157],[15,60661,60663,60666,60669,60672,60675],{"className":60662},[50],[15,60664],{"className":60665,"style":139},[54],[15,60667,37],{"className":60668,"style":61},[59,60],[15,60670,113],{"className":60671},[146],[15,60673,769],{"className":60674},[59,60],[15,60676,120],{"className":60677},[153]," 也已验算；KL 显然不满足，故不对称。",[2311,60680,60682],{"id":60681},"_44-变分表示","4.4 变分表示",[993,60684,60686,60777,61003,61006,61382],{"title":60685},"定理 4.1（变分表示 \u002F Fenchel 对偶）",[11,60687,534,60688,60747,60748,60776],{},[15,60689,60691,60709],{"className":60690,"translate":19},[18],[15,60692,60694],{"className":60693},[23],[25,60695,60696],{"xmlns":27},[29,60697,60698,60706],{},[32,60699,60700],{},[6814,60701,60702,60704],{},[35,60703,37],{},[110,60705,7573],{},[39,60707,60708],{"encoding":41},"f^*",[15,60710,60712],{"className":60711,"ariaHidden":46},[45],[15,60713,60715,60718],{"className":60714},[50],[15,60716],{"className":60717,"style":55},[54],[15,60719,60721,60724],{"className":60720},[59],[15,60722,37],{"className":60723,"style":61},[59,60],[15,60725,60727],{"className":60726},[281],[15,60728,60730],{"className":60729},[285],[15,60731,60733],{"className":60732},[290],[15,60734,60736],{"className":60735,"style":8499},[294],[15,60737,60738,60741],{"style":6865},[15,60739],{"className":60740,"style":303},[302],[15,60742,60744],{"className":60743},[307,308,309,310],[15,60745,7573],{"className":60746},[2591,310]," 为 ",[15,60749,60751,60764],{"className":60750,"translate":19},[18],[15,60752,60754],{"className":60753},[23],[25,60755,60756],{"xmlns":27},[29,60757,60758,60762],{},[32,60759,60760],{},[35,60761,37],{},[39,60763,37],{"encoding":41},[15,60765,60767],{"className":60766,"ariaHidden":46},[45],[15,60768,60770,60773],{"className":60769},[50],[15,60771],{"className":60772,"style":55},[54],[15,60774,37],{"className":60775,"style":61},[59,60]," 的凸共轭（Fenchel 共轭）",[15,60778,60780],{"className":60779,"translate":19},[180],[15,60781,60783,60845],{"className":60782,"translate":19},[18],[15,60784,60786],{"className":60785},[23],[25,60787,60788],{"xmlns":27,"display":189},[29,60789,60790,60842],{},[32,60791,60792,60798,60800,60802,60804,60806,60822,60824,60826,60828,60830,60832,60834,60836,60838,60840],{},[6814,60793,60794,60796],{},[35,60795,37],{},[110,60797,7573],{},[110,60799,113],{"stretchy":112},[35,60801,40237],{},[110,60803,120],{"stretchy":112},[110,60805,123],{},[6016,60807,60808,60814],{},[32,60809,60810,60812],{},[35,60811,35432],{},[110,60813,4103],{},[32,60815,60816,60818,60820],{},[35,60817,769],{},[110,60819,6928],{},[115,60821,126],{},[110,60823,2898],{"stretchy":112},[35,60825,40237],{},[35,60827,769],{},[110,60829,4813],{},[35,60831,37],{},[110,60833,113],{"stretchy":112},[35,60835,769],{},[110,60837,120],{"stretchy":112},[110,60839,2908],{"stretchy":112},[110,60841,551],{"separator":46},[39,60843,60844],{"encoding":41},"f^*(y)=\\sup_{t\\ge0}\\{yt-f(t)\\},",[15,60846,60848,60901,60981],{"className":60847,"ariaHidden":46},[45],[15,60849,60851,60854,60883,60886,60889,60892,60895,60898],{"className":60850},[50],[15,60852],{"className":60853,"style":139},[54],[15,60855,60857,60860],{"className":60856},[59],[15,60858,37],{"className":60859,"style":61},[59,60],[15,60861,60863],{"className":60862},[281],[15,60864,60866],{"className":60865},[285],[15,60867,60869],{"className":60868},[290],[15,60870,60872],{"className":60871,"style":8248},[294],[15,60873,60874,60877],{"style":8277},[15,60875],{"className":60876,"style":303},[302],[15,60878,60880],{"className":60879},[307,308,309,310],[15,60881,7573],{"className":60882},[2591,310],[15,60884,113],{"className":60885},[146],[15,60887,40237],{"className":60888,"style":981},[59,60],[15,60890,120],{"className":60891},[153],[15,60893],{"className":60894,"style":158},[157],[15,60896,123],{"className":60897},[162],[15,60899],{"className":60900,"style":158},[157],[15,60902,60904,60908,60963,60966,60969,60972,60975,60978],{"className":60903},[50],[15,60905],{"className":60906,"style":60907},[54],"height:1.7567em;vertical-align:-1.0067em;",[15,60909,60911],{"className":60910},[1484,13716],[15,60912,60914,60954],{"className":60913},[285,286],[15,60915,60917,60951],{"className":60916},[290],[15,60918,60920,60941],{"className":60919,"style":2345},[294],[15,60921,60923,60926],{"style":60922},"top:-2.1885em;margin-left:0em;",[15,60924],{"className":60925,"style":461},[302],[15,60927,60929],{"className":60928},[307,308,309,310],[15,60930,60932,60935,60938],{"className":60931},[59,310],[15,60933,769],{"className":60934},[59,60,310],[15,60936,6928],{"className":60937},[162,310],[15,60939,126],{"className":60940},[59,310],[15,60942,60943,60946],{"style":11863},[15,60944],{"className":60945,"style":461},[302],[15,60947,60948],{},[15,60949,35432],{"className":60950},[1484],[15,60952,318],{"className":60953},[317],[15,60955,60957],{"className":60956},[290],[15,60958,60961],{"className":60959,"style":60960},[294],"height:1.0067em;",[15,60962],{},[15,60964,2898],{"className":60965},[146],[15,60967,40237],{"className":60968,"style":981},[59,60],[15,60970,769],{"className":60971},[59,60],[15,60973],{"className":60974,"style":2587},[157],[15,60976,4813],{"className":60977},[2591],[15,60979],{"className":60980,"style":2587},[157],[15,60982,60984,60987,60990,60993,60996,61000],{"className":60983},[50],[15,60985],{"className":60986,"style":139},[54],[15,60988,37],{"className":60989,"style":61},[59,60],[15,60991,113],{"className":60992},[146],[15,60994,769],{"className":60995},[59,60],[15,60997,60999],{"className":60998},[153],")}",[15,61001,551],{"className":61002},[573],[11,61004,61005],{},"则",[15,61007,61009],{"className":61008,"translate":19},[180],[15,61010,61012,61096],{"className":61011,"translate":19},[18],[15,61013,61015],{"className":61014},[23],[25,61016,61017],{"xmlns":27,"display":189},[29,61018,61019,61093],{},[32,61020,61021,61027,61029,61031,61033,61035,61037,61039,61049,61091],{},[195,61022,61023,61025],{},[35,61024,199],{},[35,61026,37],{},[110,61028,113],{"stretchy":112},[35,61030,206],{},[35,61032,210],{"mathvariant":209},[35,61034,213],{},[110,61036,120],{"stretchy":112},[110,61038,123],{},[6016,61040,61041,61047],{},[32,61042,61043,61045],{},[35,61044,35432],{},[110,61046,4103],{},[35,61048,4158],{},[32,61050,61051,61053,61059,61061,61063,61065,61067,61073,61075,61081,61083,61085,61087,61089],{},[110,61052,2898],{"fence":46},[195,61054,61055,61057],{},[35,61056,223],{"mathvariant":222},[35,61058,206],{},[110,61060,230],{"stretchy":112},[35,61062,4158],{},[110,61064,257],{"stretchy":112},[110,61066,4813],{},[195,61068,61069,61071],{},[35,61070,223],{"mathvariant":222},[35,61072,213],{},[110,61074,230],{"stretchy":112},[6814,61076,61077,61079],{},[35,61078,37],{},[110,61080,7573],{},[110,61082,113],{"stretchy":112},[35,61084,4158],{},[110,61086,120],{"stretchy":112},[110,61088,257],{"stretchy":112},[110,61090,2908],{"fence":46},[110,61092,551],{"separator":46},[39,61094,61095],{"encoding":41},"D_f(P\\|Q)=\\sup_{g}\n\\left\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\right\\},",[15,61097,61099,61169],{"className":61098,"ariaHidden":46},[45],[15,61100,61102,61105,61145,61148,61151,61154,61157,61160,61163,61166],{"className":61101},[50],[15,61103],{"className":61104,"style":270},[54],[15,61106,61108,61111],{"className":61107},[59],[15,61109,199],{"className":61110,"style":277},[59,60],[15,61112,61114],{"className":61113},[281],[15,61115,61117,61137],{"className":61116},[285,286],[15,61118,61120,61134],{"className":61119},[290],[15,61121,61123],{"className":61122,"style":295},[294],[15,61124,61125,61128],{"style":298},[15,61126],{"className":61127,"style":303},[302],[15,61129,61131],{"className":61130},[307,308,309,310],[15,61132,37],{"className":61133,"style":61},[59,60,310],[15,61135,318],{"className":61136},[317],[15,61138,61140],{"className":61139},[290],[15,61141,61143],{"className":61142,"style":325},[294],[15,61144],{},[15,61146,113],{"className":61147},[146],[15,61149,206],{"className":61150,"style":334},[59,60],[15,61152,210],{"className":61153},[59],[15,61155,213],{"className":61156},[59,60],[15,61158,120],{"className":61159},[153],[15,61161],{"className":61162,"style":158},[157],[15,61164,123],{"className":61165},[162],[15,61167],{"className":61168,"style":158},[157],[15,61170,61172,61176,61225,61228,61376,61379],{"className":61171},[50],[15,61173],{"className":61174,"style":61175},[54],"height:1.7805em;vertical-align:-1.0305em;",[15,61177,61179],{"className":61178},[1484,13716],[15,61180,61182,61216],{"className":61181},[285,286],[15,61183,61185,61213],{"className":61184},[290],[15,61186,61188,61203],{"className":61187,"style":2345},[294],[15,61189,61191,61194],{"style":61190},"top:-2.2056em;margin-left:0em;",[15,61192],{"className":61193,"style":461},[302],[15,61195,61197],{"className":61196},[307,308,309,310],[15,61198,61200],{"className":61199},[59,310],[15,61201,4158],{"className":61202,"style":981},[59,60,310],[15,61204,61205,61208],{"style":11863},[15,61206],{"className":61207,"style":461},[302],[15,61209,61210],{},[15,61211,35432],{"className":61212},[1484],[15,61214,318],{"className":61215},[317],[15,61217,61219],{"className":61218},[290],[15,61220,61223],{"className":61221,"style":61222},[294],"height:1.0305em;",[15,61224],{},[15,61226],{"className":61227,"style":406},[157],[15,61229,61231,61234,61274,61277,61280,61283,61286,61289,61292,61332,61335,61364,61367,61370,61373],{"className":61230},[410],[15,61232,2898],{"className":61233,"style":415},[146,414],[15,61235,61237,61240],{"className":61236},[59],[15,61238,223],{"className":61239},[59,366],[15,61241,61243],{"className":61242},[281],[15,61244,61246,61266],{"className":61245},[285,286],[15,61247,61249,61263],{"className":61248},[290],[15,61250,61252],{"className":61251,"style":379},[294],[15,61253,61254,61257],{"style":382},[15,61255],{"className":61256,"style":303},[302],[15,61258,61260],{"className":61259},[307,308,309,310],[15,61261,206],{"className":61262,"style":334},[59,60,310],[15,61264,318],{"className":61265},[317],[15,61267,61269],{"className":61268},[290],[15,61270,61272],{"className":61271,"style":7968},[294],[15,61273],{},[15,61275,230],{"className":61276},[146],[15,61278,4158],{"className":61279,"style":981},[59,60],[15,61281,257],{"className":61282},[153],[15,61284],{"className":61285,"style":2587},[157],[15,61287,4813],{"className":61288},[2591],[15,61290],{"className":61291,"style":2587},[157],[15,61293,61295,61298],{"className":61294},[59],[15,61296,223],{"className":61297},[59,366],[15,61299,61301],{"className":61300},[281],[15,61302,61304,61324],{"className":61303},[285,286],[15,61305,61307,61321],{"className":61306},[290],[15,61308,61310],{"className":61309,"style":379},[294],[15,61311,61312,61315],{"style":382},[15,61313],{"className":61314,"style":303},[302],[15,61316,61318],{"className":61317},[307,308,309,310],[15,61319,213],{"className":61320},[59,60,310],[15,61322,318],{"className":61323},[317],[15,61325,61327],{"className":61326},[290],[15,61328,61330],{"className":61329,"style":325},[294],[15,61331],{},[15,61333,230],{"className":61334},[146],[15,61336,61338,61341],{"className":61337},[59],[15,61339,37],{"className":61340,"style":61},[59,60],[15,61342,61344],{"className":61343},[281],[15,61345,61347],{"className":61346},[285],[15,61348,61350],{"className":61349},[290],[15,61351,61353],{"className":61352,"style":8248},[294],[15,61354,61355,61358],{"style":8277},[15,61356],{"className":61357,"style":303},[302],[15,61359,61361],{"className":61360},[307,308,309,310],[15,61362,7573],{"className":61363},[2591,310],[15,61365,113],{"className":61366},[146],[15,61368,4158],{"className":61369,"style":981},[59,60],[15,61371,20390],{"className":61372},[153],[15,61374,2908],{"className":61375,"style":415},[153,414],[15,61377],{"className":61378,"style":406},[157],[15,61380,551],{"className":61381},[573],[11,61383,61384,61385,10180],{},"其中上确界取遍所有使两个期望都有定义的可测函数 ",[15,61386,61388,61419],{"className":61387,"translate":19},[18],[15,61389,61391],{"className":61390},[23],[25,61392,61393],{"xmlns":27},[29,61394,61395,61416],{},[32,61396,61397,61399,61401,61403,61405,61408,61410],{},[35,61398,4158],{},[110,61400,1015],{},[35,61402,598],{"mathvariant":597},[110,61404,1029],{},[35,61406,61407],{"mathvariant":209},"dom",[110,61409,4103],{},[6814,61411,61412,61414],{},[35,61413,37],{},[110,61415,7573],{},[39,61417,61418],{"encoding":41},"g:\\mathcal X\\to\\operatorname{dom} f^*",[15,61420,61422,61440,61458],{"className":61421,"ariaHidden":46},[45],[15,61423,61425,61428,61431,61434,61437],{"className":61424},[50],[15,61426],{"className":61427,"style":2276},[54],[15,61429,4158],{"className":61430,"style":981},[59,60],[15,61432],{"className":61433,"style":158},[157],[15,61435,1015],{"className":61436},[162],[15,61438],{"className":61439,"style":158},[157],[15,61441,61443,61446,61449,61452,61455],{"className":61442},[50],[15,61444],{"className":61445,"style":664},[54],[15,61447,598],{"className":61448,"style":625},[59,624],[15,61450],{"className":61451,"style":158},[157],[15,61453,1029],{"className":61454},[162],[15,61456],{"className":61457,"style":158},[157],[15,61459,61461,61464,61470,61473],{"className":61460},[50],[15,61462],{"className":61463,"style":55},[54],[15,61465,61467],{"className":61466},[1484],[15,61468,61407],{"className":61469},[59,32662],[15,61471],{"className":61472,"style":406},[157],[15,61474,61476,61479],{"className":61475},[59],[15,61477,37],{"className":61478,"style":61},[59,60],[15,61480,61482],{"className":61481},[281],[15,61483,61485],{"className":61484},[285],[15,61486,61488],{"className":61487},[290],[15,61489,61491],{"className":61490,"style":8499},[294],[15,61492,61493,61496],{"style":6865},[15,61494],{"className":61495,"style":303},[302],[15,61497,61499],{"className":61498},[307,308,309,310],[15,61500,7573],{"className":61501},[2591,310],[11,61503,61504,61507,61508,61536],{},[1225,61505,61506],{},"证明（Fenchel 对偶）。"," 由共轭函数的性质（Fenchel–Moreau，",[15,61509,61511,61524],{"className":61510,"translate":19},[18],[15,61512,61514],{"className":61513},[23],[25,61515,61516],{"xmlns":27},[29,61517,61518,61522],{},[32,61519,61520],{},[35,61521,37],{},[39,61523,37],{"encoding":41},[15,61525,61527],{"className":61526,"ariaHidden":46},[45],[15,61528,61530,61533],{"className":61529},[50],[15,61531],{"className":61532,"style":55},[54],[15,61534,37],{"className":61535,"style":61},[59,60]," 凸闭），",[15,61538,61540],{"className":61539,"translate":19},[180],[15,61541,61543,61610],{"className":61542,"translate":19},[18],[15,61544,61546],{"className":61545},[23],[25,61547,61548],{"xmlns":27,"display":189},[29,61549,61550,61607],{},[32,61551,61552,61554,61556,61558,61560,61562,61572,61574,61576,61578,61580,61586,61588,61590,61592,61594,61596,61598,61601,61603,61605],{},[35,61553,37],{},[110,61555,113],{"stretchy":112},[35,61557,769],{},[110,61559,120],{"stretchy":112},[110,61561,123],{},[6016,61563,61564,61570],{},[32,61565,61566,61568],{},[35,61567,35432],{},[110,61569,4103],{},[35,61571,40237],{},[110,61573,2898],{"stretchy":112},[35,61575,40237],{},[35,61577,769],{},[110,61579,4813],{},[6814,61581,61582,61584],{},[35,61583,37],{},[110,61585,7573],{},[110,61587,113],{"stretchy":112},[35,61589,40237],{},[110,61591,120],{"stretchy":112},[110,61593,2908],{"stretchy":112},[110,61595,551],{"separator":46},[157,61597],{"width":3262},[35,61599,61600],{"mathvariant":209},"∀",[35,61602,769],{},[110,61604,6928],{},[115,61606,5764],{},[39,61608,61609],{"encoding":41},"f(t)=\\sup_{y}\\{yt-f^*(y)\\},\n\\qquad \\forall t\\ge0 .",[15,61611,61613,61640,61711,61779],{"className":61612,"ariaHidden":46},[45],[15,61614,61616,61619,61622,61625,61628,61631,61634,61637],{"className":61615},[50],[15,61617],{"className":61618,"style":139},[54],[15,61620,37],{"className":61621,"style":61},[59,60],[15,61623,113],{"className":61624},[146],[15,61626,769],{"className":61627},[59,60],[15,61629,120],{"className":61630},[153],[15,61632],{"className":61633,"style":158},[157],[15,61635,123],{"className":61636},[162],[15,61638],{"className":61639,"style":158},[157],[15,61641,61643,61646,61693,61696,61699,61702,61705,61708],{"className":61642},[50],[15,61644],{"className":61645,"style":61175},[54],[15,61647,61649],{"className":61648},[1484,13716],[15,61650,61652,61685],{"className":61651},[285,286],[15,61653,61655,61682],{"className":61654},[290],[15,61656,61658,61672],{"className":61657,"style":2345},[294],[15,61659,61660,61663],{"style":61190},[15,61661],{"className":61662,"style":461},[302],[15,61664,61666],{"className":61665},[307,308,309,310],[15,61667,61669],{"className":61668},[59,310],[15,61670,40237],{"className":61671,"style":981},[59,60,310],[15,61673,61674,61677],{"style":11863},[15,61675],{"className":61676,"style":461},[302],[15,61678,61679],{},[15,61680,35432],{"className":61681},[1484],[15,61683,318],{"className":61684},[317],[15,61686,61688],{"className":61687},[290],[15,61689,61691],{"className":61690,"style":61222},[294],[15,61692],{},[15,61694,2898],{"className":61695},[146],[15,61697,40237],{"className":61698,"style":981},[59,60],[15,61700,769],{"className":61701},[59,60],[15,61703],{"className":61704,"style":2587},[157],[15,61706,4813],{"className":61707},[2591],[15,61709],{"className":61710,"style":2587},[157],[15,61712,61714,61717,61746,61749,61752,61755,61758,61761,61764,61767,61770,61773,61776],{"className":61713},[50],[15,61715],{"className":61716,"style":139},[54],[15,61718,61720,61723],{"className":61719},[59],[15,61721,37],{"className":61722,"style":61},[59,60],[15,61724,61726],{"className":61725},[281],[15,61727,61729],{"className":61728},[285],[15,61730,61732],{"className":61731},[290],[15,61733,61735],{"className":61734,"style":8248},[294],[15,61736,61737,61740],{"style":8277},[15,61738],{"className":61739,"style":303},[302],[15,61741,61743],{"className":61742},[307,308,309,310],[15,61744,7573],{"className":61745},[2591,310],[15,61747,113],{"className":61748},[146],[15,61750,40237],{"className":61751,"style":981},[59,60],[15,61753,60999],{"className":61754},[153],[15,61756,551],{"className":61757},[573],[15,61759],{"className":61760,"style":3634},[157],[15,61762],{"className":61763,"style":406},[157],[15,61765,61600],{"className":61766},[59],[15,61768,769],{"className":61769},[59,60],[15,61771],{"className":61772,"style":158},[157],[15,61774,6928],{"className":61775},[162],[15,61777],{"className":61778,"style":158},[157],[15,61780,61782,61785],{"className":61781},[50],[15,61783],{"className":61784,"style":172},[54],[15,61786,5764],{"className":61787},[59],[11,61789,17046,61790,61924,61925,61953],{},[15,61791,61793,61823],{"className":61792,"translate":19},[18],[15,61794,61796],{"className":61795},[23],[25,61797,61798],{"xmlns":27},[29,61799,61800,61820],{},[32,61801,61802,61804,61806],{},[35,61803,769],{},[110,61805,123],{},[238,61807,61808,61814],{},[32,61809,61810,61812],{},[35,61811,244],{},[35,61813,206],{},[32,61815,61816,61818],{},[35,61817,244],{},[35,61819,213],{},[39,61821,61822],{"encoding":41},"t=\\frac{dP}{dQ}",[15,61824,61826,61844],{"className":61825,"ariaHidden":46},[45],[15,61827,61829,61832,61835,61838,61841],{"className":61828},[50],[15,61830],{"className":61831,"style":5343},[54],[15,61833,769],{"className":61834},[59,60],[15,61836],{"className":61837,"style":158},[157],[15,61839,123],{"className":61840},[162],[15,61842],{"className":61843,"style":158},[157],[15,61845,61847,61850],{"className":61846},[50],[15,61848],{"className":61849,"style":2668},[54],[15,61851,61853,61856,61921],{"className":61852},[59],[15,61854],{"className":61855},[146,441],[15,61857,61859],{"className":61858},[238],[15,61860,61862,61913],{"className":61861},[285,286],[15,61863,61865,61910],{"className":61864},[290],[15,61866,61868,61885,61893],{"className":61867,"style":2687},[294],[15,61869,61870,61873],{"style":2527},[15,61871],{"className":61872,"style":461},[302],[15,61874,61876],{"className":61875},[307,308,309,310],[15,61877,61879,61882],{"className":61878},[59,310],[15,61880,244],{"className":61881},[59,60,310],[15,61883,213],{"className":61884},[59,60,310],[15,61886,61887,61890],{"style":473},[15,61888],{"className":61889,"style":461},[302],[15,61891],{"className":61892,"style":481},[480],[15,61894,61895,61898],{"style":2550},[15,61896],{"className":61897,"style":461},[302],[15,61899,61901],{"className":61900},[307,308,309,310],[15,61902,61904,61907],{"className":61903},[59,310],[15,61905,244],{"className":61906},[59,60,310],[15,61908,206],{"className":61909,"style":334},[59,60,310],[15,61911,318],{"className":61912},[317],[15,61914,61916],{"className":61915},[290],[15,61917,61919],{"className":61918,"style":2739},[294],[15,61920],{},[15,61922],{"className":61923},[153,441]," 代入并对 ",[15,61926,61928,61941],{"className":61927,"translate":19},[18],[15,61929,61931],{"className":61930},[23],[25,61932,61933],{"xmlns":27},[29,61934,61935,61939],{},[32,61936,61937],{},[35,61938,213],{},[39,61940,213],{"encoding":41},[15,61942,61944],{"className":61943,"ariaHidden":46},[45],[15,61945,61947,61950],{"className":61946},[50],[15,61948],{"className":61949,"style":566},[54],[15,61951,213],{"className":61952},[59,60]," 积分：",[15,61955,61957],{"className":61956,"translate":19},[180],[15,61958,61960,62202],{"className":61959,"translate":19},[18],[15,61961,61963],{"className":61962},[23],[25,61964,61965],{"xmlns":27,"display":189},[29,61966,61967,62199],{},[1243,61968,61969,62055,62129],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,61970,61971,61993],{},[1252,61972,61973],{},[1255,61974,61975],{"scriptlevel":126,"displaystyle":46},[32,61976,61977,61983,61985,61987,61989,61991],{},[195,61978,61979,61981],{},[35,61980,199],{},[35,61982,37],{},[110,61984,113],{"stretchy":112},[35,61986,206],{},[35,61988,210],{"mathvariant":209},[35,61990,213],{},[110,61992,120],{"stretchy":112},[1252,61994,61995],{},[1255,61996,61997],{"scriptlevel":126,"displaystyle":46},[32,61998,61999,62001,62003,62005,62015,62017,62019,62021,62035,62037,62043,62045,62047,62049,62051,62053],{},[32,62000],{},[110,62002,123],{},[110,62004,1287],{},[6016,62006,62007,62013],{},[32,62008,62009,62011],{},[35,62010,35432],{},[110,62012,4103],{},[35,62014,40237],{},[110,62016,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,62018,40237],{},[1297,62020,1299],{},[238,62022,62023,62029],{},[32,62024,62025,62027],{},[35,62026,244],{},[35,62028,206],{},[32,62030,62031,62033],{},[35,62032,244],{},[35,62034,213],{},[110,62036,4813],{},[6814,62038,62039,62041],{},[35,62040,37],{},[110,62042,7573],{},[110,62044,113],{"stretchy":112},[35,62046,40237],{},[110,62048,120],{"stretchy":112},[110,62050,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,62052,244],{},[35,62054,213],{},[1249,62056,62057,62063],{},[1252,62058,62059],{},[1255,62060,62061],{"scriptlevel":126,"displaystyle":46},[32,62062],{},[1252,62064,62065],{},[1255,62066,62067],{"scriptlevel":126,"displaystyle":46},[32,62068,62069,62071,62073,62075,62077,62087,62089,62091,62093,62095,62109,62111,62117,62119,62121,62123,62125,62127],{},[32,62070],{},[1297,62072,4283],{},[110,62074,6928],{},[1297,62076,4283],{},[6016,62078,62079,62085],{},[32,62080,62081,62083],{},[35,62082,35432],{},[110,62084,4103],{},[35,62086,40237],{},[110,62088,1287],{},[110,62090,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,62092,40237],{},[1297,62094,1299],{},[238,62096,62097,62103],{},[32,62098,62099,62101],{},[35,62100,244],{},[35,62102,206],{},[32,62104,62105,62107],{},[35,62106,244],{},[35,62108,213],{},[110,62110,4813],{},[6814,62112,62113,62115],{},[35,62114,37],{},[110,62116,7573],{},[110,62118,113],{"stretchy":112},[35,62120,40237],{},[110,62122,120],{"stretchy":112},[110,62124,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,62126,244],{},[35,62128,213],{},[1249,62130,62131,62137],{},[1252,62132,62133],{},[1255,62134,62135],{"scriptlevel":126,"displaystyle":46},[32,62136],{},[1252,62138,62139],{},[1255,62140,62141],{"scriptlevel":126,"displaystyle":46},[32,62142,62143,62145,62147,62157,62159,62165,62167,62169,62171,62173,62179,62181,62187,62189,62191,62193,62195,62197],{},[32,62144],{},[110,62146,123],{},[6016,62148,62149,62155],{},[32,62150,62151,62153],{},[35,62152,35432],{},[110,62154,4103],{},[35,62156,40237],{},[110,62158,2898],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,62160,62161,62163],{},[35,62162,223],{"mathvariant":222},[35,62164,206],{},[110,62166,230],{"stretchy":112},[35,62168,40237],{},[110,62170,257],{"stretchy":112},[110,62172,4813],{},[195,62174,62175,62177],{},[35,62176,223],{"mathvariant":222},[35,62178,213],{},[110,62180,230],{"stretchy":112},[6814,62182,62183,62185],{},[35,62184,37],{},[110,62186,7573],{},[110,62188,113],{"stretchy":112},[35,62190,40237],{},[110,62192,120],{"stretchy":112},[110,62194,257],{"stretchy":112},[110,62196,2908],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,62198,4375],{"mathvariant":209},[39,62200,62201],{"encoding":41},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int \\sup_y\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&\\ \\ge\\ \\sup_y\\int\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&=\\sup_y\\big\\{\\mathbb E_P[y]\n-\\mathbb E_Q[f^*(y)]\\big\\}.\n\\end{aligned}",[15,62203,62205],{"className":62204,"ariaHidden":46},[45],[15,62206,62208,62212],{"className":62207},[50],[15,62209],{"className":62210,"style":62211},[54],"height:7.2845em;vertical-align:-3.3923em;",[15,62213,62215],{"className":62214},[59],[15,62216,62218,62326],{"className":62217},[1243],[15,62219,62221],{"className":62220},[1360],[15,62222,62224,62317],{"className":62223},[285,286],[15,62225,62227,62314],{"className":62226},[290],[15,62228,62231,62296,62305],{"className":62229,"style":62230},[294],"height:3.8923em;",[15,62232,62234,62238],{"style":62233},"top:-5.8923em;",[15,62235],{"className":62236,"style":62237},[302],"height:3.3714em;",[15,62239,62241,62281,62284,62287,62290,62293],{"className":62240},[59],[15,62242,62244,62247],{"className":62243},[59],[15,62245,199],{"className":62246,"style":277},[59,60],[15,62248,62250],{"className":62249},[281],[15,62251,62253,62273],{"className":62252},[285,286],[15,62254,62256,62270],{"className":62255},[290],[15,62257,62259],{"className":62258,"style":295},[294],[15,62260,62261,62264],{"style":298},[15,62262],{"className":62263,"style":303},[302],[15,62265,62267],{"className":62266},[307,308,309,310],[15,62268,37],{"className":62269,"style":61},[59,60,310],[15,62271,318],{"className":62272},[317],[15,62274,62276],{"className":62275},[290],[15,62277,62279],{"className":62278,"style":325},[294],[15,62280],{},[15,62282,113],{"className":62283},[146],[15,62285,206],{"className":62286,"style":334},[59,60],[15,62288,210],{"className":62289},[59],[15,62291,213],{"className":62292},[59,60],[15,62294,120],{"className":62295},[153],[15,62297,62299,62302],{"style":62298},"top:-3.1903em;",[15,62300],{"className":62301,"style":62237},[302],[15,62303],{"className":62304},[59],[15,62306,62308,62311],{"style":62307},"top:-1.0097em;",[15,62309],{"className":62310,"style":62237},[302],[15,62312],{"className":62313},[59],[15,62315,318],{"className":62316},[317],[15,62318,62320],{"className":62319},[290],[15,62321,62324],{"className":62322,"style":62323},[294],"height:3.3923em;",[15,62325],{},[15,62327,62329],{"className":62328},[1451],[15,62330,62332,62992],{"className":62331},[285,286],[15,62333,62335,62989],{"className":62334},[290],[15,62336,62338,62550,62768],{"className":62337,"style":62230},[294],[15,62339,62340,62343],{"style":62233},[15,62341],{"className":62342,"style":62237},[302],[15,62344,62346,62349,62352,62355,62358,62361,62364,62408,62411,62417,62420,62423,62491,62494,62497,62500,62529,62532,62535,62538,62544,62547],{"className":62345},[59],[15,62347],{"className":62348},[59],[15,62350],{"className":62351,"style":158},[157],[15,62353,123],{"className":62354},[162],[15,62356],{"className":62357,"style":158},[157],[15,62359,1287],{"className":62360,"style":1487},[1484,1485,1486],[15,62362],{"className":62363,"style":406},[157],[15,62365,62367],{"className":62366},[1484,13716],[15,62368,62370,62400],{"className":62369},[285,286],[15,62371,62373,62397],{"className":62372},[290],[15,62374,62376,62387],{"className":62375,"style":2345},[294],[15,62377,62378,62381],{"style":61190},[15,62379],{"className":62380,"style":461},[302],[15,62382,62384],{"className":62383},[307,308,309,310],[15,62385,40237],{"className":62386,"style":981},[59,60,310],[15,62388,62389,62392],{"style":11863},[15,62390],{"className":62391,"style":461},[302],[15,62393,62394],{},[15,62395,35432],{"className":62396},[1484],[15,62398,318],{"className":62399},[317],[15,62401,62403],{"className":62402},[290],[15,62404,62406],{"className":62405,"style":61222},[294],[15,62407],{},[15,62409],{"className":62410,"style":406},[157],[15,62412,62414],{"className":62413},[59],[15,62415,2898],{"className":62416},[419,3720],[15,62418,40237],{"className":62419,"style":981},[59,60],[15,62421],{"className":62422,"style":406},[157],[15,62424,62426,62429,62488],{"className":62425},[59],[15,62427],{"className":62428},[146,441],[15,62430,62432],{"className":62431},[238],[15,62433,62435,62480],{"className":62434},[285,286],[15,62436,62438,62477],{"className":62437},[290],[15,62439,62441,62455,62463],{"className":62440,"style":454},[294],[15,62442,62443,62446],{"style":457},[15,62444],{"className":62445,"style":461},[302],[15,62447,62449,62452],{"className":62448},[59],[15,62450,244],{"className":62451},[59,60],[15,62453,213],{"className":62454},[59,60],[15,62456,62457,62460],{"style":473},[15,62458],{"className":62459,"style":461},[302],[15,62461],{"className":62462,"style":481},[480],[15,62464,62465,62468],{"style":484},[15,62466],{"className":62467,"style":461},[302],[15,62469,62471,62474],{"className":62470},[59],[15,62472,244],{"className":62473},[59,60],[15,62475,206],{"className":62476,"style":334},[59,60],[15,62478,318],{"className":62479},[317],[15,62481,62483],{"className":62482},[290],[15,62484,62486],{"className":62485,"style":506},[294],[15,62487],{},[15,62489],{"className":62490},[153,441],[15,62492],{"className":62493,"style":2587},[157],[15,62495,4813],{"className":62496},[2591],[15,62498],{"className":62499,"style":2587},[157],[15,62501,62503,62506],{"className":62502},[59],[15,62504,37],{"className":62505,"style":61},[59,60],[15,62507,62509],{"className":62508},[281],[15,62510,62512],{"className":62511},[285],[15,62513,62515],{"className":62514},[290],[15,62516,62518],{"className":62517,"style":8248},[294],[15,62519,62520,62523],{"style":8277},[15,62521],{"className":62522,"style":303},[302],[15,62524,62526],{"className":62525},[307,308,309,310],[15,62527,7573],{"className":62528},[2591,310],[15,62530,113],{"className":62531},[146],[15,62533,40237],{"className":62534,"style":981},[59,60],[15,62536,120],{"className":62537},[153],[15,62539,62541],{"className":62540},[59],[15,62542,2908],{"className":62543},[419,3720],[15,62545,244],{"className":62546},[59,60],[15,62548,213],{"className":62549},[59,60],[15,62551,62552,62555],{"style":62298},[15,62553],{"className":62554,"style":62237},[302],[15,62556,62558,62561,62564,62567,62570,62573,62576,62620,62623,62626,62629,62635,62638,62641,62709,62712,62715,62718,62747,62750,62753,62756,62762,62765],{"className":62557},[59],[15,62559],{"className":62560},[59],[15,62562,4283],{"className":62563},[157],[15,62565],{"className":62566,"style":158},[157],[15,62568,6928],{"className":62569},[162],[15,62571,4283],{"className":62572},[157],[15,62574],{"className":62575,"style":158},[157],[15,62577,62579],{"className":62578},[1484,13716],[15,62580,62582,62612],{"className":62581},[285,286],[15,62583,62585,62609],{"className":62584},[290],[15,62586,62588,62599],{"className":62587,"style":2345},[294],[15,62589,62590,62593],{"style":61190},[15,62591],{"className":62592,"style":461},[302],[15,62594,62596],{"className":62595},[307,308,309,310],[15,62597,40237],{"className":62598,"style":981},[59,60,310],[15,62600,62601,62604],{"style":11863},[15,62602],{"className":62603,"style":461},[302],[15,62605,62606],{},[15,62607,35432],{"className":62608},[1484],[15,62610,318],{"className":62611},[317],[15,62613,62615],{"className":62614},[290],[15,62616,62618],{"className":62617,"style":61222},[294],[15,62619],{},[15,62621],{"className":62622,"style":406},[157],[15,62624,1287],{"className":62625,"style":1487},[1484,1485,1486],[15,62627],{"className":62628,"style":406},[157],[15,62630,62632],{"className":62631},[59],[15,62633,2898],{"className":62634},[419,3720],[15,62636,40237],{"className":62637,"style":981},[59,60],[15,62639],{"className":62640,"style":406},[157],[15,62642,62644,62647,62706],{"className":62643},[59],[15,62645],{"className":62646},[146,441],[15,62648,62650],{"className":62649},[238],[15,62651,62653,62698],{"className":62652},[285,286],[15,62654,62656,62695],{"className":62655},[290],[15,62657,62659,62673,62681],{"className":62658,"style":454},[294],[15,62660,62661,62664],{"style":457},[15,62662],{"className":62663,"style":461},[302],[15,62665,62667,62670],{"className":62666},[59],[15,62668,244],{"className":62669},[59,60],[15,62671,213],{"className":62672},[59,60],[15,62674,62675,62678],{"style":473},[15,62676],{"className":62677,"style":461},[302],[15,62679],{"className":62680,"style":481},[480],[15,62682,62683,62686],{"style":484},[15,62684],{"className":62685,"style":461},[302],[15,62687,62689,62692],{"className":62688},[59],[15,62690,244],{"className":62691},[59,60],[15,62693,206],{"className":62694,"style":334},[59,60],[15,62696,318],{"className":62697},[317],[15,62699,62701],{"className":62700},[290],[15,62702,62704],{"className":62703,"style":506},[294],[15,62705],{},[15,62707],{"className":62708},[153,441],[15,62710],{"className":62711,"style":2587},[157],[15,62713,4813],{"className":62714},[2591],[15,62716],{"className":62717,"style":2587},[157],[15,62719,62721,62724],{"className":62720},[59],[15,62722,37],{"className":62723,"style":61},[59,60],[15,62725,62727],{"className":62726},[281],[15,62728,62730],{"className":62729},[285],[15,62731,62733],{"className":62732},[290],[15,62734,62736],{"className":62735,"style":8248},[294],[15,62737,62738,62741],{"style":8277},[15,62739],{"className":62740,"style":303},[302],[15,62742,62744],{"className":62743},[307,308,309,310],[15,62745,7573],{"className":62746},[2591,310],[15,62748,113],{"className":62749},[146],[15,62751,40237],{"className":62752,"style":981},[59,60],[15,62754,120],{"className":62755},[153],[15,62757,62759],{"className":62758},[59],[15,62760,2908],{"className":62761},[419,3720],[15,62763,244],{"className":62764},[59,60],[15,62766,213],{"className":62767},[59,60],[15,62769,62770,62773],{"style":62307},[15,62771],{"className":62772,"style":62237},[302],[15,62774,62776,62779,62782,62785,62788,62832,62835,62841,62881,62884,62887,62890,62893,62896,62899,62939,62942,62971,62974,62977,62980,62986],{"className":62775},[59],[15,62777],{"className":62778},[59],[15,62780],{"className":62781,"style":158},[157],[15,62783,123],{"className":62784},[162],[15,62786],{"className":62787,"style":158},[157],[15,62789,62791],{"className":62790},[1484,13716],[15,62792,62794,62824],{"className":62793},[285,286],[15,62795,62797,62821],{"className":62796},[290],[15,62798,62800,62811],{"className":62799,"style":2345},[294],[15,62801,62802,62805],{"style":61190},[15,62803],{"className":62804,"style":461},[302],[15,62806,62808],{"className":62807},[307,308,309,310],[15,62809,40237],{"className":62810,"style":981},[59,60,310],[15,62812,62813,62816],{"style":11863},[15,62814],{"className":62815,"style":461},[302],[15,62817,62818],{},[15,62819,35432],{"className":62820},[1484],[15,62822,318],{"className":62823},[317],[15,62825,62827],{"className":62826},[290],[15,62828,62830],{"className":62829,"style":61222},[294],[15,62831],{},[15,62833],{"className":62834,"style":406},[157],[15,62836,62838],{"className":62837},[59],[15,62839,2898],{"className":62840},[419,9674],[15,62842,62844,62847],{"className":62843},[59],[15,62845,223],{"className":62846},[59,366],[15,62848,62850],{"className":62849},[281],[15,62851,62853,62873],{"className":62852},[285,286],[15,62854,62856,62870],{"className":62855},[290],[15,62857,62859],{"className":62858,"style":379},[294],[15,62860,62861,62864],{"style":382},[15,62862],{"className":62863,"style":303},[302],[15,62865,62867],{"className":62866},[307,308,309,310],[15,62868,206],{"className":62869,"style":334},[59,60,310],[15,62871,318],{"className":62872},[317],[15,62874,62876],{"className":62875},[290],[15,62877,62879],{"className":62878,"style":7968},[294],[15,62880],{},[15,62882,230],{"className":62883},[146],[15,62885,40237],{"className":62886,"style":981},[59,60],[15,62888,257],{"className":62889},[153],[15,62891],{"className":62892,"style":2587},[157],[15,62894,4813],{"className":62895},[2591],[15,62897],{"className":62898,"style":2587},[157],[15,62900,62902,62905],{"className":62901},[59],[15,62903,223],{"className":62904},[59,366],[15,62906,62908],{"className":62907},[281],[15,62909,62911,62931],{"className":62910},[285,286],[15,62912,62914,62928],{"className":62913},[290],[15,62915,62917],{"className":62916,"style":379},[294],[15,62918,62919,62922],{"style":382},[15,62920],{"className":62921,"style":303},[302],[15,62923,62925],{"className":62924},[307,308,309,310],[15,62926,213],{"className":62927},[59,60,310],[15,62929,318],{"className":62930},[317],[15,62932,62934],{"className":62933},[290],[15,62935,62937],{"className":62936,"style":325},[294],[15,62938],{},[15,62940,230],{"className":62941},[146],[15,62943,62945,62948],{"className":62944},[59],[15,62946,37],{"className":62947,"style":61},[59,60],[15,62949,62951],{"className":62950},[281],[15,62952,62954],{"className":62953},[285],[15,62955,62957],{"className":62956},[290],[15,62958,62960],{"className":62959,"style":8248},[294],[15,62961,62962,62965],{"style":8277},[15,62963],{"className":62964,"style":303},[302],[15,62966,62968],{"className":62967},[307,308,309,310],[15,62969,7573],{"className":62970},[2591,310],[15,62972,113],{"className":62973},[146],[15,62975,40237],{"className":62976,"style":981},[59,60],[15,62978,20390],{"className":62979},[153],[15,62981,62983],{"className":62982},[59],[15,62984,2908],{"className":62985},[419,9674],[15,62987,4375],{"className":62988},[59],[15,62990,318],{"className":62991},[317],[15,62993,62995],{"className":62994},[290],[15,62996,62998],{"className":62997,"style":62323},[294],[15,62999],{},[11,63001,63002,63003,63031,63032,63060,63061,63256,63257,63285,63286,63363,63364,63463,63464,63623,63624,63652],{},"这里只能得到 ",[15,63004,63006,63019],{"className":63005,"translate":19},[18],[15,63007,63009],{"className":63008},[23],[25,63010,63011],{"xmlns":27},[29,63012,63013,63017],{},[32,63014,63015],{},[110,63016,6928],{},[39,63018,55489],{"encoding":41},[15,63020,63022],{"className":63021,"ariaHidden":46},[45],[15,63023,63025,63028],{"className":63024},[50],[15,63026],{"className":63027,"style":43188},[54],[15,63029,6928],{"className":63030},[162],"，因为「积分的上确界 ≥ 上确界的积分」。反向不等式需要一个可测选择\u002F极大值论证：由于 ",[15,63033,63035,63048],{"className":63034,"translate":19},[18],[15,63036,63038],{"className":63037},[23],[25,63039,63040],{"xmlns":27},[29,63041,63042,63046],{},[32,63043,63044],{},[35,63045,37],{},[39,63047,37],{"encoding":41},[15,63049,63051],{"className":63050,"ariaHidden":46},[45],[15,63052,63054,63057],{"className":63053},[50],[15,63055],{"className":63056,"style":55},[54],[15,63058,37],{"className":63059,"style":61},[59,60]," 凸，",[15,63062,63064,63118],{"className":63063,"translate":19},[18],[15,63065,63067],{"className":63066},[23],[25,63068,63069],{"xmlns":27},[29,63070,63071,63115],{},[32,63072,63073,63075,63077,63079,63081,63083,63093,63095,63097,63099,63101,63107,63109,63111,63113],{},[35,63074,37],{},[110,63076,113],{"stretchy":112},[35,63078,769],{},[110,63080,120],{"stretchy":112},[110,63082,123],{},[195,63084,63085,63091],{},[32,63086,63087,63089],{},[35,63088,35432],{},[110,63090,4103],{},[35,63092,40237],{},[110,63094,2898],{"stretchy":112},[35,63096,40237],{},[35,63098,769],{},[110,63100,4813],{},[6814,63102,63103,63105],{},[35,63104,37],{},[110,63106,7573],{},[110,63108,113],{"stretchy":112},[35,63110,40237],{},[110,63112,120],{"stretchy":112},[110,63114,2908],{"stretchy":112},[39,63116,63117],{"encoding":41},"f(t)=\\sup_y\\{yt-f^*(y)\\}",[15,63119,63121,63148,63212],{"className":63120,"ariaHidden":46},[45],[15,63122,63124,63127,63130,63133,63136,63139,63142,63145],{"className":63123},[50],[15,63125],{"className":63126,"style":139},[54],[15,63128,37],{"className":63129,"style":61},[59,60],[15,63131,113],{"className":63132},[146],[15,63134,769],{"className":63135},[59,60],[15,63137,120],{"className":63138},[153],[15,63140],{"className":63141,"style":158},[157],[15,63143,123],{"className":63144},[162],[15,63146],{"className":63147,"style":158},[157],[15,63149,63151,63154,63194,63197,63200,63203,63206,63209],{"className":63150},[50],[15,63152],{"className":63153,"style":57323},[54],[15,63155,63157,63160],{"className":63156},[1484],[15,63158,35432],{"className":63159},[1484],[15,63161,63163],{"className":63162},[281],[15,63164,63166,63186],{"className":63165},[285,286],[15,63167,63169,63183],{"className":63168},[290],[15,63170,63172],{"className":63171,"style":36999},[294],[15,63173,63174,63177],{"style":35578},[15,63175],{"className":63176,"style":303},[302],[15,63178,63180],{"className":63179},[307,308,309,310],[15,63181,40237],{"className":63182,"style":981},[59,60,310],[15,63184,318],{"className":63185},[317],[15,63187,63189],{"className":63188},[290],[15,63190,63192],{"className":63191,"style":57362},[294],[15,63193],{},[15,63195,2898],{"className":63196},[146],[15,63198,40237],{"className":63199,"style":981},[59,60],[15,63201,769],{"className":63202},[59,60],[15,63204],{"className":63205,"style":2587},[157],[15,63207,4813],{"className":63208},[2591],[15,63210],{"className":63211,"style":2587},[157],[15,63213,63215,63218,63247,63250,63253],{"className":63214},[50],[15,63216],{"className":63217,"style":139},[54],[15,63219,63221,63224],{"className":63220},[59],[15,63222,37],{"className":63223,"style":61},[59,60],[15,63225,63227],{"className":63226},[281],[15,63228,63230],{"className":63229},[285],[15,63231,63233],{"className":63232},[290],[15,63234,63236],{"className":63235,"style":8499},[294],[15,63237,63238,63241],{"style":6865},[15,63239],{"className":63240,"style":303},[302],[15,63242,63244],{"className":63243},[307,308,309,310],[15,63245,7573],{"className":63246},[2591,310],[15,63248,113],{"className":63249},[146],[15,63251,40237],{"className":63252,"style":981},[59,60],[15,63254,60999],{"className":63255},[153]," 中的 ",[15,63258,63260,63273],{"className":63259,"translate":19},[18],[15,63261,63263],{"className":63262},[23],[25,63264,63265],{"xmlns":27},[29,63266,63267,63271],{},[32,63268,63269],{},[35,63270,40237],{},[39,63272,40237],{"encoding":41},[15,63274,63276],{"className":63275,"ariaHidden":46},[45],[15,63277,63279,63282],{"className":63278},[50],[15,63280],{"className":63281,"style":2276},[54],[15,63283,40237],{"className":63284,"style":981},[59,60]," 可取为 ",[15,63287,63289,63313],{"className":63288,"translate":19},[18],[15,63290,63292],{"className":63291},[23],[25,63293,63294],{"xmlns":27},[29,63295,63296,63310],{},[32,63297,63298,63304,63306,63308],{},[6814,63299,63300,63302],{},[35,63301,37],{},[110,63303,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,63305,113],{"stretchy":112},[35,63307,769],{},[110,63309,120],{"stretchy":112},[39,63311,63312],{"encoding":41},"f'(t)",[15,63314,63316],{"className":63315,"ariaHidden":46},[45],[15,63317,63319,63322,63354,63357,63360],{"className":63318},[50],[15,63320],{"className":63321,"style":6843},[54],[15,63323,63325,63328],{"className":63324},[59],[15,63326,37],{"className":63327,"style":61},[59,60],[15,63329,63331],{"className":63330},[281],[15,63332,63334],{"className":63333},[285],[15,63335,63337],{"className":63336},[290],[15,63338,63340],{"className":63339,"style":6862},[294],[15,63341,63342,63345],{"style":6865},[15,63343],{"className":63344,"style":303},[302],[15,63346,63348],{"className":63347},[307,308,309,310],[15,63349,63351],{"className":63350},[59,310],[15,63352,6820],{"className":63353},[59,310],[15,63355,113],{"className":63356},[146],[15,63358,769],{"className":63359},[59,60],[15,63361,120],{"className":63362},[153],"（在可微点），而 ",[15,63365,63367,63395],{"className":63366,"translate":19},[18],[15,63368,63370],{"className":63369},[23],[25,63371,63372],{"xmlns":27},[29,63373,63374,63392],{},[32,63375,63376,63378,63380,63386,63388,63390],{},[35,63377,769],{},[110,63379,8684],{},[6814,63381,63382,63384],{},[35,63383,37],{},[110,63385,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,63387,113],{"stretchy":112},[35,63389,769],{},[110,63391,120],{"stretchy":112},[39,63393,63394],{"encoding":41},"t\\mapsto f'(t)",[15,63396,63398,63416],{"className":63397,"ariaHidden":46},[45],[15,63399,63401,63404,63407,63410,63413],{"className":63400},[50],[15,63402],{"className":63403,"style":8711},[54],[15,63405,769],{"className":63406},[59,60],[15,63408],{"className":63409,"style":158},[157],[15,63411,8684],{"className":63412},[162],[15,63414],{"className":63415,"style":158},[157],[15,63417,63419,63422,63454,63457,63460],{"className":63418},[50],[15,63420],{"className":63421,"style":6843},[54],[15,63423,63425,63428],{"className":63424},[59],[15,63426,37],{"className":63427,"style":61},[59,60],[15,63429,63431],{"className":63430},[281],[15,63432,63434],{"className":63433},[285],[15,63435,63437],{"className":63436},[290],[15,63438,63440],{"className":63439,"style":6862},[294],[15,63441,63442,63445],{"style":6865},[15,63443],{"className":63444,"style":303},[302],[15,63446,63448],{"className":63447},[307,308,309,310],[15,63449,63451],{"className":63450},[59,310],[15,63452,6820],{"className":63453},[59,310],[15,63455,113],{"className":63456},[146],[15,63458,769],{"className":63459},[59,60],[15,63461,120],{"className":63462},[153]," 单调，于是 ",[15,63465,63467,63513],{"className":63466,"translate":19},[18],[15,63468,63470],{"className":63469},[23],[25,63471,63472],{"xmlns":27},[29,63473,63474,63510],{},[32,63475,63476,63482,63484,63486,63488,63490,63492,63498,63500,63502,63504,63506,63508],{},[6814,63477,63478,63480],{},[35,63479,4158],{},[110,63481,7573],{},[110,63483,113],{"stretchy":112},[35,63485,774],{},[110,63487,120],{"stretchy":112},[110,63489,1015],{},[110,63491,123],{},[6814,63493,63494,63496],{},[35,63495,37],{},[110,63497,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,63499,113],{"stretchy":112},[35,63501,769],{},[110,63503,113],{"stretchy":112},[35,63505,774],{},[110,63507,120],{"stretchy":112},[110,63509,120],{"stretchy":112},[39,63511,63512],{"encoding":41},"g^*(x):=f'(t(x))",[15,63514,63516,63570],{"className":63515,"ariaHidden":46},[45],[15,63517,63519,63522,63551,63554,63557,63560,63563,63567],{"className":63518},[50],[15,63520],{"className":63521,"style":139},[54],[15,63523,63525,63528],{"className":63524},[59],[15,63526,4158],{"className":63527,"style":981},[59,60],[15,63529,63531],{"className":63530},[281],[15,63532,63534],{"className":63533},[285],[15,63535,63537],{"className":63536},[290],[15,63538,63540],{"className":63539,"style":8499},[294],[15,63541,63542,63545],{"style":6865},[15,63543],{"className":63544,"style":303},[302],[15,63546,63548],{"className":63547},[307,308,309,310],[15,63549,7573],{"className":63550},[2591,310],[15,63552,113],{"className":63553},[146],[15,63555,774],{"className":63556},[59,60],[15,63558,120],{"className":63559},[153],[15,63561],{"className":63562,"style":158},[157],[15,63564,63566],{"className":63565},[162],":=",[15,63568],{"className":63569,"style":158},[157],[15,63571,63573,63576,63608,63611,63614,63617,63620],{"className":63572},[50],[15,63574],{"className":63575,"style":6843},[54],[15,63577,63579,63582],{"className":63578},[59],[15,63580,37],{"className":63581,"style":61},[59,60],[15,63583,63585],{"className":63584},[281],[15,63586,63588],{"className":63587},[285],[15,63589,63591],{"className":63590},[290],[15,63592,63594],{"className":63593,"style":6862},[294],[15,63595,63596,63599],{"style":6865},[15,63597],{"className":63598,"style":303},[302],[15,63600,63602],{"className":63601},[307,308,309,310],[15,63603,63605],{"className":63604},[59,310],[15,63606,6820],{"className":63607},[59,310],[15,63609,113],{"className":63610},[146],[15,63612,769],{"className":63613},[59,60],[15,63615,113],{"className":63616},[146],[15,63618,774],{"className":63619},[59,60],[15,63621,19047],{"className":63622},[153]," 是可测的，并且对每个 ",[15,63625,63627,63640],{"className":63626,"translate":19},[18],[15,63628,63630],{"className":63629},[23],[25,63631,63632],{"xmlns":27},[29,63633,63634,63638],{},[32,63635,63636],{},[35,63637,774],{},[39,63639,774],{"encoding":41},[15,63641,63643],{"className":63642,"ariaHidden":46},[45],[15,63644,63646,63649],{"className":63645},[50],[15,63647],{"className":63648,"style":2345},[54],[15,63650,774],{"className":63651},[59,60]," 达到上确界。于是不等式取等号。",[11,63654,63655,63658],{},[1225,63656,63657],{},"最优解。"," 达到上确界的函数为",[15,63660,63662],{"className":63661,"translate":19},[180],[15,63663,63665,63727],{"className":63664,"translate":19},[18],[15,63666,63668],{"className":63667},[23],[25,63669,63670],{"xmlns":27,"display":189},[29,63671,63672,63724],{},[32,63673,63674,63680,63682,63684,63686,63688,63694,63696,63722],{},[6814,63675,63676,63678],{},[35,63677,4158],{},[110,63679,7573],{},[110,63681,113],{"stretchy":112},[35,63683,774],{},[110,63685,120],{"stretchy":112},[110,63687,123],{},[6814,63689,63690,63692],{},[35,63691,37],{},[110,63693,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[1297,63695,1304],{},[32,63697,63698,63700,63714,63716,63718,63720],{},[110,63699,113],{"fence":46},[238,63701,63702,63708],{},[32,63703,63704,63706],{},[35,63705,244],{},[35,63707,206],{},[32,63709,63710,63712],{},[35,63711,244],{},[35,63713,213],{},[110,63715,113],{"stretchy":112},[35,63717,774],{},[110,63719,120],{"stretchy":112},[110,63721,120],{"fence":46},[110,63723,551],{"separator":46},[39,63725,63726],{"encoding":41},"g^*(x)=f'\\!\\left(\\frac{dP}{dQ}(x)\\right),",[15,63728,63730,63783],{"className":63729,"ariaHidden":46},[45],[15,63731,63733,63736,63765,63768,63771,63774,63777,63780],{"className":63732},[50],[15,63734],{"className":63735,"style":139},[54],[15,63737,63739,63742],{"className":63738},[59],[15,63740,4158],{"className":63741,"style":981},[59,60],[15,63743,63745],{"className":63744},[281],[15,63746,63748],{"className":63747},[285],[15,63749,63751],{"className":63750},[290],[15,63752,63754],{"className":63753,"style":8248},[294],[15,63755,63756,63759],{"style":8277},[15,63757],{"className":63758,"style":303},[302],[15,63760,63762],{"className":63761},[307,308,309,310],[15,63763,7573],{"className":63764},[2591,310],[15,63766,113],{"className":63767},[146],[15,63769,774],{"className":63770},[59,60],[15,63772,120],{"className":63773},[153],[15,63775],{"className":63776,"style":158},[157],[15,63778,123],{"className":63779},[162],[15,63781],{"className":63782,"style":158},[157],[15,63784,63786,63789,63821,63824,63827,63919,63922],{"className":63785},[50],[15,63787],{"className":63788,"style":359},[54],[15,63790,63792,63795],{"className":63791},[59],[15,63793,37],{"className":63794,"style":61},[59,60],[15,63796,63798],{"className":63797},[281],[15,63799,63801],{"className":63800},[285],[15,63802,63804],{"className":63803},[290],[15,63805,63807],{"className":63806,"style":28971},[294],[15,63808,63809,63812],{"style":8277},[15,63810],{"className":63811,"style":303},[302],[15,63813,63815],{"className":63814},[307,308,309,310],[15,63816,63818],{"className":63817},[59,310],[15,63819,6820],{"className":63820},[59,310],[15,63822],{"className":63823,"style":1512},[157],[15,63825],{"className":63826,"style":406},[157],[15,63828,63830,63836,63904,63907,63910,63913],{"className":63829},[410],[15,63831,63833],{"className":63832,"style":415},[146,414],[15,63834,113],{"className":63835},[419,309],[15,63837,63839,63842,63901],{"className":63838},[59],[15,63840],{"className":63841},[146,441],[15,63843,63845],{"className":63844},[238],[15,63846,63848,63893],{"className":63847},[285,286],[15,63849,63851,63890],{"className":63850},[290],[15,63852,63854,63868,63876],{"className":63853,"style":454},[294],[15,63855,63856,63859],{"style":457},[15,63857],{"className":63858,"style":461},[302],[15,63860,63862,63865],{"className":63861},[59],[15,63863,244],{"className":63864},[59,60],[15,63866,213],{"className":63867},[59,60],[15,63869,63870,63873],{"style":473},[15,63871],{"className":63872,"style":461},[302],[15,63874],{"className":63875,"style":481},[480],[15,63877,63878,63881],{"style":484},[15,63879],{"className":63880,"style":461},[302],[15,63882,63884,63887],{"className":63883},[59],[15,63885,244],{"className":63886},[59,60],[15,63888,206],{"className":63889,"style":334},[59,60],[15,63891,318],{"className":63892},[317],[15,63894,63896],{"className":63895},[290],[15,63897,63899],{"className":63898,"style":506},[294],[15,63900],{},[15,63902],{"className":63903},[153,441],[15,63905,113],{"className":63906},[146],[15,63908,774],{"className":63909},[59,60],[15,63911,120],{"className":63912},[153],[15,63914,63916],{"className":63915,"style":415},[153,414],[15,63917,120],{"className":63918},[419,309],[15,63920],{"className":63921,"style":406},[157],[15,63923,551],{"className":63924},[573],[11,63926,63927,63928,3853,63956,63984,63985,64045,64046,64118,64119,45608,64238,64422],{},"条件是 ",[15,63929,63931,63944],{"className":63930,"translate":19},[18],[15,63932,63934],{"className":63933},[23],[25,63935,63936],{"xmlns":27},[29,63937,63938,63942],{},[32,63939,63940],{},[35,63941,37],{},[39,63943,37],{"encoding":41},[15,63945,63947],{"className":63946,"ariaHidden":46},[45],[15,63948,63950,63953],{"className":63949},[50],[15,63951],{"className":63952,"style":55},[54],[15,63954,37],{"className":63955,"style":61},[59,60],[15,63957,63959,63972],{"className":63958,"translate":19},[18],[15,63960,63962],{"className":63961},[23],[25,63963,63964],{"xmlns":27},[29,63965,63966,63970],{},[32,63967,63968],{},[35,63969,769],{},[39,63971,769],{"encoding":41},[15,63973,63975],{"className":63974,"ariaHidden":46},[45],[15,63976,63978,63981],{"className":63977},[50],[15,63979],{"className":63980,"style":5343},[54],[15,63982,769],{"className":63983},[59,60]," 处可微、且 ",[15,63986,63988,64006],{"className":63987,"translate":19},[18],[15,63989,63991],{"className":63990},[23],[25,63992,63993],{"xmlns":27},[29,63994,63995,64003],{},[32,63996,63997],{},[6814,63998,63999,64001],{},[35,64000,4158],{},[110,64002,7573],{},[39,64004,64005],{"encoding":41},"g^*",[15,64007,64009],{"className":64008,"ariaHidden":46},[45],[15,64010,64012,64016],{"className":64011},[50],[15,64013],{"className":64014,"style":64015},[54],"height:0.8831em;vertical-align:-0.1944em;",[15,64017,64019,64022],{"className":64018},[59],[15,64020,4158],{"className":64021,"style":981},[59,60],[15,64023,64025],{"className":64024},[281],[15,64026,64028],{"className":64027},[285],[15,64029,64031],{"className":64030},[290],[15,64032,64034],{"className":64033,"style":8499},[294],[15,64035,64036,64039],{"style":6865},[15,64037],{"className":64038,"style":303},[302],[15,64040,64042],{"className":64041},[307,308,309,310],[15,64043,7573],{"className":64044},[2591,310]," 落在 ",[15,64047,64049,64071],{"className":64048,"translate":19},[18],[15,64050,64052],{"className":64051},[23],[25,64053,64054],{"xmlns":27},[29,64055,64056,64068],{},[32,64057,64058,64060,64062],{},[35,64059,61407],{"mathvariant":209},[110,64061,4103],{},[6814,64063,64064,64066],{},[35,64065,37],{},[110,64067,7573],{},[39,64069,64070],{"encoding":41},"\\operatorname{dom} f^*",[15,64072,64074],{"className":64073,"ariaHidden":46},[45],[15,64075,64077,64080,64086,64089],{"className":64076},[50],[15,64078],{"className":64079,"style":55},[54],[15,64081,64083],{"className":64082},[1484],[15,64084,61407],{"className":64085},[59,32662],[15,64087],{"className":64088,"style":406},[157],[15,64090,64092,64095],{"className":64091},[59],[15,64093,37],{"className":64094,"style":61},[59,60],[15,64096,64098],{"className":64097},[281],[15,64099,64101],{"className":64100},[285],[15,64102,64104],{"className":64103},[290],[15,64105,64107],{"className":64106,"style":8499},[294],[15,64108,64109,64112],{"style":6865},[15,64110],{"className":64111,"style":303},[302],[15,64113,64115],{"className":64114},[307,308,309,310],[15,64116,7573],{"className":64117},[2591,310]," 内。例如 KL（",[15,64120,64122,64152],{"className":64121,"translate":19},[18],[15,64123,64125],{"className":64124},[23],[25,64126,64127],{"xmlns":27},[29,64128,64129,64149],{},[32,64130,64131,64137,64139,64141,64143,64145,64147],{},[6814,64132,64133,64135],{},[35,64134,37],{},[110,64136,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,64138,123],{},[35,64140,4100],{},[110,64142,4103],{},[35,64144,769],{},[110,64146,2470],{},[115,64148,117],{},[39,64150,64151],{"encoding":41},"f'=\\log t+1",[15,64153,64155,64203,64229],{"className":64154,"ariaHidden":46},[45],[15,64156,64158,64162,64194,64197,64200],{"className":64157},[50],[15,64159],{"className":64160,"style":64161},[54],"height:0.9463em;vertical-align:-0.1944em;",[15,64163,64165,64168],{"className":64164},[59],[15,64166,37],{"className":64167,"style":61},[59,60],[15,64169,64171],{"className":64170},[281],[15,64172,64174],{"className":64173},[285],[15,64175,64177],{"className":64176},[290],[15,64178,64180],{"className":64179,"style":6862},[294],[15,64181,64182,64185],{"style":6865},[15,64183],{"className":64184,"style":303},[302],[15,64186,64188],{"className":64187},[307,308,309,310],[15,64189,64191],{"className":64190},[59,310],[15,64192,6820],{"className":64193},[59,310],[15,64195],{"className":64196,"style":158},[157],[15,64198,123],{"className":64199},[162],[15,64201],{"className":64202,"style":158},[157],[15,64204,64206,64209,64214,64217,64220,64223,64226],{"className":64205},[50],[15,64207],{"className":64208,"style":55},[54],[15,64210,4154,64212],{"className":64211},[1484],[15,64213,4158],{"style":4157},[15,64215],{"className":64216,"style":406},[157],[15,64218,769],{"className":64219},[59,60],[15,64221],{"className":64222,"style":2587},[157],[15,64224,2470],{"className":64225},[2591],[15,64227],{"className":64228,"style":2587},[157],[15,64230,64232,64235],{"className":64231},[50],[15,64233],{"className":64234,"style":172},[54],[15,64236,117],{"className":64237},[59],[15,64239,64241,64275],{"className":64240,"translate":19},[18],[15,64242,64244],{"className":64243},[23],[25,64245,64246],{"xmlns":27},[29,64247,64248,64272],{},[32,64249,64250,64256,64258,64260,64262,64268,64270],{},[6814,64251,64252,64254],{},[35,64253,4158],{},[110,64255,7573],{},[110,64257,123],{},[35,64259,4100],{},[110,64261,4103],{},[238,64263,64264,64266],{},[35,64265,11],{},[35,64267,944],{},[110,64269,2470],{},[115,64271,117],{},[39,64273,64274],{"encoding":41},"g^*=\\log\\frac{p}{q}+1",[15,64276,64278,64322,64413],{"className":64277,"ariaHidden":46},[45],[15,64279,64281,64284,64313,64316,64319],{"className":64280},[50],[15,64282],{"className":64283,"style":64015},[54],[15,64285,64287,64290],{"className":64286},[59],[15,64288,4158],{"className":64289,"style":981},[59,60],[15,64291,64293],{"className":64292},[281],[15,64294,64296],{"className":64295},[285],[15,64297,64299],{"className":64298},[290],[15,64300,64302],{"className":64301,"style":8499},[294],[15,64303,64304,64307],{"style":6865},[15,64305],{"className":64306,"style":303},[302],[15,64308,64310],{"className":64309},[307,308,309,310],[15,64311,7573],{"className":64312},[2591,310],[15,64314],{"className":64315,"style":158},[157],[15,64317,123],{"className":64318},[162],[15,64320],{"className":64321,"style":158},[157],[15,64323,64325,64328,64333,64336,64404,64407,64410],{"className":64324},[50],[15,64326],{"className":64327,"style":3084},[54],[15,64329,4154,64331],{"className":64330},[1484],[15,64332,4158],{"style":4157},[15,64334],{"className":64335,"style":406},[157],[15,64337,64339,64342,64401],{"className":64338},[59],[15,64340],{"className":64341},[146,441],[15,64343,64345],{"className":64344},[238],[15,64346,64348,64393],{"className":64347},[285,286],[15,64349,64351,64390],{"className":64350},[290],[15,64352,64354,64368,64376],{"className":64353,"style":3103},[294],[15,64355,64356,64359],{"style":2527},[15,64357],{"className":64358,"style":461},[302],[15,64360,64362],{"className":64361},[307,308,309,310],[15,64363,64365],{"className":64364},[59,310],[15,64366,944],{"className":64367,"style":981},[59,60,310],[15,64369,64370,64373],{"style":473},[15,64371],{"className":64372,"style":461},[302],[15,64374],{"className":64375,"style":481},[480],[15,64377,64378,64381],{"style":2853},[15,64379],{"className":64380,"style":461},[302],[15,64382,64384],{"className":64383},[307,308,309,310],[15,64385,64387],{"className":64386},[59,310],[15,64388,11],{"className":64389},[59,60,310],[15,64391,318],{"className":64392},[317],[15,64394,64396],{"className":64395},[290],[15,64397,64399],{"className":64398,"style":2739},[294],[15,64400],{},[15,64402],{"className":64403},[153,441],[15,64405],{"className":64406,"style":2587},[157],[15,64408,2470],{"className":64409},[2591],[15,64411],{"className":64412,"style":2587},[157],[15,64414,64416,64419],{"className":64415},[50],[15,64417],{"className":64418,"style":172},[54],[15,64420,117],{"className":64421},[59],"；这解释了为什么「对判别器做 log 密度比」是 f-GAN 的最佳策略。",[11,64424,64425,64487,64488,64587,64588,45608],{},[1225,64426,64427,64428,64486],{},"常用 ",[15,64429,64431,64448],{"className":64430,"translate":19},[18],[15,64432,64434],{"className":64433},[23],[25,64435,64436],{"xmlns":27},[29,64437,64438,64446],{},[32,64439,64440],{},[6814,64441,64442,64444],{},[35,64443,37],{},[110,64445,7573],{},[39,64447,60708],{"encoding":41},[15,64449,64451],{"className":64450,"ariaHidden":46},[45],[15,64452,64454,64457],{"className":64453},[50],[15,64455],{"className":64456,"style":55},[54],[15,64458,64460,64463],{"className":64459},[59],[15,64461,37],{"className":64462,"style":61},[59,60],[15,64464,64466],{"className":64465},[281],[15,64467,64469],{"className":64468},[285],[15,64470,64472],{"className":64471},[290],[15,64473,64475],{"className":64474,"style":8499},[294],[15,64476,64477,64480],{"style":6865},[15,64478],{"className":64479,"style":303},[302],[15,64481,64483],{"className":64482},[307,308,309,310],[15,64484,7573],{"className":64485},[2591,310]," 表","（结合 ",[15,64489,64491,64521],{"className":64490,"translate":19},[18],[15,64492,64494],{"className":64493},[23],[25,64495,64496],{"xmlns":27},[29,64497,64498,64518],{},[32,64499,64500,64502,64504,64506,64508,64510,64512,64514,64516],{},[110,64501,1287],{},[35,64503,244],{},[35,64505,206],{},[110,64507,123],{},[110,64509,1287],{},[35,64511,244],{},[35,64513,213],{},[110,64515,123],{},[115,64517,117],{},[39,64519,64520],{"encoding":41},"\\int dP=\\int dQ=1",[15,64522,64524,64551,64578],{"className":64523,"ariaHidden":46},[45],[15,64525,64527,64530,64533,64536,64539,64542,64545,64548],{"className":64526},[50],[15,64528],{"className":64529,"style":5612},[54],[15,64531,1287],{"className":64532,"style":5617},[1484,1485,5616],[15,64534],{"className":64535,"style":406},[157],[15,64537,244],{"className":64538},[59,60],[15,64540,206],{"className":64541,"style":334},[59,60],[15,64543],{"className":64544,"style":158},[157],[15,64546,123],{"className":64547},[162],[15,64549],{"className":64550,"style":158},[157],[15,64552,64554,64557,64560,64563,64566,64569,64572,64575],{"className":64553},[50],[15,64555],{"className":64556,"style":5612},[54],[15,64558,1287],{"className":64559,"style":5617},[1484,1485,5616],[15,64561],{"className":64562,"style":406},[157],[15,64564,244],{"className":64565},[59,60],[15,64567,213],{"className":64568},[59,60],[15,64570],{"className":64571,"style":158},[157],[15,64573,123],{"className":64574},[162],[15,64576],{"className":64577,"style":158},[157],[15,64579,64581,64584],{"className":64580},[50],[15,64582],{"className":64583,"style":172},[54],[15,64585,117],{"className":64586},[59]," 可加任意常数 ",[15,64589,64591,64604],{"className":64590,"translate":19},[18],[15,64592,64594],{"className":64593},[23],[25,64595,64596],{"xmlns":27},[29,64597,64598,64602],{},[32,64599,64600],{},[35,64601,5906],{},[39,64603,5906],{"encoding":41},[15,64605,64607],{"className":64606,"ariaHidden":46},[45],[15,64608,64610,64613],{"className":64609},[50],[15,64611],{"className":64612,"style":2345},[54],[15,64614,5906],{"className":64615},[59,60],[52492,64617,64618,64819],{},[52495,64619,64620],{},[52498,64621,64622,64667,64743,64816],{},[52501,64623,64624],{},[15,64625,64627,64646],{"className":64626,"translate":19},[18],[15,64628,64630],{"className":64629},[23],[25,64631,64632],{"xmlns":27},[29,64633,64634,64644],{},[32,64635,64636,64638,64640,64642],{},[35,64637,37],{},[110,64639,113],{"stretchy":112},[35,64641,769],{},[110,64643,120],{"stretchy":112},[39,64645,52528],{"encoding":41},[15,64647,64649],{"className":64648,"ariaHidden":46},[45],[15,64650,64652,64655,64658,64661,64664],{"className":64651},[50],[15,64653],{"className":64654,"style":139},[54],[15,64656,37],{"className":64657,"style":61},[59,60],[15,64659,113],{"className":64660},[146],[15,64662,769],{"className":64663},[59,60],[15,64665,120],{"className":64666},[153],[52501,64668,64669],{},[15,64670,64672,64696],{"className":64671,"translate":19},[18],[15,64673,64675],{"className":64674},[23],[25,64676,64677],{"xmlns":27},[29,64678,64679,64693],{},[32,64680,64681,64687,64689,64691],{},[6814,64682,64683,64685],{},[35,64684,37],{},[110,64686,7573],{},[110,64688,113],{"stretchy":112},[35,64690,40237],{},[110,64692,120],{"stretchy":112},[39,64694,64695],{"encoding":41},"f^*(y)",[15,64697,64699],{"className":64698,"ariaHidden":46},[45],[15,64700,64702,64705,64734,64737,64740],{"className":64701},[50],[15,64703],{"className":64704,"style":139},[54],[15,64706,64708,64711],{"className":64707},[59],[15,64709,37],{"className":64710,"style":61},[59,60],[15,64712,64714],{"className":64713},[281],[15,64715,64717],{"className":64716},[285],[15,64718,64720],{"className":64719},[290],[15,64721,64723],{"className":64722,"style":8499},[294],[15,64724,64725,64728],{"style":6865},[15,64726],{"className":64727,"style":303},[302],[15,64729,64731],{"className":64730},[307,308,309,310],[15,64732,7573],{"className":64733},[2591,310],[15,64735,113],{"className":64736},[146],[15,64738,40237],{"className":64739,"style":981},[59,60],[15,64741,120],{"className":64742},[153],[52501,64744,64745],{},[15,64746,64748,64769],{"className":64747,"translate":19},[18],[15,64749,64751],{"className":64750},[23],[25,64752,64753],{"xmlns":27},[29,64754,64755,64767],{},[32,64756,64757,64759,64761],{},[35,64758,61407],{"mathvariant":209},[110,64760,4103],{},[6814,64762,64763,64765],{},[35,64764,37],{},[110,64766,7573],{},[39,64768,64070],{"encoding":41},[15,64770,64772],{"className":64771,"ariaHidden":46},[45],[15,64773,64775,64778,64784,64787],{"className":64774},[50],[15,64776],{"className":64777,"style":55},[54],[15,64779,64781],{"className":64780},[1484],[15,64782,61407],{"className":64783},[59,32662],[15,64785],{"className":64786,"style":406},[157],[15,64788,64790,64793],{"className":64789},[59],[15,64791,37],{"className":64792,"style":61},[59,60],[15,64794,64796],{"className":64795},[281],[15,64797,64799],{"className":64798},[285],[15,64800,64802],{"className":64801},[290],[15,64803,64805],{"className":64804,"style":8499},[294],[15,64806,64807,64810],{"style":6865},[15,64808],{"className":64809,"style":303},[302],[15,64811,64813],{"className":64812},[307,308,309,310],[15,64814,7573],{"className":64815},[2591,310],[52501,64817,64818],{},"对应 GAN 损失",[52590,64820,64821,64984,65225,65858,66162,66501],{},[52498,64822,64823,64874,64950,64981],{},[52595,64824,64825,64873],{},[15,64826,64828,64847],{"className":64827,"translate":19},[18],[15,64829,64831],{"className":64830},[23],[25,64832,64833],{"xmlns":27},[29,64834,64835,64845],{},[32,64836,64837,64839,64841,64843],{},[35,64838,769],{},[35,64840,4100],{},[110,64842,4103],{},[35,64844,769],{},[39,64846,52726],{"encoding":41},[15,64848,64850],{"className":64849,"ariaHidden":46},[45],[15,64851,64853,64856,64859,64862,64867,64870],{"className":64852},[50],[15,64854],{"className":64855,"style":55},[54],[15,64857,769],{"className":64858},[59,60],[15,64860],{"className":64861,"style":406},[157],[15,64863,4154,64865],{"className":64864},[1484],[15,64866,4158],{"style":4157},[15,64868],{"className":64869,"style":406},[157],[15,64871,769],{"className":64872},[59,60],"（KL）",[52595,64875,64876],{},[15,64877,64879,64903],{"className":64878,"translate":19},[18],[15,64880,64882],{"className":64881},[23],[25,64883,64884],{"xmlns":27},[29,64885,64886,64900],{},[32,64887,64888],{},[6814,64889,64890,64892],{},[35,64891,7567],{},[32,64893,64894,64896,64898],{},[35,64895,40237],{},[110,64897,4813],{},[115,64899,117],{},[39,64901,64902],{"encoding":41},"e^{y-1}",[15,64904,64906],{"className":64905,"ariaHidden":46},[45],[15,64907,64909,64912],{"className":64908},[50],[15,64910],{"className":64911,"style":20028},[54],[15,64913,64915,64918],{"className":64914},[59],[15,64916,7567],{"className":64917},[59,60],[15,64919,64921],{"className":64920},[281],[15,64922,64924],{"className":64923},[285],[15,64925,64927],{"className":64926},[290],[15,64928,64930],{"className":64929,"style":20028},[294],[15,64931,64932,64935],{"style":6865},[15,64933],{"className":64934,"style":303},[302],[15,64936,64938],{"className":64937},[307,308,309,310],[15,64939,64941,64944,64947],{"className":64940},[59,310],[15,64942,40237],{"className":64943,"style":981},[59,60,310],[15,64945,4813],{"className":64946},[2591,310],[15,64948,117],{"className":64949},[59,310],[52595,64951,64952],{},[15,64953,64955,64969],{"className":64954,"translate":19},[18],[15,64956,64958],{"className":64957},[23],[25,64959,64960],{"xmlns":27},[29,64961,64962,64966],{},[32,64963,64964],{},[35,64965,1032],{"mathvariant":222},[39,64967,64968],{"encoding":41},"\\mathbb R",[15,64970,64972],{"className":64971,"ariaHidden":46},[45],[15,64973,64975,64978],{"className":64974},[50],[15,64976],{"className":64977,"style":1096},[54],[15,64979,1032],{"className":64980},[59,366],[52595,64982,64983],{},"MINE-f \u002F f-GAN",[52498,64985,64986,65037,65119,65172],{},[52595,64987,64988,65036],{},[15,64989,64991,65010],{"className":64990,"translate":19},[18],[15,64992,64994],{"className":64993},[23],[25,64995,64996],{"xmlns":27},[29,64997,64998,65008],{},[32,64999,65000,65002,65004,65006],{},[110,65001,4813],{},[35,65003,4100],{},[110,65005,4103],{},[35,65007,769],{},[39,65009,52926],{"encoding":41},[15,65011,65013],{"className":65012,"ariaHidden":46},[45],[15,65014,65016,65019,65022,65025,65030,65033],{"className":65015},[50],[15,65017],{"className":65018,"style":55},[54],[15,65020,4813],{"className":65021},[59],[15,65023],{"className":65024,"style":406},[157],[15,65026,4154,65028],{"className":65027},[1484],[15,65029,4158],{"style":4157},[15,65031],{"className":65032,"style":406},[157],[15,65034,769],{"className":65035},[59,60],"（反向 KL）",[52595,65038,65039],{},[15,65040,65042,65072],{"className":65041,"translate":19},[18],[15,65043,65045],{"className":65044},[23],[25,65046,65047],{"xmlns":27},[29,65048,65049,65069],{},[32,65050,65051,65053,65055,65057,65059,65061,65063,65065,65067],{},[110,65052,4813],{},[115,65054,117],{},[110,65056,4813],{},[35,65058,4100],{},[110,65060,4103],{},[110,65062,113],{"stretchy":112},[110,65064,4813],{},[35,65066,40237],{},[110,65068,120],{"stretchy":112},[39,65070,65071],{"encoding":41},"-1-\\log(-y)",[15,65073,65075,65096],{"className":65074,"ariaHidden":46},[45],[15,65076,65078,65081,65084,65087,65090,65093],{"className":65077},[50],[15,65079],{"className":65080,"style":12578},[54],[15,65082,4813],{"className":65083},[59],[15,65085,117],{"className":65086},[59],[15,65088],{"className":65089,"style":2587},[157],[15,65091,4813],{"className":65092},[2591],[15,65094],{"className":65095,"style":2587},[157],[15,65097,65099,65102,65107,65110,65113,65116],{"className":65098},[50],[15,65100],{"className":65101,"style":139},[54],[15,65103,4154,65105],{"className":65104},[1484],[15,65106,4158],{"style":4157},[15,65108,113],{"className":65109},[146],[15,65111,4813],{"className":65112},[59],[15,65114,40237],{"className":65115,"style":981},[59,60],[15,65117,120],{"className":65118},[153],[52595,65120,65121],{},[15,65122,65124,65142],{"className":65123,"translate":19},[18],[15,65125,65127],{"className":65126},[23],[25,65128,65129],{"xmlns":27},[29,65130,65131,65139],{},[32,65132,65133,65135,65137],{},[35,65134,40237],{},[110,65136,7251],{},[115,65138,126],{},[39,65140,65141],{"encoding":41},"y\u003C0",[15,65143,65145,65163],{"className":65144,"ariaHidden":46},[45],[15,65146,65148,65151,65154,65157,65160],{"className":65147},[50],[15,65149],{"className":65150,"style":31692},[54],[15,65152,40237],{"className":65153,"style":981},[59,60],[15,65155],{"className":65156,"style":158},[157],[15,65158,7251],{"className":65159},[162],[15,65161],{"className":65162,"style":158},[157],[15,65164,65166,65169],{"className":65165},[50],[15,65167],{"className":65168,"style":172},[54],[15,65170,126],{"className":65171},[59],[52595,65173,65174,65224],{},[15,65175,65177,65194],{"className":65176,"translate":19},[18],[15,65178,65180],{"className":65179},[23],[25,65181,65182],{"xmlns":27},[29,65183,65184,65192],{},[32,65185,65186,65188,65190],{},[35,65187,44754],{},[110,65189,123],{},[115,65191,126],{},[39,65193,46488],{"encoding":41},[15,65195,65197,65215],{"className":65196,"ariaHidden":46},[45],[15,65198,65200,65203,65206,65209,65212],{"className":65199},[50],[15,65201],{"className":65202,"style":2345},[54],[15,65204,44754],{"className":65205,"style":44784},[59,60],[15,65207],{"className":65208,"style":158},[157],[15,65210,123],{"className":65211},[162],[15,65213],{"className":65214,"style":158},[157],[15,65216,65218,65221],{"className":65217},[50],[15,65219],{"className":65220,"style":172},[54],[15,65222,126],{"className":65223},[59]," 端",[52498,65226,65227,65517,65711,65855],{},[52595,65228,65229,65516],{},[15,65230,65232,65289],{"className":65231,"translate":19},[18],[15,65233,65235],{"className":65234},[23],[25,65236,65237],{"xmlns":27},[29,65238,65239,65287],{},[32,65240,65241,65247,65249,65251,65253,65255,65257,65259,65261,65263,65265,65267,65269,65271,65273,65285],{},[238,65242,65243,65245],{},[115,65244,117],{},[115,65246,2463],{},[110,65248,230],{"stretchy":112},[35,65250,769],{},[35,65252,4100],{},[110,65254,4103],{},[35,65256,769],{},[110,65258,4813],{},[110,65260,113],{"stretchy":112},[35,65262,769],{},[110,65264,2470],{},[115,65266,117],{},[110,65268,120],{"stretchy":112},[35,65270,4100],{},[110,65272,4103],{},[238,65274,65275,65283],{},[32,65276,65277,65279,65281],{},[35,65278,769],{},[110,65280,2470],{},[115,65282,117],{},[115,65284,2463],{},[110,65286,257],{"stretchy":112},[39,65288,53187],{"encoding":41},[15,65290,65292,65395,65416],{"className":65291,"ariaHidden":46},[45],[15,65293,65295,65298,65366,65369,65372,65375,65380,65383,65386,65389,65392],{"className":65294},[50],[15,65296],{"className":65297,"style":2505},[54],[15,65299,65301,65304,65363],{"className":65300},[59],[15,65302],{"className":65303},[146,441],[15,65305,65307],{"className":65306},[238],[15,65308,65310,65355],{"className":65309},[285,286],[15,65311,65313,65352],{"className":65312},[290],[15,65314,65316,65330,65338],{"className":65315,"style":2524},[294],[15,65317,65318,65321],{"style":2527},[15,65319],{"className":65320,"style":461},[302],[15,65322,65324],{"className":65323},[307,308,309,310],[15,65325,65327],{"className":65326},[59,310],[15,65328,2463],{"className":65329},[59,310],[15,65331,65332,65335],{"style":473},[15,65333],{"className":65334,"style":461},[302],[15,65336],{"className":65337,"style":481},[480],[15,65339,65340,65343],{"style":2550},[15,65341],{"className":65342,"style":461},[302],[15,65344,65346],{"className":65345},[307,308,309,310],[15,65347,65349],{"className":65348},[59,310],[15,65350,117],{"className":65351},[59,310],[15,65353,318],{"className":65354},[317],[15,65356,65358],{"className":65357},[290],[15,65359,65361],{"className":65360,"style":2572},[294],[15,65362],{},[15,65364],{"className":65365},[153,441],[15,65367,230],{"className":65368},[146],[15,65370,769],{"className":65371},[59,60],[15,65373],{"className":65374,"style":406},[157],[15,65376,4154,65378],{"className":65377},[1484],[15,65379,4158],{"style":4157},[15,65381],{"className":65382,"style":406},[157],[15,65384,769],{"className":65385},[59,60],[15,65387],{"className":65388,"style":2587},[157],[15,65390,4813],{"className":65391},[2591],[15,65393],{"className":65394,"style":2587},[157],[15,65396,65398,65401,65404,65407,65410,65413],{"className":65397},[50],[15,65399],{"className":65400,"style":139},[54],[15,65402,113],{"className":65403},[146],[15,65405,769],{"className":65406},[59,60],[15,65408],{"className":65409,"style":2587},[157],[15,65411,2470],{"className":65412},[2591],[15,65414],{"className":65415,"style":2587},[157],[15,65417,65419,65422,65425,65428,65431,65436,65439,65513],{"className":65418},[50],[15,65420],{"className":65421,"style":2505},[54],[15,65423,117],{"className":65424},[59],[15,65426,120],{"className":65427},[153],[15,65429],{"className":65430,"style":406},[157],[15,65432,4154,65434],{"className":65433},[1484],[15,65435,4158],{"style":4157},[15,65437],{"className":65438,"style":406},[157],[15,65440,65442,65445,65510],{"className":65441},[59],[15,65443],{"className":65444},[146,441],[15,65446,65448],{"className":65447},[238],[15,65449,65451,65502],{"className":65450},[285,286],[15,65452,65454,65499],{"className":65453},[290],[15,65455,65457,65471,65479],{"className":65456,"style":2524},[294],[15,65458,65459,65462],{"style":2527},[15,65460],{"className":65461,"style":461},[302],[15,65463,65465],{"className":65464},[307,308,309,310],[15,65466,65468],{"className":65467},[59,310],[15,65469,2463],{"className":65470},[59,310],[15,65472,65473,65476],{"style":473},[15,65474],{"className":65475,"style":461},[302],[15,65477],{"className":65478,"style":481},[480],[15,65480,65481,65484],{"style":2550},[15,65482],{"className":65483,"style":461},[302],[15,65485,65487],{"className":65486},[307,308,309,310],[15,65488,65490,65493,65496],{"className":65489},[59,310],[15,65491,769],{"className":65492},[59,60,310],[15,65494,2470],{"className":65495},[2591,310],[15,65497,117],{"className":65498},[59,310],[15,65500,318],{"className":65501},[317],[15,65503,65505],{"className":65504},[290],[15,65506,65508],{"className":65507,"style":2572},[294],[15,65509],{},[15,65511],{"className":65512},[153,441],[15,65514,257],{"className":65515},[153],"（JS）",[52595,65518,65519],{},[15,65520,65522,65564],{"className":65521,"translate":19},[18],[15,65523,65525],{"className":65524},[23],[25,65526,65527],{"xmlns":27},[29,65528,65529,65561],{},[32,65530,65531,65533,65539,65541,65543,65545,65547,65549,65559],{},[110,65532,4813],{},[238,65534,65535,65537],{},[115,65536,117],{},[115,65538,2463],{},[35,65540,4100],{},[110,65542,4103],{},[110,65544,113],{"stretchy":112},[115,65546,2463],{},[110,65548,4813],{},[6814,65550,65551,65553],{},[35,65552,7567],{},[32,65554,65555,65557],{},[115,65556,2463],{},[35,65558,40237],{},[110,65560,120],{"stretchy":112},[39,65562,65563],{"encoding":41},"-\\frac12\\log(2-e^{2y})",[15,65565,65567,65667],{"className":65566,"ariaHidden":46},[45],[15,65568,65570,65573,65576,65644,65647,65652,65655,65658,65661,65664],{"className":65569},[50],[15,65571],{"className":65572,"style":2505},[54],[15,65574,4813],{"className":65575},[59],[15,65577,65579,65582,65641],{"className":65578},[59],[15,65580],{"className":65581},[146,441],[15,65583,65585],{"className":65584},[238],[15,65586,65588,65633],{"className":65587},[285,286],[15,65589,65591,65630],{"className":65590},[290],[15,65592,65594,65608,65616],{"className":65593,"style":2524},[294],[15,65595,65596,65599],{"style":2527},[15,65597],{"className":65598,"style":461},[302],[15,65600,65602],{"className":65601},[307,308,309,310],[15,65603,65605],{"className":65604},[59,310],[15,65606,2463],{"className":65607},[59,310],[15,65609,65610,65613],{"style":473},[15,65611],{"className":65612,"style":461},[302],[15,65614],{"className":65615,"style":481},[480],[15,65617,65618,65621],{"style":2550},[15,65619],{"className":65620,"style":461},[302],[15,65622,65624],{"className":65623},[307,308,309,310],[15,65625,65627],{"className":65626},[59,310],[15,65628,117],{"className":65629},[59,310],[15,65631,318],{"className":65632},[317],[15,65634,65636],{"className":65635},[290],[15,65637,65639],{"className":65638,"style":2572},[294],[15,65640],{},[15,65642],{"className":65643},[153,441],[15,65645],{"className":65646,"style":406},[157],[15,65648,4154,65650],{"className":65649},[1484],[15,65651,4158],{"style":4157},[15,65653,113],{"className":65654},[146],[15,65656,2463],{"className":65657},[59],[15,65659],{"className":65660,"style":2587},[157],[15,65662,4813],{"className":65663},[2591],[15,65665],{"className":65666,"style":2587},[157],[15,65668,65670,65673,65708],{"className":65669},[50],[15,65671],{"className":65672,"style":20003},[54],[15,65674,65676,65679],{"className":65675},[59],[15,65677,7567],{"className":65678},[59,60],[15,65680,65682],{"className":65681},[281],[15,65683,65685],{"className":65684},[285],[15,65686,65688],{"className":65687},[290],[15,65689,65691],{"className":65690,"style":20028},[294],[15,65692,65693,65696],{"style":6865},[15,65694],{"className":65695,"style":303},[302],[15,65697,65699],{"className":65698},[307,308,309,310],[15,65700,65702,65705],{"className":65701},[59,310],[15,65703,2463],{"className":65704},[59,310],[15,65706,40237],{"className":65707,"style":981},[59,60,310],[15,65709,120],{"className":65710},[153],[52595,65712,65713],{},[15,65714,65716,65744],{"className":65715,"translate":19},[18],[15,65717,65719],{"className":65718},[23],[25,65720,65721],{"xmlns":27},[29,65722,65723,65741],{},[32,65724,65725,65727,65729],{},[35,65726,40237],{},[110,65728,7251],{},[238,65730,65731,65739],{},[32,65732,65733,65735,65737],{},[35,65734,4100],{},[110,65736,4103],{},[115,65738,2463],{},[115,65740,2463],{},[39,65742,65743],{"encoding":41},"y\u003C\\frac{\\log2}{2}",[15,65745,65747,65765],{"className":65746,"ariaHidden":46},[45],[15,65748,65750,65753,65756,65759,65762],{"className":65749},[50],[15,65751],{"className":65752,"style":31692},[54],[15,65754,40237],{"className":65755,"style":981},[59,60],[15,65757],{"className":65758,"style":158},[157],[15,65760,7251],{"className":65761},[162],[15,65763],{"className":65764,"style":158},[157],[15,65766,65768,65772],{"className":65767},[50],[15,65769],{"className":65770,"style":65771},[54],"height:1.2772em;vertical-align:-0.345em;",[15,65773,65775,65778,65852],{"className":65774},[59],[15,65776],{"className":65777},[146,441],[15,65779,65781],{"className":65780},[238],[15,65782,65784,65844],{"className":65783},[285,286],[15,65785,65787,65841],{"className":65786},[290],[15,65788,65790,65804,65812],{"className":65789,"style":2825},[294],[15,65791,65792,65795],{"style":2527},[15,65793],{"className":65794,"style":461},[302],[15,65796,65798],{"className":65797},[307,308,309,310],[15,65799,65801],{"className":65800},[59,310],[15,65802,2463],{"className":65803},[59,310],[15,65805,65806,65809],{"style":473},[15,65807],{"className":65808,"style":461},[302],[15,65810],{"className":65811,"style":481},[480],[15,65813,65814,65817],{"style":2853},[15,65815],{"className":65816,"style":461},[302],[15,65818,65820],{"className":65819},[307,308,309,310],[15,65821,65823,65835,65838],{"className":65822},[59,310],[15,65824,65826,65829,65832],{"className":65825},[1484,310],[15,65827,47658],{"className":65828},[310],[15,65830,47662],{"className":65831},[310],[15,65833,4158],{"className":65834,"style":4157},[310],[15,65836],{"className":65837,"style":42366},[157,310],[15,65839,2463],{"className":65840},[59,310],[15,65842,318],{"className":65843},[317],[15,65845,65847],{"className":65846},[290],[15,65848,65850],{"className":65849,"style":2572},[294],[15,65851],{},[15,65853],{"className":65854},[153,441],[52595,65856,65857],{},"原始 GAN",[52498,65859,65860,65997,66027,66159],{},[52595,65861,65862,65996],{},[15,65863,65865,65892],{"className":65864,"translate":19},[18],[15,65866,65868],{"className":65867},[23],[25,65869,65870],{"xmlns":27},[29,65871,65872,65890],{},[32,65873,65874,65880,65882,65884,65886,65888],{},[238,65875,65876,65878],{},[115,65877,117],{},[115,65879,2463],{},[110,65881,4808],{"stretchy":112},[35,65883,769],{},[110,65885,4813],{},[115,65887,117],{},[110,65889,4808],{"stretchy":112},[39,65891,53555],{"encoding":41},[15,65893,65895,65984],{"className":65894,"ariaHidden":46},[45],[15,65896,65898,65901,65969,65972,65975,65978,65981],{"className":65897},[50],[15,65899],{"className":65900,"style":2505},[54],[15,65902,65904,65907,65966],{"className":65903},[59],[15,65905],{"className":65906},[146,441],[15,65908,65910],{"className":65909},[238],[15,65911,65913,65958],{"className":65912},[285,286],[15,65914,65916,65955],{"className":65915},[290],[15,65917,65919,65933,65941],{"className":65918,"style":2524},[294],[15,65920,65921,65924],{"style":2527},[15,65922],{"className":65923,"style":461},[302],[15,65925,65927],{"className":65926},[307,308,309,310],[15,65928,65930],{"className":65929},[59,310],[15,65931,2463],{"className":65932},[59,310],[15,65934,65935,65938],{"style":473},[15,65936],{"className":65937,"style":461},[302],[15,65939],{"className":65940,"style":481},[480],[15,65942,65943,65946],{"style":2550},[15,65944],{"className":65945,"style":461},[302],[15,65947,65949],{"className":65948},[307,308,309,310],[15,65950,65952],{"className":65951},[59,310],[15,65953,117],{"className":65954},[59,310],[15,65956,318],{"className":65957},[317],[15,65959,65961],{"className":65960},[290],[15,65962,65964],{"className":65963,"style":2572},[294],[15,65965],{},[15,65967],{"className":65968},[153,441],[15,65970,4808],{"className":65971},[146],[15,65973,769],{"className":65974},[59,60],[15,65976],{"className":65977,"style":2587},[157],[15,65979,4813],{"className":65980},[2591],[15,65982],{"className":65983,"style":2587},[157],[15,65985,65987,65990,65993],{"className":65986},[50],[15,65988],{"className":65989,"style":139},[54],[15,65991,117],{"className":65992},[59],[15,65994,4808],{"className":65995},[153],"（TV）",[52595,65998,65999],{},[15,66000,66002,66015],{"className":66001,"translate":19},[18],[15,66003,66005],{"className":66004},[23],[25,66006,66007],{"xmlns":27},[29,66008,66009,66013],{},[32,66010,66011],{},[35,66012,40237],{},[39,66014,40237],{"encoding":41},[15,66016,66018],{"className":66017,"ariaHidden":46},[45],[15,66019,66021,66024],{"className":66020},[50],[15,66022],{"className":66023,"style":2276},[54],[15,66025,40237],{"className":66026,"style":981},[59,60],[52595,66028,66029],{},[15,66030,66032,66058],{"className":66031,"translate":19},[18],[15,66033,66035],{"className":66034},[23],[25,66036,66037],{"xmlns":27},[29,66038,66039,66055],{},[32,66040,66041,66043,66045,66047,66049],{},[110,66042,4808],{"stretchy":112},[35,66044,40237],{},[110,66046,4808],{"stretchy":112},[110,66048,9952],{},[238,66050,66051,66053],{},[115,66052,117],{},[115,66054,2463],{},[39,66056,66057],{"encoding":41},"\\lvert y\\rvert\\le\\frac12",[15,66059,66061,66085],{"className":66060,"ariaHidden":46},[45],[15,66062,66064,66067,66070,66073,66076,66079,66082],{"className":66063},[50],[15,66065],{"className":66066,"style":139},[54],[15,66068,4808],{"className":66069},[146],[15,66071,40237],{"className":66072,"style":981},[59,60],[15,66074,4808],{"className":66075},[153],[15,66077],{"className":66078,"style":158},[157],[15,66080,9952],{"className":66081},[162],[15,66083],{"className":66084,"style":158},[157],[15,66086,66088,66091],{"className":66087},[50],[15,66089],{"className":66090,"style":2505},[54],[15,66092,66094,66097,66156],{"className":66093},[59],[15,66095],{"className":66096},[146,441],[15,66098,66100],{"className":66099},[238],[15,66101,66103,66148],{"className":66102},[285,286],[15,66104,66106,66145],{"className":66105},[290],[15,66107,66109,66123,66131],{"className":66108,"style":2524},[294],[15,66110,66111,66114],{"style":2527},[15,66112],{"className":66113,"style":461},[302],[15,66115,66117],{"className":66116},[307,308,309,310],[15,66118,66120],{"className":66119},[59,310],[15,66121,2463],{"className":66122},[59,310],[15,66124,66125,66128],{"style":473},[15,66126],{"className":66127,"style":461},[302],[15,66129],{"className":66130,"style":481},[480],[15,66132,66133,66136],{"style":2550},[15,66134],{"className":66135,"style":461},[302],[15,66137,66139],{"className":66138},[307,308,309,310],[15,66140,66142],{"className":66141},[59,310],[15,66143,117],{"className":66144},[59,310],[15,66146,318],{"className":66147},[317],[15,66149,66151],{"className":66150},[290],[15,66152,66154],{"className":66153,"style":2572},[294],[15,66155],{},[15,66157],{"className":66158},[153,441],[52595,66160,66161],{},"—",[52498,66163,66164,66314,66468,66498],{},[52595,66165,66166,15795,66256,53475],{},[15,66167,66169,66194],{"className":66168,"translate":19},[18],[15,66170,66172],{"className":66171},[23],[25,66173,66174],{"xmlns":27},[29,66175,66176,66192],{},[32,66177,66178,66180,66182,66184,66186],{},[110,66179,113],{"stretchy":112},[35,66181,769],{},[110,66183,4813],{},[115,66185,117],{},[6814,66187,66188,66190],{},[110,66189,120],{"stretchy":112},[115,66191,2463],{},[39,66193,53830],{"encoding":41},[15,66195,66197,66218],{"className":66196,"ariaHidden":46},[45],[15,66198,66200,66203,66206,66209,66212,66215],{"className":66199},[50],[15,66201],{"className":66202,"style":139},[54],[15,66204,113],{"className":66205},[146],[15,66207,769],{"className":66208},[59,60],[15,66210],{"className":66211,"style":2587},[157],[15,66213,4813],{"className":66214},[2591],[15,66216],{"className":66217,"style":2587},[157],[15,66219,66221,66224,66227],{"className":66220},[50],[15,66222],{"className":66223,"style":20003},[54],[15,66225,117],{"className":66226},[59],[15,66228,66230,66233],{"className":66229},[153],[15,66231,120],{"className":66232},[153],[15,66234,66236],{"className":66235},[281],[15,66237,66239],{"className":66238},[285],[15,66240,66242],{"className":66241},[290],[15,66243,66245],{"className":66244,"style":20028},[294],[15,66246,66247,66250],{"style":6865},[15,66248],{"className":66249,"style":303},[302],[15,66251,66253],{"className":66252},[307,308,309,310],[15,66254,2463],{"className":66255},[59,310],[15,66257,66259,66276],{"className":66258,"translate":19},[18],[15,66260,66262],{"className":66261},[23],[25,66263,66264],{"xmlns":27},[29,66265,66266,66274],{},[32,66267,66268],{},[6814,66269,66270,66272],{},[35,66271,37449],{},[115,66273,2463],{},[39,66275,40394],{"encoding":41},[15,66277,66279],{"className":66278,"ariaHidden":46},[45],[15,66280,66282,66285],{"className":66281},[50],[15,66283],{"className":66284,"style":40404},[54],[15,66286,66288,66291],{"className":66287},[59],[15,66289,37449],{"className":66290},[59,60],[15,66292,66294],{"className":66293},[281],[15,66295,66297],{"className":66296},[285],[15,66298,66300],{"className":66299},[290],[15,66301,66303],{"className":66302,"style":20028},[294],[15,66304,66305,66308],{"style":6865},[15,66306],{"className":66307,"style":303},[302],[15,66309,66311],{"className":66310},[307,308,309,310],[15,66312,2463],{"className":66313},[59,310],[52595,66315,66316],{},[15,66317,66319,66345],{"className":66318,"translate":19},[18],[15,66320,66322],{"className":66321},[23],[25,66323,66324],{"xmlns":27},[29,66325,66326,66342],{},[32,66327,66328,66330,66332],{},[35,66329,40237],{},[110,66331,2470],{},[238,66333,66334,66340],{},[6814,66335,66336,66338],{},[35,66337,40237],{},[115,66339,2463],{},[115,66341,38989],{},[39,66343,66344],{"encoding":41},"y+\\frac{y^2}{4}",[15,66346,66348,66366],{"className":66347,"ariaHidden":46},[45],[15,66349,66351,66354,66357,66360,66363],{"className":66350},[50],[15,66352],{"className":66353,"style":40321},[54],[15,66355,40237],{"className":66356,"style":981},[59,60],[15,66358],{"className":66359,"style":2587},[157],[15,66361,2470],{"className":66362},[2591],[15,66364],{"className":66365,"style":2587},[157],[15,66367,66369,66373],{"className":66368},[50],[15,66370],{"className":66371,"style":66372},[54],"height:1.415em;vertical-align:-0.345em;",[15,66374,66376,66379,66465],{"className":66375},[59],[15,66377],{"className":66378},[146,441],[15,66380,66382],{"className":66381},[238],[15,66383,66385,66457],{"className":66384},[285,286],[15,66386,66388,66454],{"className":66387},[290],[15,66389,66392,66406,66414],{"className":66390,"style":66391},[294],"height:1.07em;",[15,66393,66394,66397],{"style":2527},[15,66395],{"className":66396,"style":461},[302],[15,66398,66400],{"className":66399},[307,308,309,310],[15,66401,66403],{"className":66402},[59,310],[15,66404,38989],{"className":66405},[59,310],[15,66407,66408,66411],{"style":473},[15,66409],{"className":66410,"style":461},[302],[15,66412],{"className":66413,"style":481},[480],[15,66415,66416,66419],{"style":2853},[15,66417],{"className":66418,"style":461},[302],[15,66420,66422],{"className":66421},[307,308,309,310],[15,66423,66425],{"className":66424},[59,310],[15,66426,66428,66431],{"className":66427},[59,310],[15,66429,40237],{"className":66430,"style":981},[59,60,310],[15,66432,66434],{"className":66433},[281],[15,66435,66437],{"className":66436},[285],[15,66438,66440],{"className":66439},[290],[15,66441,66443],{"className":66442,"style":38512},[294],[15,66444,66445,66448],{"style":38515},[15,66446],{"className":66447,"style":30206},[302],[15,66449,66451],{"className":66450},[307,30210,9674,310],[15,66452,2463],{"className":66453},[59,310],[15,66455,318],{"className":66456},[317],[15,66458,66460],{"className":66459},[290],[15,66461,66463],{"className":66462,"style":2572},[294],[15,66464],{},[15,66466],{"className":66467},[153,441],[52595,66469,66470],{},[15,66471,66473,66486],{"className":66472,"translate":19},[18],[15,66474,66476],{"className":66475},[23],[25,66477,66478],{"xmlns":27},[29,66479,66480,66484],{},[32,66481,66482],{},[35,66483,1032],{"mathvariant":222},[39,66485,64968],{"encoding":41},[15,66487,66489],{"className":66488,"ariaHidden":46},[45],[15,66490,66492,66495],{"className":66491},[50],[15,66493],{"className":66494,"style":1096},[54],[15,66496,1032],{"className":66497},[59,366],[52595,66499,66500],{},"LSGAN",[52498,66502,66503,66639,66751,66804],{},[52595,66504,66505,66638],{},[15,66506,66508,66535],{"className":66507,"translate":19},[18],[15,66509,66511],{"className":66510},[23],[25,66512,66513],{"xmlns":27},[29,66514,66515,66533],{},[32,66516,66517,66519,66523,66525,66527],{},[110,66518,113],{"stretchy":112},[34339,66520,66521],{},[35,66522,769],{},[110,66524,4813],{},[115,66526,117],{},[6814,66528,66529,66531],{},[110,66530,120],{"stretchy":112},[115,66532,2463],{},[39,66534,54307],{"encoding":41},[15,66536,66538,66600],{"className":66537,"ariaHidden":46},[45],[15,66539,66541,66544,66547,66591,66594,66597],{"className":66540},[50],[15,66542],{"className":66543,"style":42667},[54],[15,66545,113],{"className":66546},[146],[15,66548,66550],{"className":66549},[59,34367],[15,66551,66553,66583],{"className":66552},[285,286],[15,66554,66556,66580],{"className":66555},[290],[15,66557,66559,66568],{"className":66558,"style":42683},[294],[15,66560,66562,66565],{"className":66561,"style":11863},[6307],[15,66563],{"className":66564,"style":461},[302],[15,66566,769],{"className":66567,"style":34387},[59,60],[15,66569,66570,66573],{"style":42695},[15,66571],{"className":66572,"style":461},[302],[15,66574,66576],{"className":66575,"style":34444},[34443],[6323,66577,66578],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,66579],{"d":34451},[15,66581,318],{"className":66582},[317],[15,66584,66586],{"className":66585},[290],[15,66587,66589],{"className":66588,"style":42715},[294],[15,66590],{},[15,66592],{"className":66593,"style":2587},[157],[15,66595,4813],{"className":66596},[2591],[15,66598],{"className":66599,"style":2587},[157],[15,66601,66603,66606,66609],{"className":66602},[50],[15,66604],{"className":66605,"style":20003},[54],[15,66607,117],{"className":66608},[59],[15,66610,66612,66615],{"className":66611},[153],[15,66613,120],{"className":66614},[153],[15,66616,66618],{"className":66617},[281],[15,66619,66621],{"className":66620},[285],[15,66622,66624],{"className":66623},[290],[15,66625,66627],{"className":66626,"style":20028},[294],[15,66628,66629,66632],{"style":6865},[15,66630],{"className":66631,"style":303},[302],[15,66633,66635],{"className":66634},[307,308,309,310],[15,66636,2463],{"className":66637},[59,310],"（Hellinger²）",[52595,66640,66641],{},[15,66642,66644,66668],{"className":66643,"translate":19},[18],[15,66645,66647],{"className":66646},[23],[25,66648,66649],{"xmlns":27},[29,66650,66651,66665],{},[32,66652,66653],{},[238,66654,66655,66657],{},[35,66656,40237],{},[32,66658,66659,66661,66663],{},[115,66660,117],{},[110,66662,4813],{},[35,66664,40237],{},[39,66666,66667],{"encoding":41},"\\frac{y}{1-y}",[15,66669,66671],{"className":66670,"ariaHidden":46},[45],[15,66672,66674,66677],{"className":66673},[50],[15,66675],{"className":66676,"style":3084},[54],[15,66678,66680,66683,66748],{"className":66679},[59],[15,66681],{"className":66682},[146,441],[15,66684,66686],{"className":66685},[238],[15,66687,66689,66740],{"className":66688},[285,286],[15,66690,66692,66737],{"className":66691},[290],[15,66693,66695,66715,66723],{"className":66694,"style":3103},[294],[15,66696,66697,66700],{"style":2527},[15,66698],{"className":66699,"style":461},[302],[15,66701,66703],{"className":66702},[307,308,309,310],[15,66704,66706,66709,66712],{"className":66705},[59,310],[15,66707,117],{"className":66708},[59,310],[15,66710,4813],{"className":66711},[2591,310],[15,66713,40237],{"className":66714,"style":981},[59,60,310],[15,66716,66717,66720],{"style":473},[15,66718],{"className":66719,"style":461},[302],[15,66721],{"className":66722,"style":481},[480],[15,66724,66725,66728],{"style":2853},[15,66726],{"className":66727,"style":461},[302],[15,66729,66731],{"className":66730},[307,308,309,310],[15,66732,66734],{"className":66733},[59,310],[15,66735,40237],{"className":66736,"style":981},[59,60,310],[15,66738,318],{"className":66739},[317],[15,66741,66743],{"className":66742},[290],[15,66744,66746],{"className":66745,"style":2739},[294],[15,66747],{},[15,66749],{"className":66750},[153,441],[52595,66752,66753],{},[15,66754,66756,66774],{"className":66755,"translate":19},[18],[15,66757,66759],{"className":66758},[23],[25,66760,66761],{"xmlns":27},[29,66762,66763,66771],{},[32,66764,66765,66767,66769],{},[35,66766,40237],{},[110,66768,7251],{},[115,66770,117],{},[39,66772,66773],{"encoding":41},"y\u003C1",[15,66775,66777,66795],{"className":66776,"ariaHidden":46},[45],[15,66778,66780,66783,66786,66789,66792],{"className":66779},[50],[15,66781],{"className":66782,"style":31692},[54],[15,66784,40237],{"className":66785,"style":981},[59,60],[15,66787],{"className":66788,"style":158},[157],[15,66790,7251],{"className":66791},[162],[15,66793],{"className":66794,"style":158},[157],[15,66796,66798,66801],{"className":66797},[50],[15,66799],{"className":66800,"style":172},[54],[15,66802,117],{"className":66803},[59],[52595,66805,66161],{},[11,66807,66808,66809,66867,66868,67114,67115,67276,67277,67542,67543,20956,67703,67819],{},"以 ",[15,66810,66812,66829],{"className":66811,"translate":19},[18],[15,66813,66815],{"className":66814},[23],[25,66816,66817],{"xmlns":27},[29,66818,66819,66827],{},[32,66820,66821],{},[6814,66822,66823,66825],{},[35,66824,37449],{},[115,66826,2463],{},[39,66828,40394],{"encoding":41},[15,66830,66832],{"className":66831,"ariaHidden":46},[45],[15,66833,66835,66838],{"className":66834},[50],[15,66836],{"className":66837,"style":40404},[54],[15,66839,66841,66844],{"className":66840},[59],[15,66842,37449],{"className":66843},[59,60],[15,66845,66847],{"className":66846},[281],[15,66848,66850],{"className":66849},[285],[15,66851,66853],{"className":66852},[290],[15,66854,66856],{"className":66855,"style":20028},[294],[15,66857,66858,66861],{"style":6865},[15,66859],{"className":66860,"style":303},[302],[15,66862,66864],{"className":66863},[307,308,309,310],[15,66865,2463],{"className":66866},[59,310]," 为例验证：",[15,66869,66871,66931],{"className":66870,"translate":19},[18],[15,66872,66874],{"className":66873},[23],[25,66875,66876],{"xmlns":27},[29,66877,66878,66928],{},[32,66879,66880,66886,66888,66890,66892,66894,66904,66906,66908,66910,66912,66914,66916,66918,66920,66926],{},[6814,66881,66882,66884],{},[35,66883,37],{},[110,66885,7573],{},[110,66887,113],{"stretchy":112},[35,66889,40237],{},[110,66891,120],{"stretchy":112},[110,66893,123],{},[195,66895,66896,66902],{},[32,66897,66898,66900],{},[35,66899,35432],{},[110,66901,4103],{},[35,66903,769],{},[110,66905,2898],{"stretchy":112},[35,66907,769],{},[35,66909,40237],{},[110,66911,4813],{},[110,66913,113],{"stretchy":112},[35,66915,769],{},[110,66917,4813],{},[115,66919,117],{},[6814,66921,66922,66924],{},[110,66923,120],{"stretchy":112},[115,66925,2463],{},[110,66927,2908],{"stretchy":112},[39,66929,66930],{"encoding":41},"f^*(y)=\\sup_t\\{ty-(t-1)^2\\}",[15,66932,66934,66987,67052,67073],{"className":66933,"ariaHidden":46},[45],[15,66935,66937,66940,66969,66972,66975,66978,66981,66984],{"className":66936},[50],[15,66938],{"className":66939,"style":139},[54],[15,66941,66943,66946],{"className":66942},[59],[15,66944,37],{"className":66945,"style":61},[59,60],[15,66947,66949],{"className":66948},[281],[15,66950,66952],{"className":66951},[285],[15,66953,66955],{"className":66954},[290],[15,66956,66958],{"className":66957,"style":8499},[294],[15,66959,66960,66963],{"style":6865},[15,66961],{"className":66962,"style":303},[302],[15,66964,66966],{"className":66965},[307,308,309,310],[15,66967,7573],{"className":66968},[2591,310],[15,66970,113],{"className":66971},[146],[15,66973,40237],{"className":66974,"style":981},[59,60],[15,66976,120],{"className":66977},[153],[15,66979],{"className":66980,"style":158},[157],[15,66982,123],{"className":66983},[162],[15,66985],{"className":66986,"style":158},[157],[15,66988,66990,66993,67034,67037,67040,67043,67046,67049],{"className":66989},[50],[15,66991],{"className":66992,"style":139},[54],[15,66994,66996,66999],{"className":66995},[1484],[15,66997,35432],{"className":66998},[1484],[15,67000,67002],{"className":67001},[281],[15,67003,67005,67026],{"className":67004},[285,286],[15,67006,67008,67023],{"className":67007},[290],[15,67009,67012],{"className":67010,"style":67011},[294],"height:0.1864em;",[15,67013,67014,67017],{"style":35578},[15,67015],{"className":67016,"style":303},[302],[15,67018,67020],{"className":67019},[307,308,309,310],[15,67021,769],{"className":67022},[59,60,310],[15,67024,318],{"className":67025},[317],[15,67027,67029],{"className":67028},[290],[15,67030,67032],{"className":67031,"style":37020},[294],[15,67033],{},[15,67035,2898],{"className":67036},[146],[15,67038,769],{"className":67039},[59,60],[15,67041,40237],{"className":67042,"style":981},[59,60],[15,67044],{"className":67045,"style":2587},[157],[15,67047,4813],{"className":67048},[2591],[15,67050],{"className":67051,"style":2587},[157],[15,67053,67055,67058,67061,67064,67067,67070],{"className":67054},[50],[15,67056],{"className":67057,"style":139},[54],[15,67059,113],{"className":67060},[146],[15,67062,769],{"className":67063},[59,60],[15,67065],{"className":67066,"style":2587},[157],[15,67068,4813],{"className":67069},[2591],[15,67071],{"className":67072,"style":2587},[157],[15,67074,67076,67079,67082,67111],{"className":67075},[50],[15,67077],{"className":67078,"style":20003},[54],[15,67080,117],{"className":67081},[59],[15,67083,67085,67088],{"className":67084},[153],[15,67086,120],{"className":67087},[153],[15,67089,67091],{"className":67090},[281],[15,67092,67094],{"className":67093},[285],[15,67095,67097],{"className":67096},[290],[15,67098,67100],{"className":67099,"style":20028},[294],[15,67101,67102,67105],{"style":6865},[15,67103],{"className":67104,"style":303},[302],[15,67106,67108],{"className":67107},[307,308,309,310],[15,67109,2463],{"className":67110},[59,310],[15,67112,2908],{"className":67113},[153],"，驻点 ",[15,67116,67118,67162],{"className":67117,"translate":19},[18],[15,67119,67121],{"className":67120},[23],[25,67122,67123],{"xmlns":27},[29,67124,67125,67159],{},[32,67126,67127,67129,67131,67133,67135,67137,67139,67141,67143,67145,67147,67149,67151,67153,67155,67157],{},[35,67128,40237],{},[110,67130,123],{},[115,67132,2463],{},[110,67134,113],{"stretchy":112},[35,67136,769],{},[110,67138,4813],{},[115,67140,117],{},[110,67142,120],{"stretchy":112},[110,67144,10990],{},[35,67146,769],{},[110,67148,123],{},[115,67150,117],{},[110,67152,2470],{},[35,67154,40237],{},[35,67156,941],{"mathvariant":209},[115,67158,2463],{},[39,67160,67161],{"encoding":41},"y=2(t-1)\\Rightarrow t=1+y\u002F2",[15,67163,67165,67183,67207,67228,67246,67264],{"className":67164,"ariaHidden":46},[45],[15,67166,67168,67171,67174,67177,67180],{"className":67167},[50],[15,67169],{"className":67170,"style":2276},[54],[15,67172,40237],{"className":67173,"style":981},[59,60],[15,67175],{"className":67176,"style":158},[157],[15,67178,123],{"className":67179},[162],[15,67181],{"className":67182,"style":158},[157],[15,67184,67186,67189,67192,67195,67198,67201,67204],{"className":67185},[50],[15,67187],{"className":67188,"style":139},[54],[15,67190,2463],{"className":67191},[59],[15,67193,113],{"className":67194},[146],[15,67196,769],{"className":67197},[59,60],[15,67199],{"className":67200,"style":2587},[157],[15,67202,4813],{"className":67203},[2591],[15,67205],{"className":67206,"style":2587},[157],[15,67208,67210,67213,67216,67219,67222,67225],{"className":67209},[50],[15,67211],{"className":67212,"style":139},[54],[15,67214,117],{"className":67215},[59],[15,67217,120],{"className":67218},[153],[15,67220],{"className":67221,"style":158},[157],[15,67223,10990],{"className":67224},[162],[15,67226],{"className":67227,"style":158},[157],[15,67229,67231,67234,67237,67240,67243],{"className":67230},[50],[15,67232],{"className":67233,"style":5343},[54],[15,67235,769],{"className":67236},[59,60],[15,67238],{"className":67239,"style":158},[157],[15,67241,123],{"className":67242},[162],[15,67244],{"className":67245,"style":158},[157],[15,67247,67249,67252,67255,67258,67261],{"className":67248},[50],[15,67250],{"className":67251,"style":12578},[54],[15,67253,117],{"className":67254},[59],[15,67256],{"className":67257,"style":2587},[157],[15,67259,2470],{"className":67260},[2591],[15,67262],{"className":67263,"style":2587},[157],[15,67265,67267,67270,67273],{"className":67266},[50],[15,67268],{"className":67269,"style":139},[54],[15,67271,40237],{"className":67272,"style":981},[59,60],[15,67274,45150],{"className":67275},[59],"，得 ",[15,67278,67280,67344],{"className":67279,"translate":19},[18],[15,67281,67283],{"className":67282},[23],[25,67284,67285],{"xmlns":27},[29,67286,67287,67341],{},[32,67288,67289,67295,67297,67299,67301,67303,67305,67307,67309,67311,67313,67315,67321,67323,67325,67327,67329,67331,67337,67339],{},[6814,67290,67291,67293],{},[35,67292,37],{},[110,67294,7573],{},[110,67296,123],{},[35,67298,40237],{},[110,67300,113],{"stretchy":112},[115,67302,117],{},[110,67304,2470],{},[35,67306,40237],{},[35,67308,941],{"mathvariant":209},[115,67310,2463],{},[110,67312,120],{"stretchy":112},[110,67314,4813],{},[6814,67316,67317,67319],{},[35,67318,40237],{},[115,67320,2463],{},[35,67322,941],{"mathvariant":209},[115,67324,38989],{},[110,67326,123],{},[35,67328,40237],{},[110,67330,2470],{},[6814,67332,67333,67335],{},[35,67334,40237],{},[115,67336,2463],{},[35,67338,941],{"mathvariant":209},[115,67340,38989],{},[39,67342,67343],{"encoding":41},"f^*=y(1+y\u002F2)-y^2\u002F4=y+y^2\u002F4",[15,67345,67347,67391,67415,67439,67486,67504],{"className":67346,"ariaHidden":46},[45],[15,67348,67350,67353,67382,67385,67388],{"className":67349},[50],[15,67351],{"className":67352,"style":55},[54],[15,67354,67356,67359],{"className":67355},[59],[15,67357,37],{"className":67358,"style":61},[59,60],[15,67360,67362],{"className":67361},[281],[15,67363,67365],{"className":67364},[285],[15,67366,67368],{"className":67367},[290],[15,67369,67371],{"className":67370,"style":8499},[294],[15,67372,67373,67376],{"style":6865},[15,67374],{"className":67375,"style":303},[302],[15,67377,67379],{"className":67378},[307,308,309,310],[15,67380,7573],{"className":67381},[2591,310],[15,67383],{"className":67384,"style":158},[157],[15,67386,123],{"className":67387},[162],[15,67389],{"className":67390,"style":158},[157],[15,67392,67394,67397,67400,67403,67406,67409,67412],{"className":67393},[50],[15,67395],{"className":67396,"style":139},[54],[15,67398,40237],{"className":67399,"style":981},[59,60],[15,67401,113],{"className":67402},[146],[15,67404,117],{"className":67405},[59],[15,67407],{"className":67408,"style":2587},[157],[15,67410,2470],{"className":67411},[2591],[15,67413],{"className":67414,"style":2587},[157],[15,67416,67418,67421,67424,67427,67430,67433,67436],{"className":67417},[50],[15,67419],{"className":67420,"style":139},[54],[15,67422,40237],{"className":67423,"style":981},[59,60],[15,67425,45150],{"className":67426},[59],[15,67428,120],{"className":67429},[153],[15,67431],{"className":67432,"style":2587},[157],[15,67434,4813],{"className":67435},[2591],[15,67437],{"className":67438,"style":2587},[157],[15,67440,67442,67445,67474,67477,67480,67483],{"className":67441},[50],[15,67443],{"className":67444,"style":20003},[54],[15,67446,67448,67451],{"className":67447},[59],[15,67449,40237],{"className":67450,"style":981},[59,60],[15,67452,67454],{"className":67453},[281],[15,67455,67457],{"className":67456},[285],[15,67458,67460],{"className":67459},[290],[15,67461,67463],{"className":67462,"style":20028},[294],[15,67464,67465,67468],{"style":6865},[15,67466],{"className":67467,"style":303},[302],[15,67469,67471],{"className":67470},[307,308,309,310],[15,67472,2463],{"className":67473},[59,310],[15,67475,40372],{"className":67476},[59],[15,67478],{"className":67479,"style":158},[157],[15,67481,123],{"className":67482},[162],[15,67484],{"className":67485,"style":158},[157],[15,67487,67489,67492,67495,67498,67501],{"className":67488},[50],[15,67490],{"className":67491,"style":40321},[54],[15,67493,40237],{"className":67494,"style":981},[59,60],[15,67496],{"className":67497,"style":2587},[157],[15,67499,2470],{"className":67500},[2591],[15,67502],{"className":67503,"style":2587},[157],[15,67505,67507,67510,67539],{"className":67506},[50],[15,67508],{"className":67509,"style":20003},[54],[15,67511,67513,67516],{"className":67512},[59],[15,67514,40237],{"className":67515,"style":981},[59,60],[15,67517,67519],{"className":67518},[281],[15,67520,67522],{"className":67521},[285],[15,67523,67525],{"className":67524},[290],[15,67526,67528],{"className":67527,"style":20028},[294],[15,67529,67530,67533],{"style":6865},[15,67531],{"className":67532,"style":303},[302],[15,67534,67536],{"className":67535},[307,308,309,310],[15,67537,2463],{"className":67538},[59,310],[15,67540,40372],{"className":67541},[59],"。以 Hellinger² 为例：",[15,67544,67546,67582],{"className":67545,"translate":19},[18],[15,67547,67549],{"className":67548},[23],[25,67550,67551],{"xmlns":27},[29,67552,67553,67579],{},[32,67554,67555,67557,67559,67561,67563,67565,67567,67569,67571,67575,67577],{},[35,67556,37],{},[110,67558,113],{"stretchy":112},[35,67560,769],{},[110,67562,120],{"stretchy":112},[110,67564,123],{},[35,67566,769],{},[110,67568,4813],{},[115,67570,2463],{},[34339,67572,67573],{},[35,67574,769],{},[110,67576,2470],{},[115,67578,117],{},[39,67580,67581],{"encoding":41},"f(t)=t-2\\sqrt t+1",[15,67583,67585,67612,67631,67694],{"className":67584,"ariaHidden":46},[45],[15,67586,67588,67591,67594,67597,67600,67603,67606,67609],{"className":67587},[50],[15,67589],{"className":67590,"style":139},[54],[15,67592,37],{"className":67593,"style":61},[59,60],[15,67595,113],{"className":67596},[146],[15,67598,769],{"className":67599},[59,60],[15,67601,120],{"className":67602},[153],[15,67604],{"className":67605,"style":158},[157],[15,67607,123],{"className":67608},[162],[15,67610],{"className":67611,"style":158},[157],[15,67613,67615,67619,67622,67625,67628],{"className":67614},[50],[15,67616],{"className":67617,"style":67618},[54],"height:0.6984em;vertical-align:-0.0833em;",[15,67620,769],{"className":67621},[59,60],[15,67623],{"className":67624,"style":2587},[157],[15,67626,4813],{"className":67627},[2591],[15,67629],{"className":67630,"style":2587},[157],[15,67632,67634,67638,67641,67685,67688,67691],{"className":67633},[50],[15,67635],{"className":67636,"style":67637},[54],"height:1.04em;vertical-align:-0.1475em;",[15,67639,2463],{"className":67640},[59],[15,67642,67644],{"className":67643},[59,34367],[15,67645,67647,67677],{"className":67646},[285,286],[15,67648,67650,67674],{"className":67649},[290],[15,67651,67653,67662],{"className":67652,"style":42683},[294],[15,67654,67656,67659],{"className":67655,"style":11863},[6307],[15,67657],{"className":67658,"style":461},[302],[15,67660,769],{"className":67661,"style":34387},[59,60],[15,67663,67664,67667],{"style":42695},[15,67665],{"className":67666,"style":461},[302],[15,67668,67670],{"className":67669,"style":34444},[34443],[6323,67671,67672],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,67673],{"d":34451},[15,67675,318],{"className":67676},[317],[15,67678,67680],{"className":67679},[290],[15,67681,67683],{"className":67682,"style":42715},[294],[15,67684],{},[15,67686],{"className":67687,"style":2587},[157],[15,67689,2470],{"className":67690},[2591],[15,67692],{"className":67693,"style":2587},[157],[15,67695,67697,67700],{"className":67696},[50],[15,67698],{"className":67699,"style":172},[54],[15,67701,117],{"className":67702},[59],[15,67704,67706,67730],{"className":67705,"translate":19},[18],[15,67707,67709],{"className":67708},[23],[25,67710,67711],{"xmlns":27},[29,67712,67713,67727],{},[32,67714,67715,67717,67719,67723,67725],{},[35,67716,15400],{},[110,67718,123],{},[34339,67720,67721],{},[35,67722,769],{},[110,67724,6928],{},[115,67726,126],{},[39,67728,67729],{"encoding":41},"u=\\sqrt t\\ge0",[15,67731,67733,67751,67810],{"className":67732,"ariaHidden":46},[45],[15,67734,67736,67739,67742,67745,67748],{"className":67735},[50],[15,67737],{"className":67738,"style":2345},[54],[15,67740,15400],{"className":67741},[59,60],[15,67743],{"className":67744,"style":158},[157],[15,67746,123],{"className":67747},[162],[15,67749],{"className":67750,"style":158},[157],[15,67752,67754,67757,67801,67804,67807],{"className":67753},[50],[15,67755],{"className":67756,"style":67637},[54],[15,67758,67760],{"className":67759},[59,34367],[15,67761,67763,67793],{"className":67762},[285,286],[15,67764,67766,67790],{"className":67765},[290],[15,67767,67769,67778],{"className":67768,"style":42683},[294],[15,67770,67772,67775],{"className":67771,"style":11863},[6307],[15,67773],{"className":67774,"style":461},[302],[15,67776,769],{"className":67777,"style":34387},[59,60],[15,67779,67780,67783],{"style":42695},[15,67781],{"className":67782,"style":461},[302],[15,67784,67786],{"className":67785,"style":34444},[34443],[6323,67787,67788],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,67789],{"d":34451},[15,67791,318],{"className":67792},[317],[15,67794,67796],{"className":67795},[290],[15,67797,67799],{"className":67798,"style":42715},[294],[15,67800],{},[15,67802],{"className":67803,"style":158},[157],[15,67805,6928],{"className":67806},[162],[15,67808],{"className":67809,"style":158},[157],[15,67811,67813,67816],{"className":67812},[50],[15,67814],{"className":67815,"style":172},[54],[15,67817,126],{"className":67818},[59],"，把共轭写成有限上确界",[15,67821,67823],{"className":67822,"translate":19},[180],[15,67824,67826,67900],{"className":67825,"translate":19},[18],[15,67827,67829],{"className":67828},[23],[25,67830,67831],{"xmlns":27,"display":189},[29,67832,67833,67897],{},[32,67834,67835,67841,67843,67845,67847,67849,67865,67867,67869,67871,67873,67875,67877,67883,67885,67887,67889,67891,67893,67895],{},[6814,67836,67837,67839],{},[35,67838,37],{},[110,67840,7573],{},[110,67842,113],{"stretchy":112},[35,67844,40237],{},[110,67846,120],{"stretchy":112},[110,67848,123],{},[6016,67850,67851,67857],{},[32,67852,67853,67855],{},[35,67854,35432],{},[110,67856,4103],{},[32,67858,67859,67861,67863],{},[35,67860,15400],{},[110,67862,6928],{},[115,67864,126],{},[110,67866,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,67868,113],{"stretchy":112},[35,67870,40237],{},[110,67872,4813],{},[115,67874,117],{},[110,67876,120],{"stretchy":112},[6814,67878,67879,67881],{},[35,67880,15400],{},[115,67882,2463],{},[110,67884,2470],{},[115,67886,2463],{},[35,67888,15400],{},[110,67890,4813],{},[115,67892,117],{},[110,67894,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,67896,551],{"separator":46},[39,67898,67899],{"encoding":41},"f^*(y)=\\sup_{u\\ge0}\\Big\\{(y-1)u^2+2u-1\\Big\\},",[15,67901,67903,67956,68040,68090,68111],{"className":67902,"ariaHidden":46},[45],[15,67904,67906,67909,67938,67941,67944,67947,67950,67953],{"className":67905},[50],[15,67907],{"className":67908,"style":139},[54],[15,67910,67912,67915],{"className":67911},[59],[15,67913,37],{"className":67914,"style":61},[59,60],[15,67916,67918],{"className":67917},[281],[15,67919,67921],{"className":67920},[285],[15,67922,67924],{"className":67923},[290],[15,67925,67927],{"className":67926,"style":8248},[294],[15,67928,67929,67932],{"style":8277},[15,67930],{"className":67931,"style":303},[302],[15,67933,67935],{"className":67934},[307,308,309,310],[15,67936,7573],{"className":67937},[2591,310],[15,67939,113],{"className":67940},[146],[15,67942,40237],{"className":67943,"style":981},[59,60],[15,67945,120],{"className":67946},[153],[15,67948],{"className":67949,"style":158},[157],[15,67951,123],{"className":67952},[162],[15,67954],{"className":67955,"style":158},[157],[15,67957,67959,67963,68016,68019,68025,68028,68031,68034,68037],{"className":67958},[50],[15,67960],{"className":67961,"style":67962},[54],"height:2.1567em;vertical-align:-1.0067em;",[15,67964,67966],{"className":67965},[1484,13716],[15,67967,67969,68008],{"className":67968},[285,286],[15,67970,67972,68005],{"className":67971},[290],[15,67973,67975,67995],{"className":67974,"style":2345},[294],[15,67976,67977,67980],{"style":60922},[15,67978],{"className":67979,"style":461},[302],[15,67981,67983],{"className":67982},[307,308,309,310],[15,67984,67986,67989,67992],{"className":67985},[59,310],[15,67987,15400],{"className":67988},[59,60,310],[15,67990,6928],{"className":67991},[162,310],[15,67993,126],{"className":67994},[59,310],[15,67996,67997,68000],{"style":11863},[15,67998],{"className":67999,"style":461},[302],[15,68001,68002],{},[15,68003,35432],{"className":68004},[1484],[15,68006,318],{"className":68007},[317],[15,68009,68011],{"className":68010},[290],[15,68012,68014],{"className":68013,"style":60960},[294],[15,68015],{},[15,68017],{"className":68018,"style":406},[157],[15,68020,68022],{"className":68021},[59],[15,68023,2898],{"className":68024},[419,3720],[15,68026,113],{"className":68027},[146],[15,68029,40237],{"className":68030,"style":981},[59,60],[15,68032],{"className":68033,"style":2587},[157],[15,68035,4813],{"className":68036},[2591],[15,68038],{"className":68039,"style":2587},[157],[15,68041,68043,68046,68049,68052,68081,68084,68087],{"className":68042},[50],[15,68044],{"className":68045,"style":37251},[54],[15,68047,117],{"className":68048},[59],[15,68050,120],{"className":68051},[153],[15,68053,68055,68058],{"className":68054},[59],[15,68056,15400],{"className":68057},[59,60],[15,68059,68061],{"className":68060},[281],[15,68062,68064],{"className":68063},[285],[15,68065,68067],{"className":68066},[290],[15,68068,68070],{"className":68069,"style":19735},[294],[15,68071,68072,68075],{"style":8277},[15,68073],{"className":68074,"style":303},[302],[15,68076,68078],{"className":68077},[307,308,309,310],[15,68079,2463],{"className":68080},[59,310],[15,68082],{"className":68083,"style":2587},[157],[15,68085,2470],{"className":68086},[2591],[15,68088],{"className":68089,"style":2587},[157],[15,68091,68093,68096,68099,68102,68105,68108],{"className":68092},[50],[15,68094],{"className":68095,"style":12578},[54],[15,68097,2463],{"className":68098},[59],[15,68100,15400],{"className":68101},[59,60],[15,68103],{"className":68104,"style":2587},[157],[15,68106,4813],{"className":68107},[2591],[15,68109],{"className":68110,"style":2587},[157],[15,68112,68114,68118,68121,68127],{"className":68113},[50],[15,68115],{"className":68116,"style":68117},[54],"height:1.8em;vertical-align:-0.65em;",[15,68119,117],{"className":68120},[59],[15,68122,68124],{"className":68123},[59],[15,68125,2908],{"className":68126},[419,3720],[15,68128,551],{"className":68129},[573],[11,68131,68132,68133,68184,68185,68218,68219,68269,68270,68404],{},"当 ",[15,68134,68136,68154],{"className":68135,"translate":19},[18],[15,68137,68139],{"className":68138},[23],[25,68140,68141],{"xmlns":27},[29,68142,68143,68151],{},[32,68144,68145,68147,68149],{},[35,68146,40237],{},[110,68148,6928],{},[115,68150,117],{},[39,68152,68153],{"encoding":41},"y\\ge1",[15,68155,68157,68175],{"className":68156,"ariaHidden":46},[45],[15,68158,68160,68163,68166,68169,68172],{"className":68159},[50],[15,68161],{"className":68162,"style":15417},[54],[15,68164,40237],{"className":68165,"style":981},[59,60],[15,68167],{"className":68168,"style":158},[157],[15,68170,6928],{"className":68171},[162],[15,68173],{"className":68174,"style":158},[157],[15,68176,68178,68181],{"className":68177},[50],[15,68179],{"className":68180,"style":172},[54],[15,68182,117],{"className":68183},[59]," 时上确界为 ",[15,68186,68188,68203],{"className":68187,"translate":19},[18],[15,68189,68191],{"className":68190},[23],[25,68192,68193],{"xmlns":27},[29,68194,68195,68201],{},[32,68196,68197,68199],{},[110,68198,2470],{},[35,68200,1024],{"mathvariant":209},[39,68202,4241],{"encoding":41},[15,68204,68206],{"className":68205,"ariaHidden":46},[45],[15,68207,68209,68212,68215],{"className":68208},[50],[15,68210],{"className":68211,"style":4251},[54],[15,68213,2470],{"className":68214},[59],[15,68216,1024],{"className":68217},[59],"；当 ",[15,68220,68222,68239],{"className":68221,"translate":19},[18],[15,68223,68225],{"className":68224},[23],[25,68226,68227],{"xmlns":27},[29,68228,68229,68237],{},[32,68230,68231,68233,68235],{},[35,68232,40237],{},[110,68234,7251],{},[115,68236,117],{},[39,68238,66773],{"encoding":41},[15,68240,68242,68260],{"className":68241,"ariaHidden":46},[45],[15,68243,68245,68248,68251,68254,68257],{"className":68244},[50],[15,68246],{"className":68247,"style":31692},[54],[15,68249,40237],{"className":68250,"style":981},[59,60],[15,68252],{"className":68253,"style":158},[157],[15,68255,7251],{"className":68256},[162],[15,68258],{"className":68259,"style":158},[157],[15,68261,68263,68266],{"className":68262},[50],[15,68264],{"className":68265,"style":172},[54],[15,68267,117],{"className":68268},[59]," 时上式是开口向下的二次函数，最大点 ",[15,68271,68273,68303],{"className":68272,"translate":19},[18],[15,68274,68276],{"className":68275},[23],[25,68277,68278],{"xmlns":27},[29,68279,68280,68300],{},[32,68281,68282,68284,68286],{},[35,68283,15400],{},[110,68285,123],{},[1255,68287,68288],{"scriptlevel":126,"displaystyle":46},[238,68289,68290,68292],{},[115,68291,117],{},[32,68293,68294,68296,68298],{},[115,68295,117],{},[110,68297,4813],{},[35,68299,40237],{},[39,68301,68302],{"encoding":41},"u=\\dfrac{1}{1-y}",[15,68304,68306,68324],{"className":68305,"ariaHidden":46},[45],[15,68307,68309,68312,68315,68318,68321],{"className":68308},[50],[15,68310],{"className":68311,"style":2345},[54],[15,68313,15400],{"className":68314},[59,60],[15,68316],{"className":68317,"style":158},[157],[15,68319,123],{"className":68320},[162],[15,68322],{"className":68323,"style":158},[157],[15,68325,68327,68330],{"className":68326},[50],[15,68328],{"className":68329,"style":31303},[54],[15,68331,68333,68336,68401],{"className":68332},[59],[15,68334],{"className":68335},[146,441],[15,68337,68339],{"className":68338},[238],[15,68340,68342,68393],{"className":68341},[285,286],[15,68343,68345,68390],{"className":68344},[290],[15,68346,68348,68371,68379],{"className":68347,"style":22889},[294],[15,68349,68350,68353],{"style":457},[15,68351],{"className":68352,"style":461},[302],[15,68354,68356,68359,68362,68365,68368],{"className":68355},[59],[15,68357,117],{"className":68358},[59],[15,68360],{"className":68361,"style":2587},[157],[15,68363,4813],{"className":68364},[2591],[15,68366],{"className":68367,"style":2587},[157],[15,68369,40237],{"className":68370,"style":981},[59,60],[15,68372,68373,68376],{"style":473},[15,68374],{"className":68375,"style":461},[302],[15,68377],{"className":68378,"style":481},[480],[15,68380,68381,68384],{"style":484},[15,68382],{"className":68383,"style":461},[302],[15,68385,68387],{"className":68386},[59],[15,68388,117],{"className":68389},[59],[15,68391,318],{"className":68392},[317],[15,68394,68396],{"className":68395},[290],[15,68397,68399],{"className":68398,"style":506},[294],[15,68400],{},[15,68402],{"className":68403},[153,441],"，代回得",[15,68406,68408],{"className":68407,"translate":19},[180],[15,68409,68411,68507],{"className":68410,"translate":19},[18],[15,68412,68414],{"className":68413},[23],[25,68415,68416],{"xmlns":27,"display":189},[29,68417,68418,68504],{},[32,68419,68420,68426,68428,68430,68432,68434,68460,68462,68464,68476,68478,68480,68482,68494,68496,68498,68500,68502],{},[6814,68421,68422,68424],{},[35,68423,37],{},[110,68425,7573],{},[110,68427,113],{"stretchy":112},[35,68429,40237],{},[110,68431,120],{"stretchy":112},[110,68433,123],{},[238,68435,68436,68444],{},[32,68437,68438,68440,68442],{},[35,68439,40237],{},[110,68441,4813],{},[115,68443,117],{},[32,68445,68446,68448,68450,68452,68454],{},[110,68447,113],{"stretchy":112},[115,68449,117],{},[110,68451,4813],{},[35,68453,40237],{},[6814,68455,68456,68458],{},[110,68457,120],{"stretchy":112},[115,68459,2463],{},[110,68461,2470],{},[115,68463,2463],{},[238,68465,68466,68468],{},[115,68467,117],{},[32,68469,68470,68472,68474],{},[115,68471,117],{},[110,68473,4813],{},[35,68475,40237],{},[110,68477,4813],{},[115,68479,117],{},[110,68481,123],{},[238,68483,68484,68486],{},[35,68485,40237],{},[32,68487,68488,68490,68492],{},[115,68489,117],{},[110,68491,4813],{},[35,68493,40237],{},[110,68495,551],{"separator":46},[157,68497],{"width":3262},[35,68499,40237],{},[110,68501,7251],{},[115,68503,49510],{},[39,68505,68506],{"encoding":41},"f^*(y)=\\frac{y-1}{(1-y)^2}+2\\frac{1}{1-y}-1\n=\\frac{y}{1-y},\\qquad y\u003C1 .",[15,68508,68510,68563,68697,68789,68807,68908],{"className":68509,"ariaHidden":46},[45],[15,68511,68513,68516,68545,68548,68551,68554,68557,68560],{"className":68512},[50],[15,68514],{"className":68515,"style":139},[54],[15,68517,68519,68522],{"className":68518},[59],[15,68520,37],{"className":68521,"style":61},[59,60],[15,68523,68525],{"className":68524},[281],[15,68526,68528],{"className":68527},[285],[15,68529,68531],{"className":68530},[290],[15,68532,68534],{"className":68533,"style":8248},[294],[15,68535,68536,68539],{"style":8277},[15,68537],{"className":68538,"style":303},[302],[15,68540,68542],{"className":68541},[307,308,309,310],[15,68543,7573],{"className":68544},[2591,310],[15,68546,113],{"className":68547},[146],[15,68549,40237],{"className":68550,"style":981},[59,60],[15,68552,120],{"className":68553},[153],[15,68555],{"className":68556,"style":158},[157],[15,68558,123],{"className":68559},[162],[15,68561],{"className":68562,"style":158},[157],[15,68564,68566,68570,68688,68691,68694],{"className":68565},[50],[15,68567],{"className":68568,"style":68569},[54],"height:2.2574em;vertical-align:-0.936em;",[15,68571,68573,68576,68685],{"className":68572},[59],[15,68574],{"className":68575},[146,441],[15,68577,68579],{"className":68578},[238],[15,68580,68582,68677],{"className":68581},[285,286],[15,68583,68585,68674],{"className":68584},[290],[15,68586,68588,68643,68651],{"className":68587,"style":22889},[294],[15,68589,68590,68593],{"style":457},[15,68591],{"className":68592,"style":461},[302],[15,68594,68596,68599,68602,68605,68608,68611,68614],{"className":68595},[59],[15,68597,113],{"className":68598},[146],[15,68600,117],{"className":68601},[59],[15,68603],{"className":68604,"style":2587},[157],[15,68606,4813],{"className":68607},[2591],[15,68609],{"className":68610,"style":2587},[157],[15,68612,40237],{"className":68613,"style":981},[59,60],[15,68615,68617,68620],{"className":68616},[153],[15,68618,120],{"className":68619},[153],[15,68621,68623],{"className":68622},[281],[15,68624,68626],{"className":68625},[285],[15,68627,68629],{"className":68628},[290],[15,68630,68632],{"className":68631,"style":45032},[294],[15,68633,68634,68637],{"style":45035},[15,68635],{"className":68636,"style":303},[302],[15,68638,68640],{"className":68639},[307,308,309,310],[15,68641,2463],{"className":68642},[59,310],[15,68644,68645,68648],{"style":473},[15,68646],{"className":68647,"style":461},[302],[15,68649],{"className":68650,"style":481},[480],[15,68652,68653,68656],{"style":484},[15,68654],{"className":68655,"style":461},[302],[15,68657,68659,68662,68665,68668,68671],{"className":68658},[59],[15,68660,40237],{"className":68661,"style":981},[59,60],[15,68663],{"className":68664,"style":2587},[157],[15,68666,4813],{"className":68667},[2591],[15,68669],{"className":68670,"style":2587},[157],[15,68672,117],{"className":68673},[59],[15,68675,318],{"className":68676},[317],[15,68678,68680],{"className":68679},[290],[15,68681,68683],{"className":68682,"style":1601},[294],[15,68684],{},[15,68686],{"className":68687},[153,441],[15,68689],{"className":68690,"style":2587},[157],[15,68692,2470],{"className":68693},[2591],[15,68695],{"className":68696,"style":2587},[157],[15,68698,68700,68703,68706,68780,68783,68786],{"className":68699},[50],[15,68701],{"className":68702,"style":31303},[54],[15,68704,2463],{"className":68705},[59],[15,68707,68709,68712,68777],{"className":68708},[59],[15,68710],{"className":68711},[146,441],[15,68713,68715],{"className":68714},[238],[15,68716,68718,68769],{"className":68717},[285,286],[15,68719,68721,68766],{"className":68720},[290],[15,68722,68724,68747,68755],{"className":68723,"style":22889},[294],[15,68725,68726,68729],{"style":457},[15,68727],{"className":68728,"style":461},[302],[15,68730,68732,68735,68738,68741,68744],{"className":68731},[59],[15,68733,117],{"className":68734},[59],[15,68736],{"className":68737,"style":2587},[157],[15,68739,4813],{"className":68740},[2591],[15,68742],{"className":68743,"style":2587},[157],[15,68745,40237],{"className":68746,"style":981},[59,60],[15,68748,68749,68752],{"style":473},[15,68750],{"className":68751,"style":461},[302],[15,68753],{"className":68754,"style":481},[480],[15,68756,68757,68760],{"style":484},[15,68758],{"className":68759,"style":461},[302],[15,68761,68763],{"className":68762},[59],[15,68764,117],{"className":68765},[59],[15,68767,318],{"className":68768},[317],[15,68770,68772],{"className":68771},[290],[15,68773,68775],{"className":68774,"style":506},[294],[15,68776],{},[15,68778],{"className":68779},[153,441],[15,68781],{"className":68782,"style":2587},[157],[15,68784,4813],{"className":68785},[2591],[15,68787],{"className":68788,"style":2587},[157],[15,68790,68792,68795,68798,68801,68804],{"className":68791},[50],[15,68793],{"className":68794,"style":172},[54],[15,68796,117],{"className":68797},[59],[15,68799],{"className":68800,"style":158},[157],[15,68802,123],{"className":68803},[162],[15,68805],{"className":68806,"style":158},[157],[15,68808,68810,68813,68887,68890,68893,68896,68899,68902,68905],{"className":68809},[50],[15,68811],{"className":68812,"style":22010},[54],[15,68814,68816,68819,68884],{"className":68815},[59],[15,68817],{"className":68818},[146,441],[15,68820,68822],{"className":68821},[238],[15,68823,68825,68876],{"className":68824},[285,286],[15,68826,68828,68873],{"className":68827},[290],[15,68829,68831,68854,68862],{"className":68830,"style":3554},[294],[15,68832,68833,68836],{"style":457},[15,68834],{"className":68835,"style":461},[302],[15,68837,68839,68842,68845,68848,68851],{"className":68838},[59],[15,68840,117],{"className":68841},[59],[15,68843],{"className":68844,"style":2587},[157],[15,68846,4813],{"className":68847},[2591],[15,68849],{"className":68850,"style":2587},[157],[15,68852,40237],{"className":68853,"style":981},[59,60],[15,68855,68856,68859],{"style":473},[15,68857],{"className":68858,"style":461},[302],[15,68860],{"className":68861,"style":481},[480],[15,68863,68864,68867],{"style":484},[15,68865],{"className":68866,"style":461},[302],[15,68868,68870],{"className":68869},[59],[15,68871,40237],{"className":68872,"style":981},[59,60],[15,68874,318],{"className":68875},[317],[15,68877,68879],{"className":68878},[290],[15,68880,68882],{"className":68881,"style":506},[294],[15,68883],{},[15,68885],{"className":68886},[153,441],[15,68888,551],{"className":68889},[573],[15,68891],{"className":68892,"style":3634},[157],[15,68894],{"className":68895,"style":406},[157],[15,68897,40237],{"className":68898,"style":981},[59,60],[15,68900],{"className":68901,"style":158},[157],[15,68903,7251],{"className":68904},[162],[15,68906],{"className":68907,"style":158},[157],[15,68909,68911,68914],{"className":68910},[50],[15,68912],{"className":68913,"style":172},[54],[15,68915,49510],{"className":68916},[59],[11,68918,68919,68920,2745,69296,69608,69609,18708,69742,69921,69922,70137,70138,18708,70230,70370,70371,70604],{},"顺带把 JS 的共轭也完整算出（它是表中最容易出错的一个）：",[15,68921,68923,68999],{"className":68922,"translate":19},[18],[15,68924,68926],{"className":68925},[23],[25,68927,68928],{"xmlns":27},[29,68929,68930,68996],{},[32,68931,68932,68942,68944,68946,68948,68950,68956,68958,68960,68962,68964,68966,68968,68970,68972,68974,68976,68978,68980,68982,68994],{},[195,68933,68934,68936],{},[35,68935,37],{},[32,68937,68938,68940],{},[35,68939,23743],{},[35,68941,25737],{},[110,68943,113],{"stretchy":112},[35,68945,769],{},[110,68947,120],{"stretchy":112},[110,68949,123],{},[238,68951,68952,68954],{},[115,68953,117],{},[115,68955,2463],{},[110,68957,230],{"stretchy":112},[35,68959,769],{},[35,68961,4100],{},[110,68963,4103],{},[35,68965,769],{},[110,68967,4813],{},[110,68969,113],{"stretchy":112},[35,68971,769],{},[110,68973,2470],{},[115,68975,117],{},[110,68977,120],{"stretchy":112},[35,68979,4100],{},[110,68981,4103],{},[238,68983,68984,68992],{},[32,68985,68986,68988,68990],{},[35,68987,769],{},[110,68989,2470],{},[115,68991,117],{},[115,68993,2463],{},[110,68995,257],{"stretchy":112},[39,68997,68998],{"encoding":41},"f_{JS}(t)=\\frac12[t\\log t-(t+1)\\log\\frac{t+1}{2}]",[15,69000,69002,69072,69175,69196],{"className":69001,"ariaHidden":46},[45],[15,69003,69005,69008,69054,69057,69060,69063,69066,69069],{"className":69004},[50],[15,69006],{"className":69007,"style":139},[54],[15,69009,69011,69014],{"className":69010},[59],[15,69012,37],{"className":69013,"style":61},[59,60],[15,69015,69017],{"className":69016},[281],[15,69018,69020,69046],{"className":69019},[285,286],[15,69021,69023,69043],{"className":69022},[290],[15,69024,69026],{"className":69025,"style":379},[294],[15,69027,69028,69031],{"style":27509},[15,69029],{"className":69030,"style":303},[302],[15,69032,69034],{"className":69033},[307,308,309,310],[15,69035,69037,69040],{"className":69036},[59,310],[15,69038,23743],{"className":69039,"style":24153},[59,60,310],[15,69041,25737],{"className":69042,"style":25861},[59,60,310],[15,69044,318],{"className":69045},[317],[15,69047,69049],{"className":69048},[290],[15,69050,69052],{"className":69051,"style":7968},[294],[15,69053],{},[15,69055,113],{"className":69056},[146],[15,69058,769],{"className":69059},[59,60],[15,69061,120],{"className":69062},[153],[15,69064],{"className":69065,"style":158},[157],[15,69067,123],{"className":69068},[162],[15,69070],{"className":69071,"style":158},[157],[15,69073,69075,69078,69146,69149,69152,69155,69160,69163,69166,69169,69172],{"className":69074},[50],[15,69076],{"className":69077,"style":2505},[54],[15,69079,69081,69084,69143],{"className":69080},[59],[15,69082],{"className":69083},[146,441],[15,69085,69087],{"className":69086},[238],[15,69088,69090,69135],{"className":69089},[285,286],[15,69091,69093,69132],{"className":69092},[290],[15,69094,69096,69110,69118],{"className":69095,"style":2524},[294],[15,69097,69098,69101],{"style":2527},[15,69099],{"className":69100,"style":461},[302],[15,69102,69104],{"className":69103},[307,308,309,310],[15,69105,69107],{"className":69106},[59,310],[15,69108,2463],{"className":69109},[59,310],[15,69111,69112,69115],{"style":473},[15,69113],{"className":69114,"style":461},[302],[15,69116],{"className":69117,"style":481},[480],[15,69119,69120,69123],{"style":2550},[15,69121],{"className":69122,"style":461},[302],[15,69124,69126],{"className":69125},[307,308,309,310],[15,69127,69129],{"className":69128},[59,310],[15,69130,117],{"className":69131},[59,310],[15,69133,318],{"className":69134},[317],[15,69136,69138],{"className":69137},[290],[15,69139,69141],{"className":69140,"style":2572},[294],[15,69142],{},[15,69144],{"className":69145},[153,441],[15,69147,230],{"className":69148},[146],[15,69150,769],{"className":69151},[59,60],[15,69153],{"className":69154,"style":406},[157],[15,69156,4154,69158],{"className":69157},[1484],[15,69159,4158],{"style":4157},[15,69161],{"className":69162,"style":406},[157],[15,69164,769],{"className":69165},[59,60],[15,69167],{"className":69168,"style":2587},[157],[15,69170,4813],{"className":69171},[2591],[15,69173],{"className":69174,"style":2587},[157],[15,69176,69178,69181,69184,69187,69190,69193],{"className":69177},[50],[15,69179],{"className":69180,"style":139},[54],[15,69182,113],{"className":69183},[146],[15,69185,769],{"className":69186},[59,60],[15,69188],{"className":69189,"style":2587},[157],[15,69191,2470],{"className":69192},[2591],[15,69194],{"className":69195,"style":2587},[157],[15,69197,69199,69202,69205,69208,69211,69216,69219,69293],{"className":69198},[50],[15,69200],{"className":69201,"style":2505},[54],[15,69203,117],{"className":69204},[59],[15,69206,120],{"className":69207},[153],[15,69209],{"className":69210,"style":406},[157],[15,69212,4154,69214],{"className":69213},[1484],[15,69215,4158],{"style":4157},[15,69217],{"className":69218,"style":406},[157],[15,69220,69222,69225,69290],{"className":69221},[59],[15,69223],{"className":69224},[146,441],[15,69226,69228],{"className":69227},[238],[15,69229,69231,69282],{"className":69230},[285,286],[15,69232,69234,69279],{"className":69233},[290],[15,69235,69237,69251,69259],{"className":69236,"style":2524},[294],[15,69238,69239,69242],{"style":2527},[15,69240],{"className":69241,"style":461},[302],[15,69243,69245],{"className":69244},[307,308,309,310],[15,69246,69248],{"className":69247},[59,310],[15,69249,2463],{"className":69250},[59,310],[15,69252,69253,69256],{"style":473},[15,69254],{"className":69255,"style":461},[302],[15,69257],{"className":69258,"style":481},[480],[15,69260,69261,69264],{"style":2550},[15,69262],{"className":69263,"style":461},[302],[15,69265,69267],{"className":69266},[307,308,309,310],[15,69268,69270,69273,69276],{"className":69269},[59,310],[15,69271,769],{"className":69272},[59,60,310],[15,69274,2470],{"className":69275},[2591,310],[15,69277,117],{"className":69278},[59,310],[15,69280,318],{"className":69281},[317],[15,69283,69285],{"className":69284},[290],[15,69286,69288],{"className":69287,"style":2572},[294],[15,69289],{},[15,69291],{"className":69292},[153,441],[15,69294,257],{"className":69295},[153],[15,69297,69299,69357],{"className":69298,"translate":19},[18],[15,69300,69302],{"className":69301},[23],[25,69303,69304],{"xmlns":27},[29,69305,69306,69354],{},[32,69307,69308,69320,69322,69324,69326,69328,69334,69336,69338],{},[7553,69309,69310,69312,69318],{},[35,69311,37],{},[32,69313,69314,69316],{},[35,69315,23743],{},[35,69317,25737],{},[110,69319,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,69321,113],{"stretchy":112},[35,69323,769],{},[110,69325,120],{"stretchy":112},[110,69327,123],{},[238,69329,69330,69332],{},[115,69331,117],{},[115,69333,2463],{},[35,69335,4100],{},[110,69337,4103],{},[238,69339,69340,69346],{},[32,69341,69342,69344],{},[115,69343,2463],{},[35,69345,769],{},[32,69347,69348,69350,69352],{},[35,69349,769],{},[110,69351,2470],{},[115,69353,117],{},[39,69355,69356],{"encoding":41},"f_{JS}'(t)=\\frac12\\log\\frac{2t}{t+1}",[15,69358,69360,69446],{"className":69359,"ariaHidden":46},[45],[15,69361,69363,69367,69428,69431,69434,69437,69440,69443],{"className":69362},[50],[15,69364],{"className":69365,"style":69366},[54],"height:1.0272em;vertical-align:-0.2753em;",[15,69368,69370,69373],{"className":69369},[59],[15,69371,37],{"className":69372,"style":61},[59,60],[15,69374,69376],{"className":69375},[281],[15,69377,69379,69420],{"className":69378},[285,286],[15,69380,69382,69417],{"className":69381},[290],[15,69383,69385,69403],{"className":69384,"style":6862},[294],[15,69386,69388,69391],{"style":69387},"top:-2.4247em;margin-left:-0.1076em;margin-right:0.05em;",[15,69389],{"className":69390,"style":303},[302],[15,69392,69394],{"className":69393},[307,308,309,310],[15,69395,69397,69400],{"className":69396},[59,310],[15,69398,23743],{"className":69399,"style":24153},[59,60,310],[15,69401,25737],{"className":69402,"style":25861},[59,60,310],[15,69404,69405,69408],{"style":6865},[15,69406],{"className":69407,"style":303},[302],[15,69409,69411],{"className":69410},[307,308,309,310],[15,69412,69414],{"className":69413},[59,310],[15,69415,6820],{"className":69416},[59,310],[15,69418,318],{"className":69419},[317],[15,69421,69423],{"className":69422},[290],[15,69424,69426],{"className":69425,"style":38390},[294],[15,69427],{},[15,69429,113],{"className":69430},[146],[15,69432,769],{"className":69433},[59,60],[15,69435,120],{"className":69436},[153],[15,69438],{"className":69439,"style":158},[157],[15,69441,123],{"className":69442},[162],[15,69444],{"className":69445,"style":158},[157],[15,69447,69449,69452,69520,69523,69528,69531],{"className":69448},[50],[15,69450],{"className":69451,"style":45405},[54],[15,69453,69455,69458,69517],{"className":69454},[59],[15,69456],{"className":69457},[146,441],[15,69459,69461],{"className":69460},[238],[15,69462,69464,69509],{"className":69463},[285,286],[15,69465,69467,69506],{"className":69466},[290],[15,69468,69470,69484,69492],{"className":69469,"style":2524},[294],[15,69471,69472,69475],{"style":2527},[15,69473],{"className":69474,"style":461},[302],[15,69476,69478],{"className":69477},[307,308,309,310],[15,69479,69481],{"className":69480},[59,310],[15,69482,2463],{"className":69483},[59,310],[15,69485,69486,69489],{"style":473},[15,69487],{"className":69488,"style":461},[302],[15,69490],{"className":69491,"style":481},[480],[15,69493,69494,69497],{"style":2550},[15,69495],{"className":69496,"style":461},[302],[15,69498,69500],{"className":69499},[307,308,309,310],[15,69501,69503],{"className":69502},[59,310],[15,69504,117],{"className":69505},[59,310],[15,69507,318],{"className":69508},[317],[15,69510,69512],{"className":69511},[290],[15,69513,69515],{"className":69514,"style":2572},[294],[15,69516],{},[15,69518],{"className":69519},[153,441],[15,69521],{"className":69522,"style":406},[157],[15,69524,4154,69526],{"className":69525},[1484],[15,69527,4158],{"style":4157},[15,69529],{"className":69530,"style":406},[157],[15,69532,69534,69537,69605],{"className":69533},[59],[15,69535],{"className":69536},[146,441],[15,69538,69540],{"className":69539},[238],[15,69541,69543,69597],{"className":69542},[285,286],[15,69544,69546,69594],{"className":69545},[290],[15,69547,69549,69569,69577],{"className":69548,"style":2524},[294],[15,69550,69551,69554],{"style":2527},[15,69552],{"className":69553,"style":461},[302],[15,69555,69557],{"className":69556},[307,308,309,310],[15,69558,69560,69563,69566],{"className":69559},[59,310],[15,69561,769],{"className":69562},[59,60,310],[15,69564,2470],{"className":69565},[2591,310],[15,69567,117],{"className":69568},[59,310],[15,69570,69571,69574],{"style":473},[15,69572],{"className":69573,"style":461},[302],[15,69575],{"className":69576,"style":481},[480],[15,69578,69579,69582],{"style":2550},[15,69580],{"className":69581,"style":461},[302],[15,69583,69585],{"className":69584},[307,308,309,310],[15,69586,69588,69591],{"className":69587},[59,310],[15,69589,2463],{"className":69590},[59,310],[15,69592,769],{"className":69593},[59,60,310],[15,69595,318],{"className":69596},[317],[15,69598,69600],{"className":69599},[290],[15,69601,69603],{"className":69602,"style":16429},[294],[15,69604],{},[15,69606],{"className":69607},[153,441],"。令 ",[15,69610,69612,69646],{"className":69611,"translate":19},[18],[15,69613,69615],{"className":69614},[23],[25,69616,69617],{"xmlns":27},[29,69618,69619,69643],{},[32,69620,69621,69623,69625,69637,69639,69641],{},[35,69622,40237],{},[110,69624,123],{},[7553,69626,69627,69629,69635],{},[35,69628,37],{},[32,69630,69631,69633],{},[35,69632,23743],{},[35,69634,25737],{},[110,69636,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,69638,113],{"stretchy":112},[35,69640,769],{},[110,69642,120],{"stretchy":112},[39,69644,69645],{"encoding":41},"y=f_{JS}'(t)",[15,69647,69649,69667],{"className":69648,"ariaHidden":46},[45],[15,69650,69652,69655,69658,69661,69664],{"className":69651},[50],[15,69653],{"className":69654,"style":2276},[54],[15,69656,40237],{"className":69657,"style":981},[59,60],[15,69659],{"className":69660,"style":158},[157],[15,69662,123],{"className":69663},[162],[15,69665],{"className":69666,"style":158},[157],[15,69668,69670,69673,69733,69736,69739],{"className":69669},[50],[15,69671],{"className":69672,"style":69366},[54],[15,69674,69676,69679],{"className":69675},[59],[15,69677,37],{"className":69678,"style":61},[59,60],[15,69680,69682],{"className":69681},[281],[15,69683,69685,69725],{"className":69684},[285,286],[15,69686,69688,69722],{"className":69687},[290],[15,69689,69691,69708],{"className":69690,"style":6862},[294],[15,69692,69693,69696],{"style":69387},[15,69694],{"className":69695,"style":303},[302],[15,69697,69699],{"className":69698},[307,308,309,310],[15,69700,69702,69705],{"className":69701},[59,310],[15,69703,23743],{"className":69704,"style":24153},[59,60,310],[15,69706,25737],{"className":69707,"style":25861},[59,60,310],[15,69709,69710,69713],{"style":6865},[15,69711],{"className":69712,"style":303},[302],[15,69714,69716],{"className":69715},[307,308,309,310],[15,69717,69719],{"className":69718},[59,310],[15,69720,6820],{"className":69721},[59,310],[15,69723,318],{"className":69724},[317],[15,69726,69728],{"className":69727},[290],[15,69729,69731],{"className":69730,"style":38390},[294],[15,69732],{},[15,69734,113],{"className":69735},[146],[15,69737,769],{"className":69738},[59,60],[15,69740,120],{"className":69741},[153],[15,69743,69745,69785],{"className":69744,"translate":19},[18],[15,69746,69748],{"className":69747},[23],[25,69749,69750],{"xmlns":27},[29,69751,69752,69782],{},[32,69753,69754,69764,69766],{},[6814,69755,69756,69758],{},[35,69757,7567],{},[32,69759,69760,69762],{},[115,69761,2463],{},[35,69763,40237],{},[110,69765,123],{},[238,69767,69768,69774],{},[32,69769,69770,69772],{},[115,69771,2463],{},[35,69773,769],{},[32,69775,69776,69778,69780],{},[35,69777,769],{},[110,69779,2470],{},[115,69781,117],{},[39,69783,69784],{"encoding":41},"e^{2y}=\\frac{2t}{t+1}",[15,69786,69788,69838],{"className":69787,"ariaHidden":46},[45],[15,69789,69791,69794,69829,69832,69835],{"className":69790},[50],[15,69792],{"className":69793,"style":20028},[54],[15,69795,69797,69800],{"className":69796},[59],[15,69798,7567],{"className":69799},[59,60],[15,69801,69803],{"className":69802},[281],[15,69804,69806],{"className":69805},[285],[15,69807,69809],{"className":69808},[290],[15,69810,69812],{"className":69811,"style":20028},[294],[15,69813,69814,69817],{"style":6865},[15,69815],{"className":69816,"style":303},[302],[15,69818,69820],{"className":69819},[307,308,309,310],[15,69821,69823,69826],{"className":69822},[59,310],[15,69824,2463],{"className":69825},[59,310],[15,69827,40237],{"className":69828,"style":981},[59,60,310],[15,69830],{"className":69831,"style":158},[157],[15,69833,123],{"className":69834},[162],[15,69836],{"className":69837,"style":158},[157],[15,69839,69841,69844],{"className":69840},[50],[15,69842],{"className":69843,"style":45405},[54],[15,69845,69847,69850,69918],{"className":69846},[59],[15,69848],{"className":69849},[146,441],[15,69851,69853],{"className":69852},[238],[15,69854,69856,69910],{"className":69855},[285,286],[15,69857,69859,69907],{"className":69858},[290],[15,69860,69862,69882,69890],{"className":69861,"style":2524},[294],[15,69863,69864,69867],{"style":2527},[15,69865],{"className":69866,"style":461},[302],[15,69868,69870],{"className":69869},[307,308,309,310],[15,69871,69873,69876,69879],{"className":69872},[59,310],[15,69874,769],{"className":69875},[59,60,310],[15,69877,2470],{"className":69878},[2591,310],[15,69880,117],{"className":69881},[59,310],[15,69883,69884,69887],{"style":473},[15,69885],{"className":69886,"style":461},[302],[15,69888],{"className":69889,"style":481},[480],[15,69891,69892,69895],{"style":2550},[15,69893],{"className":69894,"style":461},[302],[15,69896,69898],{"className":69897},[307,308,309,310],[15,69899,69901,69904],{"className":69900},[59,310],[15,69902,2463],{"className":69903},[59,310],[15,69905,769],{"className":69906},[59,60,310],[15,69908,318],{"className":69909},[317],[15,69911,69913],{"className":69912},[290],[15,69914,69916],{"className":69915,"style":16429},[294],[15,69917],{},[15,69919],{"className":69920},[153,441],"，解得 ",[15,69923,69925,69971],{"className":69924,"translate":19},[18],[15,69926,69928],{"className":69927},[23],[25,69929,69930],{"xmlns":27},[29,69931,69932,69968],{},[32,69933,69934,69936,69938],{},[35,69935,769],{},[110,69937,123],{},[1255,69939,69940],{"scriptlevel":126,"displaystyle":46},[238,69941,69942,69952],{},[6814,69943,69944,69946],{},[35,69945,7567],{},[32,69947,69948,69950],{},[115,69949,2463],{},[35,69951,40237],{},[32,69953,69954,69956,69958],{},[115,69955,2463],{},[110,69957,4813],{},[6814,69959,69960,69962],{},[35,69961,7567],{},[32,69963,69964,69966],{},[115,69965,2463],{},[35,69967,40237],{},[39,69969,69970],{"encoding":41},"t=\\dfrac{e^{2y}}{2-e^{2y}}",[15,69972,69974,69992],{"className":69973,"ariaHidden":46},[45],[15,69975,69977,69980,69983,69986,69989],{"className":69976},[50],[15,69978],{"className":69979,"style":5343},[54],[15,69981,769],{"className":69982},[59,60],[15,69984],{"className":69985,"style":158},[157],[15,69987,123],{"className":69988},[162],[15,69990],{"className":69991,"style":158},[157],[15,69993,69995,69999],{"className":69994},[50],[15,69996],{"className":69997,"style":69998},[54],"height:2.2604em;vertical-align:-0.7693em;",[15,70000,70002,70005,70134],{"className":70001},[59],[15,70003],{"className":70004},[146,441],[15,70006,70008],{"className":70007},[238],[15,70009,70011,70126],{"className":70010},[285,286],[15,70012,70014,70123],{"className":70013},[290],[15,70015,70017,70072,70080],{"className":70016,"style":37723},[294],[15,70018,70019,70022],{"style":457},[15,70020],{"className":70021,"style":461},[302],[15,70023,70025,70028,70031,70034,70037],{"className":70024},[59],[15,70026,2463],{"className":70027},[59],[15,70029],{"className":70030,"style":2587},[157],[15,70032,4813],{"className":70033},[2591],[15,70035],{"className":70036,"style":2587},[157],[15,70038,70040,70043],{"className":70039},[59],[15,70041,7567],{"className":70042},[59,60],[15,70044,70046],{"className":70045},[281],[15,70047,70049],{"className":70048},[285],[15,70050,70052],{"className":70051},[290],[15,70053,70055],{"className":70054,"style":45032},[294],[15,70056,70057,70060],{"style":45035},[15,70058],{"className":70059,"style":303},[302],[15,70061,70063],{"className":70062},[307,308,309,310],[15,70064,70066,70069],{"className":70065},[59,310],[15,70067,2463],{"className":70068},[59,310],[15,70070,40237],{"className":70071,"style":981},[59,60,310],[15,70073,70074,70077],{"style":473},[15,70075],{"className":70076,"style":461},[302],[15,70078],{"className":70079,"style":481},[480],[15,70081,70082,70085],{"style":484},[15,70083],{"className":70084,"style":461},[302],[15,70086,70088],{"className":70087},[59],[15,70089,70091,70094],{"className":70090},[59],[15,70092,7567],{"className":70093},[59,60],[15,70095,70097],{"className":70096},[281],[15,70098,70100],{"className":70099},[285],[15,70101,70103],{"className":70102},[290],[15,70104,70106],{"className":70105,"style":20028},[294],[15,70107,70108,70111],{"style":6865},[15,70109],{"className":70110,"style":303},[302],[15,70112,70114],{"className":70113},[307,308,309,310],[15,70115,70117,70120],{"className":70116},[59,310],[15,70118,2463],{"className":70119},[59,310],[15,70121,40237],{"className":70122,"style":981},[59,60,310],[15,70124,318],{"className":70125},[317],[15,70127,70129],{"className":70128},[290],[15,70130,70132],{"className":70131,"style":17015},[294],[15,70133],{},[15,70135],{"className":70136},[153,441],"（这要求 ",[15,70139,70141,70167],{"className":70140,"translate":19},[18],[15,70142,70144],{"className":70143},[23],[25,70145,70146],{"xmlns":27},[29,70147,70148,70164],{},[32,70149,70150,70160,70162],{},[6814,70151,70152,70154],{},[35,70153,7567],{},[32,70155,70156,70158],{},[115,70157,2463],{},[35,70159,40237],{},[110,70161,7251],{},[115,70163,2463],{},[39,70165,70166],{"encoding":41},"e^{2y}\u003C2",[15,70168,70170,70221],{"className":70169,"ariaHidden":46},[45],[15,70171,70173,70177,70212,70215,70218],{"className":70172},[50],[15,70174],{"className":70175,"style":70176},[54],"height:0.8532em;vertical-align:-0.0391em;",[15,70178,70180,70183],{"className":70179},[59],[15,70181,7567],{"className":70182},[59,60],[15,70184,70186],{"className":70185},[281],[15,70187,70189],{"className":70188},[285],[15,70190,70192],{"className":70191},[290],[15,70193,70195],{"className":70194,"style":20028},[294],[15,70196,70197,70200],{"style":6865},[15,70198],{"className":70199,"style":303},[302],[15,70201,70203],{"className":70202},[307,308,309,310],[15,70204,70206,70209],{"className":70205},[59,310],[15,70207,2463],{"className":70208},[59,310],[15,70210,40237],{"className":70211,"style":981},[59,60,310],[15,70213],{"className":70214,"style":158},[157],[15,70216,7251],{"className":70217},[162],[15,70219],{"className":70220,"style":158},[157],[15,70222,70224,70227],{"className":70223},[50],[15,70225],{"className":70226,"style":172},[54],[15,70228,2463],{"className":70229},[59],[15,70231,70233,70260],{"className":70232,"translate":19},[18],[15,70234,70236],{"className":70235},[23],[25,70237,70238],{"xmlns":27},[29,70239,70240,70258],{},[32,70241,70242,70244,70246],{},[35,70243,40237],{},[110,70245,7251],{},[238,70247,70248,70256],{},[32,70249,70250,70252,70254],{},[35,70251,4100],{},[110,70253,4103],{},[115,70255,2463],{},[115,70257,2463],{},[39,70259,65743],{"encoding":41},[15,70261,70263,70281],{"className":70262,"ariaHidden":46},[45],[15,70264,70266,70269,70272,70275,70278],{"className":70265},[50],[15,70267],{"className":70268,"style":31692},[54],[15,70270,40237],{"className":70271,"style":981},[59,60],[15,70273],{"className":70274,"style":158},[157],[15,70276,7251],{"className":70277},[162],[15,70279],{"className":70280,"style":158},[157],[15,70282,70284,70287],{"className":70283},[50],[15,70285],{"className":70286,"style":65771},[54],[15,70288,70290,70293,70367],{"className":70289},[59],[15,70291],{"className":70292},[146,441],[15,70294,70296],{"className":70295},[238],[15,70297,70299,70359],{"className":70298},[285,286],[15,70300,70302,70356],{"className":70301},[290],[15,70303,70305,70319,70327],{"className":70304,"style":2825},[294],[15,70306,70307,70310],{"style":2527},[15,70308],{"className":70309,"style":461},[302],[15,70311,70313],{"className":70312},[307,308,309,310],[15,70314,70316],{"className":70315},[59,310],[15,70317,2463],{"className":70318},[59,310],[15,70320,70321,70324],{"style":473},[15,70322],{"className":70323,"style":461},[302],[15,70325],{"className":70326,"style":481},[480],[15,70328,70329,70332],{"style":2853},[15,70330],{"className":70331,"style":461},[302],[15,70333,70335],{"className":70334},[307,308,309,310],[15,70336,70338,70350,70353],{"className":70337},[59,310],[15,70339,70341,70344,70347],{"className":70340},[1484,310],[15,70342,47658],{"className":70343},[310],[15,70345,47662],{"className":70346},[310],[15,70348,4158],{"className":70349,"style":4157},[310],[15,70351],{"className":70352,"style":42366},[157,310],[15,70354,2463],{"className":70355},[59,310],[15,70357,318],{"className":70358},[317],[15,70360,70362],{"className":70361},[290],[15,70363,70365],{"className":70364,"style":2572},[294],[15,70366],{},[15,70368],{"className":70369},[153,441],"）。于是 ",[15,70372,70374,70428],{"className":70373,"translate":19},[18],[15,70375,70377],{"className":70376},[23],[25,70378,70379],{"xmlns":27},[29,70380,70381,70425],{},[32,70382,70383,70385,70387,70399,70401,70403,70405,70407,70409,70411,70413,70423],{},[35,70384,4100],{},[110,70386,4103],{},[238,70388,70389,70397],{},[32,70390,70391,70393,70395],{},[35,70392,769],{},[110,70394,2470],{},[115,70396,117],{},[115,70398,2463],{},[110,70400,123],{},[110,70402,4813],{},[35,70404,4100],{},[110,70406,4103],{},[110,70408,113],{"stretchy":112},[115,70410,2463],{},[110,70412,4813],{},[6814,70414,70415,70417],{},[35,70416,7567],{},[32,70418,70419,70421],{},[115,70420,2463],{},[35,70422,40237],{},[110,70424,120],{"stretchy":112},[39,70426,70427],{"encoding":41},"\\log\\frac{t+1}{2}=-\\log(2-e^{2y})",[15,70429,70431,70528,70560],{"className":70430,"ariaHidden":46},[45],[15,70432,70434,70437,70442,70445,70519,70522,70525],{"className":70433},[50],[15,70435],{"className":70436,"style":2505},[54],[15,70438,4154,70440],{"className":70439},[1484],[15,70441,4158],{"style":4157},[15,70443],{"className":70444,"style":406},[157],[15,70446,70448,70451,70516],{"className":70447},[59],[15,70449],{"className":70450},[146,441],[15,70452,70454],{"className":70453},[238],[15,70455,70457,70508],{"className":70456},[285,286],[15,70458,70460,70505],{"className":70459},[290],[15,70461,70463,70477,70485],{"className":70462,"style":2524},[294],[15,70464,70465,70468],{"style":2527},[15,70466],{"className":70467,"style":461},[302],[15,70469,70471],{"className":70470},[307,308,309,310],[15,70472,70474],{"className":70473},[59,310],[15,70475,2463],{"className":70476},[59,310],[15,70478,70479,70482],{"style":473},[15,70480],{"className":70481,"style":461},[302],[15,70483],{"className":70484,"style":481},[480],[15,70486,70487,70490],{"style":2550},[15,70488],{"className":70489,"style":461},[302],[15,70491,70493],{"className":70492},[307,308,309,310],[15,70494,70496,70499,70502],{"className":70495},[59,310],[15,70497,769],{"className":70498},[59,60,310],[15,70500,2470],{"className":70501},[2591,310],[15,70503,117],{"className":70504},[59,310],[15,70506,318],{"className":70507},[317],[15,70509,70511],{"className":70510},[290],[15,70512,70514],{"className":70513,"style":2572},[294],[15,70515],{},[15,70517],{"className":70518},[153,441],[15,70520],{"className":70521,"style":158},[157],[15,70523,123],{"className":70524},[162],[15,70526],{"className":70527,"style":158},[157],[15,70529,70531,70534,70537,70540,70545,70548,70551,70554,70557],{"className":70530},[50],[15,70532],{"className":70533,"style":139},[54],[15,70535,4813],{"className":70536},[59],[15,70538],{"className":70539,"style":406},[157],[15,70541,4154,70543],{"className":70542},[1484],[15,70544,4158],{"style":4157},[15,70546,113],{"className":70547},[146],[15,70549,2463],{"className":70550},[59],[15,70552],{"className":70553,"style":2587},[157],[15,70555,4813],{"className":70556},[2591],[15,70558],{"className":70559,"style":2587},[157],[15,70561,70563,70566,70601],{"className":70562},[50],[15,70564],{"className":70565,"style":20003},[54],[15,70567,70569,70572],{"className":70568},[59],[15,70570,7567],{"className":70571},[59,60],[15,70573,70575],{"className":70574},[281],[15,70576,70578],{"className":70577},[285],[15,70579,70581],{"className":70580},[290],[15,70582,70584],{"className":70583,"style":20028},[294],[15,70585,70586,70589],{"style":6865},[15,70587],{"className":70588,"style":303},[302],[15,70590,70592],{"className":70591},[307,308,309,310],[15,70593,70595,70598],{"className":70594},[59,310],[15,70596,2463],{"className":70597},[59,310],[15,70599,40237],{"className":70600,"style":981},[59,60,310],[15,70602,120],{"className":70603},[153],"，代入",[15,70606,70608],{"className":70607,"translate":19},[180],[15,70609,70611,70809],{"className":70610,"translate":19},[18],[15,70612,70614],{"className":70613},[23],[25,70615,70616],{"xmlns":27,"display":189},[29,70617,70618,70806],{},[1243,70619,70620,70672,70754],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,70621,70622,70640],{},[1252,70623,70624],{},[1255,70625,70626],{"scriptlevel":126,"displaystyle":46},[32,70627,70628,70634,70636,70638],{},[6814,70629,70630,70632],{},[35,70631,37],{},[110,70633,7573],{},[110,70635,113],{"stretchy":112},[35,70637,40237],{},[110,70639,120],{"stretchy":112},[1252,70641,70642],{},[1255,70643,70644],{"scriptlevel":126,"displaystyle":46},[32,70645,70646,70648,70650,70652,70654,70656,70666,70668,70670],{},[32,70647],{},[110,70649,123],{},[35,70651,40237],{},[35,70653,769],{},[110,70655,4813],{},[195,70657,70658,70660],{},[35,70659,37],{},[32,70661,70662,70664],{},[35,70663,23743],{},[35,70665,25737],{},[110,70667,113],{"stretchy":112},[35,70669,769],{},[110,70671,120],{"stretchy":112},[1249,70673,70674,70680],{},[1252,70675,70676],{},[1255,70677,70678],{"scriptlevel":126,"displaystyle":46},[32,70679],{},[1252,70681,70682],{},[1255,70683,70684],{"scriptlevel":126,"displaystyle":46},[32,70685,70686,70688,70690,70696,70698,70700,70702,70704,70706,70716,70718,70720,70732,70734,70736,70738,70740,70742,70752],{},[32,70687],{},[110,70689,123],{},[238,70691,70692,70694],{},[35,70693,769],{},[115,70695,2463],{},[35,70697,4100],{},[110,70699,4103],{},[110,70701,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,70703,2463],{},[110,70705,4813],{},[6814,70707,70708,70710],{},[35,70709,7567],{},[32,70711,70712,70714],{},[115,70713,2463],{},[35,70715,40237],{},[110,70717,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,70719,4813],{},[238,70721,70722,70730],{},[32,70723,70724,70726,70728],{},[35,70725,769],{},[110,70727,2470],{},[115,70729,117],{},[115,70731,2463],{},[35,70733,4100],{},[110,70735,4103],{},[110,70737,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,70739,2463],{},[110,70741,4813],{},[6814,70743,70744,70746],{},[35,70745,7567],{},[32,70747,70748,70750],{},[115,70749,2463],{},[35,70751,40237],{},[110,70753,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,70755,70756,70762],{},[1252,70757,70758],{},[1255,70759,70760],{"scriptlevel":126,"displaystyle":46},[32,70761],{},[1252,70763,70764],{},[1255,70765,70766],{"scriptlevel":126,"displaystyle":46},[32,70767,70768,70770,70772,70774,70780,70782,70784,70786,70788,70790,70792,70802,70804],{},[32,70769],{},[110,70771,123],{},[110,70773,4813],{},[238,70775,70776,70778],{},[115,70777,117],{},[115,70779,2463],{},[35,70781,4100],{},[110,70783,4103],{},[1297,70785,1304],{},[110,70787,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,70789,2463],{},[110,70791,4813],{},[6814,70793,70794,70796],{},[35,70795,7567],{},[32,70797,70798,70800],{},[115,70799,2463],{},[35,70801,40237],{},[110,70803,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,70805,4375],{"mathvariant":209},[39,70807,70808],{"encoding":41},"\\begin{aligned}\nf^*(y)&=yt-f_{JS}(t)\\\\\n&=\\frac{t}{2}\\log\\big(2-e^{2y}\\big)\n-\\frac{t+1}{2}\\log\\big(2-e^{2y}\\big)\\\\\n&=-\\frac12\\log\\!\\big(2-e^{2y}\\big).\n\\end{aligned}",[15,70810,70812],{"className":70811,"ariaHidden":46},[45],[15,70813,70815,70819],{"className":70814},[50],[15,70816],{"className":70817,"style":70818},[54],"height:5.8149em;vertical-align:-2.6574em;",[15,70820,70822],{"className":70821},[59],[15,70823,70825,70915],{"className":70824},[1243],[15,70826,70828],{"className":70827},[1360],[15,70829,70831,70906],{"className":70830},[285,286],[15,70832,70834,70903],{"className":70833},[290],[15,70835,70838,70885,70894],{"className":70836,"style":70837},[294],"height:3.1574em;",[15,70839,70841,70844],{"style":70840},"top:-5.6389em;",[15,70842],{"className":70843,"style":22666},[302],[15,70845,70847,70876,70879,70882],{"className":70846},[59],[15,70848,70850,70853],{"className":70849},[59],[15,70851,37],{"className":70852,"style":61},[59,60],[15,70854,70856],{"className":70855},[281],[15,70857,70859],{"className":70858},[285],[15,70860,70862],{"className":70861},[290],[15,70863,70865],{"className":70864,"style":8248},[294],[15,70866,70867,70870],{"style":8277},[15,70868],{"className":70869,"style":303},[302],[15,70871,70873],{"className":70872},[307,308,309,310],[15,70874,7573],{"className":70875},[2591,310],[15,70877,113],{"className":70878},[146],[15,70880,40237],{"className":70881,"style":981},[59,60],[15,70883,120],{"className":70884},[153],[15,70886,70888,70891],{"style":70887},"top:-3.6574em;",[15,70889],{"className":70890,"style":22666},[302],[15,70892],{"className":70893},[59],[15,70895,70897,70900],{"style":70896},"top:-1.35em;",[15,70898],{"className":70899,"style":22666},[302],[15,70901],{"className":70902},[59],[15,70904,318],{"className":70905},[317],[15,70907,70909],{"className":70908},[290],[15,70910,70913],{"className":70911,"style":70912},[294],"height:2.6574em;",[15,70914],{},[15,70916,70918],{"className":70917},[1451],[15,70919,70921,71487],{"className":70920},[285,286],[15,70922,70924,71484],{"className":70923},[290],[15,70925,70927,71017,71323],{"className":70926,"style":70837},[294],[15,70928,70929,70932],{"style":70840},[15,70930],{"className":70931,"style":22666},[302],[15,70933,70935,70938,70941,70944,70947,70950,70953,70956,70959,70962,71008,71011,71014],{"className":70934},[59],[15,70936],{"className":70937},[59],[15,70939],{"className":70940,"style":158},[157],[15,70942,123],{"className":70943},[162],[15,70945],{"className":70946,"style":158},[157],[15,70948,40237],{"className":70949,"style":981},[59,60],[15,70951,769],{"className":70952},[59,60],[15,70954],{"className":70955,"style":2587},[157],[15,70957,4813],{"className":70958},[2591],[15,70960],{"className":70961,"style":2587},[157],[15,70963,70965,70968],{"className":70964},[59],[15,70966,37],{"className":70967,"style":61},[59,60],[15,70969,70971],{"className":70970},[281],[15,70972,70974,71000],{"className":70973},[285,286],[15,70975,70977,70997],{"className":70976},[290],[15,70978,70980],{"className":70979,"style":379},[294],[15,70981,70982,70985],{"style":27509},[15,70983],{"className":70984,"style":303},[302],[15,70986,70988],{"className":70987},[307,308,309,310],[15,70989,70991,70994],{"className":70990},[59,310],[15,70992,23743],{"className":70993,"style":24153},[59,60,310],[15,70995,25737],{"className":70996,"style":25861},[59,60,310],[15,70998,318],{"className":70999},[317],[15,71001,71003],{"className":71002},[290],[15,71004,71006],{"className":71005,"style":7968},[294],[15,71007],{},[15,71009,113],{"className":71010},[146],[15,71012,769],{"className":71013},[59,60],[15,71015,120],{"className":71016},[153],[15,71018,71019,71022],{"style":70887},[15,71020],{"className":71021,"style":22666},[302],[15,71023,71025,71028,71031,71034,71037,71100,71103,71108,71111,71117,71120,71123,71126,71129,71164,71170,71173,71176,71179,71253,71256,71261,71264,71270,71273,71276,71279,71282,71317],{"className":71024},[59],[15,71026],{"className":71027},[59],[15,71029],{"className":71030,"style":158},[157],[15,71032,123],{"className":71033},[162],[15,71035],{"className":71036,"style":158},[157],[15,71038,71040,71043,71097],{"className":71039},[59],[15,71041],{"className":71042},[146,441],[15,71044,71046],{"className":71045},[238],[15,71047,71049,71089],{"className":71048},[285,286],[15,71050,71052,71086],{"className":71051},[290],[15,71053,71056,71067,71075],{"className":71054,"style":71055},[294],"height:1.2921em;",[15,71057,71058,71061],{"style":457},[15,71059],{"className":71060,"style":461},[302],[15,71062,71064],{"className":71063},[59],[15,71065,2463],{"className":71066},[59],[15,71068,71069,71072],{"style":473},[15,71070],{"className":71071,"style":461},[302],[15,71073],{"className":71074,"style":481},[480],[15,71076,71077,71080],{"style":484},[15,71078],{"className":71079,"style":461},[302],[15,71081,71083],{"className":71082},[59],[15,71084,769],{"className":71085},[59,60],[15,71087,318],{"className":71088},[317],[15,71090,71092],{"className":71091},[290],[15,71093,71095],{"className":71094,"style":3778},[294],[15,71096],{},[15,71098],{"className":71099},[153,441],[15,71101],{"className":71102,"style":406},[157],[15,71104,4154,71106],{"className":71105},[1484],[15,71107,4158],{"style":4157},[15,71109],{"className":71110,"style":406},[157],[15,71112,71114],{"className":71113},[59],[15,71115,113],{"className":71116},[419,9674],[15,71118,2463],{"className":71119},[59],[15,71121],{"className":71122,"style":2587},[157],[15,71124,4813],{"className":71125},[2591],[15,71127],{"className":71128,"style":2587},[157],[15,71130,71132,71135],{"className":71131},[59],[15,71133,7567],{"className":71134},[59,60],[15,71136,71138],{"className":71137},[281],[15,71139,71141],{"className":71140},[285],[15,71142,71144],{"className":71143},[290],[15,71145,71147],{"className":71146,"style":19735},[294],[15,71148,71149,71152],{"style":8277},[15,71150],{"className":71151,"style":303},[302],[15,71153,71155],{"className":71154},[307,308,309,310],[15,71156,71158,71161],{"className":71157},[59,310],[15,71159,2463],{"className":71160},[59,310],[15,71162,40237],{"className":71163,"style":981},[59,60,310],[15,71165,71167],{"className":71166},[59],[15,71168,120],{"className":71169},[419,9674],[15,71171],{"className":71172,"style":2587},[157],[15,71174,4813],{"className":71175},[2591],[15,71177],{"className":71178,"style":2587},[157],[15,71180,71182,71185,71250],{"className":71181},[59],[15,71183],{"className":71184},[146,441],[15,71186,71188],{"className":71187},[238],[15,71189,71191,71242],{"className":71190},[285,286],[15,71192,71194,71239],{"className":71193},[290],[15,71195,71197,71208,71216],{"className":71196,"style":22889},[294],[15,71198,71199,71202],{"style":457},[15,71200],{"className":71201,"style":461},[302],[15,71203,71205],{"className":71204},[59],[15,71206,2463],{"className":71207},[59],[15,71209,71210,71213],{"style":473},[15,71211],{"className":71212,"style":461},[302],[15,71214],{"className":71215,"style":481},[480],[15,71217,71218,71221],{"style":484},[15,71219],{"className":71220,"style":461},[302],[15,71222,71224,71227,71230,71233,71236],{"className":71223},[59],[15,71225,769],{"className":71226},[59,60],[15,71228],{"className":71229,"style":2587},[157],[15,71231,2470],{"className":71232},[2591],[15,71234],{"className":71235,"style":2587},[157],[15,71237,117],{"className":71238},[59],[15,71240,318],{"className":71241},[317],[15,71243,71245],{"className":71244},[290],[15,71246,71248],{"className":71247,"style":3778},[294],[15,71249],{},[15,71251],{"className":71252},[153,441],[15,71254],{"className":71255,"style":406},[157],[15,71257,4154,71259],{"className":71258},[1484],[15,71260,4158],{"style":4157},[15,71262],{"className":71263,"style":406},[157],[15,71265,71267],{"className":71266},[59],[15,71268,113],{"className":71269},[419,9674],[15,71271,2463],{"className":71272},[59],[15,71274],{"className":71275,"style":2587},[157],[15,71277,4813],{"className":71278},[2591],[15,71280],{"className":71281,"style":2587},[157],[15,71283,71285,71288],{"className":71284},[59],[15,71286,7567],{"className":71287},[59,60],[15,71289,71291],{"className":71290},[281],[15,71292,71294],{"className":71293},[285],[15,71295,71297],{"className":71296},[290],[15,71298,71300],{"className":71299,"style":19735},[294],[15,71301,71302,71305],{"style":8277},[15,71303],{"className":71304,"style":303},[302],[15,71306,71308],{"className":71307},[307,308,309,310],[15,71309,71311,71314],{"className":71310},[59,310],[15,71312,2463],{"className":71313},[59,310],[15,71315,40237],{"className":71316,"style":981},[59,60,310],[15,71318,71320],{"className":71319},[59],[15,71321,120],{"className":71322},[419,9674],[15,71324,71325,71328],{"style":70896},[15,71326],{"className":71327,"style":22666},[302],[15,71329,71331,71334,71337,71340,71343,71346,71408,71411,71416,71419,71422,71428,71431,71434,71437,71440,71475,71481],{"className":71330},[59],[15,71332],{"className":71333},[59],[15,71335],{"className":71336,"style":158},[157],[15,71338,123],{"className":71339},[162],[15,71341],{"className":71342,"style":158},[157],[15,71344,4813],{"className":71345},[59],[15,71347,71349,71352,71405],{"className":71348},[59],[15,71350],{"className":71351},[146,441],[15,71353,71355],{"className":71354},[238],[15,71356,71358,71397],{"className":71357},[285,286],[15,71359,71361,71394],{"className":71360},[290],[15,71362,71364,71375,71383],{"className":71363,"style":22889},[294],[15,71365,71366,71369],{"style":457},[15,71367],{"className":71368,"style":461},[302],[15,71370,71372],{"className":71371},[59],[15,71373,2463],{"className":71374},[59],[15,71376,71377,71380],{"style":473},[15,71378],{"className":71379,"style":461},[302],[15,71381],{"className":71382,"style":481},[480],[15,71384,71385,71388],{"style":484},[15,71386],{"className":71387,"style":461},[302],[15,71389,71391],{"className":71390},[59],[15,71392,117],{"className":71393},[59],[15,71395,318],{"className":71396},[317],[15,71398,71400],{"className":71399},[290],[15,71401,71403],{"className":71402,"style":3778},[294],[15,71404],{},[15,71406],{"className":71407},[153,441],[15,71409],{"className":71410,"style":406},[157],[15,71412,4154,71414],{"className":71413},[1484],[15,71415,4158],{"style":4157},[15,71417],{"className":71418,"style":1512},[157],[15,71420],{"className":71421,"style":406},[157],[15,71423,71425],{"className":71424},[59],[15,71426,113],{"className":71427},[419,9674],[15,71429,2463],{"className":71430},[59],[15,71432],{"className":71433,"style":2587},[157],[15,71435,4813],{"className":71436},[2591],[15,71438],{"className":71439,"style":2587},[157],[15,71441,71443,71446],{"className":71442},[59],[15,71444,7567],{"className":71445},[59,60],[15,71447,71449],{"className":71448},[281],[15,71450,71452],{"className":71451},[285],[15,71453,71455],{"className":71454},[290],[15,71456,71458],{"className":71457,"style":19735},[294],[15,71459,71460,71463],{"style":8277},[15,71461],{"className":71462,"style":303},[302],[15,71464,71466],{"className":71465},[307,308,309,310],[15,71467,71469,71472],{"className":71468},[59,310],[15,71470,2463],{"className":71471},[59,310],[15,71473,40237],{"className":71474,"style":981},[59,60,310],[15,71476,71478],{"className":71477},[59],[15,71479,120],{"className":71480},[419,9674],[15,71482,4375],{"className":71483},[59],[15,71485,318],{"className":71486},[317],[15,71488,71490],{"className":71489},[290],[15,71491,71493],{"className":71492,"style":70912},[294],[15,71494],{},[11,71496,71497,71498,71802,71803,71854,71855,72211,72212,71854,72263,72619,72620,72749,72750,72801,72802,68218,72830,72950,72951,68218,72984,73109,73110,72801,73161,73264],{},"TV 的共轭也很干净：",[15,71499,71501,71569],{"className":71500,"translate":19},[18],[15,71502,71504],{"className":71503},[23],[25,71505,71506],{"xmlns":27},[29,71507,71508,71566],{},[32,71509,71510,71516,71518,71520,71522,71524,71540,71542,71544,71546,71548,71554,71556,71558,71560,71562,71564],{},[6814,71511,71512,71514],{},[35,71513,37],{},[110,71515,7573],{},[110,71517,113],{"stretchy":112},[35,71519,40237],{},[110,71521,120],{"stretchy":112},[110,71523,123],{},[195,71525,71526,71532],{},[32,71527,71528,71530],{},[35,71529,35432],{},[110,71531,4103],{},[32,71533,71534,71536,71538],{},[35,71535,769],{},[110,71537,6928],{},[115,71539,126],{},[110,71541,2898],{"stretchy":112},[35,71543,40237],{},[35,71545,769],{},[110,71547,4813],{},[238,71549,71550,71552],{},[115,71551,117],{},[115,71553,2463],{},[35,71555,4808],{"mathvariant":209},[35,71557,769],{},[110,71559,4813],{},[115,71561,117],{},[35,71563,4808],{"mathvariant":209},[110,71565,2908],{"stretchy":112},[39,71567,71568],{"encoding":41},"f^*(y)=\\sup_{t\\ge0}\\{yt-\\frac12|t-1|\\}",[15,71570,71572,71625,71701,71790],{"className":71571,"ariaHidden":46},[45],[15,71573,71575,71578,71607,71610,71613,71616,71619,71622],{"className":71574},[50],[15,71576],{"className":71577,"style":139},[54],[15,71579,71581,71584],{"className":71580},[59],[15,71582,37],{"className":71583,"style":61},[59,60],[15,71585,71587],{"className":71586},[281],[15,71588,71590],{"className":71589},[285],[15,71591,71593],{"className":71592},[290],[15,71594,71596],{"className":71595,"style":8499},[294],[15,71597,71598,71601],{"style":6865},[15,71599],{"className":71600,"style":303},[302],[15,71602,71604],{"className":71603},[307,308,309,310],[15,71605,7573],{"className":71606},[2591,310],[15,71608,113],{"className":71609},[146],[15,71611,40237],{"className":71612,"style":981},[59,60],[15,71614,120],{"className":71615},[153],[15,71617],{"className":71618,"style":158},[157],[15,71620,123],{"className":71621},[162],[15,71623],{"className":71624,"style":158},[157],[15,71626,71628,71632,71683,71686,71689,71692,71695,71698],{"className":71627},[50],[15,71629],{"className":71630,"style":71631},[54],"height:1.0893em;vertical-align:-0.3393em;",[15,71633,71635,71638],{"className":71634},[1484],[15,71636,35432],{"className":71637},[1484],[15,71639,71641],{"className":71640},[281],[15,71642,71644,71674],{"className":71643},[285,286],[15,71645,71647,71671],{"className":71646},[290],[15,71648,71651],{"className":71649,"style":71650},[294],"height:0.207em;",[15,71652,71653,71656],{"style":35578},[15,71654],{"className":71655,"style":303},[302],[15,71657,71659],{"className":71658},[307,308,309,310],[15,71660,71662,71665,71668],{"className":71661},[59,310],[15,71663,769],{"className":71664},[59,60,310],[15,71666,6928],{"className":71667},[162,310],[15,71669,126],{"className":71670},[59,310],[15,71672,318],{"className":71673},[317],[15,71675,71677],{"className":71676},[290],[15,71678,71681],{"className":71679,"style":71680},[294],"height:0.3393em;",[15,71682],{},[15,71684,2898],{"className":71685},[146],[15,71687,40237],{"className":71688,"style":981},[59,60],[15,71690,769],{"className":71691},[59,60],[15,71693],{"className":71694,"style":2587},[157],[15,71696,4813],{"className":71697},[2591],[15,71699],{"className":71700,"style":2587},[157],[15,71702,71704,71707,71775,71778,71781,71784,71787],{"className":71703},[50],[15,71705],{"className":71706,"style":2505},[54],[15,71708,71710,71713,71772],{"className":71709},[59],[15,71711],{"className":71712},[146,441],[15,71714,71716],{"className":71715},[238],[15,71717,71719,71764],{"className":71718},[285,286],[15,71720,71722,71761],{"className":71721},[290],[15,71723,71725,71739,71747],{"className":71724,"style":2524},[294],[15,71726,71727,71730],{"style":2527},[15,71728],{"className":71729,"style":461},[302],[15,71731,71733],{"className":71732},[307,308,309,310],[15,71734,71736],{"className":71735},[59,310],[15,71737,2463],{"className":71738},[59,310],[15,71740,71741,71744],{"style":473},[15,71742],{"className":71743,"style":461},[302],[15,71745],{"className":71746,"style":481},[480],[15,71748,71749,71752],{"style":2550},[15,71750],{"className":71751,"style":461},[302],[15,71753,71755],{"className":71754},[307,308,309,310],[15,71756,71758],{"className":71757},[59,310],[15,71759,117],{"className":71760},[59,310],[15,71762,318],{"className":71763},[317],[15,71765,71767],{"className":71766},[290],[15,71768,71770],{"className":71769,"style":2572},[294],[15,71771],{},[15,71773],{"className":71774},[153,441],[15,71776,4808],{"className":71777},[59],[15,71779,769],{"className":71780},[59,60],[15,71782],{"className":71783,"style":2587},[157],[15,71785,4813],{"className":71786},[2591],[15,71788],{"className":71789,"style":2587},[157],[15,71791,71793,71796,71799],{"className":71792},[50],[15,71794],{"className":71795,"style":139},[54],[15,71797,34679],{"className":71798},[59],[15,71800,2908],{"className":71801},[153],"。在 ",[15,71804,71806,71824],{"className":71805,"translate":19},[18],[15,71807,71809],{"className":71808},[23],[25,71810,71811],{"xmlns":27},[29,71812,71813,71821],{},[32,71814,71815,71817,71819],{},[35,71816,769],{},[110,71818,9952],{},[115,71820,117],{},[39,71822,71823],{"encoding":41},"t\\le1",[15,71825,71827,71845],{"className":71826,"ariaHidden":46},[45],[15,71828,71830,71833,71836,71839,71842],{"className":71829},[50],[15,71831],{"className":71832,"style":43188},[54],[15,71834,769],{"className":71835},[59,60],[15,71837],{"className":71838,"style":158},[157],[15,71840,9952],{"className":71841},[162],[15,71843],{"className":71844,"style":158},[157],[15,71846,71848,71851],{"className":71847},[50],[15,71849],{"className":71850,"style":172},[54],[15,71852,117],{"className":71853},[59]," 一侧，",[15,71856,71858,71914],{"className":71857,"translate":19},[18],[15,71859,71861],{"className":71860},[23],[25,71862,71863],{"xmlns":27},[29,71864,71865,71911],{},[32,71866,71867,71869,71871,71873,71885,71887,71889,71891,71893,71895,71901,71903,71905],{},[35,71868,40237],{},[35,71870,769],{},[110,71872,4813],{},[238,71874,71875,71883],{},[32,71876,71877,71879,71881],{},[115,71878,117],{},[110,71880,4813],{},[35,71882,769],{},[115,71884,2463],{},[110,71886,123],{},[35,71888,769],{},[110,71890,113],{"stretchy":112},[35,71892,40237],{},[110,71894,2470],{},[238,71896,71897,71899],{},[115,71898,117],{},[115,71900,2463],{},[110,71902,120],{"stretchy":112},[110,71904,4813],{},[238,71906,71907,71909],{},[115,71908,117],{},[115,71910,2463],{},[39,71912,71913],{"encoding":41},"yt-\\frac{1-t}{2}=t(y+\\frac12)-\\frac12",[15,71915,71917,71938,72027,72051,72137],{"className":71916,"ariaHidden":46},[45],[15,71918,71920,71923,71926,71929,71932,71935],{"className":71919},[50],[15,71921],{"className":71922,"style":26274},[54],[15,71924,40237],{"className":71925,"style":981},[59,60],[15,71927,769],{"className":71928},[59,60],[15,71930],{"className":71931,"style":2587},[157],[15,71933,4813],{"className":71934},[2591],[15,71936],{"className":71937,"style":2587},[157],[15,71939,71941,71944,72018,72021,72024],{"className":71940},[50],[15,71942],{"className":71943,"style":2505},[54],[15,71945,71947,71950,72015],{"className":71946},[59],[15,71948],{"className":71949},[146,441],[15,71951,71953],{"className":71952},[238],[15,71954,71956,72007],{"className":71955},[285,286],[15,71957,71959,72004],{"className":71958},[290],[15,71960,71962,71976,71984],{"className":71961,"style":2524},[294],[15,71963,71964,71967],{"style":2527},[15,71965],{"className":71966,"style":461},[302],[15,71968,71970],{"className":71969},[307,308,309,310],[15,71971,71973],{"className":71972},[59,310],[15,71974,2463],{"className":71975},[59,310],[15,71977,71978,71981],{"style":473},[15,71979],{"className":71980,"style":461},[302],[15,71982],{"className":71983,"style":481},[480],[15,71985,71986,71989],{"style":2550},[15,71987],{"className":71988,"style":461},[302],[15,71990,71992],{"className":71991},[307,308,309,310],[15,71993,71995,71998,72001],{"className":71994},[59,310],[15,71996,117],{"className":71997},[59,310],[15,71999,4813],{"className":72000},[2591,310],[15,72002,769],{"className":72003},[59,60,310],[15,72005,318],{"className":72006},[317],[15,72008,72010],{"className":72009},[290],[15,72011,72013],{"className":72012,"style":2572},[294],[15,72014],{},[15,72016],{"className":72017},[153,441],[15,72019],{"className":72020,"style":158},[157],[15,72022,123],{"className":72023},[162],[15,72025],{"className":72026,"style":158},[157],[15,72028,72030,72033,72036,72039,72042,72045,72048],{"className":72029},[50],[15,72031],{"className":72032,"style":139},[54],[15,72034,769],{"className":72035},[59,60],[15,72037,113],{"className":72038},[146],[15,72040,40237],{"className":72041,"style":981},[59,60],[15,72043],{"className":72044,"style":2587},[157],[15,72046,2470],{"className":72047},[2591],[15,72049],{"className":72050,"style":2587},[157],[15,72052,72054,72057,72125,72128,72131,72134],{"className":72053},[50],[15,72055],{"className":72056,"style":2505},[54],[15,72058,72060,72063,72122],{"className":72059},[59],[15,72061],{"className":72062},[146,441],[15,72064,72066],{"className":72065},[238],[15,72067,72069,72114],{"className":72068},[285,286],[15,72070,72072,72111],{"className":72071},[290],[15,72073,72075,72089,72097],{"className":72074,"style":2524},[294],[15,72076,72077,72080],{"style":2527},[15,72078],{"className":72079,"style":461},[302],[15,72081,72083],{"className":72082},[307,308,309,310],[15,72084,72086],{"className":72085},[59,310],[15,72087,2463],{"className":72088},[59,310],[15,72090,72091,72094],{"style":473},[15,72092],{"className":72093,"style":461},[302],[15,72095],{"className":72096,"style":481},[480],[15,72098,72099,72102],{"style":2550},[15,72100],{"className":72101,"style":461},[302],[15,72103,72105],{"className":72104},[307,308,309,310],[15,72106,72108],{"className":72107},[59,310],[15,72109,117],{"className":72110},[59,310],[15,72112,318],{"className":72113},[317],[15,72115,72117],{"className":72116},[290],[15,72118,72120],{"className":72119,"style":2572},[294],[15,72121],{},[15,72123],{"className":72124},[153,441],[15,72126,120],{"className":72127},[153],[15,72129],{"className":72130,"style":2587},[157],[15,72132,4813],{"className":72133},[2591],[15,72135],{"className":72136,"style":2587},[157],[15,72138,72140,72143],{"className":72139},[50],[15,72141],{"className":72142,"style":2505},[54],[15,72144,72146,72149,72208],{"className":72145},[59],[15,72147],{"className":72148},[146,441],[15,72150,72152],{"className":72151},[238],[15,72153,72155,72200],{"className":72154},[285,286],[15,72156,72158,72197],{"className":72157},[290],[15,72159,72161,72175,72183],{"className":72160,"style":2524},[294],[15,72162,72163,72166],{"style":2527},[15,72164],{"className":72165,"style":461},[302],[15,72167,72169],{"className":72168},[307,308,309,310],[15,72170,72172],{"className":72171},[59,310],[15,72173,2463],{"className":72174},[59,310],[15,72176,72177,72180],{"style":473},[15,72178],{"className":72179,"style":461},[302],[15,72181],{"className":72182,"style":481},[480],[15,72184,72185,72188],{"style":2550},[15,72186],{"className":72187,"style":461},[302],[15,72189,72191],{"className":72190},[307,308,309,310],[15,72192,72194],{"className":72193},[59,310],[15,72195,117],{"className":72196},[59,310],[15,72198,318],{"className":72199},[317],[15,72201,72203],{"className":72202},[290],[15,72204,72206],{"className":72205,"style":2572},[294],[15,72207],{},[15,72209],{"className":72210},[153,441],"；在 ",[15,72213,72215,72233],{"className":72214,"translate":19},[18],[15,72216,72218],{"className":72217},[23],[25,72219,72220],{"xmlns":27},[29,72221,72222,72230],{},[32,72223,72224,72226,72228],{},[35,72225,769],{},[110,72227,6928],{},[115,72229,117],{},[39,72231,72232],{"encoding":41},"t\\ge1",[15,72234,72236,72254],{"className":72235,"ariaHidden":46},[45],[15,72237,72239,72242,72245,72248,72251],{"className":72238},[50],[15,72240],{"className":72241,"style":43188},[54],[15,72243,769],{"className":72244},[59,60],[15,72246],{"className":72247,"style":158},[157],[15,72249,6928],{"className":72250},[162],[15,72252],{"className":72253,"style":158},[157],[15,72255,72257,72260],{"className":72256},[50],[15,72258],{"className":72259,"style":172},[54],[15,72261,117],{"className":72262},[59],[15,72264,72266,72322],{"className":72265,"translate":19},[18],[15,72267,72269],{"className":72268},[23],[25,72270,72271],{"xmlns":27},[29,72272,72273,72319],{},[32,72274,72275,72277,72279,72281,72293,72295,72297,72299,72301,72303,72309,72311,72313],{},[35,72276,40237],{},[35,72278,769],{},[110,72280,4813],{},[238,72282,72283,72291],{},[32,72284,72285,72287,72289],{},[35,72286,769],{},[110,72288,4813],{},[115,72290,117],{},[115,72292,2463],{},[110,72294,123],{},[35,72296,769],{},[110,72298,113],{"stretchy":112},[35,72300,40237],{},[110,72302,4813],{},[238,72304,72305,72307],{},[115,72306,117],{},[115,72308,2463],{},[110,72310,120],{"stretchy":112},[110,72312,2470],{},[238,72314,72315,72317],{},[115,72316,117],{},[115,72318,2463],{},[39,72320,72321],{"encoding":41},"yt-\\frac{t-1}{2}=t(y-\\frac12)+\\frac12",[15,72323,72325,72346,72435,72459,72545],{"className":72324,"ariaHidden":46},[45],[15,72326,72328,72331,72334,72337,72340,72343],{"className":72327},[50],[15,72329],{"className":72330,"style":26274},[54],[15,72332,40237],{"className":72333,"style":981},[59,60],[15,72335,769],{"className":72336},[59,60],[15,72338],{"className":72339,"style":2587},[157],[15,72341,4813],{"className":72342},[2591],[15,72344],{"className":72345,"style":2587},[157],[15,72347,72349,72352,72426,72429,72432],{"className":72348},[50],[15,72350],{"className":72351,"style":2505},[54],[15,72353,72355,72358,72423],{"className":72354},[59],[15,72356],{"className":72357},[146,441],[15,72359,72361],{"className":72360},[238],[15,72362,72364,72415],{"className":72363},[285,286],[15,72365,72367,72412],{"className":72366},[290],[15,72368,72370,72384,72392],{"className":72369,"style":2524},[294],[15,72371,72372,72375],{"style":2527},[15,72373],{"className":72374,"style":461},[302],[15,72376,72378],{"className":72377},[307,308,309,310],[15,72379,72381],{"className":72380},[59,310],[15,72382,2463],{"className":72383},[59,310],[15,72385,72386,72389],{"style":473},[15,72387],{"className":72388,"style":461},[302],[15,72390],{"className":72391,"style":481},[480],[15,72393,72394,72397],{"style":2550},[15,72395],{"className":72396,"style":461},[302],[15,72398,72400],{"className":72399},[307,308,309,310],[15,72401,72403,72406,72409],{"className":72402},[59,310],[15,72404,769],{"className":72405},[59,60,310],[15,72407,4813],{"className":72408},[2591,310],[15,72410,117],{"className":72411},[59,310],[15,72413,318],{"className":72414},[317],[15,72416,72418],{"className":72417},[290],[15,72419,72421],{"className":72420,"style":2572},[294],[15,72422],{},[15,72424],{"className":72425},[153,441],[15,72427],{"className":72428,"style":158},[157],[15,72430,123],{"className":72431},[162],[15,72433],{"className":72434,"style":158},[157],[15,72436,72438,72441,72444,72447,72450,72453,72456],{"className":72437},[50],[15,72439],{"className":72440,"style":139},[54],[15,72442,769],{"className":72443},[59,60],[15,72445,113],{"className":72446},[146],[15,72448,40237],{"className":72449,"style":981},[59,60],[15,72451],{"className":72452,"style":2587},[157],[15,72454,4813],{"className":72455},[2591],[15,72457],{"className":72458,"style":2587},[157],[15,72460,72462,72465,72533,72536,72539,72542],{"className":72461},[50],[15,72463],{"className":72464,"style":2505},[54],[15,72466,72468,72471,72530],{"className":72467},[59],[15,72469],{"className":72470},[146,441],[15,72472,72474],{"className":72473},[238],[15,72475,72477,72522],{"className":72476},[285,286],[15,72478,72480,72519],{"className":72479},[290],[15,72481,72483,72497,72505],{"className":72482,"style":2524},[294],[15,72484,72485,72488],{"style":2527},[15,72486],{"className":72487,"style":461},[302],[15,72489,72491],{"className":72490},[307,308,309,310],[15,72492,72494],{"className":72493},[59,310],[15,72495,2463],{"className":72496},[59,310],[15,72498,72499,72502],{"style":473},[15,72500],{"className":72501,"style":461},[302],[15,72503],{"className":72504,"style":481},[480],[15,72506,72507,72510],{"style":2550},[15,72508],{"className":72509,"style":461},[302],[15,72511,72513],{"className":72512},[307,308,309,310],[15,72514,72516],{"className":72515},[59,310],[15,72517,117],{"className":72518},[59,310],[15,72520,318],{"className":72521},[317],[15,72523,72525],{"className":72524},[290],[15,72526,72528],{"className":72527,"style":2572},[294],[15,72529],{},[15,72531],{"className":72532},[153,441],[15,72534,120],{"className":72535},[153],[15,72537],{"className":72538,"style":2587},[157],[15,72540,2470],{"className":72541},[2591],[15,72543],{"className":72544,"style":2587},[157],[15,72546,72548,72551],{"className":72547},[50],[15,72549],{"className":72550,"style":2505},[54],[15,72552,72554,72557,72616],{"className":72553},[59],[15,72555],{"className":72556},[146,441],[15,72558,72560],{"className":72559},[238],[15,72561,72563,72608],{"className":72562},[285,286],[15,72564,72566,72605],{"className":72565},[290],[15,72567,72569,72583,72591],{"className":72568,"style":2524},[294],[15,72570,72571,72574],{"style":2527},[15,72572],{"className":72573,"style":461},[302],[15,72575,72577],{"className":72576},[307,308,309,310],[15,72578,72580],{"className":72579},[59,310],[15,72581,2463],{"className":72582},[59,310],[15,72584,72585,72588],{"style":473},[15,72586],{"className":72587,"style":461},[302],[15,72589],{"className":72590,"style":481},[480],[15,72592,72593,72596],{"style":2550},[15,72594],{"className":72595,"style":461},[302],[15,72597,72599],{"className":72598},[307,308,309,310],[15,72600,72602],{"className":72601},[59,310],[15,72603,117],{"className":72604},[59,310],[15,72606,318],{"className":72607},[317],[15,72609,72611],{"className":72610},[290],[15,72612,72614],{"className":72613,"style":2572},[294],[15,72615],{},[15,72617],{"className":72618},[153,441],"。两段都是线性的：当 ",[15,72621,72623,72648],{"className":72622,"translate":19},[18],[15,72624,72626],{"className":72625},[23],[25,72627,72628],{"xmlns":27},[29,72629,72630,72646],{},[32,72631,72632,72634,72636,72638,72640],{},[110,72633,4808],{"stretchy":112},[35,72635,40237],{},[110,72637,4808],{"stretchy":112},[110,72639,9952],{},[238,72641,72642,72644],{},[115,72643,117],{},[115,72645,2463],{},[39,72647,66057],{"encoding":41},[15,72649,72651,72675],{"className":72650,"ariaHidden":46},[45],[15,72652,72654,72657,72660,72663,72666,72669,72672],{"className":72653},[50],[15,72655],{"className":72656,"style":139},[54],[15,72658,4808],{"className":72659},[146],[15,72661,40237],{"className":72662,"style":981},[59,60],[15,72664,4808],{"className":72665},[153],[15,72667],{"className":72668,"style":158},[157],[15,72670,9952],{"className":72671},[162],[15,72673],{"className":72674,"style":158},[157],[15,72676,72678,72681],{"className":72677},[50],[15,72679],{"className":72680,"style":2505},[54],[15,72682,72684,72687,72746],{"className":72683},[59],[15,72685],{"className":72686},[146,441],[15,72688,72690],{"className":72689},[238],[15,72691,72693,72738],{"className":72692},[285,286],[15,72694,72696,72735],{"className":72695},[290],[15,72697,72699,72713,72721],{"className":72698,"style":2524},[294],[15,72700,72701,72704],{"style":2527},[15,72702],{"className":72703,"style":461},[302],[15,72705,72707],{"className":72706},[307,308,309,310],[15,72708,72710],{"className":72709},[59,310],[15,72711,2463],{"className":72712},[59,310],[15,72714,72715,72718],{"style":473},[15,72716],{"className":72717,"style":461},[302],[15,72719],{"className":72720,"style":481},[480],[15,72722,72723,72726],{"style":2550},[15,72724],{"className":72725,"style":461},[302],[15,72727,72729],{"className":72728},[307,308,309,310],[15,72730,72732],{"className":72731},[59,310],[15,72733,117],{"className":72734},[59,310],[15,72736,318],{"className":72737},[317],[15,72739,72741],{"className":72740},[290],[15,72742,72744],{"className":72743,"style":2572},[294],[15,72745],{},[15,72747],{"className":72748},[153,441]," 时两段的最大值都在 ",[15,72751,72753,72771],{"className":72752,"translate":19},[18],[15,72754,72756],{"className":72755},[23],[25,72757,72758],{"xmlns":27},[29,72759,72760,72768],{},[32,72761,72762,72764,72766],{},[35,72763,769],{},[110,72765,123],{},[115,72767,117],{},[39,72769,72770],{"encoding":41},"t=1",[15,72772,72774,72792],{"className":72773,"ariaHidden":46},[45],[15,72775,72777,72780,72783,72786,72789],{"className":72776},[50],[15,72778],{"className":72779,"style":5343},[54],[15,72781,769],{"className":72782},[59,60],[15,72784],{"className":72785,"style":158},[157],[15,72787,123],{"className":72788},[162],[15,72790],{"className":72791,"style":158},[157],[15,72793,72795,72798],{"className":72794},[50],[15,72796],{"className":72797,"style":172},[54],[15,72799,117],{"className":72800},[59]," 取到，为 ",[15,72803,72805,72818],{"className":72804,"translate":19},[18],[15,72806,72808],{"className":72807},[23],[25,72809,72810],{"xmlns":27},[29,72811,72812,72816],{},[32,72813,72814],{},[35,72815,40237],{},[39,72817,40237],{"encoding":41},[15,72819,72821],{"className":72820,"ariaHidden":46},[45],[15,72822,72824,72827],{"className":72823},[50],[15,72825],{"className":72826,"style":2276},[54],[15,72828,40237],{"className":72829,"style":981},[59,60],[15,72831,72833,72855],{"className":72832,"translate":19},[18],[15,72834,72836],{"className":72835},[23],[25,72837,72838],{"xmlns":27},[29,72839,72840,72852],{},[32,72841,72842,72844,72846],{},[35,72843,40237],{},[110,72845,2903],{},[238,72847,72848,72850],{},[115,72849,117],{},[115,72851,2463],{},[39,72853,72854],{"encoding":41},"y>\\frac12",[15,72856,72858,72876],{"className":72857,"ariaHidden":46},[45],[15,72859,72861,72864,72867,72870,72873],{"className":72860},[50],[15,72862],{"className":72863,"style":31692},[54],[15,72865,40237],{"className":72866,"style":981},[59,60],[15,72868],{"className":72869,"style":158},[157],[15,72871,2903],{"className":72872},[162],[15,72874],{"className":72875,"style":158},[157],[15,72877,72879,72882],{"className":72878},[50],[15,72880],{"className":72881,"style":2505},[54],[15,72883,72885,72888,72947],{"className":72884},[59],[15,72886],{"className":72887},[146,441],[15,72889,72891],{"className":72890},[238],[15,72892,72894,72939],{"className":72893},[285,286],[15,72895,72897,72936],{"className":72896},[290],[15,72898,72900,72914,72922],{"className":72899,"style":2524},[294],[15,72901,72902,72905],{"style":2527},[15,72903],{"className":72904,"style":461},[302],[15,72906,72908],{"className":72907},[307,308,309,310],[15,72909,72911],{"className":72910},[59,310],[15,72912,2463],{"className":72913},[59,310],[15,72915,72916,72919],{"style":473},[15,72917],{"className":72918,"style":461},[302],[15,72920],{"className":72921,"style":481},[480],[15,72923,72924,72927],{"style":2550},[15,72925],{"className":72926,"style":461},[302],[15,72928,72930],{"className":72929},[307,308,309,310],[15,72931,72933],{"className":72932},[59,310],[15,72934,117],{"className":72935},[59,310],[15,72937,318],{"className":72938},[317],[15,72940,72942],{"className":72941},[290],[15,72943,72945],{"className":72944,"style":2572},[294],[15,72946],{},[15,72948],{"className":72949},[153,441]," 时第二段严格递增，上确界为 ",[15,72952,72954,72969],{"className":72953,"translate":19},[18],[15,72955,72957],{"className":72956},[23],[25,72958,72959],{"xmlns":27},[29,72960,72961,72967],{},[32,72962,72963,72965],{},[110,72964,2470],{},[35,72966,1024],{"mathvariant":209},[39,72968,4241],{"encoding":41},[15,72970,72972],{"className":72971,"ariaHidden":46},[45],[15,72973,72975,72978,72981],{"className":72974},[50],[15,72976],{"className":72977,"style":4251},[54],[15,72979,2470],{"className":72980},[59],[15,72982,1024],{"className":72983},[59],[15,72985,72987,73011],{"className":72986,"translate":19},[18],[15,72988,72990],{"className":72989},[23],[25,72991,72992],{"xmlns":27},[29,72993,72994,73008],{},[32,72995,72996,72998,73000,73002],{},[35,72997,40237],{},[110,72999,7251],{},[110,73001,4813],{},[238,73003,73004,73006],{},[115,73005,117],{},[115,73007,2463],{},[39,73009,73010],{"encoding":41},"y\u003C-\\frac12",[15,73012,73014,73032],{"className":73013,"ariaHidden":46},[45],[15,73015,73017,73020,73023,73026,73029],{"className":73016},[50],[15,73018],{"className":73019,"style":31692},[54],[15,73021,40237],{"className":73022,"style":981},[59,60],[15,73024],{"className":73025,"style":158},[157],[15,73027,7251],{"className":73028},[162],[15,73030],{"className":73031,"style":158},[157],[15,73033,73035,73038,73041],{"className":73034},[50],[15,73036],{"className":73037,"style":2505},[54],[15,73039,4813],{"className":73040},[59],[15,73042,73044,73047,73106],{"className":73043},[59],[15,73045],{"className":73046},[146,441],[15,73048,73050],{"className":73049},[238],[15,73051,73053,73098],{"className":73052},[285,286],[15,73054,73056,73095],{"className":73055},[290],[15,73057,73059,73073,73081],{"className":73058,"style":2524},[294],[15,73060,73061,73064],{"style":2527},[15,73062],{"className":73063,"style":461},[302],[15,73065,73067],{"className":73066},[307,308,309,310],[15,73068,73070],{"className":73069},[59,310],[15,73071,2463],{"className":73072},[59,310],[15,73074,73075,73078],{"style":473},[15,73076],{"className":73077,"style":461},[302],[15,73079],{"className":73080,"style":481},[480],[15,73082,73083,73086],{"style":2550},[15,73084],{"className":73085,"style":461},[302],[15,73087,73089],{"className":73088},[307,308,309,310],[15,73090,73092],{"className":73091},[59,310],[15,73093,117],{"className":73094},[59,310],[15,73096,318],{"className":73097},[317],[15,73099,73101],{"className":73100},[290],[15,73102,73104],{"className":73103,"style":2572},[294],[15,73105],{},[15,73107],{"className":73108},[153,441]," 时第一段严格递减，上确界在 ",[15,73111,73113,73131],{"className":73112,"translate":19},[18],[15,73114,73116],{"className":73115},[23],[25,73117,73118],{"xmlns":27},[29,73119,73120,73128],{},[32,73121,73122,73124,73126],{},[35,73123,769],{},[110,73125,123],{},[115,73127,126],{},[39,73129,73130],{"encoding":41},"t=0",[15,73132,73134,73152],{"className":73133,"ariaHidden":46},[45],[15,73135,73137,73140,73143,73146,73149],{"className":73136},[50],[15,73138],{"className":73139,"style":5343},[54],[15,73141,769],{"className":73142},[59,60],[15,73144],{"className":73145,"style":158},[157],[15,73147,123],{"className":73148},[162],[15,73150],{"className":73151,"style":158},[157],[15,73153,73155,73158],{"className":73154},[50],[15,73156],{"className":73157,"style":172},[54],[15,73159,126],{"className":73160},[59],[15,73162,73164,73184],{"className":73163,"translate":19},[18],[15,73165,73167],{"className":73166},[23],[25,73168,73169],{"xmlns":27},[29,73170,73171,73181],{},[32,73172,73173,73175],{},[110,73174,4813],{},[238,73176,73177,73179],{},[115,73178,117],{},[115,73180,2463],{},[39,73182,73183],{"encoding":41},"-\\frac12",[15,73185,73187],{"className":73186,"ariaHidden":46},[45],[15,73188,73190,73193,73196],{"className":73189},[50],[15,73191],{"className":73192,"style":2505},[54],[15,73194,4813],{"className":73195},[59],[15,73197,73199,73202,73261],{"className":73198},[59],[15,73200],{"className":73201},[146,441],[15,73203,73205],{"className":73204},[238],[15,73206,73208,73253],{"className":73207},[285,286],[15,73209,73211,73250],{"className":73210},[290],[15,73212,73214,73228,73236],{"className":73213,"style":2524},[294],[15,73215,73216,73219],{"style":2527},[15,73217],{"className":73218,"style":461},[302],[15,73220,73222],{"className":73221},[307,308,309,310],[15,73223,73225],{"className":73224},[59,310],[15,73226,2463],{"className":73227},[59,310],[15,73229,73230,73233],{"style":473},[15,73231],{"className":73232,"style":461},[302],[15,73234],{"className":73235,"style":481},[480],[15,73237,73238,73241],{"style":2550},[15,73239],{"className":73240,"style":461},[302],[15,73242,73244],{"className":73243},[307,308,309,310],[15,73245,73247],{"className":73246},[59,310],[15,73248,117],{"className":73249},[59,310],[15,73251,318],{"className":73252},[317],[15,73254,73256],{"className":73255},[290],[15,73257,73259],{"className":73258,"style":2572},[294],[15,73260],{},[15,73262],{"className":73263},[153,441],"。于是",[15,73266,73268],{"className":73267,"translate":19},[180],[15,73269,73271,73407],{"className":73270,"translate":19},[18],[15,73272,73274],{"className":73273},[23],[25,73275,73276],{"xmlns":27,"display":189},[29,73277,73278,73404],{},[32,73279,73280,73286,73288,73290,73292,73294],{},[6814,73281,73282,73284],{},[35,73283,37],{},[110,73285,7573],{},[110,73287,113],{"stretchy":112},[35,73289,40237],{},[110,73291,120],{"stretchy":112},[110,73293,123],{},[32,73295,73296,73298],{},[110,73297,2898],{"fence":46},[1243,73299,73300,73334,73372],{"rowspacing":4313,"columnalign":4314,"columnspacing":4315},[1249,73301,73302,73312],{},[1252,73303,73304],{},[1255,73305,73306],{"scriptlevel":126,"displaystyle":112},[32,73307,73308,73310],{},[35,73309,40237],{},[110,73311,551],{"separator":46},[1252,73313,73314],{},[1255,73315,73316],{"scriptlevel":126,"displaystyle":112},[32,73317,73318,73320,73322,73324,73326,73332],{},[110,73319,4808],{"stretchy":112},[35,73321,40237],{},[110,73323,4808],{"stretchy":112},[110,73325,9952],{},[238,73327,73328,73330],{},[115,73329,117],{},[115,73331,2463],{},[110,73333,551],{"separator":46},[1249,73335,73336,73352],{},[1252,73337,73338],{},[1255,73339,73340],{"scriptlevel":126,"displaystyle":112},[32,73341,73342,73344,73350],{},[110,73343,4813],{},[238,73345,73346,73348],{},[115,73347,117],{},[115,73349,2463],{},[110,73351,551],{"separator":46},[1252,73353,73354],{},[1255,73355,73356],{"scriptlevel":126,"displaystyle":112},[32,73357,73358,73360,73362,73364,73370],{},[35,73359,40237],{},[110,73361,9952],{},[110,73363,4813],{},[238,73365,73366,73368],{},[115,73367,117],{},[115,73369,2463],{},[110,73371,551],{"separator":46},[1249,73373,73374,73386],{},[1252,73375,73376],{},[1255,73377,73378],{"scriptlevel":126,"displaystyle":112},[32,73379,73380,73382,73384],{},[110,73381,2470],{},[35,73383,1024],{"mathvariant":209},[110,73385,551],{"separator":46},[1252,73387,73388],{},[1255,73389,73390],{"scriptlevel":126,"displaystyle":112},[32,73391,73392,73394,73396,73402],{},[35,73393,40237],{},[110,73395,2903],{},[238,73397,73398,73400],{},[115,73399,117],{},[115,73401,2463],{},[35,73403,4375],{"mathvariant":209},[39,73405,73406],{"encoding":41},"f^*(y)=\n\\begin{cases}\ny, & \\lvert y\\rvert\\le\\frac12,\\\\[2pt]\n-\\frac12, & y\\le-\\frac12,\\\\[2pt]\n+\\infty, & y>\\frac12.\n\\end{cases}",[15,73408,73410,73463],{"className":73409,"ariaHidden":46},[45],[15,73411,73413,73416,73445,73448,73451,73454,73457,73460],{"className":73412},[50],[15,73414],{"className":73415,"style":139},[54],[15,73417,73419,73422],{"className":73418},[59],[15,73420,37],{"className":73421,"style":61},[59,60],[15,73423,73425],{"className":73424},[281],[15,73426,73428],{"className":73427},[285],[15,73429,73431],{"className":73430},[290],[15,73432,73434],{"className":73433,"style":8248},[294],[15,73435,73436,73439],{"style":8277},[15,73437],{"className":73438,"style":303},[302],[15,73440,73442],{"className":73441},[307,308,309,310],[15,73443,7573],{"className":73444},[2591,310],[15,73446,113],{"className":73447},[146],[15,73449,40237],{"className":73450,"style":981},[59,60],[15,73452,120],{"className":73453},[153],[15,73455],{"className":73456,"style":158},[157],[15,73458,123],{"className":73459},[162],[15,73461],{"className":73462,"style":158},[157],[15,73464,73466,73470],{"className":73465},[50],[15,73467],{"className":73468,"style":73469},[54],"height:4.8em;vertical-align:-2.15em;",[15,73471,73473,73570,74025],{"className":73472},[410],[15,73474,73476],{"className":73475},[146],[15,73477,73479],{"className":73478},[419,14829],[15,73480,73482,73561],{"className":73481},[285,286],[15,73483,73485,73558],{"className":73484},[290],[15,73486,73489,73503,73522,73534,73546],{"className":73487,"style":73488},[294],"height:2.65em;",[15,73490,73492,73495],{"style":73491},"top:-1.9em;",[15,73493],{"className":73494,"style":17588},[302],[15,73496,73500],{"className":73497},[73498,73499],"delimsizinginner","delim-size4",[15,73501,73502],{},"⎩",[15,73504,73506,73509],{"style":73505},"top:-1.892em;",[15,73507],{"className":73508,"style":17588},[302],[15,73510,73512],{"style":73511},"height:0.616em;width:0.8889em;",[6323,73513,73519],{"xmlns":6325,"width":73514,"height":73515,"style":73516,"viewBox":73517,"preserveAspectRatio":73518},"0.8889em","0.616em","width:0.8889em","0 0 888.89 616","xMinYMin",[6331,73520],{"d":73521},"M384 0 H504 V616 H384z M384 0 H504 V616 H384z",[15,73523,73525,73528],{"style":73524},"top:-3.15em;",[15,73526],{"className":73527,"style":17588},[302],[15,73529,73531],{"className":73530},[73498,73499],[15,73532,73533],{},"⎨",[15,73535,73537,73540],{"style":73536},"top:-4.292em;",[15,73538],{"className":73539,"style":17588},[302],[15,73541,73542],{"style":73511},[6323,73543,73544],{"xmlns":6325,"width":73514,"height":73515,"style":73516,"viewBox":73517,"preserveAspectRatio":73518},[6331,73545],{"d":73521},[15,73547,73549,73552],{"style":73548},"top:-4.9em;",[15,73550],{"className":73551,"style":17588},[302],[15,73553,73555],{"className":73554},[73498,73499],[15,73556,73557],{},"⎧",[15,73559,318],{"className":73560},[317],[15,73562,73564],{"className":73563},[290],[15,73565,73568],{"className":73566,"style":73567},[294],"height:2.15em;",[15,73569],{},[15,73571,73573],{"className":73572},[59],[15,73574,73576,73717,73720],{"className":73575},[1243],[15,73577,73579],{"className":73578},[1451],[15,73580,73582,73708],{"className":73581},[285,286],[15,73583,73585,73705],{"className":73584},[290],[15,73586,73589,73604,73687],{"className":73587,"style":73588},[294],"height:2.61em;",[15,73590,73592,73595],{"style":73591},"top:-4.61em;",[15,73593],{"className":73594,"style":4573},[302],[15,73596,73598,73601],{"className":73597},[59],[15,73599,40237],{"className":73600,"style":981},[59,60],[15,73602,551],{"className":73603},[573],[15,73605,73607,73610],{"style":73606},"top:-2.97em;",[15,73608],{"className":73609,"style":4573},[302],[15,73611,73613,73616,73684],{"className":73612},[59],[15,73614,4813],{"className":73615},[59],[15,73617,73619,73622,73681],{"className":73618},[59],[15,73620],{"className":73621},[146,441],[15,73623,73625],{"className":73624},[238],[15,73626,73628,73673],{"className":73627},[285,286],[15,73629,73631,73670],{"className":73630},[290],[15,73632,73634,73648,73656],{"className":73633,"style":2524},[294],[15,73635,73636,73639],{"style":2527},[15,73637],{"className":73638,"style":461},[302],[15,73640,73642],{"className":73641},[307,308,309,310],[15,73643,73645],{"className":73644},[59,310],[15,73646,2463],{"className":73647},[59,310],[15,73649,73650,73653],{"style":473},[15,73651],{"className":73652,"style":461},[302],[15,73654],{"className":73655,"style":481},[480],[15,73657,73658,73661],{"style":2550},[15,73659],{"className":73660,"style":461},[302],[15,73662,73664],{"className":73663},[307,308,309,310],[15,73665,73667],{"className":73666},[59,310],[15,73668,117],{"className":73669},[59,310],[15,73671,318],{"className":73672},[317],[15,73674,73676],{"className":73675},[290],[15,73677,73679],{"className":73678,"style":2572},[294],[15,73680],{},[15,73682],{"className":73683},[153,441],[15,73685,551],{"className":73686},[573],[15,73688,73690,73693],{"style":73689},"top:-1.33em;",[15,73691],{"className":73692,"style":4573},[302],[15,73694,73696,73699,73702],{"className":73695},[59],[15,73697,2470],{"className":73698},[59],[15,73700,1024],{"className":73701},[59],[15,73703,551],{"className":73704},[573],[15,73706,318],{"className":73707},[317],[15,73709,73711],{"className":73710},[290],[15,73712,73715],{"className":73713,"style":73714},[294],"height:2.11em;",[15,73716],{},[15,73718],{"className":73719,"style":4622},[4621],[15,73721,73723],{"className":73722},[1451],[15,73724,73726,74017],{"className":73725},[285,286],[15,73727,73729,74014],{"className":73728},[290],[15,73730,73732,73829,73923],{"className":73731,"style":73588},[294],[15,73733,73734,73737],{"style":73591},[15,73735],{"className":73736,"style":4573},[302],[15,73738,73740,73743,73746,73749,73752,73755,73758,73826],{"className":73739},[59],[15,73741,4808],{"className":73742},[146],[15,73744,40237],{"className":73745,"style":981},[59,60],[15,73747,4808],{"className":73748},[153],[15,73750],{"className":73751,"style":158},[157],[15,73753,9952],{"className":73754},[162],[15,73756],{"className":73757,"style":158},[157],[15,73759,73761,73764,73823],{"className":73760},[59],[15,73762],{"className":73763},[146,441],[15,73765,73767],{"className":73766},[238],[15,73768,73770,73815],{"className":73769},[285,286],[15,73771,73773,73812],{"className":73772},[290],[15,73774,73776,73790,73798],{"className":73775,"style":2524},[294],[15,73777,73778,73781],{"style":2527},[15,73779],{"className":73780,"style":461},[302],[15,73782,73784],{"className":73783},[307,308,309,310],[15,73785,73787],{"className":73786},[59,310],[15,73788,2463],{"className":73789},[59,310],[15,73791,73792,73795],{"style":473},[15,73793],{"className":73794,"style":461},[302],[15,73796],{"className":73797,"style":481},[480],[15,73799,73800,73803],{"style":2550},[15,73801],{"className":73802,"style":461},[302],[15,73804,73806],{"className":73805},[307,308,309,310],[15,73807,73809],{"className":73808},[59,310],[15,73810,117],{"className":73811},[59,310],[15,73813,318],{"className":73814},[317],[15,73816,73818],{"className":73817},[290],[15,73819,73821],{"className":73820,"style":2572},[294],[15,73822],{},[15,73824],{"className":73825},[153,441],[15,73827,551],{"className":73828},[573],[15,73830,73831,73834],{"style":73606},[15,73832],{"className":73833,"style":4573},[302],[15,73835,73837,73840,73843,73846,73849,73852,73920],{"className":73836},[59],[15,73838,40237],{"className":73839,"style":981},[59,60],[15,73841],{"className":73842,"style":158},[157],[15,73844,9952],{"className":73845},[162],[15,73847],{"className":73848,"style":158},[157],[15,73850,4813],{"className":73851},[59],[15,73853,73855,73858,73917],{"className":73854},[59],[15,73856],{"className":73857},[146,441],[15,73859,73861],{"className":73860},[238],[15,73862,73864,73909],{"className":73863},[285,286],[15,73865,73867,73906],{"className":73866},[290],[15,73868,73870,73884,73892],{"className":73869,"style":2524},[294],[15,73871,73872,73875],{"style":2527},[15,73873],{"className":73874,"style":461},[302],[15,73876,73878],{"className":73877},[307,308,309,310],[15,73879,73881],{"className":73880},[59,310],[15,73882,2463],{"className":73883},[59,310],[15,73885,73886,73889],{"style":473},[15,73887],{"className":73888,"style":461},[302],[15,73890],{"className":73891,"style":481},[480],[15,73893,73894,73897],{"style":2550},[15,73895],{"className":73896,"style":461},[302],[15,73898,73900],{"className":73899},[307,308,309,310],[15,73901,73903],{"className":73902},[59,310],[15,73904,117],{"className":73905},[59,310],[15,73907,318],{"className":73908},[317],[15,73910,73912],{"className":73911},[290],[15,73913,73915],{"className":73914,"style":2572},[294],[15,73916],{},[15,73918],{"className":73919},[153,441],[15,73921,551],{"className":73922},[573],[15,73924,73925,73928],{"style":73689},[15,73926],{"className":73927,"style":4573},[302],[15,73929,73931,73934,73937,73940,73943,74011],{"className":73930},[59],[15,73932,40237],{"className":73933,"style":981},[59,60],[15,73935],{"className":73936,"style":158},[157],[15,73938,2903],{"className":73939},[162],[15,73941],{"className":73942,"style":158},[157],[15,73944,73946,73949,74008],{"className":73945},[59],[15,73947],{"className":73948},[146,441],[15,73950,73952],{"className":73951},[238],[15,73953,73955,74000],{"className":73954},[285,286],[15,73956,73958,73997],{"className":73957},[290],[15,73959,73961,73975,73983],{"className":73960,"style":2524},[294],[15,73962,73963,73966],{"style":2527},[15,73964],{"className":73965,"style":461},[302],[15,73967,73969],{"className":73968},[307,308,309,310],[15,73970,73972],{"className":73971},[59,310],[15,73973,2463],{"className":73974},[59,310],[15,73976,73977,73980],{"style":473},[15,73978],{"className":73979,"style":461},[302],[15,73981],{"className":73982,"style":481},[480],[15,73984,73985,73988],{"style":2550},[15,73986],{"className":73987,"style":461},[302],[15,73989,73991],{"className":73990},[307,308,309,310],[15,73992,73994],{"className":73993},[59,310],[15,73995,117],{"className":73996},[59,310],[15,73998,318],{"className":73999},[317],[15,74001,74003],{"className":74002},[290],[15,74004,74006],{"className":74005,"style":2572},[294],[15,74007],{},[15,74009],{"className":74010},[153,441],[15,74012,4375],{"className":74013},[59],[15,74015,318],{"className":74016},[317],[15,74018,74020],{"className":74019},[290],[15,74021,74023],{"className":74022,"style":73714},[294],[15,74024],{},[15,74026],{"className":74027},[153,441],[11,74029,74030],{},"这正对应经典表示",[15,74032,74034],{"className":74033,"translate":19},[180],[15,74035,74037,74125],{"className":74036,"translate":19},[18],[15,74038,74040],{"className":74039},[23],[25,74041,74042],{"xmlns":27,"display":189},[29,74043,74044,74122],{},[32,74045,74046,74056,74058,74060,74062,74064,74066,74068,74092,74094,74100,74102,74104,74106,74108,74114,74116,74118,74120],{},[195,74047,74048,74050],{},[35,74049,199],{},[32,74051,74052,74054],{},[35,74053,5392],{},[35,74055,34850],{},[110,74057,113],{"stretchy":112},[35,74059,206],{},[110,74061,551],{"separator":46},[35,74063,213],{},[110,74065,120],{"stretchy":112},[110,74067,123],{},[6016,74069,74070,74076],{},[32,74071,74072,74074],{},[35,74073,35432],{},[110,74075,4103],{},[32,74077,74078,74080,74082,74088,74090],{},[110,74079,210],{"stretchy":112},[35,74081,4158],{},[195,74083,74084,74086],{},[110,74085,210],{"stretchy":112},[35,74087,1024],{"mathvariant":209},[110,74089,9952],{},[115,74091,117],{},[110,74093,2898],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,74095,74096,74098],{},[35,74097,223],{"mathvariant":222},[35,74099,206],{},[110,74101,230],{"stretchy":112},[35,74103,4158],{},[110,74105,257],{"stretchy":112},[110,74107,4813],{},[195,74109,74110,74112],{},[35,74111,223],{"mathvariant":222},[35,74113,213],{},[110,74115,230],{"stretchy":112},[35,74117,4158],{},[110,74119,257],{"stretchy":112},[110,74121,2908],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[39,74123,74124],{"encoding":41},"D_{TV}(P,Q)=\\sup_{\\lVert g\\rVert_\\infty\\le1}\n\\big\\{\\mathbb E_P[g]-\\mathbb E_Q[g]\\big\\}",[15,74126,74128,74207,74381],{"className":74127,"ariaHidden":46},[45],[15,74129,74131,74134,74180,74183,74186,74189,74192,74195,74198,74201,74204],{"className":74130},[50],[15,74132],{"className":74133,"style":139},[54],[15,74135,74137,74140],{"className":74136},[59],[15,74138,199],{"className":74139,"style":277},[59,60],[15,74141,74143],{"className":74142},[281],[15,74144,74146,74172],{"className":74145},[285,286],[15,74147,74149,74169],{"className":74148},[290],[15,74150,74152],{"className":74151,"style":379},[294],[15,74153,74154,74157],{"style":298},[15,74155],{"className":74156,"style":303},[302],[15,74158,74160],{"className":74159},[307,308,309,310],[15,74161,74163,74166],{"className":74162},[59,310],[15,74164,5392],{"className":74165,"style":334},[59,60,310],[15,74167,34850],{"className":74168,"style":2587},[59,60,310],[15,74170,318],{"className":74171},[317],[15,74173,74175],{"className":74174},[290],[15,74176,74178],{"className":74177,"style":7968},[294],[15,74179],{},[15,74181,113],{"className":74182},[146],[15,74184,206],{"className":74185,"style":334},[59,60],[15,74187,551],{"className":74188},[573],[15,74190],{"className":74191,"style":406},[157],[15,74193,213],{"className":74194},[59,60],[15,74196,120],{"className":74197},[153],[15,74199],{"className":74200,"style":158},[157],[15,74202,123],{"className":74203},[162],[15,74205],{"className":74206,"style":158},[157],[15,74208,74210,74214,74314,74317,74323,74363,74366,74369,74372,74375,74378],{"className":74209},[50],[15,74211],{"className":74212,"style":74213},[54],"height:2.0104em;vertical-align:-1.1604em;",[15,74215,74217],{"className":74216},[1484,13716],[15,74218,74220,74305],{"className":74219},[285,286],[15,74221,74223,74302],{"className":74222},[290],[15,74224,74226,74292],{"className":74225,"style":2345},[294],[15,74227,74229,74232],{"style":74228},"top:-2.1146em;margin-left:0em;",[15,74230],{"className":74231,"style":461},[302],[15,74233,74235],{"className":74234},[307,308,309,310],[15,74236,74238,74241,74244,74286,74289],{"className":74237},[59,310],[15,74239,210],{"className":74240},[146,310],[15,74242,4158],{"className":74243,"style":981},[59,60,310],[15,74245,74247,74250],{"className":74246},[153,310],[15,74248,210],{"className":74249},[153,310],[15,74251,74253],{"className":74252},[281],[15,74254,74256,74278],{"className":74255},[285,286],[15,74257,74259,74275],{"className":74258},[290],[15,74260,74263],{"className":74261,"style":74262},[294],"height:0.1645em;",[15,74264,74266,74269],{"style":74265},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[15,74267],{"className":74268,"style":30206},[302],[15,74270,74272],{"className":74271},[307,30210,9674,310],[15,74273,1024],{"className":74274},[59,310],[15,74276,318],{"className":74277},[317],[15,74279,74281],{"className":74280},[290],[15,74282,74284],{"className":74283,"style":39770},[294],[15,74285],{},[15,74287,9952],{"className":74288},[162,310],[15,74290,117],{"className":74291},[59,310],[15,74293,74294,74297],{"style":11863},[15,74295],{"className":74296,"style":461},[302],[15,74298,74299],{},[15,74300,35432],{"className":74301},[1484],[15,74303,318],{"className":74304},[317],[15,74306,74308],{"className":74307},[290],[15,74309,74312],{"className":74310,"style":74311},[294],"height:1.1604em;",[15,74313],{},[15,74315],{"className":74316,"style":406},[157],[15,74318,74320],{"className":74319},[59],[15,74321,2898],{"className":74322},[419,9674],[15,74324,74326,74329],{"className":74325},[59],[15,74327,223],{"className":74328},[59,366],[15,74330,74332],{"className":74331},[281],[15,74333,74335,74355],{"className":74334},[285,286],[15,74336,74338,74352],{"className":74337},[290],[15,74339,74341],{"className":74340,"style":379},[294],[15,74342,74343,74346],{"style":382},[15,74344],{"className":74345,"style":303},[302],[15,74347,74349],{"className":74348},[307,308,309,310],[15,74350,206],{"className":74351,"style":334},[59,60,310],[15,74353,318],{"className":74354},[317],[15,74356,74358],{"className":74357},[290],[15,74359,74361],{"className":74360,"style":7968},[294],[15,74362],{},[15,74364,230],{"className":74365},[146],[15,74367,4158],{"className":74368,"style":981},[59,60],[15,74370,257],{"className":74371},[153],[15,74373],{"className":74374,"style":2587},[157],[15,74376,4813],{"className":74377},[2591],[15,74379],{"className":74380,"style":2587},[157],[15,74382,74384,74387,74427,74430,74433,74436],{"className":74383},[50],[15,74385],{"className":74386,"style":20563},[54],[15,74388,74390,74393],{"className":74389},[59],[15,74391,223],{"className":74392},[59,366],[15,74394,74396],{"className":74395},[281],[15,74397,74399,74419],{"className":74398},[285,286],[15,74400,74402,74416],{"className":74401},[290],[15,74403,74405],{"className":74404,"style":379},[294],[15,74406,74407,74410],{"style":382},[15,74408],{"className":74409,"style":303},[302],[15,74411,74413],{"className":74412},[307,308,309,310],[15,74414,213],{"className":74415},[59,60,310],[15,74417,318],{"className":74418},[317],[15,74420,74422],{"className":74421},[290],[15,74423,74425],{"className":74424,"style":325},[294],[15,74426],{},[15,74428,230],{"className":74429},[146],[15,74431,4158],{"className":74432,"style":981},[59,60],[15,74434,257],{"className":74435},[153],[15,74437,74439],{"className":74438},[59],[15,74440,2908],{"className":74441},[419,9674],[11,74443,74444],{},"的 Kantorovich 型对偶。",[11,74446,74447],{},"这个对偶表示在机器学习中非常有用，例如 f-GAN 就是基于此构造的（第 5 节详述）。",[2311,74449,74451],{"id":74450},"_45-数据处理不等式","4.5 数据处理不等式",[993,74453,74455,74555],{"title":74454},"命题 4.4（数据处理不等式）",[11,74456,534,74457,74485,74486,5645,74520,74554],{},[15,74458,74460,74473],{"className":74459,"translate":19},[18],[15,74461,74463],{"className":74462},[23],[25,74464,74465],{"xmlns":27},[29,74466,74467,74471],{},[32,74468,74469],{},[35,74470,10694],{},[39,74472,10694],{"encoding":41},[15,74474,74476],{"className":74475,"ariaHidden":46},[45],[15,74477,74479,74482],{"className":74478},[50],[15,74480],{"className":74481,"style":664},[54],[15,74483,10694],{"className":74484,"style":10782},[59,60]," 是一个马尔可夫核（随机变换），记 ",[15,74487,74489,74505],{"className":74488,"translate":19},[18],[15,74490,74492],{"className":74491},[23],[25,74493,74494],{"xmlns":27},[29,74495,74496,74502],{},[32,74497,74498,74500],{},[35,74499,206],{},[35,74501,10694],{},[39,74503,74504],{"encoding":41},"PK",[15,74506,74508],{"className":74507,"ariaHidden":46},[45],[15,74509,74511,74514,74517],{"className":74510},[50],[15,74512],{"className":74513,"style":664},[54],[15,74515,206],{"className":74516,"style":334},[59,60],[15,74518,10694],{"className":74519,"style":10782},[59,60],[15,74521,74523,74539],{"className":74522,"translate":19},[18],[15,74524,74526],{"className":74525},[23],[25,74527,74528],{"xmlns":27},[29,74529,74530,74536],{},[32,74531,74532,74534],{},[35,74533,213],{},[35,74535,10694],{},[39,74537,74538],{"encoding":41},"QK",[15,74540,74542],{"className":74541,"ariaHidden":46},[45],[15,74543,74545,74548,74551],{"className":74544},[50],[15,74546],{"className":74547,"style":566},[54],[15,74549,213],{"className":74550},[59,60],[15,74552,10694],{"className":74553,"style":10782},[59,60]," 为输出分布，则",[15,74556,74558],{"className":74557,"translate":19},[180],[15,74559,74561,74613],{"className":74560,"translate":19},[18],[15,74562,74564],{"className":74563},[23],[25,74565,74566],{"xmlns":27,"display":189},[29,74567,74568,74610],{},[32,74569,74570,74576,74578,74580,74582,74584,74586,74588,74590,74592,74598,74600,74602,74604,74606,74608],{},[195,74571,74572,74574],{},[35,74573,199],{},[35,74575,37],{},[110,74577,113],{"stretchy":112},[35,74579,206],{},[35,74581,10694],{},[35,74583,210],{"mathvariant":209},[35,74585,213],{},[35,74587,10694],{},[110,74589,120],{"stretchy":112},[110,74591,9952],{},[195,74593,74594,74596],{},[35,74595,199],{},[35,74597,37],{},[110,74599,113],{"stretchy":112},[35,74601,206],{},[35,74603,210],{"mathvariant":209},[35,74605,213],{},[110,74607,120],{"stretchy":112},[35,74609,4375],{"mathvariant":209},[39,74611,74612],{"encoding":41},"D_f(PK\\|QK)\\le D_f(P\\|Q).",[15,74614,74616,74692],{"className":74615,"ariaHidden":46},[45],[15,74617,74619,74622,74662,74665,74668,74671,74674,74677,74680,74683,74686,74689],{"className":74618},[50],[15,74620],{"className":74621,"style":270},[54],[15,74623,74625,74628],{"className":74624},[59],[15,74626,199],{"className":74627,"style":277},[59,60],[15,74629,74631],{"className":74630},[281],[15,74632,74634,74654],{"className":74633},[285,286],[15,74635,74637,74651],{"className":74636},[290],[15,74638,74640],{"className":74639,"style":295},[294],[15,74641,74642,74645],{"style":298},[15,74643],{"className":74644,"style":303},[302],[15,74646,74648],{"className":74647},[307,308,309,310],[15,74649,37],{"className":74650,"style":61},[59,60,310],[15,74652,318],{"className":74653},[317],[15,74655,74657],{"className":74656},[290],[15,74658,74660],{"className":74659,"style":325},[294],[15,74661],{},[15,74663,113],{"className":74664},[146],[15,74666,206],{"className":74667,"style":334},[59,60],[15,74669,10694],{"className":74670,"style":10782},[59,60],[15,74672,210],{"className":74673},[59],[15,74675,213],{"className":74676},[59,60],[15,74678,10694],{"className":74679,"style":10782},[59,60],[15,74681,120],{"className":74682},[153],[15,74684],{"className":74685,"style":158},[157],[15,74687,9952],{"className":74688},[162],[15,74690],{"className":74691,"style":158},[157],[15,74693,74695,74698,74738,74741,74744,74747,74750,74753],{"className":74694},[50],[15,74696],{"className":74697,"style":270},[54],[15,74699,74701,74704],{"className":74700},[59],[15,74702,199],{"className":74703,"style":277},[59,60],[15,74705,74707],{"className":74706},[281],[15,74708,74710,74730],{"className":74709},[285,286],[15,74711,74713,74727],{"className":74712},[290],[15,74714,74716],{"className":74715,"style":295},[294],[15,74717,74718,74721],{"style":298},[15,74719],{"className":74720,"style":303},[302],[15,74722,74724],{"className":74723},[307,308,309,310],[15,74725,37],{"className":74726,"style":61},[59,60,310],[15,74728,318],{"className":74729},[317],[15,74731,74733],{"className":74732},[290],[15,74734,74736],{"className":74735,"style":325},[294],[15,74737],{},[15,74739,113],{"className":74740},[146],[15,74742,206],{"className":74743,"style":334},[59,60],[15,74745,210],{"className":74746},[59],[15,74748,213],{"className":74749},[59,60],[15,74751,120],{"className":74752},[153],[15,74754,4375],{"className":74755},[59],[11,74757,74758,11060,74761,2745,74817,2745,74867,55740,74953,75003,75004,75065,75066,9400],{},[1225,74759,74760],{},"证明（条件 Jensen）。",[15,74762,74764,74784],{"className":74763,"translate":19},[18],[15,74765,74767],{"className":74766},[23],[25,74768,74769],{"xmlns":27},[29,74770,74771,74781],{},[32,74772,74773,74775,74777,74779],{},[35,74774,5401],{},[110,74776,8869],{},[35,74778,213],{},[35,74780,10694],{},[39,74782,74783],{"encoding":41},"Y\\sim QK",[15,74785,74787,74805],{"className":74786,"ariaHidden":46},[45],[15,74788,74790,74793,74796,74799,74802],{"className":74789},[50],[15,74791],{"className":74792,"style":664},[54],[15,74794,5401],{"className":74795,"style":2587},[59,60],[15,74797],{"className":74798,"style":158},[157],[15,74800,8869],{"className":74801},[162],[15,74803],{"className":74804,"style":158},[157],[15,74806,74808,74811,74814],{"className":74807},[50],[15,74809],{"className":74810,"style":566},[54],[15,74812,213],{"className":74813},[59,60],[15,74815,10694],{"className":74816,"style":10782},[59,60],[15,74818,74820,74837],{"className":74819,"translate":19},[18],[15,74821,74823],{"className":74822},[23],[25,74824,74825],{"xmlns":27},[29,74826,74827,74835],{},[32,74828,74829,74831,74833],{},[35,74830,598],{},[110,74832,8869],{},[35,74834,213],{},[39,74836,8874],{"encoding":41},[15,74838,74840,74858],{"className":74839,"ariaHidden":46},[45],[15,74841,74843,74846,74849,74852,74855],{"className":74842},[50],[15,74844],{"className":74845,"style":664},[54],[15,74847,598],{"className":74848,"style":8887},[59,60],[15,74850],{"className":74851,"style":158},[157],[15,74853,8869],{"className":74854},[162],[15,74856],{"className":74857,"style":158},[157],[15,74859,74861,74864],{"className":74860},[50],[15,74862],{"className":74863,"style":566},[54],[15,74865,213],{"className":74866},[59,60],[15,74868,74870,74902],{"className":74869,"translate":19},[18],[15,74871,74873],{"className":74872},[23],[25,74874,74875],{"xmlns":27},[29,74876,74877,74899],{},[32,74878,74879,74881,74883,74885,74887,74889,74891,74893,74895,74897],{},[35,74880,5401],{},[35,74882,4808],{"mathvariant":209},[35,74884,598],{},[110,74886,8869],{},[35,74888,10694],{},[110,74890,113],{"stretchy":112},[110,74892,3299],{},[35,74894,4808],{"mathvariant":209},[35,74896,598],{},[110,74898,120],{"stretchy":112},[39,74900,74901],{"encoding":41},"Y|X\\sim K(\\cdot|X)",[15,74903,74905,74929],{"className":74904,"ariaHidden":46},[45],[15,74906,74908,74911,74914,74917,74920,74923,74926],{"className":74907},[50],[15,74909],{"className":74910,"style":139},[54],[15,74912,5401],{"className":74913,"style":2587},[59,60],[15,74915,4808],{"className":74916},[59],[15,74918,598],{"className":74919,"style":8887},[59,60],[15,74921],{"className":74922,"style":158},[157],[15,74924,8869],{"className":74925},[162],[15,74927],{"className":74928,"style":158},[157],[15,74930,74932,74935,74938,74941,74944,74947,74950],{"className":74931},[50],[15,74933],{"className":74934,"style":139},[54],[15,74936,10694],{"className":74937,"style":10782},[59,60],[15,74939,113],{"className":74940},[146],[15,74942,3299],{"className":74943},[59],[15,74945,4808],{"className":74946},[59],[15,74948,598],{"className":74949,"style":8887},[59,60],[15,74951,120],{"className":74952},[153],[15,74954,74956,74973],{"className":74955,"translate":19},[18],[15,74957,74959],{"className":74958},[23],[25,74960,74961],{"xmlns":27},[29,74962,74963,74971],{},[32,74964,74965,74967,74969],{},[35,74966,206],{},[110,74968,714],{},[35,74970,213],{},[39,74972,719],{"encoding":41},[15,74974,74976,74994],{"className":74975,"ariaHidden":46},[45],[15,74977,74979,74982,74985,74988,74991],{"className":74978},[50],[15,74980],{"className":74981,"style":729},[54],[15,74983,206],{"className":74984,"style":334},[59,60],[15,74986],{"className":74987,"style":158},[157],[15,74989,714],{"className":74990},[162],[15,74992],{"className":74993,"style":158},[157],[15,74995,74997,75000],{"className":74996},[50],[15,74998],{"className":74999,"style":566},[54],[15,75001,213],{"className":75002},[59,60]," 则 ",[15,75005,75007,75029],{"className":75006,"translate":19},[18],[15,75008,75010],{"className":75009},[23],[25,75011,75012],{"xmlns":27},[29,75013,75014,75026],{},[32,75015,75016,75018,75020,75022,75024],{},[35,75017,206],{},[35,75019,10694],{},[110,75021,714],{},[35,75023,213],{},[35,75025,10694],{},[39,75027,75028],{"encoding":41},"PK\\ll QK",[15,75030,75032,75053],{"className":75031,"ariaHidden":46},[45],[15,75033,75035,75038,75041,75044,75047,75050],{"className":75034},[50],[15,75036],{"className":75037,"style":729},[54],[15,75039,206],{"className":75040,"style":334},[59,60],[15,75042,10694],{"className":75043,"style":10782},[59,60],[15,75045],{"className":75046,"style":158},[157],[15,75048,714],{"className":75049},[162],[15,75051],{"className":75052,"style":158},[157],[15,75054,75056,75059,75062],{"className":75055},[50],[15,75057],{"className":75058,"style":566},[54],[15,75060,213],{"className":75061},[59,60],[15,75063,10694],{"className":75064,"style":10782},[59,60],"，且对任意可测集 ",[15,75067,75069,75082],{"className":75068,"translate":19},[18],[15,75070,75072],{"className":75071},[23],[25,75073,75074],{"xmlns":27},[29,75075,75076,75080],{},[32,75077,75078],{},[35,75079,603],{},[39,75081,603],{"encoding":41},[15,75083,75085],{"className":75084,"ariaHidden":46},[45],[15,75086,75088,75091],{"className":75087},[50],[15,75089],{"className":75090,"style":664},[54],[15,75092,603],{"className":75093},[59,60],[15,75095,75097],{"className":75096,"translate":19},[180],[15,75098,75100,75299],{"className":75099,"translate":19},[18],[15,75101,75103],{"className":75102},[23],[25,75104,75105],{"xmlns":27,"display":189},[29,75106,75107,75296],{},[1243,75108,75109,75173,75228],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,75110,75111,75127],{},[1252,75112,75113],{},[1255,75114,75115],{"scriptlevel":126,"displaystyle":46},[32,75116,75117,75119,75121,75123,75125],{},[35,75118,206],{},[35,75120,10694],{},[110,75122,113],{"stretchy":112},[35,75124,603],{},[110,75126,120],{"stretchy":112},[1252,75128,75129],{},[1255,75130,75131],{"scriptlevel":126,"displaystyle":46},[32,75132,75133,75135,75137,75139,75141,75143,75145,75147,75149,75151,75153,75155,75157,75159,75161,75163,75165,75167,75169,75171],{},[32,75134],{},[110,75136,123],{},[110,75138,1287],{},[35,75140,10694],{},[110,75142,113],{"stretchy":112},[35,75144,603],{},[35,75146,4808],{"mathvariant":209},[35,75148,774],{},[110,75150,120],{"stretchy":112},[1297,75152,1299],{},[35,75154,769],{},[110,75156,113],{"stretchy":112},[35,75158,774],{},[110,75160,120],{"stretchy":112},[1297,75162,1299],{},[35,75164,244],{},[35,75166,213],{},[110,75168,113],{"stretchy":112},[35,75170,774],{},[110,75172,120],{"stretchy":112},[1249,75174,75175,75181],{},[1252,75176,75177],{},[1255,75178,75179],{"scriptlevel":126,"displaystyle":46},[32,75180],{},[1252,75182,75183],{},[1255,75184,75185],{"scriptlevel":126,"displaystyle":46},[32,75186,75187,75189,75191,75197,75199,75201,75203,75205,75207,75209,75226],{},[32,75188],{},[110,75190,123],{},[195,75192,75193,75195],{},[35,75194,223],{"mathvariant":222},[35,75196,213],{},[110,75198,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,75200,769],{},[110,75202,113],{"stretchy":112},[35,75204,598],{},[110,75206,120],{"stretchy":112},[1297,75208,1299],{},[195,75210,75211,75214],{},[115,75212,117],{"mathvariant":75213},"bold",[32,75215,75216,75218,75220,75222,75224],{},[110,75217,2898],{"stretchy":112},[35,75219,5401],{},[110,75221,5909],{},[35,75223,603],{},[110,75225,2908],{"stretchy":112},[110,75227,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,75229,75230,75236],{},[1252,75231,75232],{},[1255,75233,75234],{"scriptlevel":126,"displaystyle":46},[32,75235],{},[1252,75237,75238],{},[1255,75239,75240],{"scriptlevel":126,"displaystyle":46},[32,75241,75242,75244,75246,75256,75258,75264,75266,75268,75270,75272,75274,75276,75278,75280,75282,75284,75286,75292,75294],{},[32,75243],{},[110,75245,123],{},[195,75247,75248,75250],{},[35,75249,223],{"mathvariant":222},[32,75251,75252,75254],{},[35,75253,213],{},[35,75255,10694],{},[110,75257,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,75259,75260,75262],{},[35,75261,223],{"mathvariant":222},[35,75263,213],{},[110,75265,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,75267,769],{},[110,75269,113],{"stretchy":112},[35,75271,598],{},[110,75273,120],{"stretchy":112},[1297,75275,1299],{},[110,75277,4808],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,75279,1299],{},[35,75281,5401],{},[110,75283,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,75285,1299],{},[195,75287,75288,75290],{},[115,75289,117],{"mathvariant":75213},[35,75291,603],{},[110,75293,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,75295,551],{"separator":46},[39,75297,75298],{"encoding":41},"\\begin{aligned}\nPK(A)\n&=\\int K(A|x)\\,t(x)\\,dQ(x)\\\\[2pt]\n&=\\mathbb E_Q\\big[t(X)\\,\n\\mathbf 1_{\\{Y\\in A\\}}\\big]\\\\\n&=\\mathbb E_{QK}\\Big[\n\\mathbb E_Q\\big[t(X)\\,\\big|\\,Y\\big]\\,\n\\mathbf 1_A\\Big],\n\\end{aligned}",[15,75300,75302],{"className":75301,"ariaHidden":46},[45],[15,75303,75305,75309],{"className":75304},[50],[15,75306],{"className":75307,"style":75308},[54],"height:5.8323em;vertical-align:-2.6661em;",[15,75310,75312],{"className":75311},[59],[15,75313,75315,75382],{"className":75314},[1243],[15,75316,75318],{"className":75317},[1360],[15,75319,75321,75373],{"className":75320},[285,286],[15,75322,75324,75370],{"className":75323},[290],[15,75325,75328,75352,75361],{"className":75326,"style":75327},[294],"height:3.1661em;",[15,75329,75331,75334],{"style":75330},"top:-5.1661em;",[15,75332],{"className":75333,"style":6273},[302],[15,75335,75337,75340,75343,75346,75349],{"className":75336},[59],[15,75338,206],{"className":75339,"style":334},[59,60],[15,75341,10694],{"className":75342,"style":10782},[59,60],[15,75344,113],{"className":75345},[146],[15,75347,603],{"className":75348},[59,60],[15,75350,120],{"className":75351},[153],[15,75353,75355,75358],{"style":75354},"top:-3.1539em;",[15,75356],{"className":75357,"style":6273},[302],[15,75359],{"className":75360},[59],[15,75362,75364,75367],{"style":75363},"top:-1.3439em;",[15,75365],{"className":75366,"style":6273},[302],[15,75368],{"className":75369},[59],[15,75371,318],{"className":75372},[317],[15,75374,75376],{"className":75375},[290],[15,75377,75380],{"className":75378,"style":75379},[294],"height:2.6661em;",[15,75381],{},[15,75383,75385],{"className":75384},[1451],[15,75386,75388,75852],{"className":75387},[285,286],[15,75389,75391,75849],{"className":75390},[290],[15,75392,75394,75471,75615],{"className":75393,"style":75327},[294],[15,75395,75396,75399],{"style":75330},[15,75397],{"className":75398,"style":6273},[302],[15,75400,75402,75405,75408,75411,75414,75417,75420,75423,75426,75429,75432,75435,75438,75441,75444,75447,75450,75453,75456,75459,75462,75465,75468],{"className":75401},[59],[15,75403],{"className":75404},[59],[15,75406],{"className":75407,"style":158},[157],[15,75409,123],{"className":75410},[162],[15,75412],{"className":75413,"style":158},[157],[15,75415,1287],{"className":75416,"style":1487},[1484,1485,1486],[15,75418],{"className":75419,"style":406},[157],[15,75421,10694],{"className":75422,"style":10782},[59,60],[15,75424,113],{"className":75425},[146],[15,75427,603],{"className":75428},[59,60],[15,75430,4808],{"className":75431},[59],[15,75433,774],{"className":75434},[59,60],[15,75436,120],{"className":75437},[153],[15,75439],{"className":75440,"style":406},[157],[15,75442,769],{"className":75443},[59,60],[15,75445,113],{"className":75446},[146],[15,75448,774],{"className":75449},[59,60],[15,75451,120],{"className":75452},[153],[15,75454],{"className":75455,"style":406},[157],[15,75457,244],{"className":75458},[59,60],[15,75460,213],{"className":75461},[59,60],[15,75463,113],{"className":75464},[146],[15,75466,774],{"className":75467},[59,60],[15,75469,120],{"className":75470},[153],[15,75472,75473,75476],{"style":75354},[15,75474],{"className":75475,"style":6273},[302],[15,75477,75479,75482,75485,75488,75491,75531,75537,75540,75543,75546,75549,75552,75609],{"className":75478},[59],[15,75480],{"className":75481},[59],[15,75483],{"className":75484,"style":158},[157],[15,75486,123],{"className":75487},[162],[15,75489],{"className":75490,"style":158},[157],[15,75492,75494,75497],{"className":75493},[59],[15,75495,223],{"className":75496},[59,366],[15,75498,75500],{"className":75499},[281],[15,75501,75503,75523],{"className":75502},[285,286],[15,75504,75506,75520],{"className":75505},[290],[15,75507,75509],{"className":75508,"style":379},[294],[15,75510,75511,75514],{"style":382},[15,75512],{"className":75513,"style":303},[302],[15,75515,75517],{"className":75516},[307,308,309,310],[15,75518,213],{"className":75519},[59,60,310],[15,75521,318],{"className":75522},[317],[15,75524,75526],{"className":75525},[290],[15,75527,75529],{"className":75528,"style":325},[294],[15,75530],{},[15,75532,75534],{"className":75533},[59],[15,75535,230],{"className":75536},[419,9674],[15,75538,769],{"className":75539},[59,60],[15,75541,113],{"className":75542},[146],[15,75544,598],{"className":75545,"style":8887},[59,60],[15,75547,120],{"className":75548},[153],[15,75550],{"className":75551,"style":406},[157],[15,75553,75555,75559],{"className":75554},[59],[15,75556,117],{"className":75557},[59,75558],"mathbf",[15,75560,75562],{"className":75561},[281],[15,75563,75565,75601],{"className":75564},[285,286],[15,75566,75568,75598],{"className":75567},[290],[15,75569,75571],{"className":75570,"style":6098},[294],[15,75572,75574,75577],{"style":75573},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[15,75575],{"className":75576,"style":303},[302],[15,75578,75580],{"className":75579},[307,308,309,310],[15,75581,75583,75586,75589,75592,75595],{"className":75582},[59,310],[15,75584,2898],{"className":75585},[146,310],[15,75587,5401],{"className":75588,"style":2587},[59,60,310],[15,75590,5909],{"className":75591},[162,310],[15,75593,603],{"className":75594},[59,60,310],[15,75596,2908],{"className":75597},[153,310],[15,75599,318],{"className":75600},[317],[15,75602,75604],{"className":75603},[290],[15,75605,75607],{"className":75606,"style":6144},[294],[15,75608],{},[15,75610,75612],{"className":75611},[59],[15,75613,257],{"className":75614},[419,9674],[15,75616,75617,75620],{"style":75363},[15,75618],{"className":75619,"style":6273},[302],[15,75621,75623,75626,75629,75632,75635,75681,75687,75727,75733,75736,75739,75742,75745,75748,75785,75788,75791,75797,75800,75840,75846],{"className":75622},[59],[15,75624],{"className":75625},[59],[15,75627],{"className":75628,"style":158},[157],[15,75630,123],{"className":75631},[162],[15,75633],{"className":75634,"style":158},[157],[15,75636,75638,75641],{"className":75637},[59],[15,75639,223],{"className":75640},[59,366],[15,75642,75644],{"className":75643},[281],[15,75645,75647,75673],{"className":75646},[285,286],[15,75648,75650,75670],{"className":75649},[290],[15,75651,75653],{"className":75652,"style":379},[294],[15,75654,75655,75658],{"style":382},[15,75656],{"className":75657,"style":303},[302],[15,75659,75661],{"className":75660},[307,308,309,310],[15,75662,75664,75667],{"className":75663},[59,310],[15,75665,213],{"className":75666},[59,60,310],[15,75668,10694],{"className":75669,"style":10782},[59,60,310],[15,75671,318],{"className":75672},[317],[15,75674,75676],{"className":75675},[290],[15,75677,75679],{"className":75678,"style":325},[294],[15,75680],{},[15,75682,75684],{"className":75683},[59],[15,75685,230],{"className":75686},[419,3720],[15,75688,75690,75693],{"className":75689},[59],[15,75691,223],{"className":75692},[59,366],[15,75694,75696],{"className":75695},[281],[15,75697,75699,75719],{"className":75698},[285,286],[15,75700,75702,75716],{"className":75701},[290],[15,75703,75705],{"className":75704,"style":379},[294],[15,75706,75707,75710],{"style":382},[15,75708],{"className":75709,"style":303},[302],[15,75711,75713],{"className":75712},[307,308,309,310],[15,75714,213],{"className":75715},[59,60,310],[15,75717,318],{"className":75718},[317],[15,75720,75722],{"className":75721},[290],[15,75723,75725],{"className":75724,"style":325},[294],[15,75726],{},[15,75728,75730],{"className":75729},[59],[15,75731,230],{"className":75732},[419,9674],[15,75734,769],{"className":75735},[59,60],[15,75737,113],{"className":75738},[146],[15,75740,598],{"className":75741,"style":8887},[59,60],[15,75743,120],{"className":75744},[153],[15,75746],{"className":75747,"style":406},[157],[15,75749,75751],{"className":75750},[59],[15,75752,75754],{"className":75753},[419,14829],[15,75755,75757,75777],{"className":75756},[285,286],[15,75758,75760,75774],{"className":75759},[290],[15,75761,75763],{"className":75762,"style":14839},[294],[15,75764,75765,75768],{"style":14842},[15,75766],{"className":75767,"style":14846},[302],[15,75769,75770],{"style":36434},[6323,75771,75772],{"xmlns":6325,"width":35051,"height":9450,"viewBox":36437},[6331,75773],{"d":36440},[15,75775,318],{"className":75776},[317],[15,75778,75780],{"className":75779},[290],[15,75781,75783],{"className":75782,"style":14866},[294],[15,75784],{},[15,75786],{"className":75787,"style":406},[157],[15,75789,5401],{"className":75790,"style":2587},[59,60],[15,75792,75794],{"className":75793},[59],[15,75795,257],{"className":75796},[419,9674],[15,75798],{"className":75799,"style":406},[157],[15,75801,75803,75806],{"className":75802},[59],[15,75804,117],{"className":75805},[59,75558],[15,75807,75809],{"className":75808},[281],[15,75810,75812,75832],{"className":75811},[285,286],[15,75813,75815,75829],{"className":75814},[290],[15,75816,75818],{"className":75817,"style":379},[294],[15,75819,75820,75823],{"style":382},[15,75821],{"className":75822,"style":303},[302],[15,75824,75826],{"className":75825},[307,308,309,310],[15,75827,603],{"className":75828},[59,60,310],[15,75830,318],{"className":75831},[317],[15,75833,75835],{"className":75834},[290],[15,75836,75838],{"className":75837,"style":7968},[294],[15,75839],{},[15,75841,75843],{"className":75842},[59],[15,75844,257],{"className":75845},[419,3720],[15,75847,551],{"className":75848},[573],[15,75850,318],{"className":75851},[317],[15,75853,75855],{"className":75854},[290],[15,75856,75858],{"className":75857,"style":75379},[294],[15,75859],{},[11,75861,75862],{},"故",[15,75864,75866],{"className":75865,"translate":19},[180],[15,75867,75869,75964],{"className":75868,"translate":19},[18],[15,75870,75872],{"className":75871},[23],[25,75873,75874],{"xmlns":27,"display":189},[29,75875,75876,75961],{},[1243,75877,75879],{"width":75878},"100%",[1249,75880,75881,75884,75946,75948],{},[1252,75882],{"width":75883},"50%",[1252,75885,75886],{},[32,75887,75888,75906,75908,75910,75912,75914,75920,75922,75924,75926,75928,75930,75932,75934,75936,75938,75940,75942,75944],{},[238,75889,75890,75898],{},[32,75891,75892,75894,75896],{},[35,75893,244],{},[35,75895,206],{},[35,75897,10694],{},[32,75899,75900,75902,75904],{},[35,75901,244],{},[35,75903,213],{},[35,75905,10694],{},[110,75907,113],{"stretchy":112},[35,75909,40237],{},[110,75911,120],{"stretchy":112},[110,75913,123],{},[195,75915,75916,75918],{},[35,75917,223],{"mathvariant":222},[35,75919,213],{},[110,75921,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,75923,769],{},[110,75925,113],{"stretchy":112},[35,75927,598],{},[110,75929,120],{"stretchy":112},[1297,75931,1299],{},[110,75933,4808],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,75935,1299],{},[35,75937,5401],{},[110,75939,123],{},[35,75941,40237],{},[110,75943,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,75945,4375],{"mathvariant":209},[1252,75947],{"width":75883},[1252,75949,75950],{},[32,75951,75952,75954,75959],{},[1297,75953,113],{},[1255,75955,75956],{"scriptlevel":126,"displaystyle":112},[110,75957,75958],{},"⋆",[1297,75960,120],{},[39,75962,75963],{"encoding":41},"\\frac{dPK}{dQK}(y)\n=\\mathbb E_Q\\big[t(X)\\,\\big|\\,Y=y\\big].\n\\tag{$\\star$}",[15,75965,75967,76065,76184,76202],{"className":75966,"ariaHidden":46},[45],[15,75968,75970,75973,76047,76050,76053,76056,76059,76062],{"className":75969},[50],[15,75971],{"className":75972,"style":838},[54],[15,75974,75976,75979,76044],{"className":75975},[59],[15,75977],{"className":75978},[146,441],[15,75980,75982],{"className":75981},[238],[15,75983,75985,76036],{"className":75984},[285,286],[15,75986,75988,76033],{"className":75987},[290],[15,75989,75991,76008,76016],{"className":75990,"style":454},[294],[15,75992,75993,75996],{"style":457},[15,75994],{"className":75995,"style":461},[302],[15,75997,75999,76002,76005],{"className":75998},[59],[15,76000,244],{"className":76001},[59,60],[15,76003,213],{"className":76004},[59,60],[15,76006,10694],{"className":76007,"style":10782},[59,60],[15,76009,76010,76013],{"style":473},[15,76011],{"className":76012,"style":461},[302],[15,76014],{"className":76015,"style":481},[480],[15,76017,76018,76021],{"style":484},[15,76019],{"className":76020,"style":461},[302],[15,76022,76024,76027,76030],{"className":76023},[59],[15,76025,244],{"className":76026},[59,60],[15,76028,206],{"className":76029,"style":334},[59,60],[15,76031,10694],{"className":76032,"style":10782},[59,60],[15,76034,318],{"className":76035},[317],[15,76037,76039],{"className":76038},[290],[15,76040,76042],{"className":76041,"style":506},[294],[15,76043],{},[15,76045],{"className":76046},[153,441],[15,76048,113],{"className":76049},[146],[15,76051,40237],{"className":76052,"style":981},[59,60],[15,76054,120],{"className":76055},[153],[15,76057],{"className":76058,"style":158},[157],[15,76060,123],{"className":76061},[162],[15,76063],{"className":76064,"style":158},[157],[15,76066,76068,76071,76111,76117,76120,76123,76126,76129,76132,76169,76172,76175,76178,76181],{"className":76067},[50],[15,76069],{"className":76070,"style":20563},[54],[15,76072,76074,76077],{"className":76073},[59],[15,76075,223],{"className":76076},[59,366],[15,76078,76080],{"className":76079},[281],[15,76081,76083,76103],{"className":76082},[285,286],[15,76084,76086,76100],{"className":76085},[290],[15,76087,76089],{"className":76088,"style":379},[294],[15,76090,76091,76094],{"style":382},[15,76092],{"className":76093,"style":303},[302],[15,76095,76097],{"className":76096},[307,308,309,310],[15,76098,213],{"className":76099},[59,60,310],[15,76101,318],{"className":76102},[317],[15,76104,76106],{"className":76105},[290],[15,76107,76109],{"className":76108,"style":325},[294],[15,76110],{},[15,76112,76114],{"className":76113},[59],[15,76115,230],{"className":76116},[419,9674],[15,76118,769],{"className":76119},[59,60],[15,76121,113],{"className":76122},[146],[15,76124,598],{"className":76125,"style":8887},[59,60],[15,76127,120],{"className":76128},[153],[15,76130],{"className":76131,"style":406},[157],[15,76133,76135],{"className":76134},[59],[15,76136,76138],{"className":76137},[419,14829],[15,76139,76141,76161],{"className":76140},[285,286],[15,76142,76144,76158],{"className":76143},[290],[15,76145,76147],{"className":76146,"style":14839},[294],[15,76148,76149,76152],{"style":14842},[15,76150],{"className":76151,"style":14846},[302],[15,76153,76154],{"style":36434},[6323,76155,76156],{"xmlns":6325,"width":35051,"height":9450,"viewBox":36437},[6331,76157],{"d":36440},[15,76159,318],{"className":76160},[317],[15,76162,76164],{"className":76163},[290],[15,76165,76167],{"className":76166,"style":14866},[294],[15,76168],{},[15,76170],{"className":76171,"style":406},[157],[15,76173,5401],{"className":76174,"style":2587},[59,60],[15,76176],{"className":76177,"style":158},[157],[15,76179,123],{"className":76180},[162],[15,76182],{"className":76183,"style":158},[157],[15,76185,76187,76190,76193,76199],{"className":76186},[50],[15,76188],{"className":76189,"style":20563},[54],[15,76191,40237],{"className":76192,"style":981},[59,60],[15,76194,76196],{"className":76195},[59],[15,76197,257],{"className":76198},[419,9674],[15,76200,4375],{"className":76201},[59],[15,76203,76206,76209],{"className":76204},[76205],"tag",[15,76207],{"className":76208,"style":838},[54],[15,76210,76212,76215,76221],{"className":76211},[59,4598],[15,76213,113],{"className":76214},[59],[15,76216,76218],{"className":76217},[59],[15,76219,75958],{"className":76220},[59],[15,76222,120],{"className":76223},[59],[11,76225,76226,76227,76255],{},"由 ",[15,76228,76230,76243],{"className":76229,"translate":19},[18],[15,76231,76233],{"className":76232},[23],[25,76234,76235],{"xmlns":27},[29,76236,76237,76241],{},[32,76238,76239],{},[35,76240,37],{},[39,76242,37],{"encoding":41},[15,76244,76246],{"className":76245,"ariaHidden":46},[45],[15,76247,76249,76252],{"className":76248},[50],[15,76250],{"className":76251,"style":55},[54],[15,76253,37],{"className":76254,"style":61},[59,60]," 凸及条件 Jensen：",[15,76257,76259],{"className":76258,"translate":19},[180],[15,76260,76262,76374],{"className":76261,"translate":19},[18],[15,76263,76265],{"className":76264},[23],[25,76266,76267],{"xmlns":27,"display":189},[29,76268,76269,76371],{},[32,76270,76271,76273,76275,76305,76307,76309,76311,76317,76319,76321,76323,76325,76327,76329,76331,76333,76335,76337,76339,76345,76347,76349,76351,76353,76355,76357,76359,76361,76363,76365,76367,76369],{},[35,76272,37],{},[1297,76274,1304],{},[32,76276,76277,76279,76297,76299,76301,76303],{},[110,76278,113],{"fence":46},[238,76280,76281,76289],{},[32,76282,76283,76285,76287],{},[35,76284,244],{},[35,76286,206],{},[35,76288,10694],{},[32,76290,76291,76293,76295],{},[35,76292,244],{},[35,76294,213],{},[35,76296,10694],{},[110,76298,113],{"stretchy":112},[35,76300,40237],{},[110,76302,120],{"stretchy":112},[110,76304,120],{"fence":46},[110,76306,123],{},[35,76308,37],{},[110,76310,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,76312,76313,76315],{},[35,76314,223],{"mathvariant":222},[35,76316,213],{},[110,76318,230],{"stretchy":112},[35,76320,769],{},[1297,76322,1299],{},[35,76324,4808],{"mathvariant":209},[1297,76326,1299],{},[35,76328,5401],{},[110,76330,123],{},[35,76332,40237],{},[110,76334,257],{"stretchy":112},[110,76336,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,76338,9952],{},[195,76340,76341,76343],{},[35,76342,223],{"mathvariant":222},[35,76344,213],{},[110,76346,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,76348,37],{},[110,76350,113],{"stretchy":112},[35,76352,769],{},[110,76354,120],{"stretchy":112},[1297,76356,1299],{},[110,76358,4808],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1297,76360,1299],{},[35,76362,5401],{},[110,76364,123],{},[35,76366,40237],{},[110,76368,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,76370,4375],{"mathvariant":209},[39,76372,76373],{"encoding":41},"f\\!\\left(\\frac{dPK}{dQK}(y)\\right)\n=f\\Big(\\mathbb E_Q[t\\,|\\,Y=y]\\Big)\n\\le \\mathbb E_Q\\big[f(t)\\,\\big|\\,Y=y\\big].",[15,76375,76377,76499,76581,76608,76727],{"className":76376,"ariaHidden":46},[45],[15,76378,76380,76383,76386,76389,76392,76490,76493,76496],{"className":76379},[50],[15,76381],{"className":76382,"style":359},[54],[15,76384,37],{"className":76385,"style":61},[59,60],[15,76387],{"className":76388,"style":1512},[157],[15,76390],{"className":76391,"style":406},[157],[15,76393,76395,76401,76475,76478,76481,76484],{"className":76394},[410],[15,76396,76398],{"className":76397,"style":415},[146,414],[15,76399,113],{"className":76400},[419,309],[15,76402,76404,76407,76472],{"className":76403},[59],[15,76405],{"className":76406},[146,441],[15,76408,76410],{"className":76409},[238],[15,76411,76413,76464],{"className":76412},[285,286],[15,76414,76416,76461],{"className":76415},[290],[15,76417,76419,76436,76444],{"className":76418,"style":454},[294],[15,76420,76421,76424],{"style":457},[15,76422],{"className":76423,"style":461},[302],[15,76425,76427,76430,76433],{"className":76426},[59],[15,76428,244],{"className":76429},[59,60],[15,76431,213],{"className":76432},[59,60],[15,76434,10694],{"className":76435,"style":10782},[59,60],[15,76437,76438,76441],{"style":473},[15,76439],{"className":76440,"style":461},[302],[15,76442],{"className":76443,"style":481},[480],[15,76445,76446,76449],{"style":484},[15,76447],{"className":76448,"style":461},[302],[15,76450,76452,76455,76458],{"className":76451},[59],[15,76453,244],{"className":76454},[59,60],[15,76456,206],{"className":76457,"style":334},[59,60],[15,76459,10694],{"className":76460,"style":10782},[59,60],[15,76462,318],{"className":76463},[317],[15,76465,76467],{"className":76466},[290],[15,76468,76470],{"className":76469,"style":506},[294],[15,76471],{},[15,76473],{"className":76474},[153,441],[15,76476,113],{"className":76477},[146],[15,76479,40237],{"className":76480,"style":981},[59,60],[15,76482,120],{"className":76483},[153],[15,76485,76487],{"className":76486,"style":415},[153,414],[15,76488,120],{"className":76489},[419,309],[15,76491],{"className":76492,"style":158},[157],[15,76494,123],{"className":76495},[162],[15,76497],{"className":76498,"style":158},[157],[15,76500,76502,76505,76508,76514,76554,76557,76560,76563,76566,76569,76572,76575,76578],{"className":76501},[50],[15,76503],{"className":76504,"style":68117},[54],[15,76506,37],{"className":76507,"style":61},[59,60],[15,76509,76511],{"className":76510},[59],[15,76512,113],{"className":76513},[419,3720],[15,76515,76517,76520],{"className":76516},[59],[15,76518,223],{"className":76519},[59,366],[15,76521,76523],{"className":76522},[281],[15,76524,76526,76546],{"className":76525},[285,286],[15,76527,76529,76543],{"className":76528},[290],[15,76530,76532],{"className":76531,"style":379},[294],[15,76533,76534,76537],{"style":382},[15,76535],{"className":76536,"style":303},[302],[15,76538,76540],{"className":76539},[307,308,309,310],[15,76541,213],{"className":76542},[59,60,310],[15,76544,318],{"className":76545},[317],[15,76547,76549],{"className":76548},[290],[15,76550,76552],{"className":76551,"style":325},[294],[15,76553],{},[15,76555,230],{"className":76556},[146],[15,76558,769],{"className":76559},[59,60],[15,76561],{"className":76562,"style":406},[157],[15,76564,4808],{"className":76565},[59],[15,76567],{"className":76568,"style":406},[157],[15,76570,5401],{"className":76571,"style":2587},[59,60],[15,76573],{"className":76574,"style":158},[157],[15,76576,123],{"className":76577},[162],[15,76579],{"className":76580,"style":158},[157],[15,76582,76584,76587,76590,76593,76599,76602,76605],{"className":76583},[50],[15,76585],{"className":76586,"style":68117},[54],[15,76588,40237],{"className":76589,"style":981},[59,60],[15,76591,257],{"className":76592},[153],[15,76594,76596],{"className":76595},[59],[15,76597,120],{"className":76598},[419,3720],[15,76600],{"className":76601,"style":158},[157],[15,76603,9952],{"className":76604},[162],[15,76606],{"className":76607,"style":158},[157],[15,76609,76611,76614,76654,76660,76663,76666,76669,76672,76675,76712,76715,76718,76721,76724],{"className":76610},[50],[15,76612],{"className":76613,"style":20563},[54],[15,76615,76617,76620],{"className":76616},[59],[15,76618,223],{"className":76619},[59,366],[15,76621,76623],{"className":76622},[281],[15,76624,76626,76646],{"className":76625},[285,286],[15,76627,76629,76643],{"className":76628},[290],[15,76630,76632],{"className":76631,"style":379},[294],[15,76633,76634,76637],{"style":382},[15,76635],{"className":76636,"style":303},[302],[15,76638,76640],{"className":76639},[307,308,309,310],[15,76641,213],{"className":76642},[59,60,310],[15,76644,318],{"className":76645},[317],[15,76647,76649],{"className":76648},[290],[15,76650,76652],{"className":76651,"style":325},[294],[15,76653],{},[15,76655,76657],{"className":76656},[59],[15,76658,230],{"className":76659},[419,9674],[15,76661,37],{"className":76662,"style":61},[59,60],[15,76664,113],{"className":76665},[146],[15,76667,769],{"className":76668},[59,60],[15,76670,120],{"className":76671},[153],[15,76673],{"className":76674,"style":406},[157],[15,76676,76678],{"className":76677},[59],[15,76679,76681],{"className":76680},[419,14829],[15,76682,76684,76704],{"className":76683},[285,286],[15,76685,76687,76701],{"className":76686},[290],[15,76688,76690],{"className":76689,"style":14839},[294],[15,76691,76692,76695],{"style":14842},[15,76693],{"className":76694,"style":14846},[302],[15,76696,76697],{"style":36434},[6323,76698,76699],{"xmlns":6325,"width":35051,"height":9450,"viewBox":36437},[6331,76700],{"d":36440},[15,76702,318],{"className":76703},[317],[15,76705,76707],{"className":76706},[290],[15,76708,76710],{"className":76709,"style":14866},[294],[15,76711],{},[15,76713],{"className":76714,"style":406},[157],[15,76716,5401],{"className":76717,"style":2587},[59,60],[15,76719],{"className":76720,"style":158},[157],[15,76722,123],{"className":76723},[162],[15,76725],{"className":76726,"style":158},[157],[15,76728,76730,76733,76736,76742],{"className":76729},[50],[15,76731],{"className":76732,"style":20563},[54],[15,76734,40237],{"className":76735,"style":981},[59,60],[15,76737,76739],{"className":76738},[59],[15,76740,257],{"className":76741},[419,9674],[15,76743,4375],{"className":76744},[59],[11,76746,14261,76747,668,76775,61953],{},[15,76748,76750,76763],{"className":76749,"translate":19},[18],[15,76751,76753],{"className":76752},[23],[25,76754,76755],{"xmlns":27},[29,76756,76757,76761],{},[32,76758,76759],{},[35,76760,40237],{},[39,76762,40237],{"encoding":41},[15,76764,76766],{"className":76765,"ariaHidden":46},[45],[15,76767,76769,76772],{"className":76768},[50],[15,76770],{"className":76771,"style":2276},[54],[15,76773,40237],{"className":76774,"style":981},[59,60],[15,76776,76778,76793],{"className":76777,"translate":19},[18],[15,76779,76781],{"className":76780},[23],[25,76782,76783],{"xmlns":27},[29,76784,76785,76791],{},[32,76786,76787,76789],{},[35,76788,213],{},[35,76790,10694],{},[39,76792,74538],{"encoding":41},[15,76794,76796],{"className":76795,"ariaHidden":46},[45],[15,76797,76799,76802,76805],{"className":76798},[50],[15,76800],{"className":76801,"style":566},[54],[15,76803,213],{"className":76804},[59,60],[15,76806,10694],{"className":76807,"style":10782},[59,60],[15,76809,76811],{"className":76810,"translate":19},[180],[15,76812,76814,77014],{"className":76813,"translate":19},[18],[15,76815,76817],{"className":76816},[23],[25,76818,76819],{"xmlns":27,"display":189},[29,76820,76821,77011],{},[1243,76822,76823,76897,76951],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,76824,76825,76851],{},[1252,76826,76827],{},[1255,76828,76829],{"scriptlevel":126,"displaystyle":46},[32,76830,76831,76837,76839,76841,76843,76845,76847,76849],{},[195,76832,76833,76835],{},[35,76834,199],{},[35,76836,37],{},[110,76838,113],{"stretchy":112},[35,76840,206],{},[35,76842,10694],{},[35,76844,210],{"mathvariant":209},[35,76846,213],{},[35,76848,10694],{},[110,76850,120],{"stretchy":112},[1252,76852,76853],{},[1255,76854,76855],{"scriptlevel":126,"displaystyle":46},[32,76856,76857,76859,76861,76871,76873,76875,76877,76883,76885,76887,76889,76891,76893,76895],{},[32,76858],{},[110,76860,123],{},[195,76862,76863,76865],{},[35,76864,223],{"mathvariant":222},[32,76866,76867,76869],{},[35,76868,213],{},[35,76870,10694],{},[110,76872,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,76874,37],{},[110,76876,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,76878,76879,76881],{},[35,76880,223],{"mathvariant":222},[35,76882,213],{},[110,76884,230],{"stretchy":112},[35,76886,769],{},[35,76888,4808],{"mathvariant":209},[35,76890,5401],{},[110,76892,257],{"stretchy":112},[110,76894,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,76896,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,76898,76899,76905],{},[1252,76900,76901],{},[1255,76902,76903],{"scriptlevel":126,"displaystyle":46},[32,76904],{},[1252,76906,76907],{},[1255,76908,76909],{"scriptlevel":126,"displaystyle":46},[32,76910,76911,76913,76915,76925,76927,76933,76935,76937,76939,76941,76943,76945,76947,76949],{},[32,76912],{},[110,76914,9952],{},[195,76916,76917,76919],{},[35,76918,223],{"mathvariant":222},[32,76920,76921,76923],{},[35,76922,213],{},[35,76924,10694],{},[110,76926,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,76928,76929,76931],{},[35,76930,223],{"mathvariant":222},[35,76932,213],{},[110,76934,230],{"stretchy":112},[35,76936,37],{},[110,76938,113],{"stretchy":112},[35,76940,769],{},[110,76942,120],{"stretchy":112},[35,76944,4808],{"mathvariant":209},[35,76946,5401],{},[110,76948,257],{"stretchy":112},[110,76950,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,76952,76953,76959],{},[1252,76954,76955],{},[1255,76956,76957],{"scriptlevel":126,"displaystyle":46},[32,76958],{},[1252,76960,76961],{},[1255,76962,76963],{"scriptlevel":126,"displaystyle":46},[32,76964,76965,76967,76969,76975,76977,76979,76981,76983,76985,76987,76989,76995,76997,76999,77001,77003,77005,77007,77009],{},[32,76966],{},[110,76968,123],{},[195,76970,76971,76973],{},[35,76972,223],{"mathvariant":222},[35,76974,213],{},[110,76976,230],{"stretchy":112},[35,76978,37],{},[110,76980,113],{"stretchy":112},[35,76982,769],{},[110,76984,120],{"stretchy":112},[110,76986,257],{"stretchy":112},[110,76988,123],{},[195,76990,76991,76993],{},[35,76992,199],{},[35,76994,37],{},[110,76996,113],{"stretchy":112},[35,76998,206],{},[35,77000,210],{"mathvariant":209},[35,77002,213],{},[110,77004,120],{"stretchy":112},[35,77006,4375],{"mathvariant":209},[157,77008],{"width":3262},[35,77010,59252],{"mathvariant":209},[39,77012,77013],{"encoding":41},"\\begin{aligned}\nD_f(PK\\|QK)\n&=\\mathbb E_{QK}\\Big[\nf\\big(\\mathbb E_Q[t|Y]\\big)\\Big]\\\\\n&\\le \\mathbb E_{QK}\\Big[\n\\mathbb E_Q[f(t)|Y]\\Big]\\\\\n&=\\mathbb E_Q[f(t)]=D_f(P\\|Q).\\qquad\\square\n\\end{aligned}",[15,77015,77017],{"className":77016,"ariaHidden":46},[45],[15,77018,77020,77024],{"className":77019},[50],[15,77021],{"className":77022,"style":77023},[54],"height:5.4em;vertical-align:-2.45em;",[15,77025,77027],{"className":77026},[59],[15,77028,77030,77142],{"className":77029},[1243],[15,77031,77033],{"className":77032},[1360],[15,77034,77036,77133],{"className":77035},[285,286],[15,77037,77039,77130],{"className":77038},[290],[15,77040,77043,77113,77121],{"className":77041,"style":77042},[294],"height:2.95em;",[15,77044,77046,77049],{"style":77045},"top:-4.95em;",[15,77047],{"className":77048,"style":17588},[302],[15,77050,77052,77092,77095,77098,77101,77104,77107,77110],{"className":77051},[59],[15,77053,77055,77058],{"className":77054},[59],[15,77056,199],{"className":77057,"style":277},[59,60],[15,77059,77061],{"className":77060},[281],[15,77062,77064,77084],{"className":77063},[285,286],[15,77065,77067,77081],{"className":77066},[290],[15,77068,77070],{"className":77069,"style":295},[294],[15,77071,77072,77075],{"style":298},[15,77073],{"className":77074,"style":303},[302],[15,77076,77078],{"className":77077},[307,308,309,310],[15,77079,37],{"className":77080,"style":61},[59,60,310],[15,77082,318],{"className":77083},[317],[15,77085,77087],{"className":77086},[290],[15,77088,77090],{"className":77089,"style":325},[294],[15,77091],{},[15,77093,113],{"className":77094},[146],[15,77096,206],{"className":77097,"style":334},[59,60],[15,77099,10694],{"className":77100,"style":10782},[59,60],[15,77102,210],{"className":77103},[59],[15,77105,213],{"className":77106},[59,60],[15,77108,10694],{"className":77109,"style":10782},[59,60],[15,77111,120],{"className":77112},[153],[15,77114,77115,77118],{"style":14842},[15,77116],{"className":77117,"style":17588},[302],[15,77119],{"className":77120},[59],[15,77122,77124,77127],{"style":77123},"top:-1.06em;",[15,77125],{"className":77126,"style":17588},[302],[15,77128],{"className":77129},[59],[15,77131,318],{"className":77132},[317],[15,77134,77136],{"className":77135},[290],[15,77137,77140],{"className":77138,"style":77139},[294],"height:2.45em;",[15,77141],{},[15,77143,77145],{"className":77144},[1451],[15,77146,77148,77595],{"className":77147},[285,286],[15,77149,77151,77592],{"className":77150},[290],[15,77152,77154,77302,77444],{"className":77153,"style":77042},[294],[15,77155,77156,77159],{"style":77045},[15,77157],{"className":77158,"style":17588},[302],[15,77160,77162,77165,77168,77171,77174,77220,77226,77229,77235,77275,77278,77281,77284,77287,77290,77296],{"className":77161},[59],[15,77163],{"className":77164},[59],[15,77166],{"className":77167,"style":158},[157],[15,77169,123],{"className":77170},[162],[15,77172],{"className":77173,"style":158},[157],[15,77175,77177,77180],{"className":77176},[59],[15,77178,223],{"className":77179},[59,366],[15,77181,77183],{"className":77182},[281],[15,77184,77186,77212],{"className":77185},[285,286],[15,77187,77189,77209],{"className":77188},[290],[15,77190,77192],{"className":77191,"style":379},[294],[15,77193,77194,77197],{"style":382},[15,77195],{"className":77196,"style":303},[302],[15,77198,77200],{"className":77199},[307,308,309,310],[15,77201,77203,77206],{"className":77202},[59,310],[15,77204,213],{"className":77205},[59,60,310],[15,77207,10694],{"className":77208,"style":10782},[59,60,310],[15,77210,318],{"className":77211},[317],[15,77213,77215],{"className":77214},[290],[15,77216,77218],{"className":77217,"style":325},[294],[15,77219],{},[15,77221,77223],{"className":77222},[59],[15,77224,230],{"className":77225},[419,3720],[15,77227,37],{"className":77228,"style":61},[59,60],[15,77230,77232],{"className":77231},[59],[15,77233,113],{"className":77234},[419,9674],[15,77236,77238,77241],{"className":77237},[59],[15,77239,223],{"className":77240},[59,366],[15,77242,77244],{"className":77243},[281],[15,77245,77247,77267],{"className":77246},[285,286],[15,77248,77250,77264],{"className":77249},[290],[15,77251,77253],{"className":77252,"style":379},[294],[15,77254,77255,77258],{"style":382},[15,77256],{"className":77257,"style":303},[302],[15,77259,77261],{"className":77260},[307,308,309,310],[15,77262,213],{"className":77263},[59,60,310],[15,77265,318],{"className":77266},[317],[15,77268,77270],{"className":77269},[290],[15,77271,77273],{"className":77272,"style":325},[294],[15,77274],{},[15,77276,230],{"className":77277},[146],[15,77279,769],{"className":77280},[59,60],[15,77282,4808],{"className":77283},[59],[15,77285,5401],{"className":77286,"style":2587},[59,60],[15,77288,257],{"className":77289},[153],[15,77291,77293],{"className":77292},[59],[15,77294,120],{"className":77295},[419,9674],[15,77297,77299],{"className":77298},[59],[15,77300,257],{"className":77301},[419,3720],[15,77303,77304,77307],{"style":14842},[15,77305],{"className":77306,"style":17588},[302],[15,77308,77310,77313,77316,77319,77322,77368,77374,77414,77417,77420,77423,77426,77429,77432,77435,77438],{"className":77309},[59],[15,77311],{"className":77312},[59],[15,77314],{"className":77315,"style":158},[157],[15,77317,9952],{"className":77318},[162],[15,77320],{"className":77321,"style":158},[157],[15,77323,77325,77328],{"className":77324},[59],[15,77326,223],{"className":77327},[59,366],[15,77329,77331],{"className":77330},[281],[15,77332,77334,77360],{"className":77333},[285,286],[15,77335,77337,77357],{"className":77336},[290],[15,77338,77340],{"className":77339,"style":379},[294],[15,77341,77342,77345],{"style":382},[15,77343],{"className":77344,"style":303},[302],[15,77346,77348],{"className":77347},[307,308,309,310],[15,77349,77351,77354],{"className":77350},[59,310],[15,77352,213],{"className":77353},[59,60,310],[15,77355,10694],{"className":77356,"style":10782},[59,60,310],[15,77358,318],{"className":77359},[317],[15,77361,77363],{"className":77362},[290],[15,77364,77366],{"className":77365,"style":325},[294],[15,77367],{},[15,77369,77371],{"className":77370},[59],[15,77372,230],{"className":77373},[419,3720],[15,77375,77377,77380],{"className":77376},[59],[15,77378,223],{"className":77379},[59,366],[15,77381,77383],{"className":77382},[281],[15,77384,77386,77406],{"className":77385},[285,286],[15,77387,77389,77403],{"className":77388},[290],[15,77390,77392],{"className":77391,"style":379},[294],[15,77393,77394,77397],{"style":382},[15,77395],{"className":77396,"style":303},[302],[15,77398,77400],{"className":77399},[307,308,309,310],[15,77401,213],{"className":77402},[59,60,310],[15,77404,318],{"className":77405},[317],[15,77407,77409],{"className":77408},[290],[15,77410,77412],{"className":77411,"style":325},[294],[15,77413],{},[15,77415,230],{"className":77416},[146],[15,77418,37],{"className":77419,"style":61},[59,60],[15,77421,113],{"className":77422},[146],[15,77424,769],{"className":77425},[59,60],[15,77427,120],{"className":77428},[153],[15,77430,4808],{"className":77431},[59],[15,77433,5401],{"className":77434,"style":2587},[59,60],[15,77436,257],{"className":77437},[153],[15,77439,77441],{"className":77440},[59],[15,77442,257],{"className":77443},[419,3720],[15,77445,77446,77449],{"style":77123},[15,77447],{"className":77448,"style":17588},[302],[15,77450,77452,77455,77458,77461,77464,77504,77507,77510,77513,77516,77519,77522,77525,77528,77568,77571,77574,77577,77580,77583,77586,77589],{"className":77451},[59],[15,77453],{"className":77454},[59],[15,77456],{"className":77457,"style":158},[157],[15,77459,123],{"className":77460},[162],[15,77462],{"className":77463,"style":158},[157],[15,77465,77467,77470],{"className":77466},[59],[15,77468,223],{"className":77469},[59,366],[15,77471,77473],{"className":77472},[281],[15,77474,77476,77496],{"className":77475},[285,286],[15,77477,77479,77493],{"className":77478},[290],[15,77480,77482],{"className":77481,"style":379},[294],[15,77483,77484,77487],{"style":382},[15,77485],{"className":77486,"style":303},[302],[15,77488,77490],{"className":77489},[307,308,309,310],[15,77491,213],{"className":77492},[59,60,310],[15,77494,318],{"className":77495},[317],[15,77497,77499],{"className":77498},[290],[15,77500,77502],{"className":77501,"style":325},[294],[15,77503],{},[15,77505,230],{"className":77506},[146],[15,77508,37],{"className":77509,"style":61},[59,60],[15,77511,113],{"className":77512},[146],[15,77514,769],{"className":77515},[59,60],[15,77517,20390],{"className":77518},[153],[15,77520],{"className":77521,"style":158},[157],[15,77523,123],{"className":77524},[162],[15,77526],{"className":77527,"style":158},[157],[15,77529,77531,77534],{"className":77530},[59],[15,77532,199],{"className":77533,"style":277},[59,60],[15,77535,77537],{"className":77536},[281],[15,77538,77540,77560],{"className":77539},[285,286],[15,77541,77543,77557],{"className":77542},[290],[15,77544,77546],{"className":77545,"style":295},[294],[15,77547,77548,77551],{"style":298},[15,77549],{"className":77550,"style":303},[302],[15,77552,77554],{"className":77553},[307,308,309,310],[15,77555,37],{"className":77556,"style":61},[59,60,310],[15,77558,318],{"className":77559},[317],[15,77561,77563],{"className":77562},[290],[15,77564,77566],{"className":77565,"style":325},[294],[15,77567],{},[15,77569,113],{"className":77570},[146],[15,77572,206],{"className":77573,"style":334},[59,60],[15,77575,210],{"className":77576},[59],[15,77578,213],{"className":77579},[59,60],[15,77581,120],{"className":77582},[153],[15,77584,4375],{"className":77585},[59],[15,77587],{"className":77588,"style":3634},[157],[15,77590,59252],{"className":77591},[59,59794],[15,77593,318],{"className":77594},[317],[15,77596,77598],{"className":77597},[290],[15,77599,77601],{"className":77600,"style":77139},[294],[15,77602],{},[11,77604,77605,77608,77609,77637,77638,77733,77734,77778,77779,77807,77808,77878,77879,77907,77908,77936,77937,33825,77978,77981],{},[1225,77606,77607],{},"等号条件。"," 若 ",[15,77610,77612,77625],{"className":77611,"translate":19},[18],[15,77613,77615],{"className":77614},[23],[25,77616,77617],{"xmlns":27},[29,77618,77619,77623],{},[32,77620,77621],{},[35,77622,37],{},[39,77624,37],{"encoding":41},[15,77626,77628],{"className":77627,"ariaHidden":46},[45],[15,77629,77631,77634],{"className":77630},[50],[15,77632],{"className":77633,"style":55},[54],[15,77635,37],{"className":77636,"style":61},[59,60]," 严格凸，等号成立当且仅当 ",[15,77639,77641,77669],{"className":77640,"translate":19},[18],[15,77642,77644],{"className":77643},[23],[25,77645,77646],{"xmlns":27},[29,77647,77648,77666],{},[32,77649,77650,77656,77658,77660,77662,77664],{},[195,77651,77652,77654],{},[35,77653,223],{"mathvariant":222},[35,77655,213],{},[110,77657,230],{"stretchy":112},[35,77659,769],{},[35,77661,4808],{"mathvariant":209},[35,77663,5401],{},[110,77665,257],{"stretchy":112},[39,77667,77668],{"encoding":41},"\\mathbb E_Q[t|Y]",[15,77670,77672],{"className":77671,"ariaHidden":46},[45],[15,77673,77675,77678,77718,77721,77724,77727,77730],{"className":77674},[50],[15,77676],{"className":77677,"style":270},[54],[15,77679,77681,77684],{"className":77680},[59],[15,77682,223],{"className":77683},[59,366],[15,77685,77687],{"className":77686},[281],[15,77688,77690,77710],{"className":77689},[285,286],[15,77691,77693,77707],{"className":77692},[290],[15,77694,77696],{"className":77695,"style":379},[294],[15,77697,77698,77701],{"style":382},[15,77699],{"className":77700,"style":303},[302],[15,77702,77704],{"className":77703},[307,308,309,310],[15,77705,213],{"className":77706},[59,60,310],[15,77708,318],{"className":77709},[317],[15,77711,77713],{"className":77712},[290],[15,77714,77716],{"className":77715,"style":325},[294],[15,77717],{},[15,77719,230],{"className":77720},[146],[15,77722,769],{"className":77723},[59,60],[15,77725,4808],{"className":77726},[59],[15,77728,5401],{"className":77729,"style":2587},[59,60],[15,77731,257],{"className":77732},[153]," 本身是 ",[15,77735,77737,77757],{"className":77736,"translate":19},[18],[15,77738,77740],{"className":77739},[23],[25,77741,77742],{"xmlns":27},[29,77743,77744,77754],{},[32,77745,77746,77748,77750,77752],{},[35,77747,2332],{},[110,77749,113],{"stretchy":112},[35,77751,5401],{},[110,77753,120],{"stretchy":112},[39,77755,77756],{"encoding":41},"\\sigma(Y)",[15,77758,77760],{"className":77759,"ariaHidden":46},[45],[15,77761,77763,77766,77769,77772,77775],{"className":77762},[50],[15,77764],{"className":77765,"style":139},[54],[15,77767,2332],{"className":77768,"style":981},[59,60],[15,77770,113],{"className":77771},[146],[15,77773,5401],{"className":77774,"style":2587},[59,60],[15,77776,120],{"className":77777},[153],"-可测的（对每个 ",[15,77780,77782,77795],{"className":77781,"translate":19},[18],[15,77783,77785],{"className":77784},[23],[25,77786,77787],{"xmlns":27},[29,77788,77789,77793],{},[32,77790,77791],{},[35,77792,40237],{},[39,77794,40237],{"encoding":41},[15,77796,77798],{"className":77797,"ariaHidden":46},[45],[15,77799,77801,77804],{"className":77800},[50],[15,77802],{"className":77803,"style":2276},[54],[15,77805,40237],{"className":77806,"style":981},[59,60]," 是常数），即 ",[15,77809,77811,77836],{"className":77810,"translate":19},[18],[15,77812,77814],{"className":77813},[23],[25,77815,77816],{"xmlns":27},[29,77817,77818,77834],{},[32,77819,77820,77822,77824,77826,77828,77830,77832],{},[35,77821,769],{},[110,77823,123],{},[35,77825,244],{},[35,77827,206],{},[35,77829,941],{"mathvariant":209},[35,77831,244],{},[35,77833,213],{},[39,77835,5333],{"encoding":41},[15,77837,77839,77857],{"className":77838,"ariaHidden":46},[45],[15,77840,77842,77845,77848,77851,77854],{"className":77841},[50],[15,77843],{"className":77844,"style":5343},[54],[15,77846,769],{"className":77847},[59,60],[15,77849],{"className":77850,"style":158},[157],[15,77852,123],{"className":77853},[162],[15,77855],{"className":77856,"style":158},[157],[15,77858,77860,77863,77866,77869,77872,77875],{"className":77859},[50],[15,77861],{"className":77862,"style":139},[54],[15,77864,244],{"className":77865},[59,60],[15,77867,206],{"className":77868,"style":334},[59,60],[15,77870,941],{"className":77871},[59],[15,77873,244],{"className":77874},[59,60],[15,77876,213],{"className":77877},[59,60]," 可表为 ",[15,77880,77882,77895],{"className":77881,"translate":19},[18],[15,77883,77885],{"className":77884},[23],[25,77886,77887],{"xmlns":27},[29,77888,77889,77893],{},[32,77890,77891],{},[35,77892,5401],{},[39,77894,5401],{"encoding":41},[15,77896,77898],{"className":77897,"ariaHidden":46},[45],[15,77899,77901,77904],{"className":77900},[50],[15,77902],{"className":77903,"style":664},[54],[15,77905,5401],{"className":77906,"style":2587},[59,60]," 的函数。此时 ",[15,77909,77911,77924],{"className":77910,"translate":19},[18],[15,77912,77914],{"className":77913},[23],[25,77915,77916],{"xmlns":27},[29,77917,77918,77922],{},[32,77919,77920],{},[35,77921,5401],{},[39,77923,5401],{"encoding":41},[15,77925,77927],{"className":77926,"ariaHidden":46},[45],[15,77928,77930,77933],{"className":77929},[50],[15,77931],{"className":77932,"style":664},[54],[15,77934,5401],{"className":77935,"style":2587},[59,60]," 是关于 ",[15,77938,77940,77957],{"className":77939,"translate":19},[18],[15,77941,77943],{"className":77942},[23],[25,77944,77945],{"xmlns":27},[29,77946,77947,77955],{},[32,77948,77949,77951,77953],{},[35,77950,206],{},[110,77952,551],{"separator":46},[35,77954,213],{},[39,77956,556],{"encoding":41},[15,77958,77960],{"className":77959,"ariaHidden":46},[45],[15,77961,77963,77966,77969,77972,77975],{"className":77962},[50],[15,77964],{"className":77965,"style":566},[54],[15,77967,206],{"className":77968,"style":334},[59,60],[15,77970,551],{"className":77971},[573],[15,77973],{"className":77974,"style":406},[157],[15,77976,213],{"className":77977},[59,60],[1225,77979,77980],{},"充分统计量","：随机变换没有丢信息。这正是 f-散度能担当「信息量」的原因。",[11,77983,77984,77987,77988,78029],{},[1225,77985,77986],{},"信息单调性（Csiszár 的更进一步结果）。"," 对 α-散度族，还有更强的「信息单调性」：把 ",[15,77989,77991,78008],{"className":77990,"translate":19},[18],[15,77992,77994],{"className":77993},[23],[25,77995,77996],{"xmlns":27},[29,77997,77998,78006],{},[32,77999,78000,78002,78004],{},[35,78001,206],{},[110,78003,551],{"separator":46},[35,78005,213],{},[39,78007,556],{"encoding":41},[15,78009,78011],{"className":78010,"ariaHidden":46},[45],[15,78012,78014,78017,78020,78023,78026],{"className":78013},[50],[15,78015],{"className":78016,"style":566},[54],[15,78018,206],{"className":78019,"style":334},[59,60],[15,78021,551],{"className":78022},[573],[15,78024],{"className":78025,"style":406},[157],[15,78027,213],{"className":78028},[59,60]," 粗粒化（把样本空间划分得更粗）时散度不增，且存在严格单调的「信息序」。这构成了 Chentsov–Morozova 定理与信息几何中单调度量的基础。",[2311,78031,78033],{"id":78032},"_46-局部二次展开","4.6 局部二次展开",[993,78035,78037,78447],{"title":78036},"命题 4.5（局部二次展开）",[11,78038,534,78039,78067,78068,5645,78142,20956,78246,78395,78396,29933],{},[15,78040,78042,78055],{"className":78041,"translate":19},[18],[15,78043,78045],{"className":78044},[23],[25,78046,78047],{"xmlns":27},[29,78048,78049,78053],{},[32,78050,78051],{},[35,78052,38665],{},[39,78054,38665],{"encoding":41},[15,78056,78058],{"className":78057,"ariaHidden":46},[45],[15,78059,78061,78064],{"className":78060},[50],[15,78062],{"className":78063,"style":12597},[54],[15,78065,38665],{"className":78066},[59,60]," 满足 ",[15,78069,78071,78097],{"className":78070,"translate":19},[18],[15,78072,78074],{"className":78073},[23],[25,78075,78076],{"xmlns":27},[29,78077,78078,78094],{},[32,78079,78080,78082,78084,78086,78088,78090,78092],{},[110,78081,1287],{},[35,78083,38665],{},[1297,78085,1299],{},[35,78087,244],{},[35,78089,206],{},[110,78091,123],{},[115,78093,126],{},[39,78095,78096],{"encoding":41},"\\int h\\,dP=0",[15,78098,78100,78133],{"className":78099,"ariaHidden":46},[45],[15,78101,78103,78106,78109,78112,78115,78118,78121,78124,78127,78130],{"className":78102},[50],[15,78104],{"className":78105,"style":5612},[54],[15,78107,1287],{"className":78108,"style":5617},[1484,1485,5616],[15,78110],{"className":78111,"style":406},[157],[15,78113,38665],{"className":78114},[59,60],[15,78116],{"className":78117,"style":406},[157],[15,78119,244],{"className":78120},[59,60],[15,78122,206],{"className":78123,"style":334},[59,60],[15,78125],{"className":78126,"style":158},[157],[15,78128,123],{"className":78129},[162],[15,78131],{"className":78132,"style":158},[157],[15,78134,78136,78139],{"className":78135},[50],[15,78137],{"className":78138,"style":172},[54],[15,78140,126],{"className":78141},[59],[15,78143,78145,78175],{"className":78144,"translate":19},[18],[15,78146,78148],{"className":78147},[23],[25,78149,78150],{"xmlns":27},[29,78151,78152,78172],{},[32,78153,78154,78156,78162,78164,78166,78168,78170],{},[110,78155,1287],{},[6814,78157,78158,78160],{},[35,78159,38665],{},[115,78161,2463],{},[1297,78163,1299],{},[35,78165,244],{},[35,78167,206],{},[110,78169,7251],{},[35,78171,1024],{"mathvariant":209},[39,78173,78174],{"encoding":41},"\\int h^2\\,dP\u003C\\infty",[15,78176,78178,78237],{"className":78177,"ariaHidden":46},[45],[15,78179,78181,78184,78187,78190,78219,78222,78225,78228,78231,78234],{"className":78180},[50],[15,78182],{"className":78183,"style":50328},[54],[15,78185,1287],{"className":78186,"style":5617},[1484,1485,5616],[15,78188],{"className":78189,"style":406},[157],[15,78191,78193,78196],{"className":78192},[59],[15,78194,38665],{"className":78195},[59,60],[15,78197,78199],{"className":78198},[281],[15,78200,78202],{"className":78201},[285],[15,78203,78205],{"className":78204},[290],[15,78206,78208],{"className":78207,"style":20028},[294],[15,78209,78210,78213],{"style":6865},[15,78211],{"className":78212,"style":303},[302],[15,78214,78216],{"className":78215},[307,308,309,310],[15,78217,2463],{"className":78218},[59,310],[15,78220],{"className":78221,"style":406},[157],[15,78223,244],{"className":78224},[59,60],[15,78226,206],{"className":78227,"style":334},[59,60],[15,78229],{"className":78230,"style":158},[157],[15,78232,7251],{"className":78233},[162],[15,78235],{"className":78236,"style":158},[157],[15,78238,78240,78243],{"className":78239},[50],[15,78241],{"className":78242,"style":2345},[54],[15,78244,1024],{"className":78245},[59],[15,78247,78249,78289],{"className":78248,"translate":19},[18],[15,78250,78252],{"className":78251},[23],[25,78253,78254],{"xmlns":27},[29,78255,78256,78286],{},[32,78257,78258,78260,78266,78268,78270,78272,78274,78276,78278,78280,78282,78284],{},[35,78259,244],{},[195,78261,78262,78264],{},[35,78263,213],{},[35,78265,38662],{},[110,78267,123],{},[110,78269,113],{"stretchy":112},[115,78271,117],{},[110,78273,2470],{},[35,78275,38662],{},[35,78277,38665],{},[110,78279,120],{"stretchy":112},[1297,78281,1299],{},[35,78283,244],{},[35,78285,206],{},[39,78287,78288],{"encoding":41},"dQ_\\varepsilon=(1+\\varepsilon h)\\,dP",[15,78290,78292,78350,78371],{"className":78291,"ariaHidden":46},[45],[15,78293,78295,78298,78301,78341,78344,78347],{"className":78294},[50],[15,78296],{"className":78297,"style":55},[54],[15,78299,244],{"className":78300},[59,60],[15,78302,78304,78307],{"className":78303},[59],[15,78305,213],{"className":78306},[59,60],[15,78308,78310],{"className":78309},[281],[15,78311,78313,78333],{"className":78312},[285,286],[15,78314,78316,78330],{"className":78315},[290],[15,78317,78319],{"className":78318,"style":44929},[294],[15,78320,78321,78324],{"style":382},[15,78322],{"className":78323,"style":303},[302],[15,78325,78327],{"className":78326},[307,308,309,310],[15,78328,38662],{"className":78329},[59,60,310],[15,78331,318],{"className":78332},[317],[15,78334,78336],{"className":78335},[290],[15,78337,78339],{"className":78338,"style":7968},[294],[15,78340],{},[15,78342],{"className":78343,"style":158},[157],[15,78345,123],{"className":78346},[162],[15,78348],{"className":78349,"style":158},[157],[15,78351,78353,78356,78359,78362,78365,78368],{"className":78352},[50],[15,78354],{"className":78355,"style":139},[54],[15,78357,113],{"className":78358},[146],[15,78360,117],{"className":78361},[59],[15,78363],{"className":78364,"style":2587},[157],[15,78366,2470],{"className":78367},[2591],[15,78369],{"className":78370,"style":2587},[157],[15,78372,78374,78377,78380,78383,78386,78389,78392],{"className":78373},[50],[15,78375],{"className":78376,"style":139},[54],[15,78378,38662],{"className":78379},[59,60],[15,78381,38665],{"className":78382},[59,60],[15,78384,120],{"className":78385},[153],[15,78387],{"className":78388,"style":406},[157],[15,78390,244],{"className":78391},[59,60],[15,78393,206],{"className":78394,"style":334},[59,60],"，则当 ",[15,78397,78399,78417],{"className":78398,"translate":19},[18],[15,78400,78402],{"className":78401},[23],[25,78403,78404],{"xmlns":27},[29,78405,78406,78414],{},[32,78407,78408,78410,78412],{},[35,78409,38662],{},[110,78411,1029],{},[115,78413,126],{},[39,78415,78416],{"encoding":41},"\\varepsilon\\to0",[15,78418,78420,78438],{"className":78419,"ariaHidden":46},[45],[15,78421,78423,78426,78429,78432,78435],{"className":78422},[50],[15,78424],{"className":78425,"style":2345},[54],[15,78427,38662],{"className":78428},[59,60],[15,78430],{"className":78431,"style":158},[157],[15,78433,1029],{"className":78434},[162],[15,78436],{"className":78437,"style":158},[157],[15,78439,78441,78444],{"className":78440},[50],[15,78442],{"className":78443,"style":172},[54],[15,78445,126],{"className":78446},[59],[15,78448,78450],{"className":78449,"translate":19},[180],[15,78451,78453,78549],{"className":78452,"translate":19},[18],[15,78454,78456],{"className":78455},[23],[25,78457,78458],{"xmlns":27,"display":189},[29,78459,78460,78546],{},[32,78461,78462,78468,78470,78476,78478,78480,78482,78484,78506,78508,78514,78516,78518,78524,78526,78528,78530,78532,78534,78536,78542,78544],{},[195,78463,78464,78466],{},[35,78465,199],{},[35,78467,37],{},[110,78469,113],{"stretchy":112},[195,78471,78472,78474],{},[35,78473,213],{},[35,78475,38662],{},[35,78477,210],{"mathvariant":209},[35,78479,206],{},[110,78481,120],{"stretchy":112},[110,78483,123],{},[238,78485,78486,78504],{},[32,78487,78488,78498,78500,78502],{},[6814,78489,78490,78492],{},[35,78491,37],{},[32,78493,78494,78496],{},[110,78495,6820],{"mathvariant":209},[110,78497,6820],{"mathvariant":209},[110,78499,113],{"stretchy":112},[115,78501,117],{},[110,78503,120],{"stretchy":112},[115,78505,2463],{},[1297,78507,1299],{},[6814,78509,78510,78512],{},[35,78511,38662],{},[115,78513,2463],{},[1297,78515,1304],{},[110,78517,1287],{},[6814,78519,78520,78522],{},[35,78521,38665],{},[115,78523,2463],{},[1297,78525,1299],{},[35,78527,244],{},[35,78529,206],{},[110,78531,2470],{},[35,78533,19221],{},[110,78535,113],{"stretchy":112},[6814,78537,78538,78540],{},[35,78539,38662],{},[115,78541,40735],{},[110,78543,120],{"stretchy":112},[35,78545,4375],{"mathvariant":209},[39,78547,78548],{"encoding":41},"D_f(Q_\\varepsilon\\|P)\n=\\frac{f''(1)}{2}\\,\\varepsilon^{2}\\!\n\\int h^{2}\\,dP\n+O(\\varepsilon^{3}).",[15,78550,78552,78659,78864],{"className":78551,"ariaHidden":46},[45],[15,78553,78555,78558,78598,78601,78641,78644,78647,78650,78653,78656],{"className":78554},[50],[15,78556],{"className":78557,"style":270},[54],[15,78559,78561,78564],{"className":78560},[59],[15,78562,199],{"className":78563,"style":277},[59,60],[15,78565,78567],{"className":78566},[281],[15,78568,78570,78590],{"className":78569},[285,286],[15,78571,78573,78587],{"className":78572},[290],[15,78574,78576],{"className":78575,"style":295},[294],[15,78577,78578,78581],{"style":298},[15,78579],{"className":78580,"style":303},[302],[15,78582,78584],{"className":78583},[307,308,309,310],[15,78585,37],{"className":78586,"style":61},[59,60,310],[15,78588,318],{"className":78589},[317],[15,78591,78593],{"className":78592},[290],[15,78594,78596],{"className":78595,"style":325},[294],[15,78597],{},[15,78599,113],{"className":78600},[146],[15,78602,78604,78607],{"className":78603},[59],[15,78605,213],{"className":78606},[59,60],[15,78608,78610],{"className":78609},[281],[15,78611,78613,78633],{"className":78612},[285,286],[15,78614,78616,78630],{"className":78615},[290],[15,78617,78619],{"className":78618,"style":44929},[294],[15,78620,78621,78624],{"style":382},[15,78622],{"className":78623,"style":303},[302],[15,78625,78627],{"className":78626},[307,308,309,310],[15,78628,38662],{"className":78629},[59,60,310],[15,78631,318],{"className":78632},[317],[15,78634,78636],{"className":78635},[290],[15,78637,78639],{"className":78638,"style":7968},[294],[15,78640],{},[15,78642,210],{"className":78643},[59],[15,78645,206],{"className":78646,"style":334},[59,60],[15,78648,120],{"className":78649},[153],[15,78651],{"className":78652,"style":158},[157],[15,78654,123],{"className":78655},[162],[15,78657],{"className":78658,"style":158},[157],[15,78660,78662,78666,78767,78770,78802,78805,78808,78811,78814,78846,78849,78852,78855,78858,78861],{"className":78661},[50],[15,78663],{"className":78664,"style":78665},[54],"height:2.2911em;vertical-align:-0.8622em;",[15,78667,78669,78672,78764],{"className":78668},[59],[15,78670],{"className":78671},[146,441],[15,78673,78675],{"className":78674},[238],[15,78676,78678,78756],{"className":78677},[285,286],[15,78679,78681,78753],{"className":78680},[290],[15,78682,78685,78696,78704],{"className":78683,"style":78684},[294],"height:1.4289em;",[15,78686,78687,78690],{"style":457},[15,78688],{"className":78689,"style":461},[302],[15,78691,78693],{"className":78692},[59],[15,78694,2463],{"className":78695},[59],[15,78697,78698,78701],{"style":473},[15,78699],{"className":78700,"style":461},[302],[15,78702],{"className":78703,"style":481},[480],[15,78705,78706,78709],{"style":484},[15,78707],{"className":78708,"style":461},[302],[15,78710,78712,78744,78747,78750],{"className":78711},[59],[15,78713,78715,78718],{"className":78714},[59],[15,78716,37],{"className":78717,"style":61},[59,60],[15,78719,78721],{"className":78720},[281],[15,78722,78724],{"className":78723},[285],[15,78725,78727],{"className":78726},[290],[15,78728,78730],{"className":78729,"style":6862},[294],[15,78731,78732,78735],{"style":6865},[15,78733],{"className":78734,"style":303},[302],[15,78736,78738],{"className":78737},[307,308,309,310],[15,78739,78741],{"className":78740},[59,310],[15,78742,21748],{"className":78743},[59,310],[15,78745,113],{"className":78746},[146],[15,78748,117],{"className":78749},[59],[15,78751,120],{"className":78752},[153],[15,78754,318],{"className":78755},[317],[15,78757,78759],{"className":78758},[290],[15,78760,78762],{"className":78761,"style":3778},[294],[15,78763],{},[15,78765],{"className":78766},[153,441],[15,78768],{"className":78769,"style":406},[157],[15,78771,78773,78776],{"className":78772},[59],[15,78774,38662],{"className":78775},[59,60],[15,78777,78779],{"className":78778},[281],[15,78780,78782],{"className":78781},[285],[15,78783,78785],{"className":78784},[290],[15,78786,78788],{"className":78787,"style":19735},[294],[15,78789,78790,78793],{"style":8277},[15,78791],{"className":78792,"style":303},[302],[15,78794,78796],{"className":78795},[307,308,309,310],[15,78797,78799],{"className":78798},[59,310],[15,78800,2463],{"className":78801},[59,310],[15,78803],{"className":78804,"style":1512},[157],[15,78806],{"className":78807,"style":406},[157],[15,78809,1287],{"className":78810,"style":1487},[1484,1485,1486],[15,78812],{"className":78813,"style":406},[157],[15,78815,78817,78820],{"className":78816},[59],[15,78818,38665],{"className":78819},[59,60],[15,78821,78823],{"className":78822},[281],[15,78824,78826],{"className":78825},[285],[15,78827,78829],{"className":78828},[290],[15,78830,78832],{"className":78831,"style":19735},[294],[15,78833,78834,78837],{"style":8277},[15,78835],{"className":78836,"style":303},[302],[15,78838,78840],{"className":78839},[307,308,309,310],[15,78841,78843],{"className":78842},[59,310],[15,78844,2463],{"className":78845},[59,310],[15,78847],{"className":78848,"style":406},[157],[15,78850,244],{"className":78851},[59,60],[15,78853,206],{"className":78854,"style":334},[59,60],[15,78856],{"className":78857,"style":2587},[157],[15,78859,2470],{"className":78860},[2591],[15,78862],{"className":78863,"style":2587},[157],[15,78865,78867,78870,78873,78876,78908,78911],{"className":78866},[50],[15,78868],{"className":78869,"style":37251},[54],[15,78871,19221],{"className":78872,"style":277},[59,60],[15,78874,113],{"className":78875},[146],[15,78877,78879,78882],{"className":78878},[59],[15,78880,38662],{"className":78881},[59,60],[15,78883,78885],{"className":78884},[281],[15,78886,78888],{"className":78887},[285],[15,78889,78891],{"className":78890},[290],[15,78892,78894],{"className":78893,"style":19735},[294],[15,78895,78896,78899],{"style":8277},[15,78897],{"className":78898,"style":303},[302],[15,78900,78902],{"className":78901},[307,308,309,310],[15,78903,78905],{"className":78904},[59,310],[15,78906,40735],{"className":78907},[59,310],[15,78909,120],{"className":78910},[153],[15,78912,4375],{"className":78913},[59],[11,78915,78916,78918,78919,79080,79081,5645,79146,79219],{},[1225,78917,55471],{}," 记 ",[15,78920,78922,78962],{"className":78921,"translate":19},[18],[15,78923,78925],{"className":78924},[23],[25,78926,78927],{"xmlns":27},[29,78928,78929,78959],{},[32,78930,78931,78933,78935,78937,78943,78945,78947,78949,78951,78953,78955,78957],{},[35,78932,769],{},[110,78934,123],{},[35,78936,244],{},[195,78938,78939,78941],{},[35,78940,213],{},[35,78942,38662],{},[35,78944,941],{"mathvariant":209},[35,78946,244],{},[35,78948,206],{},[110,78950,123],{},[115,78952,117],{},[110,78954,2470],{},[35,78956,38662],{},[35,78958,38665],{},[39,78960,78961],{"encoding":41},"t=dQ_\\varepsilon\u002FdP=1+\\varepsilon h",[15,78963,78965,78983,79050,79068],{"className":78964,"ariaHidden":46},[45],[15,78966,78968,78971,78974,78977,78980],{"className":78967},[50],[15,78969],{"className":78970,"style":5343},[54],[15,78972,769],{"className":78973},[59,60],[15,78975],{"className":78976,"style":158},[157],[15,78978,123],{"className":78979},[162],[15,78981],{"className":78982,"style":158},[157],[15,78984,78986,78989,78992,79032,79035,79038,79041,79044,79047],{"className":78985},[50],[15,78987],{"className":78988,"style":139},[54],[15,78990,244],{"className":78991},[59,60],[15,78993,78995,78998],{"className":78994},[59],[15,78996,213],{"className":78997},[59,60],[15,78999,79001],{"className":79000},[281],[15,79002,79004,79024],{"className":79003},[285,286],[15,79005,79007,79021],{"className":79006},[290],[15,79008,79010],{"className":79009,"style":44929},[294],[15,79011,79012,79015],{"style":382},[15,79013],{"className":79014,"style":303},[302],[15,79016,79018],{"className":79017},[307,308,309,310],[15,79019,38662],{"className":79020},[59,60,310],[15,79022,318],{"className":79023},[317],[15,79025,79027],{"className":79026},[290],[15,79028,79030],{"className":79029,"style":7968},[294],[15,79031],{},[15,79033,941],{"className":79034},[59],[15,79036,244],{"className":79037},[59,60],[15,79039,206],{"className":79040,"style":334},[59,60],[15,79042],{"className":79043,"style":158},[157],[15,79045,123],{"className":79046},[162],[15,79048],{"className":79049,"style":158},[157],[15,79051,79053,79056,79059,79062,79065],{"className":79052},[50],[15,79054],{"className":79055,"style":12578},[54],[15,79057,117],{"className":79058},[59],[15,79060],{"className":79061,"style":2587},[157],[15,79063,2470],{"className":79064},[2591],[15,79066],{"className":79067,"style":2587},[157],[15,79069,79071,79074,79077],{"className":79070},[50],[15,79072],{"className":79073,"style":12597},[54],[15,79075,38662],{"className":79076},[59,60],[15,79078,38665],{"className":79079},[59,60],"，由 ",[15,79082,79084,79107],{"className":79083,"translate":19},[18],[15,79085,79087],{"className":79086},[23],[25,79088,79089],{"xmlns":27},[29,79090,79091,79105],{},[32,79092,79093,79095,79097,79099,79101,79103],{},[35,79094,37],{},[110,79096,113],{"stretchy":112},[115,79098,117],{},[110,79100,120],{"stretchy":112},[110,79102,123],{},[115,79104,126],{},[39,79106,129],{"encoding":41},[15,79108,79110,79137],{"className":79109,"ariaHidden":46},[45],[15,79111,79113,79116,79119,79122,79125,79128,79131,79134],{"className":79112},[50],[15,79114],{"className":79115,"style":139},[54],[15,79117,37],{"className":79118,"style":61},[59,60],[15,79120,113],{"className":79121},[146],[15,79123,117],{"className":79124},[59],[15,79126,120],{"className":79127},[153],[15,79129],{"className":79130,"style":158},[157],[15,79132,123],{"className":79133},[162],[15,79135],{"className":79136,"style":158},[157],[15,79138,79140,79143],{"className":79139},[50],[15,79141],{"className":79142,"style":172},[54],[15,79144,126],{"className":79145},[59],[15,79147,79149,79174],{"className":79148,"translate":19},[18],[15,79150,79152],{"className":79151},[23],[25,79153,79154],{"xmlns":27},[29,79155,79156,79172],{},[32,79157,79158,79160,79162,79164,79166,79168,79170],{},[110,79159,1287],{},[35,79161,38665],{},[1297,79163,1299],{},[35,79165,244],{},[35,79167,206],{},[110,79169,123],{},[115,79171,126],{},[39,79173,78096],{"encoding":41},[15,79175,79177,79210],{"className":79176,"ariaHidden":46},[45],[15,79178,79180,79183,79186,79189,79192,79195,79198,79201,79204,79207],{"className":79179},[50],[15,79181],{"className":79182,"style":5612},[54],[15,79184,1287],{"className":79185,"style":5617},[1484,1485,5616],[15,79187],{"className":79188,"style":406},[157],[15,79190,38665],{"className":79191},[59,60],[15,79193],{"className":79194,"style":406},[157],[15,79196,244],{"className":79197},[59,60],[15,79199,206],{"className":79200,"style":334},[59,60],[15,79202],{"className":79203,"style":158},[157],[15,79205,123],{"className":79206},[162],[15,79208],{"className":79209,"style":158},[157],[15,79211,79213,79216],{"className":79212},[50],[15,79214],{"className":79215,"style":172},[54],[15,79217,126],{"className":79218},[59]," 做 Taylor 展开：",[15,79221,79223],{"className":79222,"translate":19},[180],[15,79224,79226,79454],{"className":79225,"translate":19},[18],[15,79227,79229],{"className":79228},[23],[25,79230,79231],{"xmlns":27,"display":189},[29,79232,79233,79451],{},[1243,79234,79235,79297,79371],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,79236,79237,79263],{},[1252,79238,79239],{},[1255,79240,79241],{"scriptlevel":126,"displaystyle":46},[32,79242,79243,79249,79251,79257,79259,79261],{},[195,79244,79245,79247],{},[35,79246,199],{},[35,79248,37],{},[110,79250,113],{"stretchy":112},[195,79252,79253,79255],{},[35,79254,213],{},[35,79256,38662],{},[35,79258,210],{"mathvariant":209},[35,79260,206],{},[110,79262,120],{"stretchy":112},[1252,79264,79265],{},[1255,79266,79267],{"scriptlevel":126,"displaystyle":46},[32,79268,79269,79271,79273,79279,79281,79283,79285,79287,79289,79291,79293,79295],{},[32,79270],{},[110,79272,123],{},[195,79274,79275,79277],{},[35,79276,223],{"mathvariant":222},[35,79278,206],{},[110,79280,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,79282,37],{},[110,79284,113],{"stretchy":112},[115,79286,117],{},[110,79288,2470],{},[35,79290,38662],{},[35,79292,38665],{},[110,79294,120],{"stretchy":112},[110,79296,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[1249,79298,79299,79305],{},[1252,79300,79301],{},[1255,79302,79303],{"scriptlevel":126,"displaystyle":46},[32,79304],{},[1252,79306,79307],{},[1255,79308,79309],{"scriptlevel":126,"displaystyle":46},[32,79310,79311,79313,79315,79333,79335,79337,79343,79345,79347,79349],{},[32,79312],{},[110,79314,123],{},[6016,79316,79317,79331],{},[6016,79318,79319,79329],{},[32,79320,79321,79323,79325,79327],{},[35,79322,37],{},[110,79324,113],{"stretchy":112},[115,79326,117],{},[110,79328,120],{"stretchy":112},[110,79330,6040],{"stretchy":46},[115,79332,126],{},[110,79334,2470],{},[35,79336,38662],{},[6814,79338,79339,79341],{},[35,79340,37],{},[110,79342,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,79344,113],{"stretchy":112},[115,79346,117],{},[110,79348,120],{"stretchy":112},[6016,79350,79351,79369],{},[6016,79352,79353,79367],{},[32,79354,79355,79361,79363,79365],{},[195,79356,79357,79359],{},[35,79358,223],{"mathvariant":222},[35,79360,206],{},[110,79362,230],{"stretchy":112},[35,79364,38665],{},[110,79366,257],{"stretchy":112},[110,79368,6040],{"stretchy":46},[115,79370,126],{},[1249,79372,79373,79379],{},[1252,79374,79375],{},[1255,79376,79377],{"scriptlevel":126,"displaystyle":46},[32,79378],{},[1252,79380,79381],{},[1255,79382,79383],{"scriptlevel":126,"displaystyle":46},[32,79384,79385,79387,79389,79391,79401,79411,79413,79415,79417,79419,79425,79427,79433,79435,79437,79439,79441,79447,79449],{},[32,79386],{},[157,79388],{"width":3262},[110,79390,2470],{},[238,79392,79393,79399],{},[6814,79394,79395,79397],{},[35,79396,38662],{},[115,79398,2463],{},[115,79400,2463],{},[6814,79402,79403,79405],{},[35,79404,37],{},[32,79406,79407,79409],{},[110,79408,6820],{"mathvariant":209},[110,79410,6820],{"mathvariant":209},[110,79412,113],{"stretchy":112},[115,79414,117],{},[110,79416,120],{"stretchy":112},[1297,79418,1299],{},[195,79420,79421,79423],{},[35,79422,223],{"mathvariant":222},[35,79424,206],{},[110,79426,230],{"stretchy":112},[6814,79428,79429,79431],{},[35,79430,38665],{},[115,79432,2463],{},[110,79434,257],{"stretchy":112},[110,79436,2470],{},[35,79438,19221],{},[110,79440,113],{"stretchy":112},[6814,79442,79443,79445],{},[35,79444,38662],{},[115,79446,40735],{},[110,79448,120],{"stretchy":112},[35,79450,4375],{"mathvariant":209},[39,79452,79453],{"encoding":41},"\\begin{aligned}\nD_f(Q_\\varepsilon\\|P)\n&=\\mathbb E_P\\big[f(1+\\varepsilon h)\\big]\\\\[2pt]\n&=\\underbrace{f(1)}_{0}\n+\\varepsilon f'(1)\n\\underbrace{\\mathbb E_P[h]}_{0}\\\\\n&\\qquad+\\frac{\\varepsilon^2}{2}f''(1)\\,\n\\mathbb E_P[h^2]\n+O(\\varepsilon^3).\n\\end{aligned}",[15,79455,79457],{"className":79456,"ariaHidden":46},[45],[15,79458,79460,79464],{"className":79459},[50],[15,79461],{"className":79462,"style":79463},[54],"height:6.5762em;vertical-align:-3.0381em;",[15,79465,79467],{"className":79466},[59],[15,79468,79470,79615],{"className":79469},[1243],[15,79471,79473],{"className":79472},[1360],[15,79474,79476,79606],{"className":79475},[285,286],[15,79477,79479,79603],{"className":79478},[290],[15,79480,79483,79585,79594],{"className":79481,"style":79482},[294],"height:3.5381em;",[15,79484,79486,79490],{"style":79485},"top:-6.1792em;",[15,79487],{"className":79488,"style":79489},[302],"height:3.4911em;",[15,79491,79493,79533,79536,79576,79579,79582],{"className":79492},[59],[15,79494,79496,79499],{"className":79495},[59],[15,79497,199],{"className":79498,"style":277},[59,60],[15,79500,79502],{"className":79501},[281],[15,79503,79505,79525],{"className":79504},[285,286],[15,79506,79508,79522],{"className":79507},[290],[15,79509,79511],{"className":79510,"style":295},[294],[15,79512,79513,79516],{"style":298},[15,79514],{"className":79515,"style":303},[302],[15,79517,79519],{"className":79518},[307,308,309,310],[15,79520,37],{"className":79521,"style":61},[59,60,310],[15,79523,318],{"className":79524},[317],[15,79526,79528],{"className":79527},[290],[15,79529,79531],{"className":79530,"style":325},[294],[15,79532],{},[15,79534,113],{"className":79535},[146],[15,79537,79539,79542],{"className":79538},[59],[15,79540,213],{"className":79541},[59,60],[15,79543,79545],{"className":79544},[281],[15,79546,79548,79568],{"className":79547},[285,286],[15,79549,79551,79565],{"className":79550},[290],[15,79552,79554],{"className":79553,"style":44929},[294],[15,79555,79556,79559],{"style":382},[15,79557],{"className":79558,"style":303},[302],[15,79560,79562],{"className":79561},[307,308,309,310],[15,79563,38662],{"className":79564},[59,60,310],[15,79566,318],{"className":79567},[317],[15,79569,79571],{"className":79570},[290],[15,79572,79574],{"className":79573,"style":7968},[294],[15,79575],{},[15,79577,210],{"className":79578},[59],[15,79580,206],{"className":79581,"style":334},[59,60],[15,79583,120],{"className":79584},[153],[15,79586,79588,79591],{"style":79587},"top:-4.4792em;",[15,79589],{"className":79590,"style":79489},[302],[15,79592],{"className":79593},[59],[15,79595,79597,79600],{"style":79596},"top:-1.139em;",[15,79598],{"className":79599,"style":79489},[302],[15,79601],{"className":79602},[59],[15,79604,318],{"className":79605},[317],[15,79607,79609],{"className":79608},[290],[15,79610,79613],{"className":79611,"style":79612},[294],"height:3.0381em;",[15,79614],{},[15,79616,79618],{"className":79617},[1451],[15,79619,79621,80354],{"className":79620},[285,286],[15,79622,79624,80351],{"className":79623},[290],[15,79625,79627,79726,80071],{"className":79626,"style":79482},[294],[15,79628,79629,79632],{"style":79485},[15,79630],{"className":79631,"style":79489},[302],[15,79633,79635,79638,79641,79644,79647,79687,79693,79696,79699,79702,79705,79708,79711,79714,79717,79720],{"className":79634},[59],[15,79636],{"className":79637},[59],[15,79639],{"className":79640,"style":158},[157],[15,79642,123],{"className":79643},[162],[15,79645],{"className":79646,"style":158},[157],[15,79648,79650,79653],{"className":79649},[59],[15,79651,223],{"className":79652},[59,366],[15,79654,79656],{"className":79655},[281],[15,79657,79659,79679],{"className":79658},[285,286],[15,79660,79662,79676],{"className":79661},[290],[15,79663,79665],{"className":79664,"style":379},[294],[15,79666,79667,79670],{"style":382},[15,79668],{"className":79669,"style":303},[302],[15,79671,79673],{"className":79672},[307,308,309,310],[15,79674,206],{"className":79675,"style":334},[59,60,310],[15,79677,318],{"className":79678},[317],[15,79680,79682],{"className":79681},[290],[15,79683,79685],{"className":79684,"style":7968},[294],[15,79686],{},[15,79688,79690],{"className":79689},[59],[15,79691,230],{"className":79692},[419,9674],[15,79694,37],{"className":79695,"style":61},[59,60],[15,79697,113],{"className":79698},[146],[15,79700,117],{"className":79701},[59],[15,79703],{"className":79704,"style":2587},[157],[15,79706,2470],{"className":79707},[2591],[15,79709],{"className":79710,"style":2587},[157],[15,79712,38662],{"className":79713},[59,60],[15,79715,38665],{"className":79716},[59,60],[15,79718,120],{"className":79719},[153],[15,79721,79723],{"className":79722},[59],[15,79724,257],{"className":79725},[419,9674],[15,79727,79728,79731],{"style":79587},[15,79729],{"className":79730,"style":79489},[302],[15,79732,79734,79737,79740,79743,79746,79863,79866,79869,79872,79875,79907,79910,79913,79916,79919],{"className":79733},[59],[15,79735],{"className":79736},[59],[15,79738],{"className":79739,"style":158},[157],[15,79741,123],{"className":79742},[162],[15,79744],{"className":79745,"style":158},[157],[15,79747,79749],{"className":79748},[410,6016],[15,79750,79752,79854],{"className":79751},[285,286],[15,79753,79755,79851],{"className":79754},[290],[15,79756,79758,79773],{"className":79757,"style":24799},[294],[15,79759,79761,79764],{"style":79760},"top:-1.4509em;",[15,79762],{"className":79763,"style":461},[302],[15,79765,79767],{"className":79766},[307,308,309,310],[15,79768,79770],{"className":79769},[59,310],[15,79771,126],{"className":79772},[59,310],[15,79774,79775,79778],{"style":11863},[15,79776],{"className":79777,"style":461},[302],[15,79779,79781],{"className":79780},[410,6016],[15,79782,79784,79843],{"className":79783},[285,286],[15,79785,79787,79840],{"className":79786},[290],[15,79788,79790,79820],{"className":79789,"style":24799},[294],[15,79791,79793,79796],{"className":79792,"style":24838},[6307],[15,79794],{"className":79795,"style":461},[302],[15,79797,79799,79806,79813],{"className":79798,"style":6316},[6315],[15,79800,79802],{"className":79801,"style":6321},[6320],[6323,79803,79804],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6329},[6331,79805],{"d":6333},[15,79807,79809],{"className":79808,"style":6321},[6337],[6323,79810,79811],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6340},[6331,79812],{"d":6343},[15,79814,79816],{"className":79815,"style":6321},[6347],[6323,79817,79818],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6350},[6331,79819],{"d":6353},[15,79821,79822,79825],{"style":11863},[15,79823],{"className":79824,"style":461},[302],[15,79826,79828,79831,79834,79837],{"className":79827},[59],[15,79829,37],{"className":79830,"style":61},[59,60],[15,79832,113],{"className":79833},[146],[15,79835,117],{"className":79836},[59],[15,79838,120],{"className":79839},[153],[15,79841,318],{"className":79842},[317],[15,79844,79846],{"className":79845},[290],[15,79847,79849],{"className":79848,"style":24952},[294],[15,79850],{},[15,79852,318],{"className":79853},[317],[15,79855,79857],{"className":79856},[290],[15,79858,79861],{"className":79859,"style":79860},[294],"height:1.5491em;",[15,79862],{},[15,79864],{"className":79865,"style":2587},[157],[15,79867,2470],{"className":79868},[2591],[15,79870],{"className":79871,"style":2587},[157],[15,79873,38662],{"className":79874},[59,60],[15,79876,79878,79881],{"className":79877},[59],[15,79879,37],{"className":79880,"style":61},[59,60],[15,79882,79884],{"className":79883},[281],[15,79885,79887],{"className":79886},[285],[15,79888,79890],{"className":79889},[290],[15,79891,79893],{"className":79892,"style":28971},[294],[15,79894,79895,79898],{"style":8277},[15,79896],{"className":79897,"style":303},[302],[15,79899,79901],{"className":79900},[307,308,309,310],[15,79902,79904],{"className":79903},[59,310],[15,79905,6820],{"className":79906},[59,310],[15,79908,113],{"className":79909},[146],[15,79911,117],{"className":79912},[59],[15,79914,120],{"className":79915},[153],[15,79917],{"className":79918,"style":406},[157],[15,79920,79922],{"className":79921},[410,6016],[15,79923,79925,80063],{"className":79924},[285,286],[15,79926,79928,80060],{"className":79927},[290],[15,79929,79931,79945],{"className":79930,"style":24799},[294],[15,79932,79933,79936],{"style":79760},[15,79934],{"className":79935,"style":461},[302],[15,79937,79939],{"className":79938},[307,308,309,310],[15,79940,79942],{"className":79941},[59,310],[15,79943,126],{"className":79944},[59,310],[15,79946,79947,79950],{"style":11863},[15,79948],{"className":79949,"style":461},[302],[15,79951,79953],{"className":79952},[410,6016],[15,79954,79956,80052],{"className":79955},[285,286],[15,79957,79959,80049],{"className":79958},[290],[15,79960,79962,79992],{"className":79961,"style":24799},[294],[15,79963,79965,79968],{"className":79964,"style":24838},[6307],[15,79966],{"className":79967,"style":461},[302],[15,79969,79971,79978,79985],{"className":79970,"style":6316},[6315],[15,79972,79974],{"className":79973,"style":6321},[6320],[6323,79975,79976],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6329},[6331,79977],{"d":6333},[15,79979,79981],{"className":79980,"style":6321},[6337],[6323,79982,79983],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6340},[6331,79984],{"d":6343},[15,79986,79988],{"className":79987,"style":6321},[6347],[6323,79989,79990],{"xmlns":6325,"width":6326,"height":6327,"viewBox":6328,"preserveAspectRatio":6350},[6331,79991],{"d":6353},[15,79993,79994,79997],{"style":11863},[15,79995],{"className":79996,"style":461},[302],[15,79998,80000,80040,80043,80046],{"className":79999},[59],[15,80001,80003,80006],{"className":80002},[59],[15,80004,223],{"className":80005},[59,366],[15,80007,80009],{"className":80008},[281],[15,80010,80012,80032],{"className":80011},[285,286],[15,80013,80015,80029],{"className":80014},[290],[15,80016,80018],{"className":80017,"style":379},[294],[15,80019,80020,80023],{"style":382},[15,80021],{"className":80022,"style":303},[302],[15,80024,80026],{"className":80025},[307,308,309,310],[15,80027,206],{"className":80028,"style":334},[59,60,310],[15,80030,318],{"className":80031},[317],[15,80033,80035],{"className":80034},[290],[15,80036,80038],{"className":80037,"style":7968},[294],[15,80039],{},[15,80041,230],{"className":80042},[146],[15,80044,38665],{"className":80045},[59,60],[15,80047,257],{"className":80048},[153],[15,80050,318],{"className":80051},[317],[15,80053,80055],{"className":80054},[290],[15,80056,80058],{"className":80057,"style":24952},[294],[15,80059],{},[15,80061,318],{"className":80062},[317],[15,80064,80066],{"className":80065},[290],[15,80067,80069],{"className":80068,"style":79860},[294],[15,80070],{},[15,80072,80073,80076],{"style":79596},[15,80074],{"className":80075,"style":79489},[302],[15,80077,80079,80082,80085,80088,80091,80094,80182,80214,80217,80220,80223,80226,80266,80269,80298,80301,80304,80307,80310,80313,80316,80345,80348],{"className":80078},[59],[15,80080],{"className":80081},[59],[15,80083],{"className":80084,"style":3634},[157],[15,80086],{"className":80087,"style":2587},[157],[15,80089,2470],{"className":80090},[2591],[15,80092],{"className":80093,"style":2587},[157],[15,80095,80097,80100,80179],{"className":80096},[59],[15,80098],{"className":80099},[146,441],[15,80101,80103],{"className":80102},[238],[15,80104,80106,80171],{"className":80105},[285,286],[15,80107,80109,80168],{"className":80108},[290],[15,80110,80112,80123,80131],{"className":80111,"style":37723},[294],[15,80113,80114,80117],{"style":457},[15,80115],{"className":80116,"style":461},[302],[15,80118,80120],{"className":80119},[59],[15,80121,2463],{"className":80122},[59],[15,80124,80125,80128],{"style":473},[15,80126],{"className":80127,"style":461},[302],[15,80129],{"className":80130,"style":481},[480],[15,80132,80133,80136],{"style":484},[15,80134],{"className":80135,"style":461},[302],[15,80137,80139],{"className":80138},[59],[15,80140,80142,80145],{"className":80141},[59],[15,80143,38662],{"className":80144},[59,60],[15,80146,80148],{"className":80147},[281],[15,80149,80151],{"className":80150},[285],[15,80152,80154],{"className":80153},[290],[15,80155,80157],{"className":80156,"style":20028},[294],[15,80158,80159,80162],{"style":6865},[15,80160],{"className":80161,"style":303},[302],[15,80163,80165],{"className":80164},[307,308,309,310],[15,80166,2463],{"className":80167},[59,310],[15,80169,318],{"className":80170},[317],[15,80172,80174],{"className":80173},[290],[15,80175,80177],{"className":80176,"style":3778},[294],[15,80178],{},[15,80180],{"className":80181},[153,441],[15,80183,80185,80188],{"className":80184},[59],[15,80186,37],{"className":80187,"style":61},[59,60],[15,80189,80191],{"className":80190},[281],[15,80192,80194],{"className":80193},[285],[15,80195,80197],{"className":80196},[290],[15,80198,80200],{"className":80199,"style":28971},[294],[15,80201,80202,80205],{"style":8277},[15,80203],{"className":80204,"style":303},[302],[15,80206,80208],{"className":80207},[307,308,309,310],[15,80209,80211],{"className":80210},[59,310],[15,80212,21748],{"className":80213},[59,310],[15,80215,113],{"className":80216},[146],[15,80218,117],{"className":80219},[59],[15,80221,120],{"className":80222},[153],[15,80224],{"className":80225,"style":406},[157],[15,80227,80229,80232],{"className":80228},[59],[15,80230,223],{"className":80231},[59,366],[15,80233,80235],{"className":80234},[281],[15,80236,80238,80258],{"className":80237},[285,286],[15,80239,80241,80255],{"className":80240},[290],[15,80242,80244],{"className":80243,"style":379},[294],[15,80245,80246,80249],{"style":382},[15,80247],{"className":80248,"style":303},[302],[15,80250,80252],{"className":80251},[307,308,309,310],[15,80253,206],{"className":80254,"style":334},[59,60,310],[15,80256,318],{"className":80257},[317],[15,80259,80261],{"className":80260},[290],[15,80262,80264],{"className":80263,"style":7968},[294],[15,80265],{},[15,80267,230],{"className":80268},[146],[15,80270,80272,80275],{"className":80271},[59],[15,80273,38665],{"className":80274},[59,60],[15,80276,80278],{"className":80277},[281],[15,80279,80281],{"className":80280},[285],[15,80282,80284],{"className":80283},[290],[15,80285,80287],{"className":80286,"style":19735},[294],[15,80288,80289,80292],{"style":8277},[15,80290],{"className":80291,"style":303},[302],[15,80293,80295],{"className":80294},[307,308,309,310],[15,80296,2463],{"className":80297},[59,310],[15,80299,257],{"className":80300},[153],[15,80302],{"className":80303,"style":2587},[157],[15,80305,2470],{"className":80306},[2591],[15,80308],{"className":80309,"style":2587},[157],[15,80311,19221],{"className":80312,"style":277},[59,60],[15,80314,113],{"className":80315},[146],[15,80317,80319,80322],{"className":80318},[59],[15,80320,38662],{"className":80321},[59,60],[15,80323,80325],{"className":80324},[281],[15,80326,80328],{"className":80327},[285],[15,80329,80331],{"className":80330},[290],[15,80332,80334],{"className":80333,"style":19735},[294],[15,80335,80336,80339],{"style":8277},[15,80337],{"className":80338,"style":303},[302],[15,80340,80342],{"className":80341},[307,308,309,310],[15,80343,40735],{"className":80344},[59,310],[15,80346,120],{"className":80347},[153],[15,80349,4375],{"className":80350},[59],[15,80352,318],{"className":80353},[317],[15,80355,80357],{"className":80356},[290],[15,80358,80360],{"className":80359,"style":79612},[294],[15,80361],{},[11,80363,80364,23345,80448,15795,80533,80636,80637,80843,80844,15795,81014,80636,81186,81493,81494,81550,81551,81736,81737,81970,81971,81974,81975,82055],{},[1225,80365,80366,80367,80447],{},"这说明：在无穷小尺度上，所有 f-散度都只差一个常数 ",[15,80368,80370,80397],{"className":80369,"translate":19},[18],[15,80371,80373],{"className":80372},[23],[25,80374,80375],{"xmlns":27},[29,80376,80377,80395],{},[32,80378,80379,80389,80391,80393],{},[6814,80380,80381,80383],{},[35,80382,37],{},[32,80384,80385,80387],{},[110,80386,6820],{"mathvariant":209},[110,80388,6820],{"mathvariant":209},[110,80390,113],{"stretchy":112},[115,80392,117],{},[110,80394,120],{"stretchy":112},[39,80396,39534],{"encoding":41},[15,80398,80400],{"className":80399,"ariaHidden":46},[45],[15,80401,80403,80406,80438,80441,80444],{"className":80402},[50],[15,80404],{"className":80405,"style":6843},[54],[15,80407,80409,80412],{"className":80408},[59],[15,80410,37],{"className":80411,"style":61},[59,60],[15,80413,80415],{"className":80414},[281],[15,80416,80418],{"className":80417},[285],[15,80419,80421],{"className":80420},[290],[15,80422,80424],{"className":80423,"style":6862},[294],[15,80425,80426,80429],{"style":6865},[15,80427],{"className":80428,"style":303},[302],[15,80430,80432],{"className":80431},[307,308,309,310],[15,80433,80435],{"className":80434},[59,310],[15,80436,21748],{"className":80437},[59,310],[15,80439,113],{"className":80440},[146],[15,80442,117],{"className":80443},[59],[15,80445,120],{"className":80446},[153],"，形状完全一致。",[15,80449,80451,80480],{"className":80450,"translate":19},[18],[15,80452,80454],{"className":80453},[23],[25,80455,80456],{"xmlns":27},[29,80457,80458,80478],{},[32,80459,80460,80462,80464,80466,80468,80470,80472,80474,80476],{},[35,80461,37],{},[110,80463,113],{"stretchy":112},[35,80465,769],{},[110,80467,120],{"stretchy":112},[110,80469,123],{},[35,80471,769],{},[35,80473,4100],{},[110,80475,4103],{},[35,80477,769],{},[39,80479,4108],{"encoding":41},[15,80481,80483,80510],{"className":80482,"ariaHidden":46},[45],[15,80484,80486,80489,80492,80495,80498,80501,80504,80507],{"className":80485},[50],[15,80487],{"className":80488,"style":139},[54],[15,80490,37],{"className":80491,"style":61},[59,60],[15,80493,113],{"className":80494},[146],[15,80496,769],{"className":80497},[59,60],[15,80499,120],{"className":80500},[153],[15,80502],{"className":80503,"style":158},[157],[15,80505,123],{"className":80506},[162],[15,80508],{"className":80509,"style":158},[157],[15,80511,80513,80516,80519,80522,80527,80530],{"className":80512},[50],[15,80514],{"className":80515,"style":55},[54],[15,80517,769],{"className":80518},[59,60],[15,80520],{"className":80521,"style":406},[157],[15,80523,4154,80525],{"className":80524},[1484],[15,80526,4158],{"style":4157},[15,80528],{"className":80529,"style":406},[157],[15,80531,769],{"className":80532},[59,60],[15,80534,80536,80568],{"className":80535,"translate":19},[18],[15,80537,80539],{"className":80538},[23],[25,80540,80541],{"xmlns":27},[29,80542,80543,80565],{},[32,80544,80545,80555,80557,80559,80561,80563],{},[6814,80546,80547,80549],{},[35,80548,37],{},[32,80550,80551,80553],{},[110,80552,6820],{"mathvariant":209},[110,80554,6820],{"mathvariant":209},[110,80556,113],{"stretchy":112},[115,80558,117],{},[110,80560,120],{"stretchy":112},[110,80562,123],{},[115,80564,117],{},[39,80566,80567],{"encoding":41},"f''(1)=1",[15,80569,80571,80627],{"className":80570,"ariaHidden":46},[45],[15,80572,80574,80577,80609,80612,80615,80618,80621,80624],{"className":80573},[50],[15,80575],{"className":80576,"style":6843},[54],[15,80578,80580,80583],{"className":80579},[59],[15,80581,37],{"className":80582,"style":61},[59,60],[15,80584,80586],{"className":80585},[281],[15,80587,80589],{"className":80588},[285],[15,80590,80592],{"className":80591},[290],[15,80593,80595],{"className":80594,"style":6862},[294],[15,80596,80597,80600],{"style":6865},[15,80598],{"className":80599,"style":303},[302],[15,80601,80603],{"className":80602},[307,308,309,310],[15,80604,80606],{"className":80605},[59,310],[15,80607,21748],{"className":80608},[59,310],[15,80610,113],{"className":80611},[146],[15,80613,117],{"className":80614},[59],[15,80616,120],{"className":80617},[153],[15,80619],{"className":80620,"style":158},[157],[15,80622,123],{"className":80623},[162],[15,80625],{"className":80626,"style":158},[157],[15,80628,80630,80633],{"className":80629},[50],[15,80631],{"className":80632,"style":172},[54],[15,80634,117],{"className":80635},[59],"）即得 ",[15,80638,80640,80676],{"className":80639,"translate":19},[18],[15,80641,80643],{"className":80642},[23],[25,80644,80645],{"xmlns":27},[29,80646,80647,80673],{},[32,80648,80649,80659,80661,80667],{},[195,80650,80651,80653],{},[35,80652,199],{},[32,80654,80655,80657],{},[35,80656,10694],{},[35,80658,21893],{},[110,80660,32959],{},[238,80662,80663,80665],{},[115,80664,117],{},[115,80666,2463],{},[6814,80668,80669,80671],{},[35,80670,37449],{},[115,80672,2463],{},[39,80674,80675],{"encoding":41},"D_{KL}\\approx\\frac12\\chi^2",[15,80677,80679,80740],{"className":80678,"ariaHidden":46},[45],[15,80680,80682,80685,80731,80734,80737],{"className":80681},[50],[15,80683],{"className":80684,"style":15961},[54],[15,80686,80688,80691],{"className":80687},[59],[15,80689,199],{"className":80690,"style":277},[59,60],[15,80692,80694],{"className":80693},[281],[15,80695,80697,80723],{"className":80696},[285,286],[15,80698,80700,80720],{"className":80699},[290],[15,80701,80703],{"className":80702,"style":379},[294],[15,80704,80705,80708],{"style":298},[15,80706],{"className":80707,"style":303},[302],[15,80709,80711],{"className":80710},[307,308,309,310],[15,80712,80714,80717],{"className":80713},[59,310],[15,80715,10694],{"className":80716,"style":10782},[59,60,310],[15,80718,21893],{"className":80719},[59,60,310],[15,80721,318],{"className":80722},[317],[15,80724,80726],{"className":80725},[290],[15,80727,80729],{"className":80728,"style":7968},[294],[15,80730],{},[15,80732],{"className":80733,"style":158},[157],[15,80735,32959],{"className":80736},[162],[15,80738],{"className":80739,"style":158},[157],[15,80741,80743,80746,80814],{"className":80742},[50],[15,80744],{"className":80745,"style":2505},[54],[15,80747,80749,80752,80811],{"className":80748},[59],[15,80750],{"className":80751},[146,441],[15,80753,80755],{"className":80754},[238],[15,80756,80758,80803],{"className":80757},[285,286],[15,80759,80761,80800],{"className":80760},[290],[15,80762,80764,80778,80786],{"className":80763,"style":2524},[294],[15,80765,80766,80769],{"style":2527},[15,80767],{"className":80768,"style":461},[302],[15,80770,80772],{"className":80771},[307,308,309,310],[15,80773,80775],{"className":80774},[59,310],[15,80776,2463],{"className":80777},[59,310],[15,80779,80780,80783],{"style":473},[15,80781],{"className":80782,"style":461},[302],[15,80784],{"className":80785,"style":481},[480],[15,80787,80788,80791],{"style":2550},[15,80789],{"className":80790,"style":461},[302],[15,80792,80794],{"className":80793},[307,308,309,310],[15,80795,80797],{"className":80796},[59,310],[15,80798,117],{"className":80799},[59,310],[15,80801,318],{"className":80802},[317],[15,80804,80806],{"className":80805},[290],[15,80807,80809],{"className":80808,"style":2572},[294],[15,80810],{},[15,80812],{"className":80813},[153,441],[15,80815,80817,80820],{"className":80816},[59],[15,80818,37449],{"className":80819},[59,60],[15,80821,80823],{"className":80822},[281],[15,80824,80826],{"className":80825},[285],[15,80827,80829],{"className":80828},[290],[15,80830,80832],{"className":80831,"style":20028},[294],[15,80833,80834,80837],{"style":6865},[15,80835],{"className":80836,"style":303},[302],[15,80838,80840],{"className":80839},[307,308,309,310],[15,80841,2463],{"className":80842},[59,310],"；取 ",[15,80845,80847,80884],{"className":80846,"translate":19},[18],[15,80848,80850],{"className":80849},[23],[25,80851,80852],{"xmlns":27},[29,80853,80854,80882],{},[32,80855,80856,80858,80860,80862,80864,80866,80868,80872,80874,80876],{},[35,80857,37],{},[110,80859,113],{"stretchy":112},[35,80861,769],{},[110,80863,120],{"stretchy":112},[110,80865,123],{},[110,80867,113],{"stretchy":112},[34339,80869,80870],{},[35,80871,769],{},[110,80873,4813],{},[115,80875,117],{},[6814,80877,80878,80880],{},[110,80879,120],{"stretchy":112},[115,80881,2463],{},[39,80883,42630],{"encoding":41},[15,80885,80887,80914,80976],{"className":80886,"ariaHidden":46},[45],[15,80888,80890,80893,80896,80899,80902,80905,80908,80911],{"className":80889},[50],[15,80891],{"className":80892,"style":139},[54],[15,80894,37],{"className":80895,"style":61},[59,60],[15,80897,113],{"className":80898},[146],[15,80900,769],{"className":80901},[59,60],[15,80903,120],{"className":80904},[153],[15,80906],{"className":80907,"style":158},[157],[15,80909,123],{"className":80910},[162],[15,80912],{"className":80913,"style":158},[157],[15,80915,80917,80920,80923,80967,80970,80973],{"className":80916},[50],[15,80918],{"className":80919,"style":42667},[54],[15,80921,113],{"className":80922},[146],[15,80924,80926],{"className":80925},[59,34367],[15,80927,80929,80959],{"className":80928},[285,286],[15,80930,80932,80956],{"className":80931},[290],[15,80933,80935,80944],{"className":80934,"style":42683},[294],[15,80936,80938,80941],{"className":80937,"style":11863},[6307],[15,80939],{"className":80940,"style":461},[302],[15,80942,769],{"className":80943,"style":34387},[59,60],[15,80945,80946,80949],{"style":42695},[15,80947],{"className":80948,"style":461},[302],[15,80950,80952],{"className":80951,"style":34444},[34443],[6323,80953,80954],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,80955],{"d":34451},[15,80957,318],{"className":80958},[317],[15,80960,80962],{"className":80961},[290],[15,80963,80965],{"className":80964,"style":42715},[294],[15,80966],{},[15,80968],{"className":80969,"style":2587},[157],[15,80971,4813],{"className":80972},[2591],[15,80974],{"className":80975,"style":2587},[157],[15,80977,80979,80982,80985],{"className":80978},[50],[15,80980],{"className":80981,"style":20003},[54],[15,80983,117],{"className":80984},[59],[15,80986,80988,80991],{"className":80987},[153],[15,80989,120],{"className":80990},[153],[15,80992,80994],{"className":80993},[281],[15,80995,80997],{"className":80996},[285],[15,80998,81000],{"className":80999},[290],[15,81001,81003],{"className":81002,"style":20028},[294],[15,81004,81005,81008],{"style":6865},[15,81006],{"className":81007,"style":303},[302],[15,81009,81011],{"className":81010},[307,308,309,310],[15,81012,2463],{"className":81013},[59,310],[15,81015,81017,81053],{"className":81016,"translate":19},[18],[15,81018,81020],{"className":81019},[23],[25,81021,81022],{"xmlns":27},[29,81023,81024,81050],{},[32,81025,81026,81036,81038,81040,81042,81044],{},[6814,81027,81028,81030],{},[35,81029,37],{},[32,81031,81032,81034],{},[110,81033,6820],{"mathvariant":209},[110,81035,6820],{"mathvariant":209},[110,81037,113],{"stretchy":112},[115,81039,117],{},[110,81041,120],{"stretchy":112},[110,81043,123],{},[238,81045,81046,81048],{},[115,81047,117],{},[115,81049,2463],{},[39,81051,81052],{"encoding":41},"f''(1)=\\frac12",[15,81054,81056,81112],{"className":81055,"ariaHidden":46},[45],[15,81057,81059,81062,81094,81097,81100,81103,81106,81109],{"className":81058},[50],[15,81060],{"className":81061,"style":6843},[54],[15,81063,81065,81068],{"className":81064},[59],[15,81066,37],{"className":81067,"style":61},[59,60],[15,81069,81071],{"className":81070},[281],[15,81072,81074],{"className":81073},[285],[15,81075,81077],{"className":81076},[290],[15,81078,81080],{"className":81079,"style":6862},[294],[15,81081,81082,81085],{"style":6865},[15,81083],{"className":81084,"style":303},[302],[15,81086,81088],{"className":81087},[307,308,309,310],[15,81089,81091],{"className":81090},[59,310],[15,81092,21748],{"className":81093},[59,310],[15,81095,113],{"className":81096},[146],[15,81098,117],{"className":81099},[59],[15,81101,120],{"className":81102},[153],[15,81104],{"className":81105,"style":158},[157],[15,81107,123],{"className":81108},[162],[15,81110],{"className":81111,"style":158},[157],[15,81113,81115,81118],{"className":81114},[50],[15,81116],{"className":81117,"style":2505},[54],[15,81119,81121,81124,81183],{"className":81120},[59],[15,81122],{"className":81123},[146,441],[15,81125,81127],{"className":81126},[238],[15,81128,81130,81175],{"className":81129},[285,286],[15,81131,81133,81172],{"className":81132},[290],[15,81134,81136,81150,81158],{"className":81135,"style":2524},[294],[15,81137,81138,81141],{"style":2527},[15,81139],{"className":81140,"style":461},[302],[15,81142,81144],{"className":81143},[307,308,309,310],[15,81145,81147],{"className":81146},[59,310],[15,81148,2463],{"className":81149},[59,310],[15,81151,81152,81155],{"style":473},[15,81153],{"className":81154,"style":461},[302],[15,81156],{"className":81157,"style":481},[480],[15,81159,81160,81163],{"style":2550},[15,81161],{"className":81162,"style":461},[302],[15,81164,81166],{"className":81165},[307,308,309,310],[15,81167,81169],{"className":81168},[59,310],[15,81170,117],{"className":81171},[59,310],[15,81173,318],{"className":81174},[317],[15,81176,81178],{"className":81177},[290],[15,81179,81181],{"className":81180,"style":2572},[294],[15,81182],{},[15,81184],{"className":81185},[153,441],[15,81187,81189,81234],{"className":81188,"translate":19},[18],[15,81190,81192],{"className":81191},[23],[25,81193,81194],{"xmlns":27},[29,81195,81196,81232],{},[32,81197,81198,81200,81202,81206,81208,81212,81218,81220,81226],{},[110,81199,1287],{},[110,81201,113],{"stretchy":112},[34339,81203,81204],{},[35,81205,11],{},[110,81207,4813],{},[34339,81209,81210],{},[35,81211,944],{},[6814,81213,81214,81216],{},[110,81215,120],{"stretchy":112},[115,81217,2463],{},[110,81219,32959],{},[238,81221,81222,81224],{},[115,81223,117],{},[115,81225,38989],{},[6814,81227,81228,81230],{},[35,81229,37449],{},[115,81231,2463],{},[39,81233,38998],{"encoding":41},[15,81235,81237,81302,81390],{"className":81236,"ariaHidden":46},[45],[15,81238,81240,81243,81246,81249,81293,81296,81299],{"className":81239},[50],[15,81241],{"className":81242,"style":39008},[54],[15,81244,1287],{"className":81245,"style":5617},[1484,1485,5616],[15,81247,113],{"className":81248},[146],[15,81250,81252],{"className":81251},[59,34367],[15,81253,81255,81285],{"className":81254},[285,286],[15,81256,81258,81282],{"className":81257},[290],[15,81259,81261,81270],{"className":81260,"style":39027},[294],[15,81262,81264,81267],{"className":81263,"style":11863},[6307],[15,81265],{"className":81266,"style":461},[302],[15,81268,11],{"className":81269,"style":34387},[59,60],[15,81271,81272,81275],{"style":39039},[15,81273],{"className":81274,"style":461},[302],[15,81276,81278],{"className":81277,"style":34444},[34443],[6323,81279,81280],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,81281],{"d":34451},[15,81283,318],{"className":81284},[317],[15,81286,81288],{"className":81287},[290],[15,81289,81291],{"className":81290,"style":39059},[294],[15,81292],{},[15,81294],{"className":81295,"style":2587},[157],[15,81297,4813],{"className":81298},[2591],[15,81300],{"className":81301,"style":2587},[157],[15,81303,81305,81308,81352,81381,81384,81387],{"className":81304},[50],[15,81306],{"className":81307,"style":39077},[54],[15,81309,81311],{"className":81310},[59,34367],[15,81312,81314,81344],{"className":81313},[285,286],[15,81315,81317,81341],{"className":81316},[290],[15,81318,81320,81329],{"className":81319,"style":39027},[294],[15,81321,81323,81326],{"className":81322,"style":11863},[6307],[15,81324],{"className":81325,"style":461},[302],[15,81327,944],{"className":81328,"style":39099},[59,60],[15,81330,81331,81334],{"style":39039},[15,81332],{"className":81333,"style":461},[302],[15,81335,81337],{"className":81336,"style":34444},[34443],[6323,81338,81339],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,81340],{"d":34451},[15,81342,318],{"className":81343},[317],[15,81345,81347],{"className":81346},[290],[15,81348,81350],{"className":81349,"style":39059},[294],[15,81351],{},[15,81353,81355,81358],{"className":81354},[153],[15,81356,120],{"className":81357},[153],[15,81359,81361],{"className":81360},[281],[15,81362,81364],{"className":81363},[285],[15,81365,81367],{"className":81366},[290],[15,81368,81370],{"className":81369,"style":20028},[294],[15,81371,81372,81375],{"style":6865},[15,81373],{"className":81374,"style":303},[302],[15,81376,81378],{"className":81377},[307,308,309,310],[15,81379,2463],{"className":81380},[59,310],[15,81382],{"className":81383,"style":158},[157],[15,81385,32959],{"className":81386},[162],[15,81388],{"className":81389,"style":158},[157],[15,81391,81393,81396,81464],{"className":81392},[50],[15,81394],{"className":81395,"style":2505},[54],[15,81397,81399,81402,81461],{"className":81398},[59],[15,81400],{"className":81401},[146,441],[15,81403,81405],{"className":81404},[238],[15,81406,81408,81453],{"className":81407},[285,286],[15,81409,81411,81450],{"className":81410},[290],[15,81412,81414,81428,81436],{"className":81413,"style":2524},[294],[15,81415,81416,81419],{"style":2527},[15,81417],{"className":81418,"style":461},[302],[15,81420,81422],{"className":81421},[307,308,309,310],[15,81423,81425],{"className":81424},[59,310],[15,81426,38989],{"className":81427},[59,310],[15,81429,81430,81433],{"style":473},[15,81431],{"className":81432,"style":461},[302],[15,81434],{"className":81435,"style":481},[480],[15,81437,81438,81441],{"style":2550},[15,81439],{"className":81440,"style":461},[302],[15,81442,81444],{"className":81443},[307,308,309,310],[15,81445,81447],{"className":81446},[59,310],[15,81448,117],{"className":81449},[59,310],[15,81451,318],{"className":81452},[317],[15,81454,81456],{"className":81455},[290],[15,81457,81459],{"className":81458,"style":2572},[294],[15,81460],{},[15,81462],{"className":81463},[153,441],[15,81465,81467,81470],{"className":81466},[59],[15,81468,37449],{"className":81469},[59,60],[15,81471,81473],{"className":81472},[281],[15,81474,81476],{"className":81475},[285],[15,81477,81479],{"className":81478},[290],[15,81480,81482],{"className":81481,"style":20028},[294],[15,81483,81484,81487],{"style":6865},[15,81485],{"className":81486,"style":303},[302],[15,81488,81490],{"className":81489},[307,308,309,310],[15,81491,2463],{"className":81492},[59,310],"，除以 2 或换算成 ",[15,81495,81497,81517],{"className":81496,"translate":19},[18],[15,81498,81500],{"className":81499},[23],[25,81501,81502],{"xmlns":27},[29,81503,81504,81514],{},[32,81505,81506,81508,81510,81512],{},[115,81507,117],{},[110,81509,4813],{},[35,81511,39291],{},[35,81513,39294],{},[39,81515,81516],{"encoding":41},"1-BC",[15,81518,81520,81538],{"className":81519,"ariaHidden":46},[45],[15,81521,81523,81526,81529,81532,81535],{"className":81522},[50],[15,81524],{"className":81525,"style":12578},[54],[15,81527,117],{"className":81528},[59],[15,81530],{"className":81531,"style":2587},[157],[15,81533,4813],{"className":81534},[2591],[15,81536],{"className":81537,"style":2587},[157],[15,81539,81541,81544,81547],{"className":81540},[50],[15,81542],{"className":81543,"style":664},[54],[15,81545,39291],{"className":81546,"style":39387},[59,60],[15,81548,39294],{"className":81549,"style":10782},[59,60]," 就是 3.4 节引用的 Bhattacharyya 约定 ",[15,81552,81554,81586],{"className":81553,"translate":19},[18],[15,81555,81557],{"className":81556},[23],[25,81558,81559],{"xmlns":27},[29,81560,81561,81583],{},[32,81562,81563,81569,81571,81577],{},[6814,81564,81565,81567],{},[35,81566,33884],{},[115,81568,2463],{},[110,81570,32959],{},[238,81572,81573,81575],{},[115,81574,117],{},[115,81576,39303],{},[6814,81578,81579,81581],{},[35,81580,37449],{},[115,81582,2463],{},[39,81584,81585],{"encoding":41},"H^2\\approx\\frac18\\chi^2",[15,81587,81589,81633],{"className":81588,"ariaHidden":46},[45],[15,81590,81592,81595,81624,81627,81630],{"className":81591},[50],[15,81593],{"className":81594,"style":20028},[54],[15,81596,81598,81601],{"className":81597},[59],[15,81599,33884],{"className":81600,"style":34038},[59,60],[15,81602,81604],{"className":81603},[281],[15,81605,81607],{"className":81606},[285],[15,81608,81610],{"className":81609},[290],[15,81611,81613],{"className":81612,"style":20028},[294],[15,81614,81615,81618],{"style":6865},[15,81616],{"className":81617,"style":303},[302],[15,81619,81621],{"className":81620},[307,308,309,310],[15,81622,2463],{"className":81623},[59,310],[15,81625],{"className":81626,"style":158},[157],[15,81628,32959],{"className":81629},[162],[15,81631],{"className":81632,"style":158},[157],[15,81634,81636,81639,81707],{"className":81635},[50],[15,81637],{"className":81638,"style":2505},[54],[15,81640,81642,81645,81704],{"className":81641},[59],[15,81643],{"className":81644},[146,441],[15,81646,81648],{"className":81647},[238],[15,81649,81651,81696],{"className":81650},[285,286],[15,81652,81654,81693],{"className":81653},[290],[15,81655,81657,81671,81679],{"className":81656,"style":2524},[294],[15,81658,81659,81662],{"style":2527},[15,81660],{"className":81661,"style":461},[302],[15,81663,81665],{"className":81664},[307,308,309,310],[15,81666,81668],{"className":81667},[59,310],[15,81669,39303],{"className":81670},[59,310],[15,81672,81673,81676],{"style":473},[15,81674],{"className":81675,"style":461},[302],[15,81677],{"className":81678,"style":481},[480],[15,81680,81681,81684],{"style":2550},[15,81682],{"className":81683,"style":461},[302],[15,81685,81687],{"className":81686},[307,308,309,310],[15,81688,81690],{"className":81689},[59,310],[15,81691,117],{"className":81692},[59,310],[15,81694,318],{"className":81695},[317],[15,81697,81699],{"className":81698},[290],[15,81700,81702],{"className":81701,"style":2572},[294],[15,81703],{},[15,81705],{"className":81706},[153,441],[15,81708,81710,81713],{"className":81709},[59],[15,81711,37449],{"className":81712},[59,60],[15,81714,81716],{"className":81715},[281],[15,81717,81719],{"className":81718},[285],[15,81720,81722],{"className":81721},[290],[15,81723,81725],{"className":81724,"style":20028},[294],[15,81726,81727,81730],{"style":6865},[15,81728],{"className":81729,"style":303},[302],[15,81731,81733],{"className":81732},[307,308,309,310],[15,81734,2463],{"className":81735},[59,310],"。共同因子 ",[15,81738,81740,81792],{"className":81739,"translate":19},[18],[15,81741,81743],{"className":81742},[23],[25,81744,81745],{"xmlns":27},[29,81746,81747,81789],{},[32,81748,81749,81755,81757,81763,81765,81767,81769,81775,81777,81783,81785,81787],{},[6814,81750,81751,81753],{},[35,81752,38662],{},[115,81754,2463],{},[110,81756,1287],{},[6814,81758,81759,81761],{},[35,81760,38665],{},[115,81762,2463],{},[35,81764,244],{},[35,81766,206],{},[110,81768,123],{},[6814,81770,81771,81773],{},[35,81772,37449],{},[115,81774,2463],{},[110,81776,113],{"stretchy":112},[195,81778,81779,81781],{},[35,81780,213],{},[35,81782,38662],{},[35,81784,210],{"mathvariant":209},[35,81786,206],{},[110,81788,120],{"stretchy":112},[39,81790,81791],{"encoding":41},"\\varepsilon^2\\int h^2 dP=\\chi^2(Q_\\varepsilon\\|P)",[15,81793,81795,81883],{"className":81794,"ariaHidden":46},[45],[15,81796,81798,81801,81830,81833,81836,81839,81868,81871,81874,81877,81880],{"className":81797},[50],[15,81799],{"className":81800,"style":50328},[54],[15,81802,81804,81807],{"className":81803},[59],[15,81805,38662],{"className":81806},[59,60],[15,81808,81810],{"className":81809},[281],[15,81811,81813],{"className":81812},[285],[15,81814,81816],{"className":81815},[290],[15,81817,81819],{"className":81818,"style":20028},[294],[15,81820,81821,81824],{"style":6865},[15,81822],{"className":81823,"style":303},[302],[15,81825,81827],{"className":81826},[307,308,309,310],[15,81828,2463],{"className":81829},[59,310],[15,81831],{"className":81832,"style":406},[157],[15,81834,1287],{"className":81835,"style":5617},[1484,1485,5616],[15,81837],{"className":81838,"style":406},[157],[15,81840,81842,81845],{"className":81841},[59],[15,81843,38665],{"className":81844},[59,60],[15,81846,81848],{"className":81847},[281],[15,81849,81851],{"className":81850},[285],[15,81852,81854],{"className":81853},[290],[15,81855,81857],{"className":81856,"style":20028},[294],[15,81858,81859,81862],{"style":6865},[15,81860],{"className":81861,"style":303},[302],[15,81863,81865],{"className":81864},[307,308,309,310],[15,81866,2463],{"className":81867},[59,310],[15,81869,244],{"className":81870},[59,60],[15,81872,206],{"className":81873,"style":334},[59,60],[15,81875],{"className":81876,"style":158},[157],[15,81878,123],{"className":81879},[162],[15,81881],{"className":81882,"style":158},[157],[15,81884,81886,81889,81918,81921,81961,81964,81967],{"className":81885},[50],[15,81887],{"className":81888,"style":20003},[54],[15,81890,81892,81895],{"className":81891},[59],[15,81893,37449],{"className":81894},[59,60],[15,81896,81898],{"className":81897},[281],[15,81899,81901],{"className":81900},[285],[15,81902,81904],{"className":81903},[290],[15,81905,81907],{"className":81906,"style":20028},[294],[15,81908,81909,81912],{"style":6865},[15,81910],{"className":81911,"style":303},[302],[15,81913,81915],{"className":81914},[307,308,309,310],[15,81916,2463],{"className":81917},[59,310],[15,81919,113],{"className":81920},[146],[15,81922,81924,81927],{"className":81923},[59],[15,81925,213],{"className":81926},[59,60],[15,81928,81930],{"className":81929},[281],[15,81931,81933,81953],{"className":81932},[285,286],[15,81934,81936,81950],{"className":81935},[290],[15,81937,81939],{"className":81938,"style":44929},[294],[15,81940,81941,81944],{"style":382},[15,81942],{"className":81943,"style":303},[302],[15,81945,81947],{"className":81946},[307,308,309,310],[15,81948,38662],{"className":81949},[59,60,310],[15,81951,318],{"className":81952},[317],[15,81954,81956],{"className":81955},[290],[15,81957,81959],{"className":81958,"style":7968},[294],[15,81960],{},[15,81962,210],{"className":81963},[59],[15,81965,206],{"className":81966,"style":334},[59,60],[15,81968,120],{"className":81969},[153]," 就是",[1225,81972,81973],{},"Fisher 信息度量","：它给出统计流形上的黎曼度量，而 ",[15,81976,81978,82005],{"className":81977,"translate":19},[18],[15,81979,81981],{"className":81980},[23],[25,81982,81983],{"xmlns":27},[29,81984,81985,82003],{},[32,81986,81987,81997,81999,82001],{},[6814,81988,81989,81991],{},[35,81990,37],{},[32,81992,81993,81995],{},[110,81994,6820],{"mathvariant":209},[110,81996,6820],{"mathvariant":209},[110,81998,113],{"stretchy":112},[115,82000,117],{},[110,82002,120],{"stretchy":112},[39,82004,39534],{"encoding":41},[15,82006,82008],{"className":82007,"ariaHidden":46},[45],[15,82009,82011,82014,82046,82049,82052],{"className":82010},[50],[15,82012],{"className":82013,"style":6843},[54],[15,82015,82017,82020],{"className":82016},[59],[15,82018,37],{"className":82019,"style":61},[59,60],[15,82021,82023],{"className":82022},[281],[15,82024,82026],{"className":82025},[285],[15,82027,82029],{"className":82028},[290],[15,82030,82032],{"className":82031,"style":6862},[294],[15,82033,82034,82037],{"style":6865},[15,82035],{"className":82036,"style":303},[302],[15,82038,82040],{"className":82039},[307,308,309,310],[15,82041,82043],{"className":82042},[59,310],[15,82044,21748],{"className":82045},[59,310],[15,82047,113],{"className":82048},[146],[15,82050,117],{"className":82051},[59],[15,82053,120],{"className":82054},[153]," 只是「单位选择」。这也解释了为什么 GAN 中「选 JS 还是选 KL」在小偏差区几乎无差别，差别只在远离平衡或支撑不重叠时才显现。",[2311,82057,82059],{"id":82058},"_47-不等式网络","4.7 不等式网络",[993,82061,82063,82257,82763,83224],{"title":82062},"命题 4.6（不等式网络）",[11,82064,82065,82066,82256],{},"记 ",[15,82067,82069,82107],{"className":82068,"translate":19},[18],[15,82070,82072],{"className":82071},[23],[25,82073,82074],{"xmlns":27},[29,82075,82076,82104],{},[32,82077,82078,82084,82086,82094,82096,82098,82100,82102],{},[6814,82079,82080,82082],{},[35,82081,33884],{},[115,82083,2463],{},[110,82085,123],{},[7553,82087,82088,82090,82092],{},[35,82089,33884],{},[1297,82091,42137],{},[115,82093,2463],{},[110,82095,123],{},[115,82097,117],{},[110,82099,4813],{},[35,82101,39291],{},[35,82103,39294],{},[39,82105,82106],{"encoding":41},"H^2=H^2_{\\text{Bhattacharyya}}=1-BC",[15,82108,82110,82154,82226,82244],{"className":82109,"ariaHidden":46},[45],[15,82111,82113,82116,82145,82148,82151],{"className":82112},[50],[15,82114],{"className":82115,"style":20028},[54],[15,82117,82119,82122],{"className":82118},[59],[15,82120,33884],{"className":82121,"style":34038},[59,60],[15,82123,82125],{"className":82124},[281],[15,82126,82128],{"className":82127},[285],[15,82129,82131],{"className":82130},[290],[15,82132,82134],{"className":82133,"style":20028},[294],[15,82135,82136,82139],{"style":6865},[15,82137],{"className":82138,"style":303},[302],[15,82140,82142],{"className":82141},[307,308,309,310],[15,82143,2463],{"className":82144},[59,310],[15,82146],{"className":82147,"style":158},[157],[15,82149,123],{"className":82150},[162],[15,82152],{"className":82153,"style":158},[157],[15,82155,82157,82160,82217,82220,82223],{"className":82156},[50],[15,82158],{"className":82159,"style":42885},[54],[15,82161,82163,82166],{"className":82162},[59],[15,82164,33884],{"className":82165,"style":34038},[59,60],[15,82167,82169],{"className":82168},[281],[15,82170,82172,82209],{"className":82171},[285,286],[15,82173,82175,82206],{"className":82174},[290],[15,82176,82178,82195],{"className":82177,"style":20028},[294],[15,82179,82180,82183],{"style":42909},[15,82181],{"className":82182,"style":303},[302],[15,82184,82186],{"className":82185},[307,308,309,310],[15,82187,82189],{"className":82188},[59,310],[15,82190,82192],{"className":82191},[59,4598,310],[15,82193,42137],{"className":82194},[59,310],[15,82196,82197,82200],{"style":6865},[15,82198],{"className":82199,"style":303},[302],[15,82201,82203],{"className":82202},[307,308,309,310],[15,82204,2463],{"className":82205},[59,310],[15,82207,318],{"className":82208},[317],[15,82210,82212],{"className":82211},[290],[15,82213,82215],{"className":82214,"style":42945},[294],[15,82216],{},[15,82218],{"className":82219,"style":158},[157],[15,82221,123],{"className":82222},[162],[15,82224],{"className":82225,"style":158},[157],[15,82227,82229,82232,82235,82238,82241],{"className":82228},[50],[15,82230],{"className":82231,"style":12578},[54],[15,82233,117],{"className":82234},[59],[15,82236],{"className":82237,"style":2587},[157],[15,82239,4813],{"className":82240},[2591],[15,82242],{"className":82243,"style":2587},[157],[15,82245,82247,82250,82253],{"className":82246},[50],[15,82248],{"className":82249,"style":664},[54],[15,82251,39291],{"className":82252,"style":39387},[59,60],[15,82254,39294],{"className":82255,"style":10782},[59,60],"，则对概率测度有",[15,82258,82260],{"className":82259,"translate":19},[180],[15,82261,82263,82384],{"className":82262,"translate":19},[18],[15,82264,82266],{"className":82265},[23],[25,82267,82268],{"xmlns":27,"display":189},[29,82269,82270,82381],{},[1243,82271,82272,82307],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,82273,82274,82280],{},[1252,82275,82276],{},[1255,82277,82278],{"scriptlevel":126,"displaystyle":46},[32,82279],{},[1252,82281,82282],{},[1255,82283,82284],{"scriptlevel":126,"displaystyle":46},[32,82285,82286,82288],{},[32,82287],{},[32,82289,82290,82292,82294,82297,82299,82301,82303,82305],{},[35,82291,206],{"mathvariant":209},[35,82293,11963],{"mathvariant":209},[35,82295,82296],{"mathvariant":209},"n",[35,82298,7561],{"mathvariant":209},[35,82300,7564],{"mathvariant":209},[35,82302,7567],{"mathvariant":209},[35,82304,16450],{"mathvariant":209},[110,82306,1015],{},[1249,82308,82309,82315],{},[1252,82310,82311],{},[1255,82312,82313],{"scriptlevel":126,"displaystyle":46},[32,82314],{},[1252,82316,82317],{},[1255,82318,82319],{"scriptlevel":126,"displaystyle":46},[32,82320,82321,82323,82325,82335,82337,82339,82341,82343,82345,82347,82379],{},[32,82322],{},[157,82324],{"width":3262},[195,82326,82327,82329],{},[35,82328,199],{},[32,82330,82331,82333],{},[35,82332,5392],{},[35,82334,34850],{},[110,82336,113],{"stretchy":112},[35,82338,206],{},[110,82340,551],{"separator":46},[35,82342,213],{},[110,82344,120],{"stretchy":112},[110,82346,9952],{},[34339,82348,82349],{},[32,82350,82351,82359,82369,82371,82373,82375,82377],{},[1255,82352,82353],{"scriptlevel":126,"displaystyle":112},[238,82354,82355,82357],{},[115,82356,117],{},[115,82358,2463],{},[195,82360,82361,82363],{},[35,82362,199],{},[32,82364,82365,82367],{},[35,82366,10694],{},[35,82368,21893],{},[110,82370,113],{"stretchy":112},[35,82372,206],{},[35,82374,210],{"mathvariant":209},[35,82376,213],{},[110,82378,120],{"stretchy":112},[110,82380,551],{"separator":46},[39,82382,82383],{"encoding":41},"\\begin{aligned}\n&\\mathrm{Pinsker:}\\\\\n&\\qquad D_{TV}(P,Q)\\le\n\\sqrt{\\tfrac12 D_{KL}(P\\|Q)},\n\\end{aligned}",[15,82385,82387],{"className":82386,"ariaHidden":46},[45],[15,82388,82390,82394],{"className":82389},[50],[15,82391],{"className":82392,"style":82393},[54],"height:3.34em;vertical-align:-1.42em;",[15,82395,82397],{"className":82396},[59],[15,82398,82400,82444],{"className":82399},[1243],[15,82401,82403],{"className":82402},[1360],[15,82404,82406,82435],{"className":82405},[285,286],[15,82407,82409,82432],{"className":82408},[290],[15,82410,82413,82423],{"className":82411,"style":82412},[294],"height:1.92em;",[15,82414,82416,82420],{"style":82415},"top:-4.3639em;",[15,82417],{"className":82418,"style":82419},[302],"height:3.2839em;",[15,82421],{"className":82422},[59],[15,82424,82426,82429],{"style":82425},"top:-2.42em;",[15,82427],{"className":82428,"style":82419},[302],[15,82430],{"className":82431},[59],[15,82433,318],{"className":82434},[317],[15,82436,82438],{"className":82437},[290],[15,82439,82442],{"className":82440,"style":82441},[294],"height:1.42em;",[15,82443],{},[15,82445,82447],{"className":82446},[1451],[15,82448,82450,82755],{"className":82449},[285,286],[15,82451,82453,82752],{"className":82452},[290],[15,82454,82456,82480],{"className":82455,"style":82412},[294],[15,82457,82458,82461],{"style":82415},[15,82459],{"className":82460,"style":82419},[302],[15,82462,82464,82467],{"className":82463},[59],[15,82465],{"className":82466},[59],[15,82468,82470,82474,82477],{"className":82469},[59],[15,82471,82473],{"className":82472},[59,32662],"Pinsker",[15,82475],{"className":82476,"style":158},[157],[15,82478,1015],{"className":82479},[162],[15,82481,82482,82485],{"style":82425},[15,82483],{"className":82484,"style":82419},[302],[15,82486,82488,82491,82494,82540,82543,82546,82549,82552,82555,82558,82561,82564,82567,82749],{"className":82487},[59],[15,82489],{"className":82490},[59],[15,82492],{"className":82493,"style":3634},[157],[15,82495,82497,82500],{"className":82496},[59],[15,82498,199],{"className":82499,"style":277},[59,60],[15,82501,82503],{"className":82502},[281],[15,82504,82506,82532],{"className":82505},[285,286],[15,82507,82509,82529],{"className":82508},[290],[15,82510,82512],{"className":82511,"style":379},[294],[15,82513,82514,82517],{"style":298},[15,82515],{"className":82516,"style":303},[302],[15,82518,82520],{"className":82519},[307,308,309,310],[15,82521,82523,82526],{"className":82522},[59,310],[15,82524,5392],{"className":82525,"style":334},[59,60,310],[15,82527,34850],{"className":82528,"style":2587},[59,60,310],[15,82530,318],{"className":82531},[317],[15,82533,82535],{"className":82534},[290],[15,82536,82538],{"className":82537,"style":7968},[294],[15,82539],{},[15,82541,113],{"className":82542},[146],[15,82544,206],{"className":82545,"style":334},[59,60],[15,82547,551],{"className":82548},[573],[15,82550],{"className":82551,"style":406},[157],[15,82553,213],{"className":82554},[59,60],[15,82556,120],{"className":82557},[153],[15,82559],{"className":82560,"style":158},[157],[15,82562,9952],{"className":82563},[162],[15,82565],{"className":82566,"style":158},[157],[15,82568,82570],{"className":82569},[59,34367],[15,82571,82573,82740],{"className":82572},[285,286],[15,82574,82576,82737],{"className":82575},[290],[15,82577,82580,82720],{"className":82578,"style":82579},[294],"height:1.2839em;",[15,82581,82584,82588],{"className":82582,"style":82583},[6307],"top:-3.8em;",[15,82585],{"className":82586,"style":82587},[302],"height:3.8em;",[15,82589,82591,82659,82705,82708,82711,82714,82717],{"className":82590,"style":41161},[59],[15,82592,82594,82597,82656],{"className":82593},[59],[15,82595],{"className":82596},[146,441],[15,82598,82600],{"className":82599},[238],[15,82601,82603,82648],{"className":82602},[285,286],[15,82604,82606,82645],{"className":82605},[290],[15,82607,82609,82623,82631],{"className":82608,"style":2524},[294],[15,82610,82611,82614],{"style":2527},[15,82612],{"className":82613,"style":461},[302],[15,82615,82617],{"className":82616},[307,308,309,310],[15,82618,82620],{"className":82619},[59,310],[15,82621,2463],{"className":82622},[59,310],[15,82624,82625,82628],{"style":473},[15,82626],{"className":82627,"style":461},[302],[15,82629],{"className":82630,"style":481},[480],[15,82632,82633,82636],{"style":2550},[15,82634],{"className":82635,"style":461},[302],[15,82637,82639],{"className":82638},[307,308,309,310],[15,82640,82642],{"className":82641},[59,310],[15,82643,117],{"className":82644},[59,310],[15,82646,318],{"className":82647},[317],[15,82649,82651],{"className":82650},[290],[15,82652,82654],{"className":82653,"style":2572},[294],[15,82655],{},[15,82657],{"className":82658},[153,441],[15,82660,82662,82665],{"className":82661},[59],[15,82663,199],{"className":82664,"style":277},[59,60],[15,82666,82668],{"className":82667},[281],[15,82669,82671,82697],{"className":82670},[285,286],[15,82672,82674,82694],{"className":82673},[290],[15,82675,82677],{"className":82676,"style":379},[294],[15,82678,82679,82682],{"style":298},[15,82680],{"className":82681,"style":303},[302],[15,82683,82685],{"className":82684},[307,308,309,310],[15,82686,82688,82691],{"className":82687},[59,310],[15,82689,10694],{"className":82690,"style":10782},[59,60,310],[15,82692,21893],{"className":82693},[59,60,310],[15,82695,318],{"className":82696},[317],[15,82698,82700],{"className":82699},[290],[15,82701,82703],{"className":82702,"style":7968},[294],[15,82704],{},[15,82706,113],{"className":82707},[146],[15,82709,206],{"className":82710,"style":334},[59,60],[15,82712,210],{"className":82713},[59],[15,82715,213],{"className":82716},[59,60],[15,82718,120],{"className":82719},[153],[15,82721,82723,82726],{"style":82722},"top:-3.2439em;",[15,82724],{"className":82725,"style":82587},[302],[15,82727,82730],{"className":82728,"style":82729},[34443],"min-width:1.02em;height:1.88em;",[6323,82731,82734],{"xmlns":6325,"width":6326,"height":82732,"viewBox":82733,"preserveAspectRatio":6329},"1.88em","0 0 400000 1944",[6331,82735],{"d":82736},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[15,82738,318],{"className":82739},[317],[15,82741,82743],{"className":82742},[290],[15,82744,82747],{"className":82745,"style":82746},[294],"height:0.5561em;",[15,82748],{},[15,82750,551],{"className":82751},[573],[15,82753,318],{"className":82754},[317],[15,82756,82758],{"className":82757},[290],[15,82759,82761],{"className":82760,"style":82441},[294],[15,82762],{},[15,82764,82766],{"className":82765,"translate":19},[180],[15,82767,82769,82903],{"className":82768,"translate":19},[18],[15,82770,82772],{"className":82771},[23],[25,82773,82774],{"xmlns":27,"display":189},[29,82775,82776,82900],{},[1243,82777,82778,82834],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,82779,82780,82786],{},[1252,82781,82782],{},[1255,82783,82784],{"scriptlevel":126,"displaystyle":46},[32,82785],{},[1252,82787,82788],{},[1255,82789,82790],{"scriptlevel":126,"displaystyle":46},[32,82791,82792,82794],{},[32,82793],{},[32,82795,82796,82798,82800,82802,82804,82806,82808,82810,82812,82814,82816,82818,82821,82823,82825,82828,82830,82832],{},[35,82797,39291],{"mathvariant":209},[35,82799,16450],{"mathvariant":209},[35,82801,7567],{"mathvariant":209},[35,82803,769],{"mathvariant":209},[35,82805,45180],{"mathvariant":209},[35,82807,4158],{"mathvariant":209},[35,82809,82296],{"mathvariant":209},[35,82811,47662],{"mathvariant":209},[35,82813,47658],{"mathvariant":209},[35,82815,47658],{"mathvariant":209},[35,82817,7567],{"mathvariant":209},[1297,82819,82820],{},"–",[35,82822,33884],{"mathvariant":209},[35,82824,15400],{"mathvariant":209},[35,82826,82827],{"mathvariant":209},"b",[35,82829,7567],{"mathvariant":209},[35,82831,16450],{"mathvariant":209},[110,82833,1015],{},[1249,82835,82836,82842],{},[1252,82837,82838],{},[1255,82839,82840],{"scriptlevel":126,"displaystyle":46},[32,82841],{},[1252,82843,82844],{},[1255,82845,82846],{"scriptlevel":126,"displaystyle":46},[32,82847,82848,82850,82852,82858,82860,82862,82864,82866,82868,82870,82878,82888,82890,82892,82894,82896,82898],{},[32,82849],{},[157,82851],{"width":3262},[6814,82853,82854,82856],{},[35,82855,33884],{},[115,82857,2463],{},[110,82859,113],{"stretchy":112},[35,82861,206],{},[110,82863,551],{"separator":46},[35,82865,213],{},[110,82867,120],{"stretchy":112},[110,82869,9952],{},[1255,82871,82872],{"scriptlevel":126,"displaystyle":112},[238,82873,82874,82876],{},[115,82875,117],{},[115,82877,2463],{},[195,82879,82880,82882],{},[35,82881,199],{},[32,82883,82884,82886],{},[35,82885,10694],{},[35,82887,21893],{},[110,82889,113],{"stretchy":112},[35,82891,206],{},[35,82893,210],{"mathvariant":209},[35,82895,213],{},[110,82897,120],{"stretchy":112},[110,82899,551],{"separator":46},[39,82901,82902],{"encoding":41},"\\begin{aligned}\n&\\mathrm{Bretagnolle\\text{–}Huber:}\\\\\n&\\qquad H^2(P,Q)\\le \\tfrac12 D_{KL}(P\\|Q),\n\\end{aligned}",[15,82904,82906],{"className":82905,"ariaHidden":46},[45],[15,82907,82909,82913],{"className":82908},[50],[15,82910],{"className":82911,"style":82912},[54],"height:2.7241em;vertical-align:-1.1121em;",[15,82914,82916],{"className":82915},[59],[15,82917,82919,82963],{"className":82918},[1243],[15,82920,82922],{"className":82921},[1360],[15,82923,82925,82954],{"className":82924},[285,286],[15,82926,82928,82951],{"className":82927},[290],[15,82929,82932,82942],{"className":82930,"style":82931},[294],"height:1.6121em;",[15,82933,82935,82939],{"style":82934},"top:-3.6362em;",[15,82936],{"className":82937,"style":82938},[302],"height:2.8641em;",[15,82940],{"className":82941},[59],[15,82943,82945,82948],{"style":82944},"top:-2.1121em;",[15,82946],{"className":82947,"style":82938},[302],[15,82949],{"className":82950},[59],[15,82952,318],{"className":82953},[317],[15,82955,82957],{"className":82956},[290],[15,82958,82961],{"className":82959,"style":82960},[294],"height:1.1121em;",[15,82962],{},[15,82964,82966],{"className":82965},[1451],[15,82967,82969,83216],{"className":82968},[285,286],[15,82970,82972,83213],{"className":82971},[290],[15,82973,82975,83010],{"className":82974,"style":82931},[294],[15,82976,82978,82981],{"style":82977},"top:-3.7721em;",[15,82979],{"className":82980,"style":461},[302],[15,82982,82984,82987],{"className":82983},[59],[15,82985],{"className":82986},[59],[15,82988,82990,82994,83000,83004,83007],{"className":82989},[59],[15,82991,82993],{"className":82992},[59,32662],"Bretagnolle",[15,82995,82997],{"className":82996},[59,4598],[15,82998,82820],{"className":82999},[59],[15,83001,83003],{"className":83002},[59,32662],"Huber",[15,83005],{"className":83006,"style":158},[157],[15,83008,1015],{"className":83009},[162],[15,83011,83013,83016],{"style":83012},"top:-2.2479em;",[15,83014],{"className":83015,"style":461},[302],[15,83017,83019,83022,83025,83054,83057,83060,83063,83066,83069,83072,83075,83078,83081,83149,83195,83198,83201,83204,83207,83210],{"className":83018},[59],[15,83020],{"className":83021},[59],[15,83023],{"className":83024,"style":3634},[157],[15,83026,83028,83031],{"className":83027},[59],[15,83029,33884],{"className":83030,"style":34038},[59,60],[15,83032,83034],{"className":83033},[281],[15,83035,83037],{"className":83036},[285],[15,83038,83040],{"className":83039},[290],[15,83041,83043],{"className":83042,"style":19735},[294],[15,83044,83045,83048],{"style":8277},[15,83046],{"className":83047,"style":303},[302],[15,83049,83051],{"className":83050},[307,308,309,310],[15,83052,2463],{"className":83053},[59,310],[15,83055,113],{"className":83056},[146],[15,83058,206],{"className":83059,"style":334},[59,60],[15,83061,551],{"className":83062},[573],[15,83064],{"className":83065,"style":406},[157],[15,83067,213],{"className":83068},[59,60],[15,83070,120],{"className":83071},[153],[15,83073],{"className":83074,"style":158},[157],[15,83076,9952],{"className":83077},[162],[15,83079],{"className":83080,"style":158},[157],[15,83082,83084,83087,83146],{"className":83083},[59],[15,83085],{"className":83086},[146,441],[15,83088,83090],{"className":83089},[238],[15,83091,83093,83138],{"className":83092},[285,286],[15,83094,83096,83135],{"className":83095},[290],[15,83097,83099,83113,83121],{"className":83098,"style":2524},[294],[15,83100,83101,83104],{"style":2527},[15,83102],{"className":83103,"style":461},[302],[15,83105,83107],{"className":83106},[307,308,309,310],[15,83108,83110],{"className":83109},[59,310],[15,83111,2463],{"className":83112},[59,310],[15,83114,83115,83118],{"style":473},[15,83116],{"className":83117,"style":461},[302],[15,83119],{"className":83120,"style":481},[480],[15,83122,83123,83126],{"style":2550},[15,83124],{"className":83125,"style":461},[302],[15,83127,83129],{"className":83128},[307,308,309,310],[15,83130,83132],{"className":83131},[59,310],[15,83133,117],{"className":83134},[59,310],[15,83136,318],{"className":83137},[317],[15,83139,83141],{"className":83140},[290],[15,83142,83144],{"className":83143,"style":2572},[294],[15,83145],{},[15,83147],{"className":83148},[153,441],[15,83150,83152,83155],{"className":83151},[59],[15,83153,199],{"className":83154,"style":277},[59,60],[15,83156,83158],{"className":83157},[281],[15,83159,83161,83187],{"className":83160},[285,286],[15,83162,83164,83184],{"className":83163},[290],[15,83165,83167],{"className":83166,"style":379},[294],[15,83168,83169,83172],{"style":298},[15,83170],{"className":83171,"style":303},[302],[15,83173,83175],{"className":83174},[307,308,309,310],[15,83176,83178,83181],{"className":83177},[59,310],[15,83179,10694],{"className":83180,"style":10782},[59,60,310],[15,83182,21893],{"className":83183},[59,60,310],[15,83185,318],{"className":83186},[317],[15,83188,83190],{"className":83189},[290],[15,83191,83193],{"className":83192,"style":7968},[294],[15,83194],{},[15,83196,113],{"className":83197},[146],[15,83199,206],{"className":83200,"style":334},[59,60],[15,83202,210],{"className":83203},[59],[15,83205,213],{"className":83206},[59,60],[15,83208,120],{"className":83209},[153],[15,83211,551],{"className":83212},[573],[15,83214,318],{"className":83215},[317],[15,83217,83219],{"className":83218},[290],[15,83220,83222],{"className":83221,"style":82960},[294],[15,83223],{},[15,83225,83227],{"className":83226,"translate":19},[180],[15,83228,83230,83364],{"className":83229,"translate":19},[18],[15,83231,83233],{"className":83232},[23],[25,83234,83235],{"xmlns":27,"display":189},[29,83236,83237,83361],{},[1243,83238,83239,83315],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,83240,83241,83247],{},[1252,83242,83243],{},[1255,83244,83245],{"scriptlevel":126,"displaystyle":46},[32,83246],{},[1252,83248,83249],{},[1255,83250,83251],{"scriptlevel":126,"displaystyle":46},[32,83252,83253,83255,83265,83267,83269,83271,83273,83275,83277,83301,83303],{},[32,83254],{},[195,83256,83257,83259],{},[35,83258,199],{},[32,83260,83261,83263],{},[35,83262,5392],{},[35,83264,34850],{},[110,83266,113],{"stretchy":112},[35,83268,206],{},[110,83270,551],{"separator":46},[35,83272,213],{},[110,83274,120],{"stretchy":112},[110,83276,9952],{},[34339,83278,83279],{},[32,83280,83281,83287,83289,83291,83293,83299],{},[6814,83282,83283,83285],{},[35,83284,33884],{},[115,83286,2463],{},[110,83288,113],{"stretchy":112},[115,83290,2463],{},[110,83292,4813],{},[6814,83294,83295,83297],{},[35,83296,33884],{},[115,83298,2463],{},[110,83300,120],{"stretchy":112},[110,83302,9952],{},[34339,83304,83305],{},[32,83306,83307,83309],{},[115,83308,2463],{},[6814,83310,83311,83313],{},[35,83312,33884],{},[115,83314,2463],{},[1249,83316,83317,83323],{},[1252,83318,83319],{},[1255,83320,83321],{"scriptlevel":126,"displaystyle":46},[32,83322],{},[1252,83324,83325],{},[1255,83326,83327],{"scriptlevel":126,"displaystyle":46},[32,83328,83329,83331,83333,83335,83359],{},[32,83330],{},[157,83332],{"width":3262},[110,83334,9952],{},[34339,83336,83337],{},[32,83338,83339,83349,83351,83353,83355,83357],{},[195,83340,83341,83343],{},[35,83342,199],{},[32,83344,83345,83347],{},[35,83346,10694],{},[35,83348,21893],{},[110,83350,113],{"stretchy":112},[35,83352,206],{},[35,83354,210],{"mathvariant":209},[35,83356,213],{},[110,83358,120],{"stretchy":112},[35,83360,4375],{"mathvariant":209},[39,83362,83363],{"encoding":41},"\\begin{aligned}\n&D_{TV}(P,Q)\\le\\sqrt{H^2(2-H^2)}\n\\le\\sqrt{2H^2}\\\\\n&\\qquad\\le\\sqrt{D_{KL}(P\\|Q)} .\n\\end{aligned}",[15,83365,83367],{"className":83366,"ariaHidden":46},[45],[15,83368,83370,83374],{"className":83369},[50],[15,83371],{"className":83372,"style":83373},[54],"height:3.0078em;vertical-align:-1.2539em;",[15,83375,83377],{"className":83376},[59],[15,83378,83380,83424],{"className":83379},[1243],[15,83381,83383],{"className":83382},[1360],[15,83384,83386,83415],{"className":83385},[285,286],[15,83387,83389,83412],{"className":83388},[290],[15,83390,83393,83403],{"className":83391,"style":83392},[294],"height:1.7539em;",[15,83394,83396,83400],{"style":83395},"top:-3.7539em;",[15,83397],{"className":83398,"style":83399},[302],"height:3.0039em;",[15,83401],{"className":83402},[59],[15,83404,83406,83409],{"style":83405},"top:-2.11em;",[15,83407],{"className":83408,"style":83399},[302],[15,83410],{"className":83411},[59],[15,83413,318],{"className":83414},[317],[15,83416,83418],{"className":83417},[290],[15,83419,83422],{"className":83420,"style":83421},[294],"height:1.2539em;",[15,83423],{},[15,83425,83427],{"className":83426},[1451],[15,83428,83430,83870],{"className":83429},[285,286],[15,83431,83433,83867],{"className":83432},[290],[15,83434,83436,83736],{"className":83435,"style":83392},[294],[15,83437,83438,83441],{"style":83395},[15,83439],{"className":83440,"style":83399},[302],[15,83442,83444,83447,83493,83496,83499,83502,83505,83508,83511,83514,83517,83520,83648,83651,83654,83657],{"className":83443},[59],[15,83445],{"className":83446},[59],[15,83448,83450,83453],{"className":83449},[59],[15,83451,199],{"className":83452,"style":277},[59,60],[15,83454,83456],{"className":83455},[281],[15,83457,83459,83485],{"className":83458},[285,286],[15,83460,83462,83482],{"className":83461},[290],[15,83463,83465],{"className":83464,"style":379},[294],[15,83466,83467,83470],{"style":298},[15,83468],{"className":83469,"style":303},[302],[15,83471,83473],{"className":83472},[307,308,309,310],[15,83474,83476,83479],{"className":83475},[59,310],[15,83477,5392],{"className":83478,"style":334},[59,60,310],[15,83480,34850],{"className":83481,"style":2587},[59,60,310],[15,83483,318],{"className":83484},[317],[15,83486,83488],{"className":83487},[290],[15,83489,83491],{"className":83490,"style":7968},[294],[15,83492],{},[15,83494,113],{"className":83495},[146],[15,83497,206],{"className":83498,"style":334},[59,60],[15,83500,551],{"className":83501},[573],[15,83503],{"className":83504,"style":406},[157],[15,83506,213],{"className":83507},[59,60],[15,83509,120],{"className":83510},[153],[15,83512],{"className":83513,"style":158},[157],[15,83515,9952],{"className":83516},[162],[15,83518],{"className":83519,"style":158},[157],[15,83521,83523],{"className":83522},[59,34367],[15,83524,83526,83639],{"className":83525},[285,286],[15,83527,83529,83636],{"className":83528},[290],[15,83530,83533,83619],{"className":83531,"style":83532},[294],"height:0.9839em;",[15,83534,83537,83540],{"className":83535,"style":83536},[6307],"top:-3.2em;",[15,83538],{"className":83539,"style":14846},[302],[15,83541,83543,83572,83575,83578,83581,83584,83587,83616],{"className":83542,"style":41161},[59],[15,83544,83546,83549],{"className":83545},[59],[15,83547,33884],{"className":83548,"style":34038},[59,60],[15,83550,83552],{"className":83551},[281],[15,83553,83555],{"className":83554},[285],[15,83556,83558],{"className":83557},[290],[15,83559,83561],{"className":83560,"style":45032},[294],[15,83562,83563,83566],{"style":45035},[15,83564],{"className":83565,"style":303},[302],[15,83567,83569],{"className":83568},[307,308,309,310],[15,83570,2463],{"className":83571},[59,310],[15,83573,113],{"className":83574},[146],[15,83576,2463],{"className":83577},[59],[15,83579],{"className":83580,"style":2587},[157],[15,83582,4813],{"className":83583},[2591],[15,83585],{"className":83586,"style":2587},[157],[15,83588,83590,83593],{"className":83589},[59],[15,83591,33884],{"className":83592,"style":34038},[59,60],[15,83594,83596],{"className":83595},[281],[15,83597,83599],{"className":83598},[285],[15,83600,83602],{"className":83601},[290],[15,83603,83605],{"className":83604,"style":45032},[294],[15,83606,83607,83610],{"style":45035},[15,83608],{"className":83609,"style":303},[302],[15,83611,83613],{"className":83612},[307,308,309,310],[15,83614,2463],{"className":83615},[59,310],[15,83617,120],{"className":83618},[153],[15,83620,83622,83625],{"style":83621},"top:-2.9439em;",[15,83623],{"className":83624,"style":14846},[302],[15,83626,83629],{"className":83627,"style":83628},[34443],"min-width:1.02em;height:1.28em;",[6323,83630,83633],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},"1.28em","0 0 400000 1296",[6331,83634],{"d":83635},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[15,83637,318],{"className":83638},[317],[15,83640,83642],{"className":83641},[290],[15,83643,83646],{"className":83644,"style":83645},[294],"height:0.2561em;",[15,83647],{},[15,83649],{"className":83650,"style":158},[157],[15,83652,9952],{"className":83653},[162],[15,83655],{"className":83656,"style":158},[157],[15,83658,83660],{"className":83659},[59,34367],[15,83661,83663,83727],{"className":83662},[285,286],[15,83664,83666,83724],{"className":83665},[290],[15,83667,83670,83711],{"className":83668,"style":83669},[294],"height:1.0039em;",[15,83671,83673,83676],{"className":83672,"style":11863},[6307],[15,83674],{"className":83675,"style":461},[302],[15,83677,83679,83682],{"className":83678,"style":34387},[59],[15,83680,2463],{"className":83681},[59],[15,83683,83685,83688],{"className":83684},[59],[15,83686,33884],{"className":83687,"style":34038},[59,60],[15,83689,83691],{"className":83690},[281],[15,83692,83694],{"className":83693},[285],[15,83695,83697],{"className":83696},[290],[15,83698,83700],{"className":83699,"style":45032},[294],[15,83701,83702,83705],{"style":45035},[15,83703],{"className":83704,"style":303},[302],[15,83706,83708],{"className":83707},[307,308,309,310],[15,83709,2463],{"className":83710},[59,310],[15,83712,83714,83717],{"style":83713},"top:-2.9639em;",[15,83715],{"className":83716,"style":461},[302],[15,83718,83720],{"className":83719,"style":34444},[34443],[6323,83721,83722],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,83723],{"d":34451},[15,83725,318],{"className":83726},[317],[15,83728,83730],{"className":83729},[290],[15,83731,83734],{"className":83732,"style":83733},[294],"height:0.0361em;",[15,83735],{},[15,83737,83738,83741],{"style":83405},[15,83739],{"className":83740,"style":83399},[302],[15,83742,83744,83747,83750,83753,83756,83759,83864],{"className":83743},[59],[15,83745],{"className":83746},[59],[15,83748],{"className":83749,"style":3634},[157],[15,83751],{"className":83752,"style":158},[157],[15,83754,9952],{"className":83755},[162],[15,83757],{"className":83758,"style":158},[157],[15,83760,83762],{"className":83761},[59,34367],[15,83763,83765,83856],{"className":83764},[285,286],[15,83766,83768,83853],{"className":83767},[290],[15,83769,83771,83841],{"className":83770,"style":83532},[294],[15,83772,83774,83777],{"className":83773,"style":83536},[6307],[15,83775],{"className":83776,"style":14846},[302],[15,83778,83780,83826,83829,83832,83835,83838],{"className":83779,"style":41161},[59],[15,83781,83783,83786],{"className":83782},[59],[15,83784,199],{"className":83785,"style":277},[59,60],[15,83787,83789],{"className":83788},[281],[15,83790,83792,83818],{"className":83791},[285,286],[15,83793,83795,83815],{"className":83794},[290],[15,83796,83798],{"className":83797,"style":379},[294],[15,83799,83800,83803],{"style":298},[15,83801],{"className":83802,"style":303},[302],[15,83804,83806],{"className":83805},[307,308,309,310],[15,83807,83809,83812],{"className":83808},[59,310],[15,83810,10694],{"className":83811,"style":10782},[59,60,310],[15,83813,21893],{"className":83814},[59,60,310],[15,83816,318],{"className":83817},[317],[15,83819,83821],{"className":83820},[290],[15,83822,83824],{"className":83823,"style":7968},[294],[15,83825],{},[15,83827,113],{"className":83828},[146],[15,83830,206],{"className":83831,"style":334},[59,60],[15,83833,210],{"className":83834},[59],[15,83836,213],{"className":83837},[59,60],[15,83839,120],{"className":83840},[153],[15,83842,83843,83846],{"style":83621},[15,83844],{"className":83845,"style":14846},[302],[15,83847,83849],{"className":83848,"style":83628},[34443],[6323,83850,83851],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,83852],{"d":83635},[15,83854,318],{"className":83855},[317],[15,83857,83859],{"className":83858},[290],[15,83860,83862],{"className":83861,"style":83645},[294],[15,83863],{},[15,83865,4375],{"className":83866},[59],[15,83868,318],{"className":83869},[317],[15,83871,83873],{"className":83872},[290],[15,83874,83876],{"className":83875,"style":83421},[294],[15,83877],{},[11,83879,83880,83883],{},[1225,83881,83882],{},"Pinsker 的完整推导（Vajda 型两步法）。"," 分三步：",[11,83885,83886,83889,83890,83918,83919,84027],{},[1225,83887,83888],{},"第 1 步（数据处理到二元划分）。"," 对任一事件 ",[15,83891,83893,83906],{"className":83892,"translate":19},[18],[15,83894,83896],{"className":83895},[23],[25,83897,83898],{"xmlns":27},[29,83899,83900,83904],{},[32,83901,83902],{},[35,83903,603],{},[39,83905,603],{"encoding":41},[15,83907,83909],{"className":83908,"ariaHidden":46},[45],[15,83910,83912,83915],{"className":83911},[50],[15,83913],{"className":83914,"style":664},[54],[15,83916,603],{"className":83917},[59,60],"，把样本空间经确定性映射 ",[15,83920,83922,83950],{"className":83921,"translate":19},[18],[15,83923,83925],{"className":83924},[23],[25,83926,83927],{"xmlns":27},[29,83928,83929,83947],{},[32,83930,83931,83933,83935,83941,83943,83945],{},[35,83932,774],{},[110,83934,8684],{},[195,83936,83937,83939],{},[115,83938,117],{"mathvariant":75213},[35,83940,603],{},[110,83942,113],{"stretchy":112},[35,83944,774],{},[110,83946,120],{"stretchy":112},[39,83948,83949],{"encoding":41},"x\\mapsto\\mathbf 1_A(x)",[15,83951,83953,83972],{"className":83952,"ariaHidden":46},[45],[15,83954,83956,83960,83963,83966,83969],{"className":83955},[50],[15,83957],{"className":83958,"style":83959},[54],"height:0.522em;vertical-align:-0.011em;",[15,83961,774],{"className":83962},[59,60],[15,83964],{"className":83965,"style":158},[157],[15,83967,8684],{"className":83968},[162],[15,83970],{"className":83971,"style":158},[157],[15,83973,83975,83978,84018,84021,84024],{"className":83974},[50],[15,83976],{"className":83977,"style":139},[54],[15,83979,83981,83984],{"className":83980},[59],[15,83982,117],{"className":83983},[59,75558],[15,83985,83987],{"className":83986},[281],[15,83988,83990,84010],{"className":83989},[285,286],[15,83991,83993,84007],{"className":83992},[290],[15,83994,83996],{"className":83995,"style":379},[294],[15,83997,83998,84001],{"style":382},[15,83999],{"className":84000,"style":303},[302],[15,84002,84004],{"className":84003},[307,308,309,310],[15,84005,603],{"className":84006},[59,60,310],[15,84008,318],{"className":84009},[317],[15,84011,84013],{"className":84012},[290],[15,84014,84016],{"className":84015,"style":7968},[294],[15,84017],{},[15,84019,113],{"className":84020},[146],[15,84022,774],{"className":84023},[59,60],[15,84025,120],{"className":84026},[153]," 压成两个点，用 4.5 节的 DPI：",[15,84029,84031],{"className":84030,"translate":19},[180],[15,84032,84034,84159],{"className":84033,"translate":19},[18],[15,84035,84037],{"className":84036},[23],[25,84038,84039],{"xmlns":27,"display":189},[29,84040,84041,84156],{},[32,84042,84043,84053,84055,84057,84059,84061,84063,84065,84067,84069,84079,84081,84091,84093,84095,84097,84099,84101,84103,84113,84115,84118,84120,84122,84124,84126,84128,84130,84132,84134,84136,84138,84140,84142,84144,84146,84148,84150,84152,84154],{},[195,84044,84045,84047],{},[35,84046,199],{},[32,84048,84049,84051],{},[35,84050,10694],{},[35,84052,21893],{},[110,84054,113],{"stretchy":112},[35,84056,206],{},[35,84058,210],{"mathvariant":209},[35,84060,213],{},[110,84062,120],{"stretchy":112},[1297,84064,4283],{},[110,84066,6928],{},[1297,84068,4283],{},[195,84070,84071,84073],{},[35,84072,199],{},[32,84074,84075,84077],{},[35,84076,10694],{},[35,84078,21893],{},[110,84080,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[32,84082,84083,84085,84087,84089],{},[35,84084,39291],{"mathvariant":209},[35,84086,7567],{"mathvariant":209},[35,84088,16450],{"mathvariant":209},[35,84090,82296],{"mathvariant":209},[110,84092,113],{"stretchy":112},[35,84094,44754],{},[110,84096,120],{"stretchy":112},[1297,84098,1299],{},[35,84100,210],{"mathvariant":209},[1297,84102,1299],{},[32,84104,84105,84107,84109,84111],{},[35,84106,39291],{"mathvariant":209},[35,84108,7567],{"mathvariant":209},[35,84110,16450],{"mathvariant":209},[35,84112,82296],{"mathvariant":209},[110,84114,113],{"stretchy":112},[35,84116,84117],{},"β",[110,84119,120],{"stretchy":112},[110,84121,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,84123,551],{"separator":46},[157,84125],{"width":3262},[35,84127,44754],{},[110,84129,123],{},[35,84131,206],{},[110,84133,113],{"stretchy":112},[35,84135,603],{},[110,84137,120],{"stretchy":112},[110,84139,551],{"separator":46},[1297,84141,4283],{},[35,84143,84117],{},[110,84145,123],{},[35,84147,213],{},[110,84149,113],{"stretchy":112},[35,84151,603],{},[110,84153,120],{"stretchy":112},[35,84155,4375],{"mathvariant":209},[39,84157,84158],{"encoding":41},"D_{KL}(P\\|Q)\\ \\ge\\ \nD_{KL}\\big(\\mathrm{Bern}(\\alpha)\\,\\|\\,\n\\mathrm{Bern}(\\beta)\\big),\n\\qquad \\alpha=P(A),\\ \\beta=Q(A).",[15,84160,84162,84244,84370,84409],{"className":84161,"ariaHidden":46},[45],[15,84163,84165,84168,84214,84217,84220,84223,84226,84229,84232,84235,84238,84241],{"className":84164},[50],[15,84166],{"className":84167,"style":139},[54],[15,84169,84171,84174],{"className":84170},[59],[15,84172,199],{"className":84173,"style":277},[59,60],[15,84175,84177],{"className":84176},[281],[15,84178,84180,84206],{"className":84179},[285,286],[15,84181,84183,84203],{"className":84182},[290],[15,84184,84186],{"className":84185,"style":379},[294],[15,84187,84188,84191],{"style":298},[15,84189],{"className":84190,"style":303},[302],[15,84192,84194],{"className":84193},[307,308,309,310],[15,84195,84197,84200],{"className":84196},[59,310],[15,84198,10694],{"className":84199,"style":10782},[59,60,310],[15,84201,21893],{"className":84202},[59,60,310],[15,84204,318],{"className":84205},[317],[15,84207,84209],{"className":84208},[290],[15,84210,84212],{"className":84211,"style":7968},[294],[15,84213],{},[15,84215,113],{"className":84216},[146],[15,84218,206],{"className":84219,"style":334},[59,60],[15,84221,210],{"className":84222},[59],[15,84224,213],{"className":84225},[59,60],[15,84227,120],{"className":84228},[153],[15,84230,4283],{"className":84231},[157],[15,84233],{"className":84234,"style":158},[157],[15,84236,6928],{"className":84237},[162],[15,84239,4283],{"className":84240},[157],[15,84242],{"className":84243,"style":158},[157],[15,84245,84247,84250,84296,84302,84309,84312,84315,84318,84321,84324,84327,84333,84336,84340,84343,84349,84352,84355,84358,84361,84364,84367],{"className":84246},[50],[15,84248],{"className":84249,"style":20563},[54],[15,84251,84253,84256],{"className":84252},[59],[15,84254,199],{"className":84255,"style":277},[59,60],[15,84257,84259],{"className":84258},[281],[15,84260,84262,84288],{"className":84261},[285,286],[15,84263,84265,84285],{"className":84264},[290],[15,84266,84268],{"className":84267,"style":379},[294],[15,84269,84270,84273],{"style":298},[15,84271],{"className":84272,"style":303},[302],[15,84274,84276],{"className":84275},[307,308,309,310],[15,84277,84279,84282],{"className":84278},[59,310],[15,84280,10694],{"className":84281,"style":10782},[59,60,310],[15,84283,21893],{"className":84284},[59,60,310],[15,84286,318],{"className":84287},[317],[15,84289,84291],{"className":84290},[290],[15,84292,84294],{"className":84293,"style":7968},[294],[15,84295],{},[15,84297,84299],{"className":84298},[59],[15,84300,113],{"className":84301},[419,9674],[15,84303,84305],{"className":84304},[59],[15,84306,84308],{"className":84307},[59,32662],"Bern",[15,84310,113],{"className":84311},[146],[15,84313,44754],{"className":84314,"style":44784},[59,60],[15,84316,120],{"className":84317},[153],[15,84319],{"className":84320,"style":406},[157],[15,84322,210],{"className":84323},[59],[15,84325],{"className":84326,"style":406},[157],[15,84328,84330],{"className":84329},[59],[15,84331,84308],{"className":84332},[59,32662],[15,84334,113],{"className":84335},[146],[15,84337,84117],{"className":84338,"style":84339},[59,60],"margin-right:0.0528em;",[15,84341,120],{"className":84342},[153],[15,84344,84346],{"className":84345},[59],[15,84347,120],{"className":84348},[419,9674],[15,84350,551],{"className":84351},[573],[15,84353],{"className":84354,"style":3634},[157],[15,84356],{"className":84357,"style":406},[157],[15,84359,44754],{"className":84360,"style":44784},[59,60],[15,84362],{"className":84363,"style":158},[157],[15,84365,123],{"className":84366},[162],[15,84368],{"className":84369,"style":158},[157],[15,84371,84373,84376,84379,84382,84385,84388,84391,84394,84397,84400,84403,84406],{"className":84372},[50],[15,84374],{"className":84375,"style":139},[54],[15,84377,206],{"className":84378,"style":334},[59,60],[15,84380,113],{"className":84381},[146],[15,84383,603],{"className":84384},[59,60],[15,84386,120],{"className":84387},[153],[15,84389,551],{"className":84390},[573],[15,84392,4283],{"className":84393},[157],[15,84395],{"className":84396,"style":406},[157],[15,84398,84117],{"className":84399,"style":84339},[59,60],[15,84401],{"className":84402,"style":158},[157],[15,84404,123],{"className":84405},[162],[15,84407],{"className":84408,"style":158},[157],[15,84410,84412,84415,84418,84421,84424,84427],{"className":84411},[50],[15,84413],{"className":84414,"style":139},[54],[15,84416,213],{"className":84417},[59,60],[15,84419,113],{"className":84420},[146],[15,84422,603],{"className":84423},[59,60],[15,84425,120],{"className":84426},[153],[15,84428,4375],{"className":84429},[59],[11,84431,84432,84435,84436,84531,84532,84560,84561,5645,84694,84826,84827,5645,84900,84973],{},[1225,84433,84434],{},"第 2 步（二元问题的精确最小值）。"," 固定差 ",[15,84437,84439,84465],{"className":84438,"translate":19},[18],[15,84440,84442],{"className":84441},[23],[25,84443,84444],{"xmlns":27},[29,84445,84446,84462],{},[32,84447,84448,84450,84452,84454,84456,84458,84460],{},[35,84449,15712],{},[110,84451,123],{},[35,84453,44754],{},[110,84455,4813],{},[35,84457,84117],{},[110,84459,6928],{},[115,84461,126],{},[39,84463,84464],{"encoding":41},"\\delta=\\alpha-\\beta\\ge0",[15,84466,84468,84486,84504,84522],{"className":84467,"ariaHidden":46},[45],[15,84469,84471,84474,84477,84480,84483],{"className":84470},[50],[15,84472],{"className":84473,"style":12597},[54],[15,84475,15712],{"className":84476,"style":15761},[59,60],[15,84478],{"className":84479,"style":158},[157],[15,84481,123],{"className":84482},[162],[15,84484],{"className":84485,"style":158},[157],[15,84487,84489,84492,84495,84498,84501],{"className":84488},[50],[15,84490],{"className":84491,"style":4251},[54],[15,84493,44754],{"className":84494,"style":44784},[59,60],[15,84496],{"className":84497,"style":2587},[157],[15,84499,4813],{"className":84500},[2591],[15,84502],{"className":84503,"style":2587},[157],[15,84505,84507,84510,84513,84516,84519],{"className":84506},[50],[15,84508],{"className":84509,"style":55},[54],[15,84511,84117],{"className":84512,"style":84339},[59,60],[15,84514],{"className":84515,"style":158},[157],[15,84517,6928],{"className":84518},[162],[15,84520],{"className":84521,"style":158},[157],[15,84523,84525,84528],{"className":84524},[50],[15,84526],{"className":84527,"style":172},[54],[15,84529,126],{"className":84530},[59],"（目标 TV 值），对 ",[15,84533,84535,84548],{"className":84534,"translate":19},[18],[15,84536,84538],{"className":84537},[23],[25,84539,84540],{"xmlns":27},[29,84541,84542,84546],{},[32,84543,84544],{},[35,84545,44754],{},[39,84547,49090],{"encoding":41},[15,84549,84551],{"className":84550,"ariaHidden":46},[45],[15,84552,84554,84557],{"className":84553},[50],[15,84555],{"className":84556,"style":2345},[54],[15,84558,44754],{"className":84559,"style":44784},[59,60]," 最小化二元 KL。取对称中心 ",[15,84562,84564,84592],{"className":84563,"translate":19},[18],[15,84565,84567],{"className":84566},[23],[25,84568,84569],{"xmlns":27},[29,84570,84571,84589],{},[32,84572,84573,84575,84577],{},[35,84574,44754],{},[110,84576,123],{},[238,84578,84579,84587],{},[32,84580,84581,84583,84585],{},[115,84582,117],{},[110,84584,2470],{},[35,84586,15712],{},[115,84588,2463],{},[39,84590,84591],{"encoding":41},"\\alpha=\\frac{1+\\delta}{2}",[15,84593,84595,84613],{"className":84594,"ariaHidden":46},[45],[15,84596,84598,84601,84604,84607,84610],{"className":84597},[50],[15,84599],{"className":84600,"style":2345},[54],[15,84602,44754],{"className":84603,"style":44784},[59,60],[15,84605],{"className":84606,"style":158},[157],[15,84608,123],{"className":84609},[162],[15,84611],{"className":84612,"style":158},[157],[15,84614,84616,84620],{"className":84615},[50],[15,84617],{"className":84618,"style":84619},[54],"height:1.2251em;vertical-align:-0.345em;",[15,84621,84623,84626,84691],{"className":84622},[59],[15,84624],{"className":84625},[146,441],[15,84627,84629],{"className":84628},[238],[15,84630,84632,84683],{"className":84631},[285,286],[15,84633,84635,84680],{"className":84634},[290],[15,84636,84638,84652,84660],{"className":84637,"style":2687},[294],[15,84639,84640,84643],{"style":2527},[15,84641],{"className":84642,"style":461},[302],[15,84644,84646],{"className":84645},[307,308,309,310],[15,84647,84649],{"className":84648},[59,310],[15,84650,2463],{"className":84651},[59,310],[15,84653,84654,84657],{"style":473},[15,84655],{"className":84656,"style":461},[302],[15,84658],{"className":84659,"style":481},[480],[15,84661,84662,84665],{"style":2550},[15,84663],{"className":84664,"style":461},[302],[15,84666,84668],{"className":84667},[307,308,309,310],[15,84669,84671,84674,84677],{"className":84670},[59,310],[15,84672,117],{"className":84673},[59,310],[15,84675,2470],{"className":84676},[2591,310],[15,84678,15712],{"className":84679,"style":15761},[59,60,310],[15,84681,318],{"className":84682},[317],[15,84684,84686],{"className":84685},[290],[15,84687,84689],{"className":84688,"style":2572},[294],[15,84690],{},[15,84692],{"className":84693},[153,441],[15,84695,84697,84725],{"className":84696,"translate":19},[18],[15,84698,84700],{"className":84699},[23],[25,84701,84702],{"xmlns":27},[29,84703,84704,84722],{},[32,84705,84706,84708,84710],{},[35,84707,84117],{},[110,84709,123],{},[238,84711,84712,84720],{},[32,84713,84714,84716,84718],{},[115,84715,117],{},[110,84717,4813],{},[35,84719,15712],{},[115,84721,2463],{},[39,84723,84724],{"encoding":41},"\\beta=\\frac{1-\\delta}{2}",[15,84726,84728,84746],{"className":84727,"ariaHidden":46},[45],[15,84729,84731,84734,84737,84740,84743],{"className":84730},[50],[15,84732],{"className":84733,"style":55},[54],[15,84735,84117],{"className":84736,"style":84339},[59,60],[15,84738],{"className":84739,"style":158},[157],[15,84741,123],{"className":84742},[162],[15,84744],{"className":84745,"style":158},[157],[15,84747,84749,84752],{"className":84748},[50],[15,84750],{"className":84751,"style":84619},[54],[15,84753,84755,84758,84823],{"className":84754},[59],[15,84756],{"className":84757},[146,441],[15,84759,84761],{"className":84760},[238],[15,84762,84764,84815],{"className":84763},[285,286],[15,84765,84767,84812],{"className":84766},[290],[15,84768,84770,84784,84792],{"className":84769,"style":2687},[294],[15,84771,84772,84775],{"style":2527},[15,84773],{"className":84774,"style":461},[302],[15,84776,84778],{"className":84777},[307,308,309,310],[15,84779,84781],{"className":84780},[59,310],[15,84782,2463],{"className":84783},[59,310],[15,84785,84786,84789],{"style":473},[15,84787],{"className":84788,"style":461},[302],[15,84790],{"className":84791,"style":481},[480],[15,84793,84794,84797],{"style":2550},[15,84795],{"className":84796,"style":461},[302],[15,84798,84800],{"className":84799},[307,308,309,310],[15,84801,84803,84806,84809],{"className":84802},[59,310],[15,84804,117],{"className":84805},[59,310],[15,84807,4813],{"className":84808},[2591,310],[15,84810,15712],{"className":84811,"style":15761},[59,60,310],[15,84813,318],{"className":84814},[317],[15,84816,84818],{"className":84817},[290],[15,84819,84821],{"className":84820,"style":2572},[294],[15,84822],{},[15,84824],{"className":84825},[153,441],"，此时 ",[15,84828,84830,84852],{"className":84829,"translate":19},[18],[15,84831,84833],{"className":84832},[23],[25,84834,84835],{"xmlns":27},[29,84836,84837,84849],{},[32,84838,84839,84841,84843,84845,84847],{},[115,84840,117],{},[110,84842,4813],{},[35,84844,44754],{},[110,84846,123],{},[35,84848,84117],{},[39,84850,84851],{"encoding":41},"1-\\alpha=\\beta",[15,84853,84855,84873,84891],{"className":84854,"ariaHidden":46},[45],[15,84856,84858,84861,84864,84867,84870],{"className":84857},[50],[15,84859],{"className":84860,"style":12578},[54],[15,84862,117],{"className":84863},[59],[15,84865],{"className":84866,"style":2587},[157],[15,84868,4813],{"className":84869},[2591],[15,84871],{"className":84872,"style":2587},[157],[15,84874,84876,84879,84882,84885,84888],{"className":84875},[50],[15,84877],{"className":84878,"style":2345},[54],[15,84880,44754],{"className":84881,"style":44784},[59,60],[15,84883],{"className":84884,"style":158},[157],[15,84886,123],{"className":84887},[162],[15,84889],{"className":84890,"style":158},[157],[15,84892,84894,84897],{"className":84893},[50],[15,84895],{"className":84896,"style":55},[54],[15,84898,84117],{"className":84899,"style":84339},[59,60],[15,84901,84903,84925],{"className":84902,"translate":19},[18],[15,84904,84906],{"className":84905},[23],[25,84907,84908],{"xmlns":27},[29,84909,84910,84922],{},[32,84911,84912,84914,84916,84918,84920],{},[115,84913,117],{},[110,84915,4813],{},[35,84917,84117],{},[110,84919,123],{},[35,84921,44754],{},[39,84923,84924],{"encoding":41},"1-\\beta=\\alpha",[15,84926,84928,84946,84964],{"className":84927,"ariaHidden":46},[45],[15,84929,84931,84934,84937,84940,84943],{"className":84930},[50],[15,84932],{"className":84933,"style":12578},[54],[15,84935,117],{"className":84936},[59],[15,84938],{"className":84939,"style":2587},[157],[15,84941,4813],{"className":84942},[2591],[15,84944],{"className":84945,"style":2587},[157],[15,84947,84949,84952,84955,84958,84961],{"className":84948},[50],[15,84950],{"className":84951,"style":55},[54],[15,84953,84117],{"className":84954,"style":84339},[59,60],[15,84956],{"className":84957,"style":158},[157],[15,84959,123],{"className":84960},[162],[15,84962],{"className":84963,"style":158},[157],[15,84965,84967,84970],{"className":84966},[50],[15,84968],{"className":84969,"style":2345},[54],[15,84971,44754],{"className":84972,"style":44784},[59,60],"，算得",[15,84975,84977],{"className":84976,"translate":19},[180],[15,84978,84980,85236],{"className":84979,"translate":19},[18],[15,84981,84983],{"className":84982},[23],[25,84984,84985],{"xmlns":27,"display":189},[29,84986,84987,85233],{},[1243,84988,84989,85047,85097,85171],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,84990,84991,84997],{},[1252,84992,84993],{},[1255,84994,84995],{"scriptlevel":126,"displaystyle":46},[32,84996],{},[1252,84998,84999],{},[1255,85000,85001],{"scriptlevel":126,"displaystyle":46},[32,85002,85003,85005,85015,85017,85027,85029,85043,85045],{},[32,85004],{},[195,85006,85007,85009],{},[35,85008,199],{},[32,85010,85011,85013],{},[35,85012,10694],{},[35,85014,21893],{},[110,85016,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[32,85018,85019,85021,85023,85025],{},[35,85020,39291],{"mathvariant":209},[35,85022,7567],{"mathvariant":209},[35,85024,16450],{"mathvariant":209},[35,85026,82296],{"mathvariant":209},[110,85028,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1255,85030,85031],{"scriptlevel":126,"displaystyle":112},[238,85032,85033,85041],{},[32,85034,85035,85037,85039],{},[115,85036,117],{},[110,85038,2470],{},[35,85040,15712],{},[115,85042,2463],{},[110,85044,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,85046,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,85048,85049,85055],{},[1252,85050,85051],{},[1255,85052,85053],{"scriptlevel":126,"displaystyle":46},[32,85054],{},[1252,85056,85057],{},[1255,85058,85059],{"scriptlevel":126,"displaystyle":46},[32,85060,85061,85063,85065,85067,85077,85079,85093,85095],{},[32,85062],{},[157,85064],{"width":3262},[110,85066,210],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[32,85068,85069,85071,85073,85075],{},[35,85070,39291],{"mathvariant":209},[35,85072,7567],{"mathvariant":209},[35,85074,16450],{"mathvariant":209},[35,85076,82296],{"mathvariant":209},[110,85078,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1255,85080,85081],{"scriptlevel":126,"displaystyle":112},[238,85082,85083,85091],{},[32,85084,85085,85087,85089],{},[115,85086,117],{},[110,85088,4813],{},[35,85090,15712],{},[115,85092,2463],{},[110,85094,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,85096,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1249,85098,85099,85105],{},[1252,85100,85101],{},[1255,85102,85103],{"scriptlevel":126,"displaystyle":46},[32,85104],{},[1252,85106,85107],{},[1255,85108,85109],{"scriptlevel":126,"displaystyle":46},[32,85110,85111,85113,85115,85117,85119,85121,85129,85131,85133,85135,85137,85145,85147,85149,85151,85153,85155,85157,85159,85161,85163],{},[32,85112],{},[110,85114,123],{},[35,85116,44754],{},[35,85118,4100],{},[110,85120,4103],{},[1255,85122,85123],{"scriptlevel":126,"displaystyle":112},[238,85124,85125,85127],{},[35,85126,44754],{},[35,85128,84117],{},[110,85130,2470],{},[35,85132,84117],{},[35,85134,4100],{},[110,85136,4103],{},[1255,85138,85139],{"scriptlevel":126,"displaystyle":112},[238,85140,85141,85143],{},[35,85142,84117],{},[35,85144,44754],{},[110,85146,123],{},[110,85148,113],{"stretchy":112},[35,85150,44754],{},[110,85152,4813],{},[35,85154,84117],{},[110,85156,120],{"stretchy":112},[1297,85158,1299],{},[35,85160,4100],{},[110,85162,4103],{},[1255,85164,85165],{"scriptlevel":126,"displaystyle":112},[238,85166,85167,85169],{},[35,85168,44754],{},[35,85170,84117],{},[1249,85172,85173,85179],{},[1252,85174,85175],{},[1255,85176,85177],{"scriptlevel":126,"displaystyle":46},[32,85178],{},[1252,85180,85181],{},[1255,85182,85183],{"scriptlevel":126,"displaystyle":46},[32,85184,85185,85187,85189,85191,85193,85195,85197,85217,85219,85221,85223,85225,85227,85229,85231],{},[32,85186],{},[110,85188,123],{},[35,85190,15712],{},[1297,85192,1299],{},[35,85194,4100],{},[110,85196,4103],{},[1255,85198,85199],{"scriptlevel":126,"displaystyle":112},[238,85200,85201,85209],{},[32,85202,85203,85205,85207],{},[115,85204,117],{},[110,85206,2470],{},[35,85208,15712],{},[32,85210,85211,85213,85215],{},[115,85212,117],{},[110,85214,4813],{},[35,85216,15712],{},[110,85218,123],{},[110,85220,1015],{},[1297,85222,1299],{},[35,85224,38665],{},[110,85226,113],{"stretchy":112},[35,85228,15712],{},[110,85230,120],{"stretchy":112},[35,85232,4375],{"mathvariant":209},[39,85234,85235],{"encoding":41},"\\begin{aligned}\n&D_{KL}\\Big(\\mathrm{Bern}\n\\Big(\\tfrac{1+\\delta}2\\Big)\\Big)\\\\\n&\\qquad\\Big\\|\\mathrm{Bern}\n\\Big(\\tfrac{1-\\delta}2\\Big)\\Big)\\\\\n&=\\alpha\\log\\tfrac{\\alpha}{\\beta}\n+\\beta\\log\\tfrac{\\beta}{\\alpha}\n=(\\alpha-\\beta)\\,\\log\\tfrac{\\alpha}{\\beta}\\\\\n&=\\delta\\,\\log\\tfrac{1+\\delta}{1-\\delta}\n=:\\,h(\\delta).\n\\end{aligned}",[15,85237,85239],{"className":85238,"ariaHidden":46},[45],[15,85240,85242,85246],{"className":85241},[50],[15,85243],{"className":85244,"style":85245},[54],"height:7.1968em;vertical-align:-3.3484em;",[15,85247,85249],{"className":85248},[59],[15,85250,85252,85313],{"className":85251},[1243],[15,85253,85255],{"className":85254},[1360],[15,85256,85258,85304],{"className":85257},[285,286],[15,85259,85261,85301],{"className":85260},[290],[15,85262,85265,85274,85283,85292],{"className":85263,"style":85264},[294],"height:3.8484em;",[15,85266,85268,85271],{"style":85267},"top:-5.8484em;",[15,85269],{"className":85270,"style":17588},[302],[15,85272],{"className":85273},[59],[15,85275,85277,85280],{"style":85276},"top:-3.7484em;",[15,85278],{"className":85279,"style":17588},[302],[15,85281],{"className":85282},[59],[15,85284,85286,85289],{"style":85285},"top:-1.8661em;",[15,85287],{"className":85288,"style":17588},[302],[15,85290],{"className":85291},[59],[15,85293,85295,85298],{"style":85294},"top:-0.2049em;",[15,85296],{"className":85297,"style":17588},[302],[15,85299],{"className":85300},[59],[15,85302,318],{"className":85303},[317],[15,85305,85307],{"className":85306},[290],[15,85308,85311],{"className":85309,"style":85310},[294],"height:3.3484em;",[15,85312],{},[15,85314,85316],{"className":85315},[1451],[15,85317,85319,86093],{"className":85318},[285,286],[15,85320,85322,86090],{"className":85321},[290],[15,85323,85325,85486,85640,85946],{"className":85324,"style":85264},[294],[15,85326,85327,85330],{"style":85267},[15,85328],{"className":85329,"style":17588},[302],[15,85331,85333,85336,85382,85388,85394,85400,85474,85480],{"className":85332},[59],[15,85334],{"className":85335},[59],[15,85337,85339,85342],{"className":85338},[59],[15,85340,199],{"className":85341,"style":277},[59,60],[15,85343,85345],{"className":85344},[281],[15,85346,85348,85374],{"className":85347},[285,286],[15,85349,85351,85371],{"className":85350},[290],[15,85352,85354],{"className":85353,"style":379},[294],[15,85355,85356,85359],{"style":298},[15,85357],{"className":85358,"style":303},[302],[15,85360,85362],{"className":85361},[307,308,309,310],[15,85363,85365,85368],{"className":85364},[59,310],[15,85366,10694],{"className":85367,"style":10782},[59,60,310],[15,85369,21893],{"className":85370},[59,60,310],[15,85372,318],{"className":85373},[317],[15,85375,85377],{"className":85376},[290],[15,85378,85380],{"className":85379,"style":7968},[294],[15,85381],{},[15,85383,85385],{"className":85384},[59],[15,85386,113],{"className":85387},[419,3720],[15,85389,85391],{"className":85390},[59],[15,85392,84308],{"className":85393},[59,32662],[15,85395,85397],{"className":85396},[59],[15,85398,113],{"className":85399},[419,3720],[15,85401,85403,85406,85471],{"className":85402},[59],[15,85404],{"className":85405},[146,441],[15,85407,85409],{"className":85408},[238],[15,85410,85412,85463],{"className":85411},[285,286],[15,85413,85415,85460],{"className":85414},[290],[15,85416,85418,85432,85440],{"className":85417,"style":2687},[294],[15,85419,85420,85423],{"style":2527},[15,85421],{"className":85422,"style":461},[302],[15,85424,85426],{"className":85425},[307,308,309,310],[15,85427,85429],{"className":85428},[59,310],[15,85430,2463],{"className":85431},[59,310],[15,85433,85434,85437],{"style":473},[15,85435],{"className":85436,"style":461},[302],[15,85438],{"className":85439,"style":481},[480],[15,85441,85442,85445],{"style":2550},[15,85443],{"className":85444,"style":461},[302],[15,85446,85448],{"className":85447},[307,308,309,310],[15,85449,85451,85454,85457],{"className":85450},[59,310],[15,85452,117],{"className":85453},[59,310],[15,85455,2470],{"className":85456},[2591,310],[15,85458,15712],{"className":85459,"style":15761},[59,60,310],[15,85461,318],{"className":85462},[317],[15,85464,85466],{"className":85465},[290],[15,85467,85469],{"className":85468,"style":2572},[294],[15,85470],{},[15,85472],{"className":85473},[153,441],[15,85475,85477],{"className":85476},[59],[15,85478,120],{"className":85479},[419,3720],[15,85481,85483],{"className":85482},[59],[15,85484,120],{"className":85485},[419,3720],[15,85487,85488,85491],{"style":85276},[15,85489],{"className":85490,"style":17588},[302],[15,85492,85494,85497,85500,85542,85548,85554,85628,85634],{"className":85493},[59],[15,85495],{"className":85496},[59],[15,85498],{"className":85499,"style":3634},[157],[15,85501,85503],{"className":85502},[59],[15,85504,85506],{"className":85505},[419,14829],[15,85507,85509,85533],{"className":85508},[285,286],[15,85510,85512,85530],{"className":85511},[290],[15,85513,85516],{"className":85514,"style":85515},[294],"height:1.15em;",[15,85517,85518,85521],{"style":73524},[15,85519],{"className":85520,"style":82587},[302],[15,85522,85524],{"style":85523},"width:0.556em;height:1.8em;",[6323,85525,85527],{"xmlns":6325,"width":14852,"height":17439,"viewBox":85526},"0 0 556 1800",[6331,85528],{"d":85529},"M145 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z\nM367 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M410 15 H367 v585 v600 v585 h43z",[15,85531,318],{"className":85532},[317],[15,85534,85536],{"className":85535},[290],[15,85537,85540],{"className":85538,"style":85539},[294],"height:0.65em;",[15,85541],{},[15,85543,85545],{"className":85544},[59],[15,85546,84308],{"className":85547},[59,32662],[15,85549,85551],{"className":85550},[59],[15,85552,113],{"className":85553},[419,3720],[15,85555,85557,85560,85625],{"className":85556},[59],[15,85558],{"className":85559},[146,441],[15,85561,85563],{"className":85562},[238],[15,85564,85566,85617],{"className":85565},[285,286],[15,85567,85569,85614],{"className":85568},[290],[15,85570,85572,85586,85594],{"className":85571,"style":2687},[294],[15,85573,85574,85577],{"style":2527},[15,85575],{"className":85576,"style":461},[302],[15,85578,85580],{"className":85579},[307,308,309,310],[15,85581,85583],{"className":85582},[59,310],[15,85584,2463],{"className":85585},[59,310],[15,85587,85588,85591],{"style":473},[15,85589],{"className":85590,"style":461},[302],[15,85592],{"className":85593,"style":481},[480],[15,85595,85596,85599],{"style":2550},[15,85597],{"className":85598,"style":461},[302],[15,85600,85602],{"className":85601},[307,308,309,310],[15,85603,85605,85608,85611],{"className":85604},[59,310],[15,85606,117],{"className":85607},[59,310],[15,85609,4813],{"className":85610},[2591,310],[15,85612,15712],{"className":85613,"style":15761},[59,60,310],[15,85615,318],{"className":85616},[317],[15,85618,85620],{"className":85619},[290],[15,85621,85623],{"className":85622,"style":2572},[294],[15,85624],{},[15,85626],{"className":85627},[153,441],[15,85629,85631],{"className":85630},[59],[15,85632,120],{"className":85633},[419,3720],[15,85635,85637],{"className":85636},[59],[15,85638,120],{"className":85639},[419,3720],[15,85641,85642,85645],{"style":85285},[15,85643],{"className":85644,"style":17588},[302],[15,85646,85648,85651,85654,85657,85660,85663,85666,85671,85674,85743,85746,85749,85752,85755,85758,85763,85766,85834,85837,85840,85843,85846,85849,85852,85855,85858,85861,85864,85867,85870,85875,85878],{"className":85647},[59],[15,85649],{"className":85650},[59],[15,85652],{"className":85653,"style":158},[157],[15,85655,123],{"className":85656},[162],[15,85658],{"className":85659,"style":158},[157],[15,85661,44754],{"className":85662,"style":44784},[59,60],[15,85664],{"className":85665,"style":406},[157],[15,85667,4154,85669],{"className":85668},[1484],[15,85670,4158],{"style":4157},[15,85672],{"className":85673,"style":406},[157],[15,85675,85677,85680,85740],{"className":85676},[59],[15,85678],{"className":85679},[146,441],[15,85681,85683],{"className":85682},[238],[15,85684,85686,85732],{"className":85685},[285,286],[15,85687,85689,85729],{"className":85688},[290],[15,85690,85693,85707,85715],{"className":85691,"style":85692},[294],"height:0.6954em;",[15,85694,85695,85698],{"style":2527},[15,85696],{"className":85697,"style":461},[302],[15,85699,85701],{"className":85700},[307,308,309,310],[15,85702,85704],{"className":85703},[59,310],[15,85705,84117],{"className":85706,"style":84339},[59,60,310],[15,85708,85709,85712],{"style":473},[15,85710],{"className":85711,"style":461},[302],[15,85713],{"className":85714,"style":481},[480],[15,85716,85717,85720],{"style":2550},[15,85718],{"className":85719,"style":461},[302],[15,85721,85723],{"className":85722},[307,308,309,310],[15,85724,85726],{"className":85725},[59,310],[15,85727,44754],{"className":85728,"style":44784},[59,60,310],[15,85730,318],{"className":85731},[317],[15,85733,85735],{"className":85734},[290],[15,85736,85738],{"className":85737,"style":2739},[294],[15,85739],{},[15,85741],{"className":85742},[153,441],[15,85744],{"className":85745,"style":2587},[157],[15,85747,2470],{"className":85748},[2591],[15,85750],{"className":85751,"style":2587},[157],[15,85753,84117],{"className":85754,"style":84339},[59,60],[15,85756],{"className":85757,"style":406},[157],[15,85759,4154,85761],{"className":85760},[1484],[15,85762,4158],{"style":4157},[15,85764],{"className":85765,"style":406},[157],[15,85767,85769,85772,85831],{"className":85768},[59],[15,85770],{"className":85771},[146,441],[15,85773,85775],{"className":85774},[238],[15,85776,85778,85823],{"className":85777},[285,286],[15,85779,85781,85820],{"className":85780},[290],[15,85782,85784,85798,85806],{"className":85783,"style":2825},[294],[15,85785,85786,85789],{"style":2527},[15,85787],{"className":85788,"style":461},[302],[15,85790,85792],{"className":85791},[307,308,309,310],[15,85793,85795],{"className":85794},[59,310],[15,85796,44754],{"className":85797,"style":44784},[59,60,310],[15,85799,85800,85803],{"style":473},[15,85801],{"className":85802,"style":461},[302],[15,85804],{"className":85805,"style":481},[480],[15,85807,85808,85811],{"style":2853},[15,85809],{"className":85810,"style":461},[302],[15,85812,85814],{"className":85813},[307,308,309,310],[15,85815,85817],{"className":85816},[59,310],[15,85818,84117],{"className":85819,"style":84339},[59,60,310],[15,85821,318],{"className":85822},[317],[15,85824,85826],{"className":85825},[290],[15,85827,85829],{"className":85828,"style":2572},[294],[15,85830],{},[15,85832],{"className":85833},[153,441],[15,85835],{"className":85836,"style":158},[157],[15,85838,123],{"className":85839},[162],[15,85841],{"className":85842,"style":158},[157],[15,85844,113],{"className":85845},[146],[15,85847,44754],{"className":85848,"style":44784},[59,60],[15,85850],{"className":85851,"style":2587},[157],[15,85853,4813],{"className":85854},[2591],[15,85856],{"className":85857,"style":2587},[157],[15,85859,84117],{"className":85860,"style":84339},[59,60],[15,85862,120],{"className":85863},[153],[15,85865],{"className":85866,"style":406},[157],[15,85868],{"className":85869,"style":406},[157],[15,85871,4154,85873],{"className":85872},[1484],[15,85874,4158],{"style":4157},[15,85876],{"className":85877,"style":406},[157],[15,85879,85881,85884,85943],{"className":85880},[59],[15,85882],{"className":85883},[146,441],[15,85885,85887],{"className":85886},[238],[15,85888,85890,85935],{"className":85889},[285,286],[15,85891,85893,85932],{"className":85892},[290],[15,85894,85896,85910,85918],{"className":85895,"style":85692},[294],[15,85897,85898,85901],{"style":2527},[15,85899],{"className":85900,"style":461},[302],[15,85902,85904],{"className":85903},[307,308,309,310],[15,85905,85907],{"className":85906},[59,310],[15,85908,84117],{"className":85909,"style":84339},[59,60,310],[15,85911,85912,85915],{"style":473},[15,85913],{"className":85914,"style":461},[302],[15,85916],{"className":85917,"style":481},[480],[15,85919,85920,85923],{"style":2550},[15,85921],{"className":85922,"style":461},[302],[15,85924,85926],{"className":85925},[307,308,309,310],[15,85927,85929],{"className":85928},[59,310],[15,85930,44754],{"className":85931,"style":44784},[59,60,310],[15,85933,318],{"className":85934},[317],[15,85936,85938],{"className":85937},[290],[15,85939,85941],{"className":85940,"style":2739},[294],[15,85942],{},[15,85944],{"className":85945},[153,441],[15,85947,85948,85951],{"style":85294},[15,85949],{"className":85950,"style":17588},[302],[15,85952,85954,85957,85960,85963,85966,85969,85972,85975,85980,85983,86063,86066,86069,86072,86075,86078,86081,86084,86087],{"className":85953},[59],[15,85955],{"className":85956},[59],[15,85958],{"className":85959,"style":158},[157],[15,85961,123],{"className":85962},[162],[15,85964],{"className":85965,"style":158},[157],[15,85967,15712],{"className":85968,"style":15761},[59,60],[15,85970],{"className":85971,"style":406},[157],[15,85973],{"className":85974,"style":406},[157],[15,85976,4154,85978],{"className":85977},[1484],[15,85979,4158],{"style":4157},[15,85981],{"className":85982,"style":406},[157],[15,85984,85986,85989,86060],{"className":85985},[59],[15,85987],{"className":85988},[146,441],[15,85990,85992],{"className":85991},[238],[15,85993,85995,86052],{"className":85994},[285,286],[15,85996,85998,86049],{"className":85997},[290],[15,85999,86001,86021,86029],{"className":86000,"style":2687},[294],[15,86002,86003,86006],{"style":2527},[15,86004],{"className":86005,"style":461},[302],[15,86007,86009],{"className":86008},[307,308,309,310],[15,86010,86012,86015,86018],{"className":86011},[59,310],[15,86013,117],{"className":86014},[59,310],[15,86016,4813],{"className":86017},[2591,310],[15,86019,15712],{"className":86020,"style":15761},[59,60,310],[15,86022,86023,86026],{"style":473},[15,86024],{"className":86025,"style":461},[302],[15,86027],{"className":86028,"style":481},[480],[15,86030,86031,86034],{"style":2550},[15,86032],{"className":86033,"style":461},[302],[15,86035,86037],{"className":86036},[307,308,309,310],[15,86038,86040,86043,86046],{"className":86039},[59,310],[15,86041,117],{"className":86042},[59,310],[15,86044,2470],{"className":86045},[2591,310],[15,86047,15712],{"className":86048,"style":15761},[59,60,310],[15,86050,318],{"className":86051},[317],[15,86053,86055],{"className":86054},[290],[15,86056,86058],{"className":86057,"style":16429},[294],[15,86059],{},[15,86061],{"className":86062},[153,441],[15,86064],{"className":86065,"style":158},[157],[15,86067,24114],{"className":86068},[162],[15,86070],{"className":86071,"style":406},[157],[15,86073],{"className":86074,"style":158},[157],[15,86076,38665],{"className":86077},[59,60],[15,86079,113],{"className":86080},[146],[15,86082,15712],{"className":86083,"style":15761},[59,60],[15,86085,120],{"className":86086},[153],[15,86088,4375],{"className":86089},[59],[15,86091,318],{"className":86092},[317],[15,86094,86096],{"className":86095},[290],[15,86097,86099],{"className":86098,"style":85310},[294],[15,86100],{},[11,86102,86103,86104,86229,86230,86311,86312,19966,86340,86390,86391,86469,86470,86601,86602,86605,86606,86781,86782,3853,86961,87012,87013,87041],{},"由标签交换的对称性 ",[15,86105,86107,86145],{"className":86106,"translate":19},[18],[15,86108,86110],{"className":86109},[23],[25,86111,86112],{"xmlns":27},[29,86113,86114,86142],{},[32,86115,86116,86118,86120,86122,86124,86126,86128,86130,86132,86134,86136,86138,86140],{},[35,86117,31022],{},[110,86119,113],{"stretchy":112},[35,86121,44754],{},[110,86123,120],{"stretchy":112},[110,86125,123],{},[35,86127,31022],{},[110,86129,113],{"stretchy":112},[115,86131,117],{},[110,86133,4813],{},[35,86135,44754],{},[110,86137,2470],{},[35,86139,15712],{},[110,86141,120],{"stretchy":112},[39,86143,86144],{"encoding":41},"\\varphi(\\alpha)=\\varphi(1-\\alpha+\\delta)",[15,86146,86148,86175,86199,86217],{"className":86147,"ariaHidden":46},[45],[15,86149,86151,86154,86157,86160,86163,86166,86169,86172],{"className":86150},[50],[15,86152],{"className":86153,"style":139},[54],[15,86155,31022],{"className":86156},[59,60],[15,86158,113],{"className":86159},[146],[15,86161,44754],{"className":86162,"style":44784},[59,60],[15,86164,120],{"className":86165},[153],[15,86167],{"className":86168,"style":158},[157],[15,86170,123],{"className":86171},[162],[15,86173],{"className":86174,"style":158},[157],[15,86176,86178,86181,86184,86187,86190,86193,86196],{"className":86177},[50],[15,86179],{"className":86180,"style":139},[54],[15,86182,31022],{"className":86183},[59,60],[15,86185,113],{"className":86186},[146],[15,86188,117],{"className":86189},[59],[15,86191],{"className":86192,"style":2587},[157],[15,86194,4813],{"className":86195},[2591],[15,86197],{"className":86198,"style":2587},[157],[15,86200,86202,86205,86208,86211,86214],{"className":86201},[50],[15,86203],{"className":86204,"style":4251},[54],[15,86206,44754],{"className":86207,"style":44784},[59,60],[15,86209],{"className":86210,"style":2587},[157],[15,86212,2470],{"className":86213},[2591],[15,86215],{"className":86216,"style":2587},[157],[15,86218,86220,86223,86226],{"className":86219},[50],[15,86221],{"className":86222,"style":139},[54],[15,86224,15712],{"className":86225,"style":15761},[59,60],[15,86227,120],{"className":86228},[153],"、边界值更大（",[15,86231,86233,86255],{"className":86232,"translate":19},[18],[15,86234,86236],{"className":86235},[23],[25,86237,86238],{"xmlns":27},[29,86239,86240,86252],{},[32,86241,86242,86244,86246],{},[35,86243,44754],{},[110,86245,1029],{},[6814,86247,86248,86250],{},[35,86249,15712],{},[110,86251,2470],{},[39,86253,86254],{"encoding":41},"\\alpha\\to\\delta^+",[15,86256,86258,86276],{"className":86257,"ariaHidden":46},[45],[15,86259,86261,86264,86267,86270,86273],{"className":86260},[50],[15,86262],{"className":86263,"style":2345},[54],[15,86265,44754],{"className":86266,"style":44784},[59,60],[15,86268],{"className":86269,"style":158},[157],[15,86271,1029],{"className":86272},[162],[15,86274],{"className":86275,"style":158},[157],[15,86277,86279,86282],{"className":86278},[50],[15,86280],{"className":86281,"style":21009},[54],[15,86283,86285,86288],{"className":86284},[59],[15,86286,15712],{"className":86287,"style":15761},[59,60],[15,86289,86291],{"className":86290},[281],[15,86292,86294],{"className":86293},[285],[15,86295,86297],{"className":86296},[290],[15,86298,86300],{"className":86299,"style":21009},[294],[15,86301,86302,86305],{"style":6865},[15,86303],{"className":86304,"style":303},[302],[15,86306,86308],{"className":86307},[307,308,309,310],[15,86309,2470],{"className":86310},[2591,310]," 时不平衡质量挤出 ",[15,86313,86315,86328],{"className":86314,"translate":19},[18],[15,86316,86318],{"className":86317},[23],[25,86319,86320],{"xmlns":27},[29,86321,86322,86326],{},[32,86323,86324],{},[35,86325,1024],{"mathvariant":209},[39,86327,3870],{"encoding":41},[15,86329,86331],{"className":86330,"ariaHidden":46},[45],[15,86332,86334,86337],{"className":86333},[50],[15,86335],{"className":86336,"style":2345},[54],[15,86338,1024],{"className":86339},[59],[15,86341,86343,86360],{"className":86342,"translate":19},[18],[15,86344,86346],{"className":86345},[23],[25,86347,86348],{"xmlns":27},[29,86349,86350,86358],{},[32,86351,86352,86354,86356],{},[35,86353,44754],{},[110,86355,1029],{},[115,86357,117],{},[39,86359,47215],{"encoding":41},[15,86361,86363,86381],{"className":86362,"ariaHidden":46},[45],[15,86364,86366,86369,86372,86375,86378],{"className":86365},[50],[15,86367],{"className":86368,"style":2345},[54],[15,86370,44754],{"className":86371,"style":44784},[59,60],[15,86373],{"className":86374,"style":158},[157],[15,86376,1029],{"className":86377},[162],[15,86379],{"className":86380,"style":158},[157],[15,86382,86384,86387],{"className":86383},[50],[15,86385],{"className":86386,"style":172},[54],[15,86388,117],{"className":86389},[59]," 时值为 ",[15,86392,86394,86422],{"className":86393,"translate":19},[18],[15,86395,86397],{"className":86396},[23],[25,86398,86399],{"xmlns":27},[29,86400,86401,86419],{},[32,86402,86403,86405,86407,86409,86411,86413,86415,86417],{},[110,86404,4813],{},[35,86406,4100],{},[110,86408,4103],{},[110,86410,113],{"stretchy":112},[115,86412,117],{},[110,86414,4813],{},[35,86416,15712],{},[110,86418,120],{"stretchy":112},[39,86420,86421],{"encoding":41},"-\\log(1-\\delta)",[15,86423,86425,86457],{"className":86424,"ariaHidden":46},[45],[15,86426,86428,86431,86434,86437,86442,86445,86448,86451,86454],{"className":86427},[50],[15,86429],{"className":86430,"style":139},[54],[15,86432,4813],{"className":86433},[59],[15,86435],{"className":86436,"style":406},[157],[15,86438,4154,86440],{"className":86439},[1484],[15,86441,4158],{"style":4157},[15,86443,113],{"className":86444},[146],[15,86446,117],{"className":86447},[59],[15,86449],{"className":86450,"style":2587},[157],[15,86452,4813],{"className":86453},[2591],[15,86455],{"className":86456,"style":2587},[157],[15,86458,86460,86463,86466],{"className":86459},[50],[15,86461],{"className":86462,"style":139},[54],[15,86464,15712],{"className":86465,"style":15761},[59,60],[15,86467,120],{"className":86468},[153],"，均大于中心值）可得：唯一驻点在 ",[15,86471,86473,86500],{"className":86472,"translate":19},[18],[15,86474,86476],{"className":86475},[23],[25,86477,86478],{"xmlns":27},[29,86479,86480,86498],{},[32,86481,86482,86484,86486],{},[35,86483,44754],{},[110,86485,123],{},[238,86487,86488,86496],{},[32,86489,86490,86492,86494],{},[115,86491,117],{},[110,86493,2470],{},[35,86495,15712],{},[115,86497,2463],{},[39,86499,84591],{"encoding":41},[15,86501,86503,86521],{"className":86502,"ariaHidden":46},[45],[15,86504,86506,86509,86512,86515,86518],{"className":86505},[50],[15,86507],{"className":86508,"style":2345},[54],[15,86510,44754],{"className":86511,"style":44784},[59,60],[15,86513],{"className":86514,"style":158},[157],[15,86516,123],{"className":86517},[162],[15,86519],{"className":86520,"style":158},[157],[15,86522,86524,86527],{"className":86523},[50],[15,86525],{"className":86526,"style":84619},[54],[15,86528,86530,86533,86598],{"className":86529},[59],[15,86531],{"className":86532},[146,441],[15,86534,86536],{"className":86535},[238],[15,86537,86539,86590],{"className":86538},[285,286],[15,86540,86542,86587],{"className":86541},[290],[15,86543,86545,86559,86567],{"className":86544,"style":2687},[294],[15,86546,86547,86550],{"style":2527},[15,86548],{"className":86549,"style":461},[302],[15,86551,86553],{"className":86552},[307,308,309,310],[15,86554,86556],{"className":86555},[59,310],[15,86557,2463],{"className":86558},[59,310],[15,86560,86561,86564],{"style":473},[15,86562],{"className":86563,"style":461},[302],[15,86565],{"className":86566,"style":481},[480],[15,86568,86569,86572],{"style":2550},[15,86570],{"className":86571,"style":461},[302],[15,86573,86575],{"className":86574},[307,308,309,310],[15,86576,86578,86581,86584],{"className":86577},[59,310],[15,86579,117],{"className":86580},[59,310],[15,86582,2470],{"className":86583},[2591,310],[15,86585,15712],{"className":86586,"style":15761},[59,60,310],[15,86588,318],{"className":86589},[317],[15,86591,86593],{"className":86592},[290],[15,86594,86596],{"className":86595,"style":2572},[294],[15,86597],{},[15,86599],{"className":86600},[153,441],"，且是",[1225,86603,86604],{},"精确最小值","（Vajda 界）：",[15,86607,86609,86665],{"className":86608,"translate":19},[18],[15,86610,86612],{"className":86611},[23],[25,86613,86614],{"xmlns":27},[29,86615,86616,86662],{},[32,86617,86618,86628,86630,86632,86634,86636,86638,86640,86642,86644,86650,86652,86654,86656,86658,86660],{},[195,86619,86620,86622],{},[35,86621,199],{},[32,86623,86624,86626],{},[35,86625,10694],{},[35,86627,21893],{},[110,86629,113],{"stretchy":112},[35,86631,206],{},[35,86633,210],{"mathvariant":209},[35,86635,213],{},[110,86637,120],{"stretchy":112},[110,86639,6928],{},[35,86641,38665],{},[110,86643,113],{"stretchy":112},[32,86645,86646,86648],{},[35,86647,5392],{"mathvariant":209},[35,86649,34850],{"mathvariant":209},[110,86651,113],{"stretchy":112},[35,86653,206],{},[110,86655,551],{"separator":46},[35,86657,213],{},[110,86659,120],{"stretchy":112},[110,86661,120],{"stretchy":112},[39,86663,86664],{"encoding":41},"D_{KL}(P\\|Q)\\ge h(\\mathrm{TV}(P,Q))",[15,86666,86668,86744],{"className":86667,"ariaHidden":46},[45],[15,86669,86671,86674,86720,86723,86726,86729,86732,86735,86738,86741],{"className":86670},[50],[15,86672],{"className":86673,"style":139},[54],[15,86675,86677,86680],{"className":86676},[59],[15,86678,199],{"className":86679,"style":277},[59,60],[15,86681,86683],{"className":86682},[281],[15,86684,86686,86712],{"className":86685},[285,286],[15,86687,86689,86709],{"className":86688},[290],[15,86690,86692],{"className":86691,"style":379},[294],[15,86693,86694,86697],{"style":298},[15,86695],{"className":86696,"style":303},[302],[15,86698,86700],{"className":86699},[307,308,309,310],[15,86701,86703,86706],{"className":86702},[59,310],[15,86704,10694],{"className":86705,"style":10782},[59,60,310],[15,86707,21893],{"className":86708},[59,60,310],[15,86710,318],{"className":86711},[317],[15,86713,86715],{"className":86714},[290],[15,86716,86718],{"className":86717,"style":7968},[294],[15,86719],{},[15,86721,113],{"className":86722},[146],[15,86724,206],{"className":86725,"style":334},[59,60],[15,86727,210],{"className":86728},[59],[15,86730,213],{"className":86731},[59,60],[15,86733,120],{"className":86734},[153],[15,86736],{"className":86737,"style":158},[157],[15,86739,6928],{"className":86740},[162],[15,86742],{"className":86743,"style":158},[157],[15,86745,86747,86750,86753,86756,86763,86766,86769,86772,86775,86778],{"className":86746},[50],[15,86748],{"className":86749,"style":139},[54],[15,86751,38665],{"className":86752},[59,60],[15,86754,113],{"className":86755},[146],[15,86757,86759],{"className":86758},[59],[15,86760,86762],{"className":86761,"style":4157},[59,32662],"TV",[15,86764,113],{"className":86765},[146],[15,86767,206],{"className":86768,"style":334},[59,60],[15,86770,551],{"className":86771},[573],[15,86773],{"className":86774,"style":406},[157],[15,86776,213],{"className":86777},[59,60],[15,86779,19047],{"className":86780},[153],"，其中 ",[15,86783,86785,86831],{"className":86784,"translate":19},[18],[15,86786,86788],{"className":86787},[23],[25,86789,86790],{"xmlns":27},[29,86791,86792,86828],{},[32,86793,86794,86796,86798,86800,86802,86804,86806,86808,86810],{},[35,86795,38665],{},[110,86797,113],{"stretchy":112},[35,86799,15712],{},[110,86801,120],{"stretchy":112},[110,86803,123],{},[35,86805,15712],{},[35,86807,4100],{},[110,86809,4103],{},[238,86811,86812,86820],{},[32,86813,86814,86816,86818],{},[115,86815,117],{},[110,86817,2470],{},[35,86819,15712],{},[32,86821,86822,86824,86826],{},[115,86823,117],{},[110,86825,4813],{},[35,86827,15712],{},[39,86829,86830],{"encoding":41},"h(\\delta)=\\delta\\log\\frac{1+\\delta}{1-\\delta}",[15,86832,86834,86861],{"className":86833,"ariaHidden":46},[45],[15,86835,86837,86840,86843,86846,86849,86852,86855,86858],{"className":86836},[50],[15,86838],{"className":86839,"style":139},[54],[15,86841,38665],{"className":86842},[59,60],[15,86844,113],{"className":86845},[146],[15,86847,15712],{"className":86848,"style":15761},[59,60],[15,86850,120],{"className":86851},[153],[15,86853],{"className":86854,"style":158},[157],[15,86856,123],{"className":86857},[162],[15,86859],{"className":86860,"style":158},[157],[15,86862,86864,86867,86870,86873,86878,86881],{"className":86863},[50],[15,86865],{"className":86866,"style":16353},[54],[15,86868,15712],{"className":86869,"style":15761},[59,60],[15,86871],{"className":86872,"style":406},[157],[15,86874,4154,86876],{"className":86875},[1484],[15,86877,4158],{"style":4157},[15,86879],{"className":86880,"style":406},[157],[15,86882,86884,86887,86958],{"className":86883},[59],[15,86885],{"className":86886},[146,441],[15,86888,86890],{"className":86889},[238],[15,86891,86893,86950],{"className":86892},[285,286],[15,86894,86896,86947],{"className":86895},[290],[15,86897,86899,86919,86927],{"className":86898,"style":2687},[294],[15,86900,86901,86904],{"style":2527},[15,86902],{"className":86903,"style":461},[302],[15,86905,86907],{"className":86906},[307,308,309,310],[15,86908,86910,86913,86916],{"className":86909},[59,310],[15,86911,117],{"className":86912},[59,310],[15,86914,4813],{"className":86915},[2591,310],[15,86917,15712],{"className":86918,"style":15761},[59,60,310],[15,86920,86921,86924],{"style":473},[15,86922],{"className":86923,"style":461},[302],[15,86925],{"className":86926,"style":481},[480],[15,86928,86929,86932],{"style":2550},[15,86930],{"className":86931,"style":461},[302],[15,86933,86935],{"className":86934},[307,308,309,310],[15,86936,86938,86941,86944],{"className":86937},[59,310],[15,86939,117],{"className":86940},[59,310],[15,86942,2470],{"className":86943},[2591,310],[15,86945,15712],{"className":86946,"style":15761},[59,60,310],[15,86948,318],{"className":86949},[317],[15,86951,86953],{"className":86952},[290],[15,86954,86956],{"className":86955,"style":16429},[294],[15,86957],{},[15,86959],{"className":86960},[153,441],[15,86962,86964,86982],{"className":86963,"translate":19},[18],[15,86965,86967],{"className":86966},[23],[25,86968,86969],{"xmlns":27},[29,86970,86971,86979],{},[32,86972,86973,86975,86977],{},[35,86974,15712],{},[110,86976,1029],{},[115,86978,117],{},[39,86980,86981],{"encoding":41},"\\delta\\to1",[15,86983,86985,87003],{"className":86984,"ariaHidden":46},[45],[15,86986,86988,86991,86994,86997,87000],{"className":86987},[50],[15,86989],{"className":86990,"style":12597},[54],[15,86992,15712],{"className":86993,"style":15761},[59,60],[15,86995],{"className":86996,"style":158},[157],[15,86998,1029],{"className":86999},[162],[15,87001],{"className":87002,"style":158},[157],[15,87004,87006,87009],{"className":87005},[50],[15,87007],{"className":87008,"style":172},[54],[15,87010,117],{"className":87011},[59]," 时发散（与 KL 在支撑分离时为 ",[15,87014,87016,87029],{"className":87015,"translate":19},[18],[15,87017,87019],{"className":87018},[23],[25,87020,87021],{"xmlns":27},[29,87022,87023,87027],{},[32,87024,87025],{},[35,87026,1024],{"mathvariant":209},[39,87028,3870],{"encoding":41},[15,87030,87032],{"className":87031,"ariaHidden":46},[45],[15,87033,87035,87038],{"className":87034},[50],[15,87036],{"className":87037,"style":2345},[54],[15,87039,1024],{"className":87040},[59]," 一致）。",[11,87043,87044,87047],{},[1225,87045,87046],{},"第 3 步（初等放缩）。"," 由",[15,87049,87051],{"className":87050,"translate":19},[180],[15,87052,87054,87140],{"className":87053,"translate":19},[18],[15,87055,87057],{"className":87056},[23],[25,87058,87059],{"xmlns":27,"display":189},[29,87060,87061,87137],{},[32,87062,87063,87065,87067,87085,87087,87089,87129,87131,87133,87135],{},[35,87064,4100],{},[110,87066,4103],{},[238,87068,87069,87077],{},[32,87070,87071,87073,87075],{},[115,87072,117],{},[110,87074,2470],{},[35,87076,15712],{},[32,87078,87079,87081,87083],{},[115,87080,117],{},[110,87082,4813],{},[35,87084,15712],{},[110,87086,123],{},[115,87088,2463],{},[32,87090,87091,87093,87095,87097,87107,87109,87120,87122,87125,87127],{},[110,87092,113],{"fence":46},[35,87094,15712],{},[110,87096,2470],{},[238,87098,87099,87105],{},[6814,87100,87101,87103],{},[35,87102,15712],{},[115,87104,40735],{},[115,87106,40735],{},[110,87108,2470],{},[238,87110,87111,87118],{},[6814,87112,87113,87115],{},[35,87114,15712],{},[115,87116,87117],{},"5",[115,87119,87117],{},[110,87121,2470],{},[110,87123,87124],{},"⋯",[1297,87126,1299],{},[110,87128,120],{"fence":46},[110,87130,6928],{},[115,87132,2463],{},[35,87134,15712],{},[110,87136,551],{"separator":46},[39,87138,87139],{"encoding":41},"\\log\\frac{1+\\delta}{1-\\delta}\n=2\\left(\\delta+\\frac{\\delta^3}3\n+\\frac{\\delta^5}5+\\cdots\\right)\n\\ge 2\\delta,",[15,87141,87143,87252,87501],{"className":87142,"ariaHidden":46},[45],[15,87144,87146,87149,87154,87157,87243,87246,87249],{"className":87145},[50],[15,87147],{"className":87148,"style":18051},[54],[15,87150,4154,87152],{"className":87151},[1484],[15,87153,4158],{"style":4157},[15,87155],{"className":87156,"style":406},[157],[15,87158,87160,87163,87240],{"className":87159},[59],[15,87161],{"className":87162},[146,441],[15,87164,87166],{"className":87165},[238],[15,87167,87169,87232],{"className":87168},[285,286],[15,87170,87172,87229],{"className":87171},[290],[15,87173,87175,87198,87206],{"className":87174,"style":454},[294],[15,87176,87177,87180],{"style":457},[15,87178],{"className":87179,"style":461},[302],[15,87181,87183,87186,87189,87192,87195],{"className":87182},[59],[15,87184,117],{"className":87185},[59],[15,87187],{"className":87188,"style":2587},[157],[15,87190,4813],{"className":87191},[2591],[15,87193],{"className":87194,"style":2587},[157],[15,87196,15712],{"className":87197,"style":15761},[59,60],[15,87199,87200,87203],{"style":473},[15,87201],{"className":87202,"style":461},[302],[15,87204],{"className":87205,"style":481},[480],[15,87207,87208,87211],{"style":484},[15,87209],{"className":87210,"style":461},[302],[15,87212,87214,87217,87220,87223,87226],{"className":87213},[59],[15,87215,117],{"className":87216},[59],[15,87218],{"className":87219,"style":2587},[157],[15,87221,2470],{"className":87222},[2591],[15,87224],{"className":87225,"style":2587},[157],[15,87227,15712],{"className":87228,"style":15761},[59,60],[15,87230,318],{"className":87231},[317],[15,87233,87235],{"className":87234},[290],[15,87236,87238],{"className":87237,"style":17015},[294],[15,87239],{},[15,87241],{"className":87242},[153,441],[15,87244],{"className":87245,"style":158},[157],[15,87247,123],{"className":87248},[162],[15,87250],{"className":87251,"style":158},[157],[15,87253,87255,87259,87262,87265,87492,87495,87498],{"className":87254},[50],[15,87256],{"className":87257,"style":87258},[54],"height:2.4411em;vertical-align:-0.95em;",[15,87260,2463],{"className":87261},[59],[15,87263],{"className":87264,"style":406},[157],[15,87266,87268,87274,87277,87280,87283,87286,87374,87377,87380,87383,87471,87474,87477,87480,87483,87486],{"className":87267},[410],[15,87269,87271],{"className":87270,"style":415},[146,414],[15,87272,113],{"className":87273},[419,309],[15,87275,15712],{"className":87276,"style":15761},[59,60],[15,87278],{"className":87279,"style":2587},[157],[15,87281,2470],{"className":87282},[2591],[15,87284],{"className":87285,"style":2587},[157],[15,87287,87289,87292,87371],{"className":87288},[59],[15,87290],{"className":87291},[146,441],[15,87293,87295],{"className":87294},[238],[15,87296,87298,87363],{"className":87297},[285,286],[15,87299,87301,87360],{"className":87300},[290],[15,87302,87304,87315,87323],{"className":87303,"style":37723},[294],[15,87305,87306,87309],{"style":457},[15,87307],{"className":87308,"style":461},[302],[15,87310,87312],{"className":87311},[59],[15,87313,40735],{"className":87314},[59],[15,87316,87317,87320],{"style":473},[15,87318],{"className":87319,"style":461},[302],[15,87321],{"className":87322,"style":481},[480],[15,87324,87325,87328],{"style":484},[15,87326],{"className":87327,"style":461},[302],[15,87329,87331],{"className":87330},[59],[15,87332,87334,87337],{"className":87333},[59],[15,87335,15712],{"className":87336,"style":15761},[59,60],[15,87338,87340],{"className":87339},[281],[15,87341,87343],{"className":87342},[285],[15,87344,87346],{"className":87345},[290],[15,87347,87349],{"className":87348,"style":20028},[294],[15,87350,87351,87354],{"style":6865},[15,87352],{"className":87353,"style":303},[302],[15,87355,87357],{"className":87356},[307,308,309,310],[15,87358,40735],{"className":87359},[59,310],[15,87361,318],{"className":87362},[317],[15,87364,87366],{"className":87365},[290],[15,87367,87369],{"className":87368,"style":3778},[294],[15,87370],{},[15,87372],{"className":87373},[153,441],[15,87375],{"className":87376,"style":2587},[157],[15,87378,2470],{"className":87379},[2591],[15,87381],{"className":87382,"style":2587},[157],[15,87384,87386,87389,87468],{"className":87385},[59],[15,87387],{"className":87388},[146,441],[15,87390,87392],{"className":87391},[238],[15,87393,87395,87460],{"className":87394},[285,286],[15,87396,87398,87457],{"className":87397},[290],[15,87399,87401,87412,87420],{"className":87400,"style":37723},[294],[15,87402,87403,87406],{"style":457},[15,87404],{"className":87405,"style":461},[302],[15,87407,87409],{"className":87408},[59],[15,87410,87117],{"className":87411},[59],[15,87413,87414,87417],{"style":473},[15,87415],{"className":87416,"style":461},[302],[15,87418],{"className":87419,"style":481},[480],[15,87421,87422,87425],{"style":484},[15,87423],{"className":87424,"style":461},[302],[15,87426,87428],{"className":87427},[59],[15,87429,87431,87434],{"className":87430},[59],[15,87432,15712],{"className":87433,"style":15761},[59,60],[15,87435,87437],{"className":87436},[281],[15,87438,87440],{"className":87439},[285],[15,87441,87443],{"className":87442},[290],[15,87444,87446],{"className":87445,"style":20028},[294],[15,87447,87448,87451],{"style":6865},[15,87449],{"className":87450,"style":303},[302],[15,87452,87454],{"className":87453},[307,308,309,310],[15,87455,87117],{"className":87456},[59,310],[15,87458,318],{"className":87459},[317],[15,87461,87463],{"className":87462},[290],[15,87464,87466],{"className":87465,"style":3778},[294],[15,87467],{},[15,87469],{"className":87470},[153,441],[15,87472],{"className":87473,"style":2587},[157],[15,87475,2470],{"className":87476},[2591],[15,87478],{"className":87479,"style":2587},[157],[15,87481,87124],{"className":87482},[410],[15,87484],{"className":87485,"style":406},[157],[15,87487,87489],{"className":87488,"style":415},[153,414],[15,87490,120],{"className":87491},[419,309],[15,87493],{"className":87494,"style":158},[157],[15,87496,6928],{"className":87497},[162],[15,87499],{"className":87500,"style":158},[157],[15,87502,87504,87507,87510,87513],{"className":87503},[50],[15,87505],{"className":87506,"style":55},[54],[15,87508,2463],{"className":87509},[59],[15,87511,15712],{"className":87512,"style":15761},[59,60],[15,87514,551],{"className":87515},[573],[15,87517,87519],{"className":87518,"translate":19},[180],[15,87520,87522,87701],{"className":87521,"translate":19},[18],[15,87523,87525],{"className":87524},[23],[25,87526,87527],{"xmlns":27,"display":189},[29,87528,87529,87698],{},[1243,87530,87531,87617],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,87532,87533,87539],{},[1252,87534,87535],{},[1255,87536,87537],{"scriptlevel":126,"displaystyle":46},[32,87538],{},[1252,87540,87541],{},[1255,87542,87543],{"scriptlevel":126,"displaystyle":46},[32,87544,87545,87547,87557,87559,87561,87563,87565,87567,87569,87571,87573,87575,87577,87583,87585,87587,87589,87591,87593,87595,87601,87603,87605,87607,87609,87615],{},[32,87546],{},[195,87548,87549,87551],{},[35,87550,199],{},[32,87552,87553,87555],{},[35,87554,10694],{},[35,87556,21893],{},[110,87558,113],{"stretchy":112},[35,87560,206],{},[35,87562,210],{"mathvariant":209},[35,87564,213],{},[110,87566,120],{"stretchy":112},[1297,87568,4283],{},[110,87570,6928],{},[1297,87572,4283],{},[35,87574,38665],{},[110,87576,113],{"stretchy":112},[32,87578,87579,87581],{},[35,87580,5392],{"mathvariant":209},[35,87582,34850],{"mathvariant":209},[110,87584,120],{"stretchy":112},[1297,87586,4283],{},[110,87588,6928],{},[1297,87590,4283],{},[115,87592,2463],{},[1297,87594,1299],{},[32,87596,87597,87599],{},[35,87598,5392],{"mathvariant":209},[35,87600,34850],{"mathvariant":209},[110,87602,113],{"stretchy":112},[35,87604,206],{},[110,87606,551],{"separator":46},[35,87608,213],{},[6814,87610,87611,87613],{},[110,87612,120],{"stretchy":112},[115,87614,2463],{},[110,87616,551],{"separator":46},[1249,87618,87619,87625],{},[1252,87620,87621],{},[1255,87622,87623],{"scriptlevel":126,"displaystyle":46},[32,87624],{},[1252,87626,87627],{},[1255,87628,87629],{"scriptlevel":126,"displaystyle":46},[32,87630,87631,87633,87636,87638,87644,87646,87648,87650,87652,87654,87656,87658,87660,87692,87694,87696],{},[32,87632],{},[1297,87634,87635],{},"即",[157,87637],{"width":4315},[32,87639,87640,87642],{},[35,87641,5392],{"mathvariant":209},[35,87643,34850],{"mathvariant":209},[110,87645,113],{"stretchy":112},[35,87647,206],{},[110,87649,551],{"separator":46},[35,87651,213],{},[110,87653,120],{"stretchy":112},[1297,87655,4283],{},[110,87657,9952],{},[1297,87659,4283],{},[34339,87661,87662],{},[32,87663,87664,87672,87682,87684,87686,87688,87690],{},[1255,87665,87666],{"scriptlevel":126,"displaystyle":112},[238,87667,87668,87670],{},[115,87669,117],{},[115,87671,2463],{},[195,87673,87674,87676],{},[35,87675,199],{},[32,87677,87678,87680],{},[35,87679,10694],{},[35,87681,21893],{},[110,87683,113],{"stretchy":112},[35,87685,206],{},[35,87687,210],{"mathvariant":209},[35,87689,213],{},[110,87691,120],{"stretchy":112},[35,87693,4375],{"mathvariant":209},[1297,87695,4283],{},[35,87697,59252],{"mathvariant":209},[39,87699,87700],{"encoding":41},"\\begin{aligned}\n&D_{KL}(P\\|Q)\\ \\ge\\ h(\\mathrm{TV})\n\\ \\ge\\ 2\\,\\mathrm{TV}(P,Q)^2 ,\\\\[2pt]\n&\\text{即}\\quad\n\\mathrm{TV}(P,Q)\\ \\le\\\n\\sqrt{\\tfrac12 D_{KL}(P\\|Q)} .\\ \\square\n\\end{aligned}",[15,87702,87704],{"className":87703,"ariaHidden":46},[45],[15,87705,87707,87711],{"className":87706},[50],[15,87708],{"className":87709,"style":87710},[54],"height:3.5641em;vertical-align:-1.5321em;",[15,87712,87714],{"className":87713},[59],[15,87715,87717,87760],{"className":87716},[1243],[15,87718,87720],{"className":87719},[1360],[15,87721,87723,87751],{"className":87722},[285,286],[15,87724,87726,87748],{"className":87725},[290],[15,87727,87730,87739],{"className":87728,"style":87729},[294],"height:2.0321em;",[15,87731,87733,87736],{"style":87732},"top:-4.4519em;",[15,87734],{"className":87735,"style":82419},[302],[15,87737],{"className":87738},[59],[15,87740,87742,87745],{"style":87741},"top:-2.3079em;",[15,87743],{"className":87744,"style":82419},[302],[15,87746],{"className":87747},[59],[15,87749,318],{"className":87750},[317],[15,87752,87754],{"className":87753},[290],[15,87755,87758],{"className":87756,"style":87757},[294],"height:1.5321em;",[15,87759],{},[15,87761,87763],{"className":87762},[1451],[15,87764,87766,88193],{"className":87765},[285,286],[15,87767,87769,88190],{"className":87768},[290],[15,87770,87772,87948],{"className":87771,"style":87729},[294],[15,87773,87774,87777],{"style":87732},[15,87775],{"className":87776,"style":82419},[302],[15,87778,87780,87783,87829,87832,87835,87838,87841,87844,87847,87850,87853,87856,87859,87862,87865,87871,87874,87877,87880,87883,87886,87889,87892,87895,87901,87904,87907,87910,87913,87916,87945],{"className":87779},[59],[15,87781],{"className":87782},[59],[15,87784,87786,87789],{"className":87785},[59],[15,87787,199],{"className":87788,"style":277},[59,60],[15,87790,87792],{"className":87791},[281],[15,87793,87795,87821],{"className":87794},[285,286],[15,87796,87798,87818],{"className":87797},[290],[15,87799,87801],{"className":87800,"style":379},[294],[15,87802,87803,87806],{"style":298},[15,87804],{"className":87805,"style":303},[302],[15,87807,87809],{"className":87808},[307,308,309,310],[15,87810,87812,87815],{"className":87811},[59,310],[15,87813,10694],{"className":87814,"style":10782},[59,60,310],[15,87816,21893],{"className":87817},[59,60,310],[15,87819,318],{"className":87820},[317],[15,87822,87824],{"className":87823},[290],[15,87825,87827],{"className":87826,"style":7968},[294],[15,87828],{},[15,87830,113],{"className":87831},[146],[15,87833,206],{"className":87834,"style":334},[59,60],[15,87836,210],{"className":87837},[59],[15,87839,213],{"className":87840},[59,60],[15,87842,120],{"className":87843},[153],[15,87845,4283],{"className":87846},[157],[15,87848],{"className":87849,"style":158},[157],[15,87851,6928],{"className":87852},[162],[15,87854,4283],{"className":87855},[157],[15,87857],{"className":87858,"style":158},[157],[15,87860,38665],{"className":87861},[59,60],[15,87863,113],{"className":87864},[146],[15,87866,87868],{"className":87867},[59],[15,87869,86762],{"className":87870,"style":4157},[59,32662],[15,87872,120],{"className":87873},[153],[15,87875,4283],{"className":87876},[157],[15,87878],{"className":87879,"style":158},[157],[15,87881,6928],{"className":87882},[162],[15,87884,4283],{"className":87885},[157],[15,87887],{"className":87888,"style":158},[157],[15,87890,2463],{"className":87891},[59],[15,87893],{"className":87894,"style":406},[157],[15,87896,87898],{"className":87897},[59],[15,87899,86762],{"className":87900,"style":4157},[59,32662],[15,87902,113],{"className":87903},[146],[15,87905,206],{"className":87906,"style":334},[59,60],[15,87908,551],{"className":87909},[573],[15,87911],{"className":87912,"style":406},[157],[15,87914,213],{"className":87915},[59,60],[15,87917,87919,87922],{"className":87918},[153],[15,87920,120],{"className":87921},[153],[15,87923,87925],{"className":87924},[281],[15,87926,87928],{"className":87927},[285],[15,87929,87931],{"className":87930},[290],[15,87932,87934],{"className":87933,"style":19735},[294],[15,87935,87936,87939],{"style":8277},[15,87937],{"className":87938,"style":303},[302],[15,87940,87942],{"className":87941},[307,308,309,310],[15,87943,2463],{"className":87944},[59,310],[15,87946,551],{"className":87947},[573],[15,87949,87950,87953],{"style":87741},[15,87951],{"className":87952,"style":82419},[302],[15,87954,87956,87959,87965,87969,87975,87978,87981,87984,87987,87990,87993,87996,87999,88002,88005,88008,88181,88184,88187],{"className":87955},[59],[15,87957],{"className":87958},[59],[15,87960,87962],{"className":87961},[59,4598],[15,87963,87635],{"className":87964},[59,4602],[15,87966],{"className":87967,"style":87968},[157],"margin-right:1em;",[15,87970,87972],{"className":87971},[59],[15,87973,86762],{"className":87974,"style":4157},[59,32662],[15,87976,113],{"className":87977},[146],[15,87979,206],{"className":87980,"style":334},[59,60],[15,87982,551],{"className":87983},[573],[15,87985],{"className":87986,"style":406},[157],[15,87988,213],{"className":87989},[59,60],[15,87991,120],{"className":87992},[153],[15,87994,4283],{"className":87995},[157],[15,87997],{"className":87998,"style":158},[157],[15,88000,9952],{"className":88001},[162],[15,88003,4283],{"className":88004},[157],[15,88006],{"className":88007,"style":158},[157],[15,88009,88011],{"className":88010},[59,34367],[15,88012,88014,88173],{"className":88013},[285,286],[15,88015,88017,88170],{"className":88016},[290],[15,88018,88020,88158],{"className":88019,"style":82579},[294],[15,88021,88023,88026],{"className":88022,"style":82583},[6307],[15,88024],{"className":88025,"style":82587},[302],[15,88027,88029,88097,88143,88146,88149,88152,88155],{"className":88028,"style":41161},[59],[15,88030,88032,88035,88094],{"className":88031},[59],[15,88033],{"className":88034},[146,441],[15,88036,88038],{"className":88037},[238],[15,88039,88041,88086],{"className":88040},[285,286],[15,88042,88044,88083],{"className":88043},[290],[15,88045,88047,88061,88069],{"className":88046,"style":2524},[294],[15,88048,88049,88052],{"style":2527},[15,88050],{"className":88051,"style":461},[302],[15,88053,88055],{"className":88054},[307,308,309,310],[15,88056,88058],{"className":88057},[59,310],[15,88059,2463],{"className":88060},[59,310],[15,88062,88063,88066],{"style":473},[15,88064],{"className":88065,"style":461},[302],[15,88067],{"className":88068,"style":481},[480],[15,88070,88071,88074],{"style":2550},[15,88072],{"className":88073,"style":461},[302],[15,88075,88077],{"className":88076},[307,308,309,310],[15,88078,88080],{"className":88079},[59,310],[15,88081,117],{"className":88082},[59,310],[15,88084,318],{"className":88085},[317],[15,88087,88089],{"className":88088},[290],[15,88090,88092],{"className":88091,"style":2572},[294],[15,88093],{},[15,88095],{"className":88096},[153,441],[15,88098,88100,88103],{"className":88099},[59],[15,88101,199],{"className":88102,"style":277},[59,60],[15,88104,88106],{"className":88105},[281],[15,88107,88109,88135],{"className":88108},[285,286],[15,88110,88112,88132],{"className":88111},[290],[15,88113,88115],{"className":88114,"style":379},[294],[15,88116,88117,88120],{"style":298},[15,88118],{"className":88119,"style":303},[302],[15,88121,88123],{"className":88122},[307,308,309,310],[15,88124,88126,88129],{"className":88125},[59,310],[15,88127,10694],{"className":88128,"style":10782},[59,60,310],[15,88130,21893],{"className":88131},[59,60,310],[15,88133,318],{"className":88134},[317],[15,88136,88138],{"className":88137},[290],[15,88139,88141],{"className":88140,"style":7968},[294],[15,88142],{},[15,88144,113],{"className":88145},[146],[15,88147,206],{"className":88148,"style":334},[59,60],[15,88150,210],{"className":88151},[59],[15,88153,213],{"className":88154},[59,60],[15,88156,120],{"className":88157},[153],[15,88159,88160,88163],{"style":82722},[15,88161],{"className":88162,"style":82587},[302],[15,88164,88166],{"className":88165,"style":82729},[34443],[6323,88167,88168],{"xmlns":6325,"width":6326,"height":82732,"viewBox":82733,"preserveAspectRatio":6329},[6331,88169],{"d":82736},[15,88171,318],{"className":88172},[317],[15,88174,88176],{"className":88175},[290],[15,88177,88179],{"className":88178,"style":82746},[294],[15,88180],{},[15,88182,4375],{"className":88183},[59],[15,88185,4283],{"className":88186},[157],[15,88188,59252],{"className":88189},[59,59794],[15,88191,318],{"className":88192},[317],[15,88194,88196],{"className":88195},[290],[15,88197,88199],{"className":88198,"style":87757},[294],[15,88200],{},[11,88202,88203,88206,88207,88307,88308,88416,88417,88446,88447,15795,88556,88607],{},[1225,88204,88205],{},"关于常数："," Pinsker 不等式中的 ",[15,88208,88210,88230],{"className":88209,"translate":19},[18],[15,88211,88213],{"className":88212},[23],[25,88214,88215],{"xmlns":27},[29,88216,88217,88227],{},[32,88218,88219],{},[1255,88220,88221],{"scriptlevel":126,"displaystyle":112},[238,88222,88223,88225],{},[115,88224,117],{},[115,88226,2463],{},[39,88228,88229],{"encoding":41},"\\tfrac12",[15,88231,88233],{"className":88232,"ariaHidden":46},[45],[15,88234,88236,88239],{"className":88235},[50],[15,88237],{"className":88238,"style":2505},[54],[15,88240,88242,88245,88304],{"className":88241},[59],[15,88243],{"className":88244},[146,441],[15,88246,88248],{"className":88247},[238],[15,88249,88251,88296],{"className":88250},[285,286],[15,88252,88254,88293],{"className":88253},[290],[15,88255,88257,88271,88279],{"className":88256,"style":2524},[294],[15,88258,88259,88262],{"style":2527},[15,88260],{"className":88261,"style":461},[302],[15,88263,88265],{"className":88264},[307,308,309,310],[15,88266,88268],{"className":88267},[59,310],[15,88269,2463],{"className":88270},[59,310],[15,88272,88273,88276],{"style":473},[15,88274],{"className":88275,"style":461},[302],[15,88277],{"className":88278,"style":481},[480],[15,88280,88281,88284],{"style":2550},[15,88282],{"className":88283,"style":461},[302],[15,88285,88287],{"className":88286},[307,308,309,310],[15,88288,88290],{"className":88289},[59,310],[15,88291,117],{"className":88292},[59,310],[15,88294,318],{"className":88295},[317],[15,88297,88299],{"className":88298},[290],[15,88300,88302],{"className":88301,"style":2572},[294],[15,88303],{},[15,88305],{"className":88306},[153,441],"（即 ",[15,88309,88311,88345],{"className":88310,"translate":19},[18],[15,88312,88314],{"className":88313},[23],[25,88315,88316],{"xmlns":27},[29,88317,88318,88342],{},[32,88319,88320,88326,88328,88330,88332],{},[32,88321,88322,88324],{},[35,88323,10694],{"mathvariant":209},[35,88325,21893],{"mathvariant":209},[110,88327,6928],{},[115,88329,2463],{},[1297,88331,1299],{},[6814,88333,88334,88340],{},[32,88335,88336,88338],{},[35,88337,5392],{"mathvariant":209},[35,88339,34850],{"mathvariant":209},[115,88341,2463],{},[39,88343,88344],{"encoding":41},"\\mathrm{KL}\\ge2\\,\\mathrm{TV}^2",[15,88346,88348,88370],{"className":88347,"ariaHidden":46},[45],[15,88349,88351,88355,88361,88364,88367],{"className":88350},[50],[15,88352],{"className":88353,"style":88354},[54],"height:0.8193em;vertical-align:-0.136em;",[15,88356,88358],{"className":88357},[59],[15,88359,32663],{"className":88360},[59,32662],[15,88362],{"className":88363,"style":158},[157],[15,88365,6928],{"className":88366},[162],[15,88368],{"className":88369,"style":158},[157],[15,88371,88373,88377,88380,88383],{"className":88372},[50],[15,88374],{"className":88375,"style":88376},[54],"height:0.8873em;",[15,88378,2463],{"className":88379},[59],[15,88381],{"className":88382,"style":406},[157],[15,88384,88386,88392],{"className":88385},[59],[15,88387,88389],{"className":88388},[59],[15,88390,86762],{"className":88391,"style":4157},[59,32662],[15,88393,88395],{"className":88394},[281],[15,88396,88398],{"className":88397},[285],[15,88399,88401],{"className":88400},[290],[15,88402,88404],{"className":88403,"style":88376},[294],[15,88405,88407,88410],{"style":88406},"top:-3.1362em;margin-right:0.05em;",[15,88408],{"className":88409,"style":303},[302],[15,88411,88413],{"className":88412},[307,308,309,310],[15,88414,2463],{"className":88415},[59,310]," 的系数 2）是最优的：取两分布仅在极小 ",[15,88418,88420,88434],{"className":88419,"translate":19},[18],[15,88421,88423],{"className":88422},[23],[25,88424,88425],{"xmlns":27},[29,88426,88427,88431],{},[32,88428,88429],{},[35,88430,38662],{},[39,88432,88433],{"encoding":41},"\\varepsilon",[15,88435,88437],{"className":88436,"ariaHidden":46},[45],[15,88438,88440,88443],{"className":88439},[50],[15,88441],{"className":88442,"style":2345},[54],[15,88444,38662],{"className":88445},[59,60]," 上偏离最优对称配置，可让 ",[15,88448,88450,88482],{"className":88449,"translate":19},[18],[15,88451,88453],{"className":88452},[23],[25,88454,88455],{"xmlns":27},[29,88456,88457,88479],{},[32,88458,88459,88461,88463,88465,88467,88469,88475,88477],{},[35,88460,38665],{},[110,88462,113],{"stretchy":112},[35,88464,15712],{},[110,88466,120],{"stretchy":112},[110,88468,941],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[6814,88470,88471,88473],{},[35,88472,15712],{},[115,88474,2463],{},[110,88476,1029],{},[115,88478,2463],{},[39,88480,88481],{"encoding":41},"h(\\delta)\\big\u002F\\delta^2\\to 2",[15,88483,88485,88547],{"className":88484,"ariaHidden":46},[45],[15,88486,88488,88491,88494,88497,88500,88503,88509,88538,88541,88544],{"className":88487},[50],[15,88489],{"className":88490,"style":20563},[54],[15,88492,38665],{"className":88493},[59,60],[15,88495,113],{"className":88496},[146],[15,88498,15712],{"className":88499,"style":15761},[59,60],[15,88501,120],{"className":88502},[153],[15,88504,88506],{"className":88505},[59],[15,88507,941],{"className":88508},[419,9674],[15,88510,88512,88515],{"className":88511},[59],[15,88513,15712],{"className":88514,"style":15761},[59,60],[15,88516,88518],{"className":88517},[281],[15,88519,88521],{"className":88520},[285],[15,88522,88524],{"className":88523},[290],[15,88525,88527],{"className":88526,"style":20028},[294],[15,88528,88529,88532],{"style":6865},[15,88530],{"className":88531,"style":303},[302],[15,88533,88535],{"className":88534},[307,308,309,310],[15,88536,2463],{"className":88537},[59,310],[15,88539],{"className":88540,"style":158},[157],[15,88542,1029],{"className":88543},[162],[15,88545],{"className":88546,"style":158},[157],[15,88548,88550,88553],{"className":88549},[50],[15,88551],{"className":88552,"style":172},[54],[15,88554,2463],{"className":88555},[59],[15,88557,88559,88577],{"className":88558,"translate":19},[18],[15,88560,88562],{"className":88561},[23],[25,88563,88564],{"xmlns":27},[29,88565,88566,88574],{},[32,88567,88568,88570,88572],{},[35,88569,15712],{},[110,88571,1029],{},[115,88573,126],{},[39,88575,88576],{"encoding":41},"\\delta\\to0",[15,88578,88580,88598],{"className":88579,"ariaHidden":46},[45],[15,88581,88583,88586,88589,88592,88595],{"className":88582},[50],[15,88584],{"className":88585,"style":12597},[54],[15,88587,15712],{"className":88588,"style":15761},[59,60],[15,88590],{"className":88591,"style":158},[157],[15,88593,1029],{"className":88594},[162],[15,88596],{"className":88597,"style":158},[157],[15,88599,88601,88604],{"className":88600},[50],[15,88602],{"className":88603,"style":172},[54],[15,88605,126],{"className":88606},[59],"），故常数不能改进。",[11,88609,88610,88611,88680],{},"顺便指出：对一般 f-散度也有平行的\"固定 TV 时最小化 ",[15,88612,88614,88631],{"className":88613,"translate":19},[18],[15,88615,88617],{"className":88616},[23],[25,88618,88619],{"xmlns":27},[29,88620,88621,88629],{},[32,88622,88623],{},[195,88624,88625,88627],{},[35,88626,199],{},[35,88628,37],{},[39,88630,4022],{"encoding":41},[15,88632,88634],{"className":88633,"ariaHidden":46},[45],[15,88635,88637,88640],{"className":88636},[50],[15,88638],{"className":88639,"style":4032},[54],[15,88641,88643,88646],{"className":88642},[59],[15,88644,199],{"className":88645,"style":277},[59,60],[15,88647,88649],{"className":88648},[281],[15,88650,88652,88672],{"className":88651},[285,286],[15,88653,88655,88669],{"className":88654},[290],[15,88656,88658],{"className":88657,"style":295},[294],[15,88659,88660,88663],{"style":298},[15,88661],{"className":88662,"style":303},[302],[15,88664,88666],{"className":88665},[307,308,309,310],[15,88667,37],{"className":88668,"style":61},[59,60,310],[15,88670,318],{"className":88671},[317],[15,88673,88675],{"className":88674},[290],[15,88676,88678],{"className":88677,"style":325},[294],[15,88679],{},"\"函数（Fedotov–Harremoës 2003 给出完整刻画），即每个 f-散度都自带一个 TV 的下界函数；这是 4.7 末拓扑结论的定量基础。",[11,88682,88683,88686,88687,88715,88716,88719],{},[1225,88684,88685],{},"Bretagnolle–Huber 的推导。"," 由 Rényi 散度在阶数 ",[15,88688,88690,88703],{"className":88689,"translate":19},[18],[15,88691,88693],{"className":88692},[23],[25,88694,88695],{"xmlns":27},[29,88696,88697,88701],{},[32,88698,88699],{},[35,88700,44754],{},[39,88702,49090],{"encoding":41},[15,88704,88706],{"className":88705,"ariaHidden":46},[45],[15,88707,88709,88712],{"className":88708},[50],[15,88710],{"className":88711,"style":2345},[54],[15,88713,44754],{"className":88714,"style":44784},[59,60]," 上",[1225,88717,88718],{},"单调不减","（Hölder 不等式的直接推论），",[15,88721,88723],{"className":88722,"translate":19},[180],[15,88724,88726,88824],{"className":88725,"translate":19},[18],[15,88727,88729],{"className":88728},[23],[25,88730,88731],{"xmlns":27,"display":189},[29,88732,88733,88821],{},[32,88734,88735,88745,88747,88749,88751,88753,88755,88757,88765,88767,88769,88771,88773,88775,88777,88779,88781,88795,88797,88799,88801,88803,88805,88807,88809,88811,88813,88815,88817,88819],{},[195,88736,88737,88739],{},[35,88738,199],{},[32,88740,88741,88743],{},[35,88742,10694],{},[35,88744,21893],{},[110,88746,113],{"stretchy":112},[35,88748,206],{},[35,88750,210],{"mathvariant":209},[35,88752,213],{},[110,88754,120],{"stretchy":112},[110,88756,123],{},[7553,88758,88759,88761,88763],{},[35,88760,199],{},[115,88762,117],{},[35,88764,1032],{},[110,88766,113],{"stretchy":112},[35,88768,206],{},[35,88770,210],{"mathvariant":209},[35,88772,213],{},[110,88774,120],{"stretchy":112},[1297,88776,4283],{},[110,88778,6928],{},[1297,88780,4283],{},[7553,88782,88783,88785,88793],{},[35,88784,199],{},[32,88786,88787,88789,88791],{},[115,88788,117],{},[35,88790,941],{"mathvariant":209},[115,88792,2463],{},[35,88794,1032],{},[110,88796,113],{"stretchy":112},[35,88798,206],{},[35,88800,210],{"mathvariant":209},[35,88802,213],{},[110,88804,120],{"stretchy":112},[110,88806,123],{},[110,88808,4813],{},[115,88810,2463],{},[35,88812,4100],{},[110,88814,4103],{},[35,88816,39291],{},[35,88818,39294],{},[35,88820,4375],{"mathvariant":209},[39,88822,88823],{"encoding":41},"D_{KL}(P\\|Q)=D^{R}_{1}(P\\|Q)\n\\ \\ge\\ D^{R}_{1\u002F2}(P\\|Q)=-2\\log BC .",[15,88825,88827,88903,88996,89086],{"className":88826,"ariaHidden":46},[45],[15,88828,88830,88833,88879,88882,88885,88888,88891,88894,88897,88900],{"className":88829},[50],[15,88831],{"className":88832,"style":139},[54],[15,88834,88836,88839],{"className":88835},[59],[15,88837,199],{"className":88838,"style":277},[59,60],[15,88840,88842],{"className":88841},[281],[15,88843,88845,88871],{"className":88844},[285,286],[15,88846,88848,88868],{"className":88847},[290],[15,88849,88851],{"className":88850,"style":379},[294],[15,88852,88853,88856],{"style":298},[15,88854],{"className":88855,"style":303},[302],[15,88857,88859],{"className":88858},[307,308,309,310],[15,88860,88862,88865],{"className":88861},[59,310],[15,88863,10694],{"className":88864,"style":10782},[59,60,310],[15,88866,21893],{"className":88867},[59,60,310],[15,88869,318],{"className":88870},[317],[15,88872,88874],{"className":88873},[290],[15,88875,88877],{"className":88876,"style":7968},[294],[15,88878],{},[15,88880,113],{"className":88881},[146],[15,88883,206],{"className":88884,"style":334},[59,60],[15,88886,210],{"className":88887},[59],[15,88889,213],{"className":88890},[59,60],[15,88892,120],{"className":88893},[153],[15,88895],{"className":88896,"style":158},[157],[15,88898,123],{"className":88899},[162],[15,88901],{"className":88902,"style":158},[157],[15,88904,88906,88909,88966,88969,88972,88975,88978,88981,88984,88987,88990,88993],{"className":88905},[50],[15,88907],{"className":88908,"style":50873},[54],[15,88910,88912,88915],{"className":88911},[59],[15,88913,199],{"className":88914,"style":277},[59,60],[15,88916,88918],{"className":88917},[281],[15,88919,88921,88958],{"className":88920},[285,286],[15,88922,88924,88955],{"className":88923},[290],[15,88925,88927,88941],{"className":88926,"style":38512},[294],[15,88928,88929,88932],{"style":49572},[15,88930],{"className":88931,"style":303},[302],[15,88933,88935],{"className":88934},[307,308,309,310],[15,88936,88938],{"className":88937},[59,310],[15,88939,117],{"className":88940},[59,310],[15,88942,88943,88946],{"style":8277},[15,88944],{"className":88945,"style":303},[302],[15,88947,88949],{"className":88948},[307,308,309,310],[15,88950,88952],{"className":88951},[59,310],[15,88953,1032],{"className":88954,"style":49599},[59,60,310],[15,88956,318],{"className":88957},[317],[15,88959,88961],{"className":88960},[290],[15,88962,88964],{"className":88963,"style":8299},[294],[15,88965],{},[15,88967,113],{"className":88968},[146],[15,88970,206],{"className":88971,"style":334},[59,60],[15,88973,210],{"className":88974},[59],[15,88976,213],{"className":88977},[59,60],[15,88979,120],{"className":88980},[153],[15,88982,4283],{"className":88983},[157],[15,88985],{"className":88986,"style":158},[157],[15,88988,6928],{"className":88989},[162],[15,88991,4283],{"className":88992},[157],[15,88994],{"className":88995,"style":158},[157],[15,88997,88999,89003,89062,89065,89068,89071,89074,89077,89080,89083],{"className":88998},[50],[15,89000],{"className":89001,"style":89002},[54],"height:1.3383em;vertical-align:-0.447em;",[15,89004,89006,89009],{"className":89005},[59],[15,89007,199],{"className":89008,"style":277},[59,60],[15,89010,89012],{"className":89011},[281],[15,89013,89015,89053],{"className":89014},[285,286],[15,89016,89018,89050],{"className":89017},[290],[15,89019,89021,89036],{"className":89020,"style":38512},[294],[15,89022,89024,89027],{"style":89023},"top:-2.428em;margin-left:-0.0278em;margin-right:0.05em;",[15,89025],{"className":89026,"style":303},[302],[15,89028,89030],{"className":89029},[307,308,309,310],[15,89031,89033],{"className":89032},[59,310],[15,89034,33639],{"className":89035},[59,310],[15,89037,89038,89041],{"style":8277},[15,89039],{"className":89040,"style":303},[302],[15,89042,89044],{"className":89043},[307,308,309,310],[15,89045,89047],{"className":89046},[59,310],[15,89048,1032],{"className":89049,"style":49599},[59,60,310],[15,89051,318],{"className":89052},[317],[15,89054,89056],{"className":89055},[290],[15,89057,89060],{"className":89058,"style":89059},[294],"height:0.447em;",[15,89061],{},[15,89063,113],{"className":89064},[146],[15,89066,206],{"className":89067,"style":334},[59,60],[15,89069,210],{"className":89070},[59],[15,89072,213],{"className":89073},[59,60],[15,89075,120],{"className":89076},[153],[15,89078],{"className":89079,"style":158},[157],[15,89081,123],{"className":89082},[162],[15,89084],{"className":89085,"style":158},[157],[15,89087,89089,89092,89095,89098,89101,89106,89109,89112,89115],{"className":89088},[50],[15,89090],{"className":89091,"style":55},[54],[15,89093,4813],{"className":89094},[59],[15,89096,2463],{"className":89097},[59],[15,89099],{"className":89100,"style":406},[157],[15,89102,4154,89104],{"className":89103},[1484],[15,89105,4158],{"style":4157},[15,89107],{"className":89108,"style":406},[157],[15,89110,39291],{"className":89111,"style":39387},[59,60],[15,89113,39294],{"className":89114,"style":10782},[59,60],[15,89116,4375],{"className":89117},[59],[11,89119,89120,89121,15795,89214,89265,89266,89446],{},"又由 ",[15,89122,89124,89152],{"className":89123,"translate":19},[18],[15,89125,89127],{"className":89126},[23],[25,89128,89129],{"xmlns":27},[29,89130,89131,89149],{},[32,89132,89133,89135,89137,89139,89141,89143,89145,89147],{},[110,89134,4813],{},[35,89136,4100],{},[110,89138,4103],{},[35,89140,774],{},[110,89142,6928],{},[115,89144,117],{},[110,89146,4813],{},[35,89148,774],{},[39,89150,89151],{"encoding":41},"-\\log x\\ge 1-x",[15,89153,89155,89187,89205],{"className":89154,"ariaHidden":46},[45],[15,89156,89158,89161,89164,89167,89172,89175,89178,89181,89184],{"className":89157},[50],[15,89159],{"className":89160,"style":55},[54],[15,89162,4813],{"className":89163},[59],[15,89165],{"className":89166,"style":406},[157],[15,89168,4154,89170],{"className":89169},[1484],[15,89171,4158],{"style":4157},[15,89173],{"className":89174,"style":406},[157],[15,89176,774],{"className":89177},[59,60],[15,89179],{"className":89180,"style":158},[157],[15,89182,6928],{"className":89183},[162],[15,89185],{"className":89186,"style":158},[157],[15,89188,89190,89193,89196,89199,89202],{"className":89189},[50],[15,89191],{"className":89192,"style":12578},[54],[15,89194,117],{"className":89195},[59],[15,89197],{"className":89198,"style":2587},[157],[15,89200,4813],{"className":89201},[2591],[15,89203],{"className":89204,"style":2587},[157],[15,89206,89208,89211],{"className":89207},[50],[15,89209],{"className":89210,"style":2345},[54],[15,89212,774],{"className":89213},[59,60],[15,89215,89217,89235],{"className":89216,"translate":19},[18],[15,89218,89220],{"className":89219},[23],[25,89221,89222],{"xmlns":27},[29,89223,89224,89232],{},[32,89225,89226,89228,89230],{},[35,89227,774],{},[110,89229,2903],{},[115,89231,126],{},[39,89233,89234],{"encoding":41},"x>0",[15,89236,89238,89256],{"className":89237,"ariaHidden":46},[45],[15,89239,89241,89244,89247,89250,89253],{"className":89240},[50],[15,89242],{"className":89243,"style":5924},[54],[15,89245,774],{"className":89246},[59,60],[15,89248],{"className":89249,"style":158},[157],[15,89251,2903],{"className":89252},[162],[15,89254],{"className":89255,"style":158},[157],[15,89257,89259,89262],{"className":89258},[50],[15,89260],{"className":89261,"style":172},[54],[15,89263,126],{"className":89264},[59],"），",[15,89267,89269,89319],{"className":89268,"translate":19},[18],[15,89270,89272],{"className":89271},[23],[25,89273,89274],{"xmlns":27},[29,89275,89276,89316],{},[32,89277,89278,89280,89282,89284,89286,89288,89290,89292,89294,89296,89298,89300,89302,89304,89306,89308,89310],{},[110,89279,4813],{},[115,89281,2463],{},[35,89283,4100],{},[110,89285,4103],{},[35,89287,39291],{},[35,89289,39294],{},[110,89291,6928],{},[115,89293,2463],{},[110,89295,113],{"stretchy":112},[115,89297,117],{},[110,89299,4813],{},[35,89301,39291],{},[35,89303,39294],{},[110,89305,120],{"stretchy":112},[110,89307,123],{},[115,89309,2463],{},[6814,89311,89312,89314],{},[35,89313,33884],{},[115,89315,2463],{},[39,89317,89318],{"encoding":41}," -2\\log BC\\ge 2(1-BC)=2H^2",[15,89320,89322,89360,89384,89408],{"className":89321,"ariaHidden":46},[45],[15,89323,89325,89328,89331,89334,89337,89342,89345,89348,89351,89354,89357],{"className":89324},[50],[15,89326],{"className":89327,"style":55},[54],[15,89329,4813],{"className":89330},[59],[15,89332,2463],{"className":89333},[59],[15,89335],{"className":89336,"style":406},[157],[15,89338,4154,89340],{"className":89339},[1484],[15,89341,4158],{"style":4157},[15,89343],{"className":89344,"style":406},[157],[15,89346,39291],{"className":89347,"style":39387},[59,60],[15,89349,39294],{"className":89350,"style":10782},[59,60],[15,89352],{"className":89353,"style":158},[157],[15,89355,6928],{"className":89356},[162],[15,89358],{"className":89359,"style":158},[157],[15,89361,89363,89366,89369,89372,89375,89378,89381],{"className":89362},[50],[15,89364],{"className":89365,"style":139},[54],[15,89367,2463],{"className":89368},[59],[15,89370,113],{"className":89371},[146],[15,89373,117],{"className":89374},[59],[15,89376],{"className":89377,"style":2587},[157],[15,89379,4813],{"className":89380},[2591],[15,89382],{"className":89383,"style":2587},[157],[15,89385,89387,89390,89393,89396,89399,89402,89405],{"className":89386},[50],[15,89388],{"className":89389,"style":139},[54],[15,89391,39291],{"className":89392,"style":39387},[59,60],[15,89394,39294],{"className":89395,"style":10782},[59,60],[15,89397,120],{"className":89398},[153],[15,89400],{"className":89401,"style":158},[157],[15,89403,123],{"className":89404},[162],[15,89406],{"className":89407,"style":158},[157],[15,89409,89411,89414,89417],{"className":89410},[50],[15,89412],{"className":89413,"style":20028},[54],[15,89415,2463],{"className":89416},[59],[15,89418,89420,89423],{"className":89419},[59],[15,89421,33884],{"className":89422,"style":34038},[59,60],[15,89424,89426],{"className":89425},[281],[15,89427,89429],{"className":89428},[285],[15,89430,89432],{"className":89431},[290],[15,89433,89435],{"className":89434,"style":20028},[294],[15,89436,89437,89440],{"style":6865},[15,89438],{"className":89439,"style":303},[302],[15,89441,89443],{"className":89442},[307,308,309,310],[15,89444,2463],{"className":89445},[59,310],"。合并即得",[15,89448,89450],{"className":89449,"translate":19},[180],[15,89451,89453,89507],{"className":89452,"translate":19},[18],[15,89454,89456],{"className":89455},[23],[25,89457,89458],{"xmlns":27,"display":189},[29,89459,89460,89504],{},[32,89461,89462,89468,89470,89478,89488,89490,89492,89494,89496,89498,89500,89502],{},[6814,89463,89464,89466],{},[35,89465,33884],{},[115,89467,2463],{},[110,89469,9952],{},[1255,89471,89472],{"scriptlevel":126,"displaystyle":112},[238,89473,89474,89476],{},[115,89475,117],{},[115,89477,2463],{},[195,89479,89480,89482],{},[35,89481,199],{},[32,89483,89484,89486],{},[35,89485,10694],{},[35,89487,21893],{},[110,89489,113],{"stretchy":112},[35,89491,206],{},[35,89493,210],{"mathvariant":209},[35,89495,213],{},[110,89497,120],{"stretchy":112},[35,89499,4375],{"mathvariant":209},[157,89501],{"width":3262},[35,89503,59252],{"mathvariant":209},[39,89505,89506],{"encoding":41},"H^2\\le \\tfrac12 D_{KL}(P\\|Q). \\qquad\\square",[15,89508,89510,89555],{"className":89509,"ariaHidden":46},[45],[15,89511,89513,89517,89546,89549,89552],{"className":89512},[50],[15,89514],{"className":89515,"style":89516},[54],"height:1.0001em;vertical-align:-0.136em;",[15,89518,89520,89523],{"className":89519},[59],[15,89521,33884],{"className":89522,"style":34038},[59,60],[15,89524,89526],{"className":89525},[281],[15,89527,89529],{"className":89528},[285],[15,89530,89532],{"className":89531},[290],[15,89533,89535],{"className":89534,"style":19735},[294],[15,89536,89537,89540],{"style":8277},[15,89538],{"className":89539,"style":303},[302],[15,89541,89543],{"className":89542},[307,308,309,310],[15,89544,2463],{"className":89545},[59,310],[15,89547],{"className":89548,"style":158},[157],[15,89550,9952],{"className":89551},[162],[15,89553],{"className":89554,"style":158},[157],[15,89556,89558,89561,89629,89675,89678,89681,89684,89687,89690,89693,89696],{"className":89557},[50],[15,89559],{"className":89560,"style":2505},[54],[15,89562,89564,89567,89626],{"className":89563},[59],[15,89565],{"className":89566},[146,441],[15,89568,89570],{"className":89569},[238],[15,89571,89573,89618],{"className":89572},[285,286],[15,89574,89576,89615],{"className":89575},[290],[15,89577,89579,89593,89601],{"className":89578,"style":2524},[294],[15,89580,89581,89584],{"style":2527},[15,89582],{"className":89583,"style":461},[302],[15,89585,89587],{"className":89586},[307,308,309,310],[15,89588,89590],{"className":89589},[59,310],[15,89591,2463],{"className":89592},[59,310],[15,89594,89595,89598],{"style":473},[15,89596],{"className":89597,"style":461},[302],[15,89599],{"className":89600,"style":481},[480],[15,89602,89603,89606],{"style":2550},[15,89604],{"className":89605,"style":461},[302],[15,89607,89609],{"className":89608},[307,308,309,310],[15,89610,89612],{"className":89611},[59,310],[15,89613,117],{"className":89614},[59,310],[15,89616,318],{"className":89617},[317],[15,89619,89621],{"className":89620},[290],[15,89622,89624],{"className":89623,"style":2572},[294],[15,89625],{},[15,89627],{"className":89628},[153,441],[15,89630,89632,89635],{"className":89631},[59],[15,89633,199],{"className":89634,"style":277},[59,60],[15,89636,89638],{"className":89637},[281],[15,89639,89641,89667],{"className":89640},[285,286],[15,89642,89644,89664],{"className":89643},[290],[15,89645,89647],{"className":89646,"style":379},[294],[15,89648,89649,89652],{"style":298},[15,89650],{"className":89651,"style":303},[302],[15,89653,89655],{"className":89654},[307,308,309,310],[15,89656,89658,89661],{"className":89657},[59,310],[15,89659,10694],{"className":89660,"style":10782},[59,60,310],[15,89662,21893],{"className":89663},[59,60,310],[15,89665,318],{"className":89666},[317],[15,89668,89670],{"className":89669},[290],[15,89671,89673],{"className":89672,"style":7968},[294],[15,89674],{},[15,89676,113],{"className":89677},[146],[15,89679,206],{"className":89680,"style":334},[59,60],[15,89682,210],{"className":89683},[59],[15,89685,213],{"className":89686},[59,60],[15,89688,120],{"className":89689},[153],[15,89691,4375],{"className":89692},[59],[15,89694],{"className":89695,"style":3634},[157],[15,89697,59252],{"className":89698},[59,59794],[11,89700,89701,89702,5645,89907,26279,90091,90444],{},"顺便验证与 4.6 节一致：小偏差时 ",[15,89703,89705,89740],{"className":89704,"translate":19},[18],[15,89706,89708],{"className":89707},[23],[25,89709,89710],{"xmlns":27},[29,89711,89712,89738],{},[32,89713,89714,89724,89726,89732],{},[195,89715,89716,89718],{},[35,89717,199],{},[32,89719,89720,89722],{},[35,89721,10694],{},[35,89723,21893],{},[110,89725,32959],{},[238,89727,89728,89730],{},[115,89729,117],{},[115,89731,2463],{},[6814,89733,89734,89736],{},[35,89735,37449],{},[115,89737,2463],{},[39,89739,80675],{"encoding":41},[15,89741,89743,89804],{"className":89742,"ariaHidden":46},[45],[15,89744,89746,89749,89795,89798,89801],{"className":89745},[50],[15,89747],{"className":89748,"style":15961},[54],[15,89750,89752,89755],{"className":89751},[59],[15,89753,199],{"className":89754,"style":277},[59,60],[15,89756,89758],{"className":89757},[281],[15,89759,89761,89787],{"className":89760},[285,286],[15,89762,89764,89784],{"className":89763},[290],[15,89765,89767],{"className":89766,"style":379},[294],[15,89768,89769,89772],{"style":298},[15,89770],{"className":89771,"style":303},[302],[15,89773,89775],{"className":89774},[307,308,309,310],[15,89776,89778,89781],{"className":89777},[59,310],[15,89779,10694],{"className":89780,"style":10782},[59,60,310],[15,89782,21893],{"className":89783},[59,60,310],[15,89785,318],{"className":89786},[317],[15,89788,89790],{"className":89789},[290],[15,89791,89793],{"className":89792,"style":7968},[294],[15,89794],{},[15,89796],{"className":89797,"style":158},[157],[15,89799,32959],{"className":89800},[162],[15,89802],{"className":89803,"style":158},[157],[15,89805,89807,89810,89878],{"className":89806},[50],[15,89808],{"className":89809,"style":2505},[54],[15,89811,89813,89816,89875],{"className":89812},[59],[15,89814],{"className":89815},[146,441],[15,89817,89819],{"className":89818},[238],[15,89820,89822,89867],{"className":89821},[285,286],[15,89823,89825,89864],{"className":89824},[290],[15,89826,89828,89842,89850],{"className":89827,"style":2524},[294],[15,89829,89830,89833],{"style":2527},[15,89831],{"className":89832,"style":461},[302],[15,89834,89836],{"className":89835},[307,308,309,310],[15,89837,89839],{"className":89838},[59,310],[15,89840,2463],{"className":89841},[59,310],[15,89843,89844,89847],{"style":473},[15,89845],{"className":89846,"style":461},[302],[15,89848],{"className":89849,"style":481},[480],[15,89851,89852,89855],{"style":2550},[15,89853],{"className":89854,"style":461},[302],[15,89856,89858],{"className":89857},[307,308,309,310],[15,89859,89861],{"className":89860},[59,310],[15,89862,117],{"className":89863},[59,310],[15,89865,318],{"className":89866},[317],[15,89868,89870],{"className":89869},[290],[15,89871,89873],{"className":89872,"style":2572},[294],[15,89874],{},[15,89876],{"className":89877},[153,441],[15,89879,89881,89884],{"className":89880},[59],[15,89882,37449],{"className":89883},[59,60],[15,89885,89887],{"className":89886},[281],[15,89888,89890],{"className":89889},[285],[15,89891,89893],{"className":89892},[290],[15,89894,89896],{"className":89895,"style":20028},[294],[15,89897,89898,89901],{"style":6865},[15,89899],{"className":89900,"style":303},[302],[15,89902,89904],{"className":89903},[307,308,309,310],[15,89905,2463],{"className":89906},[59,310],[15,89908,89910,89941],{"className":89909,"translate":19},[18],[15,89911,89913],{"className":89912},[23],[25,89914,89915],{"xmlns":27},[29,89916,89917,89939],{},[32,89918,89919,89925,89927,89933],{},[6814,89920,89921,89923],{},[35,89922,33884],{},[115,89924,2463],{},[110,89926,32959],{},[238,89928,89929,89931],{},[115,89930,117],{},[115,89932,39303],{},[6814,89934,89935,89937],{},[35,89936,37449],{},[115,89938,2463],{},[39,89940,81585],{"encoding":41},[15,89942,89944,89988],{"className":89943,"ariaHidden":46},[45],[15,89945,89947,89950,89979,89982,89985],{"className":89946},[50],[15,89948],{"className":89949,"style":20028},[54],[15,89951,89953,89956],{"className":89952},[59],[15,89954,33884],{"className":89955,"style":34038},[59,60],[15,89957,89959],{"className":89958},[281],[15,89960,89962],{"className":89961},[285],[15,89963,89965],{"className":89964},[290],[15,89966,89968],{"className":89967,"style":20028},[294],[15,89969,89970,89973],{"style":6865},[15,89971],{"className":89972,"style":303},[302],[15,89974,89976],{"className":89975},[307,308,309,310],[15,89977,2463],{"className":89978},[59,310],[15,89980],{"className":89981,"style":158},[157],[15,89983,32959],{"className":89984},[162],[15,89986],{"className":89987,"style":158},[157],[15,89989,89991,89994,90062],{"className":89990},[50],[15,89992],{"className":89993,"style":2505},[54],[15,89995,89997,90000,90059],{"className":89996},[59],[15,89998],{"className":89999},[146,441],[15,90001,90003],{"className":90002},[238],[15,90004,90006,90051],{"className":90005},[285,286],[15,90007,90009,90048],{"className":90008},[290],[15,90010,90012,90026,90034],{"className":90011,"style":2524},[294],[15,90013,90014,90017],{"style":2527},[15,90015],{"className":90016,"style":461},[302],[15,90018,90020],{"className":90019},[307,308,309,310],[15,90021,90023],{"className":90022},[59,310],[15,90024,39303],{"className":90025},[59,310],[15,90027,90028,90031],{"style":473},[15,90029],{"className":90030,"style":461},[302],[15,90032],{"className":90033,"style":481},[480],[15,90035,90036,90039],{"style":2550},[15,90037],{"className":90038,"style":461},[302],[15,90040,90042],{"className":90041},[307,308,309,310],[15,90043,90045],{"className":90044},[59,310],[15,90046,117],{"className":90047},[59,310],[15,90049,318],{"className":90050},[317],[15,90052,90054],{"className":90053},[290],[15,90055,90057],{"className":90056,"style":2572},[294],[15,90058],{},[15,90060],{"className":90061},[153,441],[15,90063,90065,90068],{"className":90064},[59],[15,90066,37449],{"className":90067},[59,60],[15,90069,90071],{"className":90070},[281],[15,90072,90074],{"className":90073},[285],[15,90075,90077],{"className":90076},[290],[15,90078,90080],{"className":90079,"style":20028},[294],[15,90081,90082,90085],{"style":6865},[15,90083],{"className":90084,"style":303},[302],[15,90086,90088],{"className":90087},[307,308,309,310],[15,90089,2463],{"className":90090},[59,310],[15,90092,90094,90148],{"className":90093,"translate":19},[18],[15,90095,90097],{"className":90096},[23],[25,90098,90099],{"xmlns":27},[29,90100,90101,90145],{},[32,90102,90103,90109,90111,90117,90127,90129,90135],{},[6814,90104,90105,90107],{},[35,90106,33884],{},[115,90108,2463],{},[110,90110,32959],{},[238,90112,90113,90115],{},[115,90114,117],{},[115,90116,38989],{},[195,90118,90119,90121],{},[35,90120,199],{},[32,90122,90123,90125],{},[35,90124,10694],{},[35,90126,21893],{},[110,90128,9952],{},[238,90130,90131,90133],{},[115,90132,117],{},[115,90134,2463],{},[195,90136,90137,90139],{},[35,90138,199],{},[32,90140,90141,90143],{},[35,90142,10694],{},[35,90144,21893],{},[39,90146,90147],{"encoding":41},"H^2\\approx\\frac14 D_{KL}\\le\\frac12 D_{KL}",[15,90149,90151,90195,90324],{"className":90150,"ariaHidden":46},[45],[15,90152,90154,90157,90186,90189,90192],{"className":90153},[50],[15,90155],{"className":90156,"style":20028},[54],[15,90158,90160,90163],{"className":90159},[59],[15,90161,33884],{"className":90162,"style":34038},[59,60],[15,90164,90166],{"className":90165},[281],[15,90167,90169],{"className":90168},[285],[15,90170,90172],{"className":90171},[290],[15,90173,90175],{"className":90174,"style":20028},[294],[15,90176,90177,90180],{"style":6865},[15,90178],{"className":90179,"style":303},[302],[15,90181,90183],{"className":90182},[307,308,309,310],[15,90184,2463],{"className":90185},[59,310],[15,90187],{"className":90188,"style":158},[157],[15,90190,32959],{"className":90191},[162],[15,90193],{"className":90194,"style":158},[157],[15,90196,90198,90201,90269,90315,90318,90321],{"className":90197},[50],[15,90199],{"className":90200,"style":2505},[54],[15,90202,90204,90207,90266],{"className":90203},[59],[15,90205],{"className":90206},[146,441],[15,90208,90210],{"className":90209},[238],[15,90211,90213,90258],{"className":90212},[285,286],[15,90214,90216,90255],{"className":90215},[290],[15,90217,90219,90233,90241],{"className":90218,"style":2524},[294],[15,90220,90221,90224],{"style":2527},[15,90222],{"className":90223,"style":461},[302],[15,90225,90227],{"className":90226},[307,308,309,310],[15,90228,90230],{"className":90229},[59,310],[15,90231,38989],{"className":90232},[59,310],[15,90234,90235,90238],{"style":473},[15,90236],{"className":90237,"style":461},[302],[15,90239],{"className":90240,"style":481},[480],[15,90242,90243,90246],{"style":2550},[15,90244],{"className":90245,"style":461},[302],[15,90247,90249],{"className":90248},[307,308,309,310],[15,90250,90252],{"className":90251},[59,310],[15,90253,117],{"className":90254},[59,310],[15,90256,318],{"className":90257},[317],[15,90259,90261],{"className":90260},[290],[15,90262,90264],{"className":90263,"style":2572},[294],[15,90265],{},[15,90267],{"className":90268},[153,441],[15,90270,90272,90275],{"className":90271},[59],[15,90273,199],{"className":90274,"style":277},[59,60],[15,90276,90278],{"className":90277},[281],[15,90279,90281,90307],{"className":90280},[285,286],[15,90282,90284,90304],{"className":90283},[290],[15,90285,90287],{"className":90286,"style":379},[294],[15,90288,90289,90292],{"style":298},[15,90290],{"className":90291,"style":303},[302],[15,90293,90295],{"className":90294},[307,308,309,310],[15,90296,90298,90301],{"className":90297},[59,310],[15,90299,10694],{"className":90300,"style":10782},[59,60,310],[15,90302,21893],{"className":90303},[59,60,310],[15,90305,318],{"className":90306},[317],[15,90308,90310],{"className":90309},[290],[15,90311,90313],{"className":90312,"style":7968},[294],[15,90314],{},[15,90316],{"className":90317,"style":158},[157],[15,90319,9952],{"className":90320},[162],[15,90322],{"className":90323,"style":158},[157],[15,90325,90327,90330,90398],{"className":90326},[50],[15,90328],{"className":90329,"style":2505},[54],[15,90331,90333,90336,90395],{"className":90332},[59],[15,90334],{"className":90335},[146,441],[15,90337,90339],{"className":90338},[238],[15,90340,90342,90387],{"className":90341},[285,286],[15,90343,90345,90384],{"className":90344},[290],[15,90346,90348,90362,90370],{"className":90347,"style":2524},[294],[15,90349,90350,90353],{"style":2527},[15,90351],{"className":90352,"style":461},[302],[15,90354,90356],{"className":90355},[307,308,309,310],[15,90357,90359],{"className":90358},[59,310],[15,90360,2463],{"className":90361},[59,310],[15,90363,90364,90367],{"style":473},[15,90365],{"className":90366,"style":461},[302],[15,90368],{"className":90369,"style":481},[480],[15,90371,90372,90375],{"style":2550},[15,90373],{"className":90374,"style":461},[302],[15,90376,90378],{"className":90377},[307,308,309,310],[15,90379,90381],{"className":90380},[59,310],[15,90382,117],{"className":90383},[59,310],[15,90385,318],{"className":90386},[317],[15,90388,90390],{"className":90389},[290],[15,90391,90393],{"className":90392,"style":2572},[294],[15,90394],{},[15,90396],{"className":90397},[153,441],[15,90399,90401,90404],{"className":90400},[59],[15,90402,199],{"className":90403,"style":277},[59,60],[15,90405,90407],{"className":90406},[281],[15,90408,90410,90436],{"className":90409},[285,286],[15,90411,90413,90433],{"className":90412},[290],[15,90414,90416],{"className":90415,"style":379},[294],[15,90417,90418,90421],{"style":298},[15,90419],{"className":90420,"style":303},[302],[15,90422,90424],{"className":90423},[307,308,309,310],[15,90425,90427,90430],{"className":90426},[59,310],[15,90428,10694],{"className":90429,"style":10782},[59,60,310],[15,90431,21893],{"className":90432},[59,60,310],[15,90434,318],{"className":90435},[317],[15,90437,90439],{"className":90438},[290],[15,90440,90442],{"className":90441,"style":7968},[294],[15,90443],{},"，不等式成立且留有余量。",[11,90446,90447,90509],{},[1225,90448,90449,90450,90508],{},"TV 与 ",[15,90451,90453,90470],{"className":90452,"translate":19},[18],[15,90454,90456],{"className":90455},[23],[25,90457,90458],{"xmlns":27},[29,90459,90460,90468],{},[32,90461,90462],{},[6814,90463,90464,90466],{},[35,90465,33884],{},[115,90467,2463],{},[39,90469,42070],{"encoding":41},[15,90471,90473],{"className":90472,"ariaHidden":46},[45],[15,90474,90476,90479],{"className":90475},[50],[15,90477],{"className":90478,"style":20028},[54],[15,90480,90482,90485],{"className":90481},[59],[15,90483,33884],{"className":90484,"style":34038},[59,60],[15,90486,90488],{"className":90487},[281],[15,90489,90491],{"className":90490},[285],[15,90492,90494],{"className":90493},[290],[15,90495,90497],{"className":90496,"style":20028},[294],[15,90498,90499,90502],{"style":6865},[15,90500],{"className":90501,"style":303},[302],[15,90503,90505],{"className":90504},[307,308,309,310],[15,90506,2463],{"className":90507},[59,310]," 的关系。"," 由 Cauchy–Schwarz，",[15,90511,90513],{"className":90512,"translate":19},[180],[15,90514,90516,90742],{"className":90515,"translate":19},[18],[15,90517,90519],{"className":90518},[23],[25,90520,90521],{"xmlns":27,"display":189},[29,90522,90523,90739],{},[1243,90524,90525,90591,90659],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,90526,90527,90543],{},[1252,90528,90529],{},[1255,90530,90531],{"scriptlevel":126,"displaystyle":46},[32,90532,90533,90535,90537],{},[115,90534,2463],{},[1297,90536,1299],{},[32,90538,90539,90541],{},[35,90540,5392],{"mathvariant":209},[35,90542,34850],{"mathvariant":209},[1252,90544,90545],{},[1255,90546,90547],{"scriptlevel":126,"displaystyle":46},[32,90548,90549,90551,90553,90555,90557,90561,90563,90567,90569,90571,90573,90577,90579,90583,90585,90587,90589],{},[32,90550],{},[110,90552,123],{},[110,90554,1287],{},[35,90556,4808],{"mathvariant":209},[34339,90558,90559],{},[35,90560,11],{},[110,90562,4813],{},[34339,90564,90565],{},[35,90566,944],{},[35,90568,4808],{"mathvariant":209},[1297,90570,15904],{},[35,90572,4808],{"mathvariant":209},[34339,90574,90575],{},[35,90576,11],{},[110,90578,2470],{},[34339,90580,90581],{},[35,90582,944],{},[35,90584,4808],{"mathvariant":209},[1297,90586,1299],{},[35,90588,244],{},[35,90590,774],{},[1249,90592,90593,90599],{},[1252,90594,90595],{},[1255,90596,90597],{"scriptlevel":126,"displaystyle":46},[32,90598],{},[1252,90600,90601],{},[1255,90602,90603],{"scriptlevel":126,"displaystyle":46},[32,90604,90605,90607,90609,90633,90635],{},[32,90606],{},[110,90608,9952],{},[34339,90610,90611],{},[32,90612,90613,90615,90617,90621,90623,90627],{},[110,90614,1287],{},[110,90616,113],{"stretchy":112},[34339,90618,90619],{},[35,90620,11],{},[110,90622,4813],{},[34339,90624,90625],{},[35,90626,944],{},[6814,90628,90629,90631],{},[110,90630,120],{"stretchy":112},[115,90632,2463],{},[110,90634,3299],{},[34339,90636,90637],{},[32,90638,90639,90641,90643,90647,90649,90653],{},[110,90640,1287],{},[110,90642,113],{"stretchy":112},[34339,90644,90645],{},[35,90646,11],{},[110,90648,2470],{},[34339,90650,90651],{},[35,90652,944],{},[6814,90654,90655,90657],{},[110,90656,120],{"stretchy":112},[115,90658,2463],{},[1249,90660,90661,90667],{},[1252,90662,90663],{},[1255,90664,90665],{"scriptlevel":126,"displaystyle":46},[32,90666],{},[1252,90668,90669],{},[1255,90670,90671],{"scriptlevel":126,"displaystyle":46},[32,90672,90673,90675,90677,90689,90691,90709,90711,90737],{},[32,90674],{},[110,90676,123],{},[34339,90678,90679],{},[32,90680,90681,90683],{},[115,90682,2463],{},[6814,90684,90685,90687],{},[35,90686,33884],{},[115,90688,2463],{},[110,90690,3299],{},[34339,90692,90693],{},[32,90694,90695,90697,90699,90701,90703,90705,90707],{},[115,90696,2463],{},[110,90698,113],{"stretchy":112},[115,90700,117],{},[110,90702,2470],{},[35,90704,39291],{},[35,90706,39294],{},[110,90708,120],{"stretchy":112},[110,90710,123],{},[34339,90712,90713],{},[32,90714,90715,90717,90723,90725,90727,90729,90735],{},[115,90716,38989],{},[6814,90718,90719,90721],{},[35,90720,33884],{},[115,90722,2463],{},[110,90724,113],{"stretchy":112},[115,90726,2463],{},[110,90728,4813],{},[6814,90730,90731,90733],{},[35,90732,33884],{},[115,90734,2463],{},[110,90736,120],{"stretchy":112},[110,90738,551],{"separator":46},[39,90740,90741],{"encoding":41},"\\begin{aligned}\n2\\,\\mathrm{TV}\n&=\\int|\\sqrt p-\\sqrt q|\\;|\\sqrt p+\\sqrt q|\\,dx\\\\\n&\\le\\sqrt{\\int(\\sqrt p-\\sqrt q)^2}\n\\cdot\\sqrt{\\int(\\sqrt p+\\sqrt q)^2}\\\\\n&=\\sqrt{2H^2}\\cdot\\sqrt{2(1+BC)}\n=\\sqrt{4H^2(2-H^2)},\n\\end{aligned}",[15,90743,90745],{"className":90744,"ariaHidden":46},[45],[15,90746,90748,90752],{"className":90747},[50],[15,90749],{"className":90750,"style":90751},[54],"height:7.2262em;vertical-align:-3.3631em;",[15,90753,90755],{"className":90754},[59],[15,90756,90758,90823],{"className":90757},[1243],[15,90759,90761],{"className":90760},[1360],[15,90762,90764,90814],{"className":90763},[285,286],[15,90765,90767,90811],{"className":90766},[290],[15,90768,90771,90793,90802],{"className":90769,"style":90770},[294],"height:3.8631em;",[15,90772,90774,90778],{"style":90773},"top:-6.3858em;",[15,90775],{"className":90776,"style":90777},[302],"height:3.8828em;",[15,90779,90781,90784,90787],{"className":90780},[59],[15,90782,2463],{"className":90783},[59],[15,90785],{"className":90786,"style":406},[157],[15,90788,90790],{"className":90789},[59],[15,90791,86762],{"className":90792,"style":4157},[59,32662],[15,90794,90796,90799],{"style":90795},"top:-3.3408em;",[15,90797],{"className":90798,"style":90777},[302],[15,90800],{"className":90801},[59],[15,90803,90805,90808],{"style":90804},"top:-0.8797em;",[15,90806],{"className":90807,"style":90777},[302],[15,90809],{"className":90810},[59],[15,90812,318],{"className":90813},[317],[15,90815,90817],{"className":90816},[290],[15,90818,90821],{"className":90819,"style":90820},[294],"height:3.3631em;",[15,90822],{},[15,90824,90826],{"className":90825},[1451],[15,90827,90829,91783],{"className":90828},[285,286],[15,90830,90832,91780],{"className":90831},[290],[15,90833,90835,91079,91469],{"className":90834,"style":90770},[294],[15,90836,90837,90840],{"style":90773},[15,90838],{"className":90839,"style":90777},[302],[15,90841,90843,90846,90849,90852,90855,90858,90861,90864,90908,90911,90914,90917,90961,90964,90967,90970,91014,91017,91020,91023,91067,91070,91073,91076],{"className":90842},[59],[15,90844],{"className":90845},[59],[15,90847],{"className":90848,"style":158},[157],[15,90850,123],{"className":90851},[162],[15,90853],{"className":90854,"style":158},[157],[15,90856,1287],{"className":90857,"style":1487},[1484,1485,1486],[15,90859],{"className":90860,"style":406},[157],[15,90862,4808],{"className":90863},[59],[15,90865,90867],{"className":90866},[59,34367],[15,90868,90870,90900],{"className":90869},[285,286],[15,90871,90873,90897],{"className":90872},[290],[15,90874,90876,90885],{"className":90875,"style":6862},[294],[15,90877,90879,90882],{"className":90878,"style":11863},[6307],[15,90880],{"className":90881,"style":461},[302],[15,90883,11],{"className":90884,"style":34387},[59,60],[15,90886,90887,90890],{"style":41350},[15,90888],{"className":90889,"style":461},[302],[15,90891,90893],{"className":90892,"style":34444},[34443],[6323,90894,90895],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,90896],{"d":34451},[15,90898,318],{"className":90899},[317],[15,90901,90903],{"className":90902},[290],[15,90904,90906],{"className":90905,"style":41370},[294],[15,90907],{},[15,90909],{"className":90910,"style":2587},[157],[15,90912,4813],{"className":90913},[2591],[15,90915],{"className":90916,"style":2587},[157],[15,90918,90920],{"className":90919},[59,34367],[15,90921,90923,90953],{"className":90922},[285,286],[15,90924,90926,90950],{"className":90925},[290],[15,90927,90929,90938],{"className":90928,"style":6862},[294],[15,90930,90932,90935],{"className":90931,"style":11863},[6307],[15,90933],{"className":90934,"style":461},[302],[15,90936,944],{"className":90937,"style":39099},[59,60],[15,90939,90940,90943],{"style":41350},[15,90941],{"className":90942,"style":461},[302],[15,90944,90946],{"className":90945,"style":34444},[34443],[6323,90947,90948],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,90949],{"d":34451},[15,90951,318],{"className":90952},[317],[15,90954,90956],{"className":90955},[290],[15,90957,90959],{"className":90958,"style":41370},[294],[15,90960],{},[15,90962,4808],{"className":90963},[59],[15,90965],{"className":90966,"style":158},[157],[15,90968,4808],{"className":90969},[59],[15,90971,90973],{"className":90972},[59,34367],[15,90974,90976,91006],{"className":90975},[285,286],[15,90977,90979,91003],{"className":90978},[290],[15,90980,90982,90991],{"className":90981,"style":6862},[294],[15,90983,90985,90988],{"className":90984,"style":11863},[6307],[15,90986],{"className":90987,"style":461},[302],[15,90989,11],{"className":90990,"style":34387},[59,60],[15,90992,90993,90996],{"style":41350},[15,90994],{"className":90995,"style":461},[302],[15,90997,90999],{"className":90998,"style":34444},[34443],[6323,91000,91001],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91002],{"d":34451},[15,91004,318],{"className":91005},[317],[15,91007,91009],{"className":91008},[290],[15,91010,91012],{"className":91011,"style":41370},[294],[15,91013],{},[15,91015],{"className":91016,"style":2587},[157],[15,91018,2470],{"className":91019},[2591],[15,91021],{"className":91022,"style":2587},[157],[15,91024,91026],{"className":91025},[59,34367],[15,91027,91029,91059],{"className":91028},[285,286],[15,91030,91032,91056],{"className":91031},[290],[15,91033,91035,91044],{"className":91034,"style":6862},[294],[15,91036,91038,91041],{"className":91037,"style":11863},[6307],[15,91039],{"className":91040,"style":461},[302],[15,91042,944],{"className":91043,"style":39099},[59,60],[15,91045,91046,91049],{"style":41350},[15,91047],{"className":91048,"style":461},[302],[15,91050,91052],{"className":91051,"style":34444},[34443],[6323,91053,91054],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91055],{"d":34451},[15,91057,318],{"className":91058},[317],[15,91060,91062],{"className":91061},[290],[15,91063,91065],{"className":91064,"style":41370},[294],[15,91066],{},[15,91068,4808],{"className":91069},[59],[15,91071],{"className":91072,"style":406},[157],[15,91074,244],{"className":91075},[59,60],[15,91077,774],{"className":91078},[59,60],[15,91080,91081,91084],{"style":90795},[15,91082],{"className":91083,"style":90777},[302],[15,91085,91087,91090,91093,91096,91099,91284,91287,91290,91293],{"className":91086},[59],[15,91088],{"className":91089},[59],[15,91091],{"className":91092,"style":158},[157],[15,91094,9952],{"className":91095},[162],[15,91097],{"className":91098,"style":158},[157],[15,91100,91102],{"className":91101},[59,34367],[15,91103,91105,91275],{"className":91104},[285,286],[15,91106,91108,91272],{"className":91107},[290],[15,91109,91112,91255],{"className":91110,"style":91111},[294],"height:1.8828em;",[15,91113,91116,91120],{"className":91114,"style":91115},[6307],"top:-5em;",[15,91117],{"className":91118,"style":91119},[302],"height:5em;",[15,91121,91123,91126,91129,91173,91176,91179,91182,91226],{"className":91122,"style":41161},[59],[15,91124,1287],{"className":91125,"style":1487},[1484,1485,1486],[15,91127,113],{"className":91128},[146],[15,91130,91132],{"className":91131},[59,34367],[15,91133,91135,91165],{"className":91134},[285,286],[15,91136,91138,91162],{"className":91137},[290],[15,91139,91141,91150],{"className":91140,"style":6862},[294],[15,91142,91144,91147],{"className":91143,"style":11863},[6307],[15,91145],{"className":91146,"style":461},[302],[15,91148,11],{"className":91149,"style":34387},[59,60],[15,91151,91152,91155],{"style":41350},[15,91153],{"className":91154,"style":461},[302],[15,91156,91158],{"className":91157,"style":34444},[34443],[6323,91159,91160],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91161],{"d":34451},[15,91163,318],{"className":91164},[317],[15,91166,91168],{"className":91167},[290],[15,91169,91171],{"className":91170,"style":41370},[294],[15,91172],{},[15,91174],{"className":91175,"style":2587},[157],[15,91177,4813],{"className":91178},[2591],[15,91180],{"className":91181,"style":2587},[157],[15,91183,91185],{"className":91184},[59,34367],[15,91186,91188,91218],{"className":91187},[285,286],[15,91189,91191,91215],{"className":91190},[290],[15,91192,91194,91203],{"className":91193,"style":6862},[294],[15,91195,91197,91200],{"className":91196,"style":11863},[6307],[15,91198],{"className":91199,"style":461},[302],[15,91201,944],{"className":91202,"style":39099},[59,60],[15,91204,91205,91208],{"style":41350},[15,91206],{"className":91207,"style":461},[302],[15,91209,91211],{"className":91210,"style":34444},[34443],[6323,91212,91213],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91214],{"d":34451},[15,91216,318],{"className":91217},[317],[15,91219,91221],{"className":91220},[290],[15,91222,91224],{"className":91223,"style":41370},[294],[15,91225],{},[15,91227,91229,91232],{"className":91228},[153],[15,91230,120],{"className":91231},[153],[15,91233,91235],{"className":91234},[281],[15,91236,91238],{"className":91237},[285],[15,91239,91241],{"className":91240},[290],[15,91242,91244],{"className":91243,"style":45032},[294],[15,91245,91246,91249],{"style":45035},[15,91247],{"className":91248,"style":303},[302],[15,91250,91252],{"className":91251},[307,308,309,310],[15,91253,2463],{"className":91254},[59,310],[15,91256,91258,91261],{"style":91257},"top:-3.8428em;",[15,91259],{"className":91260,"style":91119},[302],[15,91262,91265],{"className":91263,"style":91264},[34443],"min-width:1.02em;height:3.08em;",[6323,91266,91269],{"xmlns":6325,"width":6326,"height":91267,"viewBox":91268,"preserveAspectRatio":6329},"3.08em","0 0 400000 3240",[6331,91270],{"d":91271},"M473,2793\nc339.3,-1799.3,509.3,-2700,510,-2702 l0 -0\nc3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM1001 80h400000v40H1017.7z",[15,91273,318],{"className":91274},[317],[15,91276,91278],{"className":91277},[290],[15,91279,91282],{"className":91280,"style":91281},[294],"height:1.1572em;",[15,91283],{},[15,91285],{"className":91286,"style":2587},[157],[15,91288,3299],{"className":91289},[2591],[15,91291],{"className":91292,"style":2587},[157],[15,91294,91296],{"className":91295},[59,34367],[15,91297,91299,91461],{"className":91298},[285,286],[15,91300,91302,91458],{"className":91301},[290],[15,91303,91305,91446],{"className":91304,"style":91111},[294],[15,91306,91308,91311],{"className":91307,"style":91115},[6307],[15,91309],{"className":91310,"style":91119},[302],[15,91312,91314,91317,91320,91364,91367,91370,91373,91417],{"className":91313,"style":41161},[59],[15,91315,1287],{"className":91316,"style":1487},[1484,1485,1486],[15,91318,113],{"className":91319},[146],[15,91321,91323],{"className":91322},[59,34367],[15,91324,91326,91356],{"className":91325},[285,286],[15,91327,91329,91353],{"className":91328},[290],[15,91330,91332,91341],{"className":91331,"style":6862},[294],[15,91333,91335,91338],{"className":91334,"style":11863},[6307],[15,91336],{"className":91337,"style":461},[302],[15,91339,11],{"className":91340,"style":34387},[59,60],[15,91342,91343,91346],{"style":41350},[15,91344],{"className":91345,"style":461},[302],[15,91347,91349],{"className":91348,"style":34444},[34443],[6323,91350,91351],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91352],{"d":34451},[15,91354,318],{"className":91355},[317],[15,91357,91359],{"className":91358},[290],[15,91360,91362],{"className":91361,"style":41370},[294],[15,91363],{},[15,91365],{"className":91366,"style":2587},[157],[15,91368,2470],{"className":91369},[2591],[15,91371],{"className":91372,"style":2587},[157],[15,91374,91376],{"className":91375},[59,34367],[15,91377,91379,91409],{"className":91378},[285,286],[15,91380,91382,91406],{"className":91381},[290],[15,91383,91385,91394],{"className":91384,"style":6862},[294],[15,91386,91388,91391],{"className":91387,"style":11863},[6307],[15,91389],{"className":91390,"style":461},[302],[15,91392,944],{"className":91393,"style":39099},[59,60],[15,91395,91396,91399],{"style":41350},[15,91397],{"className":91398,"style":461},[302],[15,91400,91402],{"className":91401,"style":34444},[34443],[6323,91403,91404],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91405],{"d":34451},[15,91407,318],{"className":91408},[317],[15,91410,91412],{"className":91411},[290],[15,91413,91415],{"className":91414,"style":41370},[294],[15,91416],{},[15,91418,91420,91423],{"className":91419},[153],[15,91421,120],{"className":91422},[153],[15,91424,91426],{"className":91425},[281],[15,91427,91429],{"className":91428},[285],[15,91430,91432],{"className":91431},[290],[15,91433,91435],{"className":91434,"style":45032},[294],[15,91436,91437,91440],{"style":45035},[15,91438],{"className":91439,"style":303},[302],[15,91441,91443],{"className":91442},[307,308,309,310],[15,91444,2463],{"className":91445},[59,310],[15,91447,91448,91451],{"style":91257},[15,91449],{"className":91450,"style":91119},[302],[15,91452,91454],{"className":91453,"style":91264},[34443],[6323,91455,91456],{"xmlns":6325,"width":6326,"height":91267,"viewBox":91268,"preserveAspectRatio":6329},[6331,91457],{"d":91271},[15,91459,318],{"className":91460},[317],[15,91462,91464],{"className":91463},[290],[15,91465,91467],{"className":91466,"style":91281},[294],[15,91468],{},[15,91470,91471,91474],{"style":90804},[15,91472],{"className":91473,"style":90777},[302],[15,91475,91477,91480,91483,91486,91489,91565,91568,91571,91574,91645,91648,91651,91654,91777],{"className":91476},[59],[15,91478],{"className":91479},[59],[15,91481],{"className":91482,"style":158},[157],[15,91484,123],{"className":91485},[162],[15,91487],{"className":91488,"style":158},[157],[15,91490,91492],{"className":91491},[59,34367],[15,91493,91495,91557],{"className":91494},[285,286],[15,91496,91498,91554],{"className":91497},[290],[15,91499,91501,91542],{"className":91500,"style":83669},[294],[15,91502,91504,91507],{"className":91503,"style":11863},[6307],[15,91505],{"className":91506,"style":461},[302],[15,91508,91510,91513],{"className":91509,"style":34387},[59],[15,91511,2463],{"className":91512},[59],[15,91514,91516,91519],{"className":91515},[59],[15,91517,33884],{"className":91518,"style":34038},[59,60],[15,91520,91522],{"className":91521},[281],[15,91523,91525],{"className":91524},[285],[15,91526,91528],{"className":91527},[290],[15,91529,91531],{"className":91530,"style":45032},[294],[15,91532,91533,91536],{"style":45035},[15,91534],{"className":91535,"style":303},[302],[15,91537,91539],{"className":91538},[307,308,309,310],[15,91540,2463],{"className":91541},[59,310],[15,91543,91544,91547],{"style":83713},[15,91545],{"className":91546,"style":461},[302],[15,91548,91550],{"className":91549,"style":34444},[34443],[6323,91551,91552],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,91553],{"d":34451},[15,91555,318],{"className":91556},[317],[15,91558,91560],{"className":91559},[290],[15,91561,91563],{"className":91562,"style":83733},[294],[15,91564],{},[15,91566],{"className":91567,"style":2587},[157],[15,91569,3299],{"className":91570},[2591],[15,91572],{"className":91573,"style":2587},[157],[15,91575,91577],{"className":91576},[59,34367],[15,91578,91580,91637],{"className":91579},[285,286],[15,91581,91583,91634],{"className":91582},[290],[15,91584,91586,91622],{"className":91585,"style":83532},[294],[15,91587,91589,91592],{"className":91588,"style":83536},[6307],[15,91590],{"className":91591,"style":14846},[302],[15,91593,91595,91598,91601,91604,91607,91610,91613,91616,91619],{"className":91594,"style":41161},[59],[15,91596,2463],{"className":91597},[59],[15,91599,113],{"className":91600},[146],[15,91602,117],{"className":91603},[59],[15,91605],{"className":91606,"style":2587},[157],[15,91608,2470],{"className":91609},[2591],[15,91611],{"className":91612,"style":2587},[157],[15,91614,39291],{"className":91615,"style":39387},[59,60],[15,91617,39294],{"className":91618,"style":10782},[59,60],[15,91620,120],{"className":91621},[153],[15,91623,91624,91627],{"style":83621},[15,91625],{"className":91626,"style":14846},[302],[15,91628,91630],{"className":91629,"style":83628},[34443],[6323,91631,91632],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,91633],{"d":83635},[15,91635,318],{"className":91636},[317],[15,91638,91640],{"className":91639},[290],[15,91641,91643],{"className":91642,"style":83645},[294],[15,91644],{},[15,91646],{"className":91647,"style":158},[157],[15,91649,123],{"className":91650},[162],[15,91652],{"className":91653,"style":158},[157],[15,91655,91657],{"className":91656},[59,34367],[15,91658,91660,91769],{"className":91659},[285,286],[15,91661,91663,91766],{"className":91662},[290],[15,91664,91666,91754],{"className":91665,"style":83532},[294],[15,91667,91669,91672],{"className":91668,"style":83536},[6307],[15,91670],{"className":91671,"style":14846},[302],[15,91673,91675,91678,91707,91710,91713,91716,91719,91722,91751],{"className":91674,"style":41161},[59],[15,91676,38989],{"className":91677},[59],[15,91679,91681,91684],{"className":91680},[59],[15,91682,33884],{"className":91683,"style":34038},[59,60],[15,91685,91687],{"className":91686},[281],[15,91688,91690],{"className":91689},[285],[15,91691,91693],{"className":91692},[290],[15,91694,91696],{"className":91695,"style":45032},[294],[15,91697,91698,91701],{"style":45035},[15,91699],{"className":91700,"style":303},[302],[15,91702,91704],{"className":91703},[307,308,309,310],[15,91705,2463],{"className":91706},[59,310],[15,91708,113],{"className":91709},[146],[15,91711,2463],{"className":91712},[59],[15,91714],{"className":91715,"style":2587},[157],[15,91717,4813],{"className":91718},[2591],[15,91720],{"className":91721,"style":2587},[157],[15,91723,91725,91728],{"className":91724},[59],[15,91726,33884],{"className":91727,"style":34038},[59,60],[15,91729,91731],{"className":91730},[281],[15,91732,91734],{"className":91733},[285],[15,91735,91737],{"className":91736},[290],[15,91738,91740],{"className":91739,"style":45032},[294],[15,91741,91742,91745],{"style":45035},[15,91743],{"className":91744,"style":303},[302],[15,91746,91748],{"className":91747},[307,308,309,310],[15,91749,2463],{"className":91750},[59,310],[15,91752,120],{"className":91753},[153],[15,91755,91756,91759],{"style":83621},[15,91757],{"className":91758,"style":14846},[302],[15,91760,91762],{"className":91761,"style":83628},[34443],[6323,91763,91764],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,91765],{"d":83635},[15,91767,318],{"className":91768},[317],[15,91770,91772],{"className":91771},[290],[15,91773,91775],{"className":91774,"style":83645},[294],[15,91776],{},[15,91778,551],{"className":91779},[573],[15,91781,318],{"className":91782},[317],[15,91784,91786],{"className":91785},[290],[15,91787,91789],{"className":91788,"style":90820},[294],[15,91790],{},[11,91792,91793,91794,91995,91996,92203,92204,92359,92360,991],{},"故 ",[15,91795,91797,91841],{"className":91796,"translate":19},[18],[15,91798,91800],{"className":91799},[23],[25,91801,91802],{"xmlns":27},[29,91803,91804,91838],{},[32,91805,91806,91812,91814],{},[32,91807,91808,91810],{},[35,91809,5392],{"mathvariant":209},[35,91811,34850],{"mathvariant":209},[110,91813,9952],{},[34339,91815,91816],{},[32,91817,91818,91824,91826,91828,91830,91836],{},[6814,91819,91820,91822],{},[35,91821,33884],{},[115,91823,2463],{},[110,91825,113],{"stretchy":112},[115,91827,2463],{},[110,91829,4813],{},[6814,91831,91832,91834],{},[35,91833,33884],{},[115,91835,2463],{},[110,91837,120],{"stretchy":112},[39,91839,91840],{"encoding":41},"\\mathrm{TV}\\le\\sqrt{H^2(2-H^2)}",[15,91842,91844,91865],{"className":91843,"ariaHidden":46},[45],[15,91845,91847,91850,91856,91859,91862],{"className":91846},[50],[15,91848],{"className":91849,"style":88354},[54],[15,91851,91853],{"className":91852},[59],[15,91854,86762],{"className":91855,"style":4157},[59,32662],[15,91857],{"className":91858,"style":158},[157],[15,91860,9952],{"className":91861},[162],[15,91863],{"className":91864,"style":158},[157],[15,91866,91868,91872],{"className":91867},[50],[15,91869],{"className":91870,"style":91871},[54],"height:1.24em;vertical-align:-0.305em;",[15,91873,91875],{"className":91874},[59,34367],[15,91876,91878,91986],{"className":91877},[285,286],[15,91879,91881,91983],{"className":91880},[290],[15,91882,91885,91970],{"className":91883,"style":91884},[294],"height:0.935em;",[15,91886,91888,91891],{"className":91887,"style":83536},[6307],[15,91889],{"className":91890,"style":14846},[302],[15,91892,91894,91923,91926,91929,91932,91935,91938,91967],{"className":91893,"style":41161},[59],[15,91895,91897,91900],{"className":91896},[59],[15,91898,33884],{"className":91899,"style":34038},[59,60],[15,91901,91903],{"className":91902},[281],[15,91904,91906],{"className":91905},[285],[15,91907,91909],{"className":91908},[290],[15,91910,91912],{"className":91911,"style":45032},[294],[15,91913,91914,91917],{"style":45035},[15,91915],{"className":91916,"style":303},[302],[15,91918,91920],{"className":91919},[307,308,309,310],[15,91921,2463],{"className":91922},[59,310],[15,91924,113],{"className":91925},[146],[15,91927,2463],{"className":91928},[59],[15,91930],{"className":91931,"style":2587},[157],[15,91933,4813],{"className":91934},[2591],[15,91936],{"className":91937,"style":2587},[157],[15,91939,91941,91944],{"className":91940},[59],[15,91942,33884],{"className":91943,"style":34038},[59,60],[15,91945,91947],{"className":91946},[281],[15,91948,91950],{"className":91949},[285],[15,91951,91953],{"className":91952},[290],[15,91954,91956],{"className":91955,"style":45032},[294],[15,91957,91958,91961],{"style":45035},[15,91959],{"className":91960,"style":303},[302],[15,91962,91964],{"className":91963},[307,308,309,310],[15,91965,2463],{"className":91966},[59,310],[15,91968,120],{"className":91969},[153],[15,91971,91973,91976],{"style":91972},"top:-2.895em;",[15,91974],{"className":91975,"style":14846},[302],[15,91977,91979],{"className":91978,"style":83628},[34443],[6323,91980,91981],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,91982],{"d":83635},[15,91984,318],{"className":91985},[317],[15,91987,91989],{"className":91988},[290],[15,91990,91993],{"className":91991,"style":91992},[294],"height:0.305em;",[15,91994],{},"，再与 ",[15,91997,91999,92035],{"className":91998,"translate":19},[18],[15,92000,92002],{"className":92001},[23],[25,92003,92004],{"xmlns":27},[29,92005,92006,92032],{},[32,92007,92008,92014,92016,92022],{},[6814,92009,92010,92012],{},[35,92011,33884],{},[115,92013,2463],{},[110,92015,9952],{},[238,92017,92018,92020],{},[115,92019,117],{},[115,92021,2463],{},[195,92023,92024,92026],{},[35,92025,199],{},[32,92027,92028,92030],{},[35,92029,10694],{},[35,92031,21893],{},[39,92033,92034],{"encoding":41},"H^2\\le\\frac12 D_{KL}",[15,92036,92038,92083],{"className":92037,"ariaHidden":46},[45],[15,92039,92041,92045,92074,92077,92080],{"className":92040},[50],[15,92042],{"className":92043,"style":92044},[54],"height:0.9501em;vertical-align:-0.136em;",[15,92046,92048,92051],{"className":92047},[59],[15,92049,33884],{"className":92050,"style":34038},[59,60],[15,92052,92054],{"className":92053},[281],[15,92055,92057],{"className":92056},[285],[15,92058,92060],{"className":92059},[290],[15,92061,92063],{"className":92062,"style":20028},[294],[15,92064,92065,92068],{"style":6865},[15,92066],{"className":92067,"style":303},[302],[15,92069,92071],{"className":92070},[307,308,309,310],[15,92072,2463],{"className":92073},[59,310],[15,92075],{"className":92076,"style":158},[157],[15,92078,9952],{"className":92079},[162],[15,92081],{"className":92082,"style":158},[157],[15,92084,92086,92089,92157],{"className":92085},[50],[15,92087],{"className":92088,"style":2505},[54],[15,92090,92092,92095,92154],{"className":92091},[59],[15,92093],{"className":92094},[146,441],[15,92096,92098],{"className":92097},[238],[15,92099,92101,92146],{"className":92100},[285,286],[15,92102,92104,92143],{"className":92103},[290],[15,92105,92107,92121,92129],{"className":92106,"style":2524},[294],[15,92108,92109,92112],{"style":2527},[15,92110],{"className":92111,"style":461},[302],[15,92113,92115],{"className":92114},[307,308,309,310],[15,92116,92118],{"className":92117},[59,310],[15,92119,2463],{"className":92120},[59,310],[15,92122,92123,92126],{"style":473},[15,92124],{"className":92125,"style":461},[302],[15,92127],{"className":92128,"style":481},[480],[15,92130,92131,92134],{"style":2550},[15,92132],{"className":92133,"style":461},[302],[15,92135,92137],{"className":92136},[307,308,309,310],[15,92138,92140],{"className":92139},[59,310],[15,92141,117],{"className":92142},[59,310],[15,92144,318],{"className":92145},[317],[15,92147,92149],{"className":92148},[290],[15,92150,92152],{"className":92151,"style":2572},[294],[15,92153],{},[15,92155],{"className":92156},[153,441],[15,92158,92160,92163],{"className":92159},[59],[15,92161,199],{"className":92162,"style":277},[59,60],[15,92164,92166],{"className":92165},[281],[15,92167,92169,92195],{"className":92168},[285,286],[15,92170,92172,92192],{"className":92171},[290],[15,92173,92175],{"className":92174,"style":379},[294],[15,92176,92177,92180],{"style":298},[15,92178],{"className":92179,"style":303},[302],[15,92181,92183],{"className":92182},[307,308,309,310],[15,92184,92186,92189],{"className":92185},[59,310],[15,92187,10694],{"className":92188,"style":10782},[59,60,310],[15,92190,21893],{"className":92191},[59,60,310],[15,92193,318],{"className":92194},[317],[15,92196,92198],{"className":92197},[290],[15,92199,92201],{"className":92200,"style":7968},[294],[15,92202],{}," 串起来就有 ",[15,92205,92207,92239],{"className":92206,"translate":19},[18],[15,92208,92210],{"className":92209},[23],[25,92211,92212],{"xmlns":27},[29,92213,92214,92236],{},[32,92215,92216,92222,92224],{},[32,92217,92218,92220],{},[35,92219,5392],{"mathvariant":209},[35,92221,34850],{"mathvariant":209},[110,92223,9952],{},[34339,92225,92226],{},[195,92227,92228,92230],{},[35,92229,199],{},[32,92231,92232,92234],{},[35,92233,10694],{},[35,92235,21893],{},[39,92237,92238],{"encoding":41},"\\mathrm{TV}\\le\\sqrt{D_{KL}}",[15,92240,92242,92263],{"className":92241,"ariaHidden":46},[45],[15,92243,92245,92248,92254,92257,92260],{"className":92244},[50],[15,92246],{"className":92247,"style":88354},[54],[15,92249,92251],{"className":92250},[59],[15,92252,86762],{"className":92253,"style":4157},[59,32662],[15,92255],{"className":92256,"style":158},[157],[15,92258,9952],{"className":92259},[162],[15,92261],{"className":92262,"style":158},[157],[15,92264,92266,92269],{"className":92265},[50],[15,92267],{"className":92268,"style":34363},[54],[15,92270,92272],{"className":92271},[59,34367],[15,92273,92275,92351],{"className":92274},[285,286],[15,92276,92278,92348],{"className":92277},[290],[15,92279,92281,92336],{"className":92280,"style":34377},[294],[15,92282,92284,92287],{"className":92283,"style":11863},[6307],[15,92285],{"className":92286,"style":461},[302],[15,92288,92290],{"className":92289,"style":34387},[59],[15,92291,92293,92296],{"className":92292},[59],[15,92294,199],{"className":92295,"style":277},[59,60],[15,92297,92299],{"className":92298},[281],[15,92300,92302,92328],{"className":92301},[285,286],[15,92303,92305,92325],{"className":92304},[290],[15,92306,92308],{"className":92307,"style":379},[294],[15,92309,92310,92313],{"style":298},[15,92311],{"className":92312,"style":303},[302],[15,92314,92316],{"className":92315},[307,308,309,310],[15,92317,92319,92322],{"className":92318},[59,310],[15,92320,10694],{"className":92321,"style":10782},[59,60,310],[15,92323,21893],{"className":92324},[59,60,310],[15,92326,318],{"className":92327},[317],[15,92329,92331],{"className":92330},[290],[15,92332,92334],{"className":92333,"style":7968},[294],[15,92335],{},[15,92337,92338,92341],{"style":34436},[15,92339],{"className":92340,"style":461},[302],[15,92342,92344],{"className":92343,"style":34444},[34443],[6323,92345,92346],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,92347],{"d":34451},[15,92349,318],{"className":92350},[317],[15,92352,92354],{"className":92353},[290],[15,92355,92357],{"className":92356,"style":34461},[294],[15,92358],{},"（比 Pinsker 常数差一个 ",[15,92361,92363,92379],{"className":92362,"translate":19},[18],[15,92364,92366],{"className":92365},[23],[25,92367,92368],{"xmlns":27},[29,92369,92370,92376],{},[32,92371,92372],{},[34339,92373,92374],{},[115,92375,2463],{},[39,92377,92378],{"encoding":41},"\\sqrt2",[15,92380,92382],{"className":92381,"ariaHidden":46},[45],[15,92383,92385,92389],{"className":92384},[50],[15,92386],{"className":92387,"style":92388},[54],"height:1.04em;vertical-align:-0.1328em;",[15,92390,92392],{"className":92391},[59,34367],[15,92393,92395,92427],{"className":92394},[285,286],[15,92396,92398,92424],{"className":92397},[290],[15,92399,92402,92411],{"className":92400,"style":92401},[294],"height:0.9072em;",[15,92403,92405,92408],{"className":92404,"style":11863},[6307],[15,92406],{"className":92407,"style":461},[302],[15,92409,2463],{"className":92410,"style":34387},[59],[15,92412,92414,92417],{"style":92413},"top:-2.8672em;",[15,92415],{"className":92416,"style":461},[302],[15,92418,92420],{"className":92419,"style":34444},[34443],[6323,92421,92422],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,92423],{"d":34451},[15,92425,318],{"className":92426},[317],[15,92428,92430],{"className":92429},[290],[15,92431,92434],{"className":92432,"style":92433},[294],"height:0.1328em;",[15,92435],{},[993,92437,92439,92589,94117,95609,95996,96562],{"title":92438},"定理 4.2（拓扑关系的准确版）",[11,92440,534,92441,92469,92470,92535,92536,92588],{},[15,92442,92444,92457],{"className":92443,"translate":19},[18],[15,92445,92447],{"className":92446},[23],[25,92448,92449],{"xmlns":27},[29,92450,92451,92455],{},[32,92452,92453],{},[35,92454,37],{},[39,92456,37],{"encoding":41},[15,92458,92460],{"className":92459,"ariaHidden":46},[45],[15,92461,92463,92466],{"className":92462},[50],[15,92464],{"className":92465,"style":55},[54],[15,92467,37],{"className":92468,"style":61},[59,60]," 凸、",[15,92471,92473,92496],{"className":92472,"translate":19},[18],[15,92474,92476],{"className":92475},[23],[25,92477,92478],{"xmlns":27},[29,92479,92480,92494],{},[32,92481,92482,92484,92486,92488,92490,92492],{},[35,92483,37],{},[110,92485,113],{"stretchy":112},[115,92487,117],{},[110,92489,120],{"stretchy":112},[110,92491,123],{},[115,92493,126],{},[39,92495,129],{"encoding":41},[15,92497,92499,92526],{"className":92498,"ariaHidden":46},[45],[15,92500,92502,92505,92508,92511,92514,92517,92520,92523],{"className":92501},[50],[15,92503],{"className":92504,"style":139},[54],[15,92506,37],{"className":92507,"style":61},[59,60],[15,92509,113],{"className":92510},[146],[15,92512,117],{"className":92513},[59],[15,92515,120],{"className":92516},[153],[15,92518],{"className":92519,"style":158},[157],[15,92521,123],{"className":92522},[162],[15,92524],{"className":92525,"style":158},[157],[15,92527,92529,92532],{"className":92528},[50],[15,92530],{"className":92531,"style":172},[54],[15,92533,126],{"className":92534},[59]," 且在 ",[15,92537,92539,92561],{"className":92538,"translate":19},[18],[15,92540,92542],{"className":92541},[23],[25,92543,92544],{"xmlns":27},[29,92545,92546,92558],{},[32,92547,92548,92550,92552,92554,92556],{},[110,92549,113],{"stretchy":112},[115,92551,126],{},[110,92553,551],{"separator":46},[35,92555,1024],{"mathvariant":209},[110,92557,120],{"stretchy":112},[39,92559,92560],{"encoding":41},"(0,\\infty)",[15,92562,92564],{"className":92563,"ariaHidden":46},[45],[15,92565,92567,92570,92573,92576,92579,92582,92585],{"className":92566},[50],[15,92568],{"className":92569,"style":139},[54],[15,92571,113],{"className":92572},[146],[15,92574,126],{"className":92575},[59],[15,92577,551],{"className":92578},[573],[15,92580],{"className":92581,"style":406},[157],[15,92583,1024],{"className":92584},[59],[15,92586,120],{"className":92587},[153]," 上连续。",[11,92590,92591,6494,92594,92927,92928,92999,93000,5645,93107,93256,93257,93412,93413,93563,93564,93622,93623,93751,93752,93809,93810,94116],{},[1225,92592,92593],{},"(a)（\"下来\"方向，一般成立）",[15,92595,92597,92667],{"className":92596,"translate":19},[18],[15,92598,92600],{"className":92599},[23],[25,92601,92602],{"xmlns":27},[29,92603,92604,92664],{},[32,92605,92606,92612,92614,92620,92622,92624,92626,92628,92630,92632,92634,92636,92646,92648,92654,92656,92658,92660,92662],{},[195,92607,92608,92610],{},[35,92609,199],{},[35,92611,37],{},[110,92613,113],{"stretchy":112},[195,92615,92616,92618],{},[35,92617,206],{},[35,92619,82296],{},[35,92621,210],{"mathvariant":209},[35,92623,213],{},[110,92625,120],{"stretchy":112},[110,92627,1029],{},[115,92629,126],{},[1297,92631,4283],{},[110,92633,4286],{},[1297,92635,4283],{},[195,92637,92638,92640],{},[35,92639,199],{},[32,92641,92642,92644],{},[35,92643,5392],{},[35,92645,34850],{},[110,92647,113],{"stretchy":112},[195,92649,92650,92652],{},[35,92651,206],{},[35,92653,82296],{},[110,92655,551],{"separator":46},[35,92657,213],{},[110,92659,120],{"stretchy":112},[110,92661,1029],{},[115,92663,126],{},[39,92665,92666],{"encoding":41},"D_f(P_n\\|Q)\\to0\\ \\Longrightarrow\\ D_{TV}(P_n,Q)\\to0",[15,92668,92670,92777,92802,92918],{"className":92669,"ariaHidden":46},[45],[15,92671,92673,92676,92716,92719,92759,92762,92765,92768,92771,92774],{"className":92672},[50],[15,92674],{"className":92675,"style":270},[54],[15,92677,92679,92682],{"className":92678},[59],[15,92680,199],{"className":92681,"style":277},[59,60],[15,92683,92685],{"className":92684},[281],[15,92686,92688,92708],{"className":92687},[285,286],[15,92689,92691,92705],{"className":92690},[290],[15,92692,92694],{"className":92693,"style":295},[294],[15,92695,92696,92699],{"style":298},[15,92697],{"className":92698,"style":303},[302],[15,92700,92702],{"className":92701},[307,308,309,310],[15,92703,37],{"className":92704,"style":61},[59,60,310],[15,92706,318],{"className":92707},[317],[15,92709,92711],{"className":92710},[290],[15,92712,92714],{"className":92713,"style":325},[294],[15,92715],{},[15,92717,113],{"className":92718},[146],[15,92720,92722,92725],{"className":92721},[59],[15,92723,206],{"className":92724,"style":334},[59,60],[15,92726,92728],{"className":92727},[281],[15,92729,92731,92751],{"className":92730},[285,286],[15,92732,92734,92748],{"className":92733},[290],[15,92735,92737],{"className":92736,"style":44929},[294],[15,92738,92739,92742],{"style":11136},[15,92740],{"className":92741,"style":303},[302],[15,92743,92745],{"className":92744},[307,308,309,310],[15,92746,82296],{"className":92747},[59,60,310],[15,92749,318],{"className":92750},[317],[15,92752,92754],{"className":92753},[290],[15,92755,92757],{"className":92756,"style":7968},[294],[15,92758],{},[15,92760,210],{"className":92761},[59],[15,92763,213],{"className":92764},[59,60],[15,92766,120],{"className":92767},[153],[15,92769],{"className":92770,"style":158},[157],[15,92772,1029],{"className":92773},[162],[15,92775],{"className":92776,"style":158},[157],[15,92778,92780,92784,92787,92790,92793,92796,92799],{"className":92779},[50],[15,92781],{"className":92782,"style":92783},[54],"height:0.6684em;vertical-align:-0.024em;",[15,92785,126],{"className":92786},[59],[15,92788,4283],{"className":92789},[157],[15,92791],{"className":92792,"style":158},[157],[15,92794,4286],{"className":92795},[162],[15,92797,4283],{"className":92798},[157],[15,92800],{"className":92801,"style":158},[157],[15,92803,92805,92808,92854,92857,92897,92900,92903,92906,92909,92912,92915],{"className":92804},[50],[15,92806],{"className":92807,"style":139},[54],[15,92809,92811,92814],{"className":92810},[59],[15,92812,199],{"className":92813,"style":277},[59,60],[15,92815,92817],{"className":92816},[281],[15,92818,92820,92846],{"className":92819},[285,286],[15,92821,92823,92843],{"className":92822},[290],[15,92824,92826],{"className":92825,"style":379},[294],[15,92827,92828,92831],{"style":298},[15,92829],{"className":92830,"style":303},[302],[15,92832,92834],{"className":92833},[307,308,309,310],[15,92835,92837,92840],{"className":92836},[59,310],[15,92838,5392],{"className":92839,"style":334},[59,60,310],[15,92841,34850],{"className":92842,"style":2587},[59,60,310],[15,92844,318],{"className":92845},[317],[15,92847,92849],{"className":92848},[290],[15,92850,92852],{"className":92851,"style":7968},[294],[15,92853],{},[15,92855,113],{"className":92856},[146],[15,92858,92860,92863],{"className":92859},[59],[15,92861,206],{"className":92862,"style":334},[59,60],[15,92864,92866],{"className":92865},[281],[15,92867,92869,92889],{"className":92868},[285,286],[15,92870,92872,92886],{"className":92871},[290],[15,92873,92875],{"className":92874,"style":44929},[294],[15,92876,92877,92880],{"style":11136},[15,92878],{"className":92879,"style":303},[302],[15,92881,92883],{"className":92882},[307,308,309,310],[15,92884,82296],{"className":92885},[59,60,310],[15,92887,318],{"className":92888},[317],[15,92890,92892],{"className":92891},[290],[15,92893,92895],{"className":92894,"style":7968},[294],[15,92896],{},[15,92898,551],{"className":92899},[573],[15,92901],{"className":92902,"style":406},[157],[15,92904,213],{"className":92905},[59,60],[15,92907,120],{"className":92908},[153],[15,92910],{"className":92911,"style":158},[157],[15,92913,1029],{"className":92914},[162],[15,92916],{"className":92917,"style":158},[157],[15,92919,92921,92924],{"className":92920},[50],[15,92922],{"className":92923,"style":172},[54],[15,92925,126],{"className":92926},[59],"。每个适度正则的 f-散度都自带一个连续的 TV 下界函数 ",[15,92929,92931,92949],{"className":92930,"translate":19},[18],[15,92932,92934],{"className":92933},[23],[25,92935,92936],{"xmlns":27},[29,92937,92938,92946],{},[32,92939,92940],{},[195,92941,92942,92944],{},[35,92943,4158],{},[35,92945,37],{},[39,92947,92948],{"encoding":41},"g_f",[15,92950,92952],{"className":92951,"ariaHidden":46},[45],[15,92953,92955,92959],{"className":92954},[50],[15,92956],{"className":92957,"style":92958},[54],"height:0.7167em;vertical-align:-0.2861em;",[15,92960,92962,92965],{"className":92961},[59],[15,92963,4158],{"className":92964,"style":981},[59,60],[15,92966,92968],{"className":92967},[281],[15,92969,92971,92991],{"className":92970},[285,286],[15,92972,92974,92988],{"className":92973},[290],[15,92975,92977],{"className":92976,"style":295},[294],[15,92978,92979,92982],{"style":18843},[15,92980],{"className":92981,"style":303},[302],[15,92983,92985],{"className":92984},[307,308,309,310],[15,92986,37],{"className":92987,"style":61},[59,60,310],[15,92989,318],{"className":92990},[317],[15,92992,92994],{"className":92993},[290],[15,92995,92997],{"className":92996,"style":325},[294],[15,92998],{},"（Vajda \u002F Fedotov–Harremoës），",[15,93001,93003,93031],{"className":93002,"translate":19},[18],[15,93004,93006],{"className":93005},[23],[25,93007,93008],{"xmlns":27},[29,93009,93010,93028],{},[32,93011,93012,93018,93020,93022,93024,93026],{},[195,93013,93014,93016],{},[35,93015,4158],{},[35,93017,37],{},[110,93019,113],{"stretchy":112},[115,93021,126],{},[110,93023,120],{"stretchy":112},[110,93025,123],{},[115,93027,126],{},[39,93029,93030],{"encoding":41},"g_f(0)=0",[15,93032,93034,93098],{"className":93033,"ariaHidden":46},[45],[15,93035,93037,93040,93080,93083,93086,93089,93092,93095],{"className":93036},[50],[15,93038],{"className":93039,"style":270},[54],[15,93041,93043,93046],{"className":93042},[59],[15,93044,4158],{"className":93045,"style":981},[59,60],[15,93047,93049],{"className":93048},[281],[15,93050,93052,93072],{"className":93051},[285,286],[15,93053,93055,93069],{"className":93054},[290],[15,93056,93058],{"className":93057,"style":295},[294],[15,93059,93060,93063],{"style":18843},[15,93061],{"className":93062,"style":303},[302],[15,93064,93066],{"className":93065},[307,308,309,310],[15,93067,37],{"className":93068,"style":61},[59,60,310],[15,93070,318],{"className":93071},[317],[15,93073,93075],{"className":93074},[290],[15,93076,93078],{"className":93077,"style":325},[294],[15,93079],{},[15,93081,113],{"className":93082},[146],[15,93084,126],{"className":93085},[59],[15,93087,120],{"className":93088},[153],[15,93090],{"className":93091,"style":158},[157],[15,93093,123],{"className":93094},[162],[15,93096],{"className":93097,"style":158},[157],[15,93099,93101,93104],{"className":93100},[50],[15,93102],{"className":93103,"style":172},[54],[15,93105,126],{"className":93106},[59],[15,93108,93110,93150],{"className":93109,"translate":19},[18],[15,93111,93113],{"className":93112},[23],[25,93114,93115],{"xmlns":27},[29,93116,93117,93147],{},[32,93118,93119,93125,93127,93129,93131,93133,93135,93137,93139,93141,93143,93145],{},[195,93120,93121,93123],{},[35,93122,4158],{},[35,93124,37],{},[110,93126,113],{"stretchy":112},[35,93128,769],{},[110,93130,120],{"stretchy":112},[110,93132,2903],{},[115,93134,126],{},[1297,93136,4283],{},[110,93138,113],{"stretchy":112},[35,93140,769],{},[110,93142,2903],{},[115,93144,126],{},[110,93146,120],{"stretchy":112},[39,93148,93149],{"encoding":41},"g_f(t)>0\\ (t>0)",[15,93151,93153,93217,93244],{"className":93152,"ariaHidden":46},[45],[15,93154,93156,93159,93199,93202,93205,93208,93211,93214],{"className":93155},[50],[15,93157],{"className":93158,"style":270},[54],[15,93160,93162,93165],{"className":93161},[59],[15,93163,4158],{"className":93164,"style":981},[59,60],[15,93166,93168],{"className":93167},[281],[15,93169,93171,93191],{"className":93170},[285,286],[15,93172,93174,93188],{"className":93173},[290],[15,93175,93177],{"className":93176,"style":295},[294],[15,93178,93179,93182],{"style":18843},[15,93180],{"className":93181,"style":303},[302],[15,93183,93185],{"className":93184},[307,308,309,310],[15,93186,37],{"className":93187,"style":61},[59,60,310],[15,93189,318],{"className":93190},[317],[15,93192,93194],{"className":93193},[290],[15,93195,93197],{"className":93196,"style":325},[294],[15,93198],{},[15,93200,113],{"className":93201},[146],[15,93203,769],{"className":93204},[59,60],[15,93206,120],{"className":93207},[153],[15,93209],{"className":93210,"style":158},[157],[15,93212,2903],{"className":93213},[162],[15,93215],{"className":93216,"style":158},[157],[15,93218,93220,93223,93226,93229,93232,93235,93238,93241],{"className":93219},[50],[15,93221],{"className":93222,"style":139},[54],[15,93224,126],{"className":93225},[59],[15,93227,4283],{"className":93228},[157],[15,93230,113],{"className":93231},[146],[15,93233,769],{"className":93234},[59,60],[15,93236],{"className":93237,"style":158},[157],[15,93239,2903],{"className":93240},[162],[15,93242],{"className":93243,"style":158},[157],[15,93245,93247,93250,93253],{"className":93246},[50],[15,93248],{"className":93249,"style":139},[54],[15,93251,126],{"className":93252},[59],[15,93254,120],{"className":93255},[153],"，使 ",[15,93258,93260,93296],{"className":93259,"translate":19},[18],[15,93261,93263],{"className":93262},[23],[25,93264,93265],{"xmlns":27},[29,93266,93267,93293],{},[32,93268,93269,93275,93277,93283,93285,93291],{},[195,93270,93271,93273],{},[35,93272,199],{},[35,93274,37],{},[110,93276,6928],{},[195,93278,93279,93281],{},[35,93280,4158],{},[35,93282,37],{},[110,93284,113],{"stretchy":112},[32,93286,93287,93289],{},[35,93288,5392],{"mathvariant":209},[35,93290,34850],{"mathvariant":209},[110,93292,120],{"stretchy":112},[39,93294,93295],{"encoding":41},"D_f\\ge g_f(\\mathrm{TV})",[15,93297,93299,93354],{"className":93298,"ariaHidden":46},[45],[15,93300,93302,93305,93345,93348,93351],{"className":93301},[50],[15,93303],{"className":93304,"style":4032},[54],[15,93306,93308,93311],{"className":93307},[59],[15,93309,199],{"className":93310,"style":277},[59,60],[15,93312,93314],{"className":93313},[281],[15,93315,93317,93337],{"className":93316},[285,286],[15,93318,93320,93334],{"className":93319},[290],[15,93321,93323],{"className":93322,"style":295},[294],[15,93324,93325,93328],{"style":298},[15,93326],{"className":93327,"style":303},[302],[15,93329,93331],{"className":93330},[307,308,309,310],[15,93332,37],{"className":93333,"style":61},[59,60,310],[15,93335,318],{"className":93336},[317],[15,93338,93340],{"className":93339},[290],[15,93341,93343],{"className":93342,"style":325},[294],[15,93344],{},[15,93346],{"className":93347,"style":158},[157],[15,93349,6928],{"className":93350},[162],[15,93352],{"className":93353,"style":158},[157],[15,93355,93357,93360,93400,93403,93409],{"className":93356},[50],[15,93358],{"className":93359,"style":270},[54],[15,93361,93363,93366],{"className":93362},[59],[15,93364,4158],{"className":93365,"style":981},[59,60],[15,93367,93369],{"className":93368},[281],[15,93370,93372,93392],{"className":93371},[285,286],[15,93373,93375,93389],{"className":93374},[290],[15,93376,93378],{"className":93377,"style":295},[294],[15,93379,93380,93383],{"style":18843},[15,93381],{"className":93382,"style":303},[302],[15,93384,93386],{"className":93385},[307,308,309,310],[15,93387,37],{"className":93388,"style":61},[59,60,310],[15,93390,318],{"className":93391},[317],[15,93393,93395],{"className":93394},[290],[15,93396,93398],{"className":93397,"style":325},[294],[15,93399],{},[15,93401,113],{"className":93402},[146],[15,93404,93406],{"className":93405},[59],[15,93407,86762],{"className":93408,"style":4157},[59,32662],[15,93410,120],{"className":93411},[153],"；常用成员的具体形式：KL 给 ",[15,93414,93416,93454],{"className":93415,"translate":19},[18],[15,93417,93419],{"className":93418},[23],[25,93420,93421],{"xmlns":27},[29,93422,93423,93451],{},[32,93424,93425,93427,93429,93439,93441],{},[115,93426,2463],{},[1297,93428,1299],{},[6814,93430,93431,93437],{},[32,93432,93433,93435],{},[35,93434,5392],{"mathvariant":209},[35,93436,34850],{"mathvariant":209},[115,93438,2463],{},[110,93440,9952],{},[195,93442,93443,93445],{},[35,93444,199],{},[32,93446,93447,93449],{},[35,93448,10694],{},[35,93450,21893],{},[39,93452,93453],{"encoding":41},"2\\,\\mathrm{TV}^2\\le D_{KL}",[15,93455,93457,93511],{"className":93456,"ariaHidden":46},[45],[15,93458,93460,93464,93467,93470,93502,93505,93508],{"className":93459},[50],[15,93461],{"className":93462,"style":93463},[54],"height:1.0233em;vertical-align:-0.136em;",[15,93465,2463],{"className":93466},[59],[15,93468],{"className":93469,"style":406},[157],[15,93471,93473,93479],{"className":93472},[59],[15,93474,93476],{"className":93475},[59],[15,93477,86762],{"className":93478,"style":4157},[59,32662],[15,93480,93482],{"className":93481},[281],[15,93483,93485],{"className":93484},[285],[15,93486,93488],{"className":93487},[290],[15,93489,93491],{"className":93490,"style":88376},[294],[15,93492,93493,93496],{"style":88406},[15,93494],{"className":93495,"style":303},[302],[15,93497,93499],{"className":93498},[307,308,309,310],[15,93500,2463],{"className":93501},[59,310],[15,93503],{"className":93504,"style":158},[157],[15,93506,9952],{"className":93507},[162],[15,93509],{"className":93510,"style":158},[157],[15,93512,93514,93517],{"className":93513},[50],[15,93515],{"className":93516,"style":15961},[54],[15,93518,93520,93523],{"className":93519},[59],[15,93521,199],{"className":93522,"style":277},[59,60],[15,93524,93526],{"className":93525},[281],[15,93527,93529,93555],{"className":93528},[285,286],[15,93530,93532,93552],{"className":93531},[290],[15,93533,93535],{"className":93534,"style":379},[294],[15,93536,93537,93540],{"style":298},[15,93538],{"className":93539,"style":303},[302],[15,93541,93543],{"className":93542},[307,308,309,310],[15,93544,93546,93549],{"className":93545},[59,310],[15,93547,10694],{"className":93548,"style":10782},[59,60,310],[15,93550,21893],{"className":93551},[59,60,310],[15,93553,318],{"className":93554},[317],[15,93556,93558],{"className":93557},[290],[15,93559,93561],{"className":93560,"style":7968},[294],[15,93562],{},"（Pinsker），",[15,93565,93567,93584],{"className":93566,"translate":19},[18],[15,93568,93570],{"className":93569},[23],[25,93571,93572],{"xmlns":27},[29,93573,93574,93582],{},[32,93575,93576],{},[6814,93577,93578,93580],{},[35,93579,37449],{},[115,93581,2463],{},[39,93583,40394],{"encoding":41},[15,93585,93587],{"className":93586,"ariaHidden":46},[45],[15,93588,93590,93593],{"className":93589},[50],[15,93591],{"className":93592,"style":40404},[54],[15,93594,93596,93599],{"className":93595},[59],[15,93597,37449],{"className":93598},[59,60],[15,93600,93602],{"className":93601},[281],[15,93603,93605],{"className":93604},[285],[15,93606,93608],{"className":93607},[290],[15,93609,93611],{"className":93610,"style":20028},[294],[15,93612,93613,93616],{"style":6865},[15,93614],{"className":93615,"style":303},[302],[15,93617,93619],{"className":93618},[307,308,309,310],[15,93620,2463],{"className":93621},[59,310]," 给 ",[15,93624,93626,93660],{"className":93625,"translate":19},[18],[15,93627,93629],{"className":93628},[23],[25,93630,93631],{"xmlns":27},[29,93632,93633,93657],{},[32,93634,93635,93641,93643,93645,93647],{},[6814,93636,93637,93639],{},[35,93638,37449],{},[115,93640,2463],{},[110,93642,6928],{},[115,93644,38989],{},[1297,93646,1299],{},[6814,93648,93649,93655],{},[32,93650,93651,93653],{},[35,93652,5392],{"mathvariant":209},[35,93654,34850],{"mathvariant":209},[115,93656,2463],{},[39,93658,93659],{"encoding":41},"\\chi^2\\ge4\\,\\mathrm{TV}^2",[15,93661,93663,93707],{"className":93662,"ariaHidden":46},[45],[15,93664,93666,93669,93698,93701,93704],{"className":93665},[50],[15,93667],{"className":93668,"style":40404},[54],[15,93670,93672,93675],{"className":93671},[59],[15,93673,37449],{"className":93674},[59,60],[15,93676,93678],{"className":93677},[281],[15,93679,93681],{"className":93680},[285],[15,93682,93684],{"className":93683},[290],[15,93685,93687],{"className":93686,"style":20028},[294],[15,93688,93689,93692],{"style":6865},[15,93690],{"className":93691,"style":303},[302],[15,93693,93695],{"className":93694},[307,308,309,310],[15,93696,2463],{"className":93697},[59,310],[15,93699],{"className":93700,"style":158},[157],[15,93702,6928],{"className":93703},[162],[15,93705],{"className":93706,"style":158},[157],[15,93708,93710,93713,93716,93719],{"className":93709},[50],[15,93711],{"className":93712,"style":88376},[54],[15,93714,38989],{"className":93715},[59],[15,93717],{"className":93718,"style":406},[157],[15,93720,93722,93728],{"className":93721},[59],[15,93723,93725],{"className":93724},[59],[15,93726,86762],{"className":93727,"style":4157},[59,32662],[15,93729,93731],{"className":93730},[281],[15,93732,93734],{"className":93733},[285],[15,93735,93737],{"className":93736},[290],[15,93738,93740],{"className":93739,"style":88376},[294],[15,93741,93742,93745],{"style":88406},[15,93743],{"className":93744,"style":303},[302],[15,93746,93748],{"className":93747},[307,308,309,310],[15,93749,2463],{"className":93750},[59,310],"，Hellinger",[15,93753,93755,93772],{"className":93754,"translate":19},[18],[15,93756,93758],{"className":93757},[23],[25,93759,93760],{"xmlns":27},[29,93761,93762,93770],{},[32,93763,93764],{},[6814,93765,93766,93768],{},[32,93767],{},[115,93769,2463],{},[39,93771,44269],{"encoding":41},[15,93773,93775],{"className":93774,"ariaHidden":46},[45],[15,93776,93778,93781],{"className":93777},[50],[15,93779],{"className":93780,"style":20028},[54],[15,93782,93784,93786],{"className":93783},[59],[15,93785],{},[15,93787,93789],{"className":93788},[281],[15,93790,93792],{"className":93791},[285],[15,93793,93795],{"className":93794},[290],[15,93796,93798],{"className":93797,"style":20028},[294],[15,93799,93800,93803],{"style":6865},[15,93801],{"className":93802,"style":303},[302],[15,93804,93806],{"className":93805},[307,308,309,310],[15,93807,2463],{"className":93808},[59,310]," 经由 ",[15,93811,93813,93871],{"className":93812,"translate":19},[18],[15,93814,93816],{"className":93815},[23],[25,93817,93818],{"xmlns":27},[29,93819,93820,93868],{},[32,93821,93822,93828,93830,93854,93856],{},[32,93823,93824,93826],{},[35,93825,5392],{"mathvariant":209},[35,93827,34850],{"mathvariant":209},[110,93829,9952],{},[34339,93831,93832],{},[32,93833,93834,93840,93842,93844,93846,93852],{},[6814,93835,93836,93838],{},[35,93837,33884],{},[115,93839,2463],{},[110,93841,113],{"stretchy":112},[115,93843,2463],{},[110,93845,4813],{},[6814,93847,93848,93850],{},[35,93849,33884],{},[115,93851,2463],{},[110,93853,120],{"stretchy":112},[110,93855,9952],{},[34339,93857,93858],{},[32,93859,93860,93862],{},[115,93861,2463],{},[6814,93863,93864,93866],{},[35,93865,33884],{},[115,93867,2463],{},[39,93869,93870],{"encoding":41},"\\mathrm{TV}\\le\\sqrt{H^2(2-H^2)}\\le\\sqrt{2H^2}",[15,93872,93874,93895,94030],{"className":93873,"ariaHidden":46},[45],[15,93875,93877,93880,93886,93889,93892],{"className":93876},[50],[15,93878],{"className":93879,"style":88354},[54],[15,93881,93883],{"className":93882},[59],[15,93884,86762],{"className":93885,"style":4157},[59,32662],[15,93887],{"className":93888,"style":158},[157],[15,93890,9952],{"className":93891},[162],[15,93893],{"className":93894,"style":158},[157],[15,93896,93898,93901,94021,94024,94027],{"className":93897},[50],[15,93899],{"className":93900,"style":91871},[54],[15,93902,93904],{"className":93903},[59,34367],[15,93905,93907,94013],{"className":93906},[285,286],[15,93908,93910,94010],{"className":93909},[290],[15,93911,93913,93998],{"className":93912,"style":91884},[294],[15,93914,93916,93919],{"className":93915,"style":83536},[6307],[15,93917],{"className":93918,"style":14846},[302],[15,93920,93922,93951,93954,93957,93960,93963,93966,93995],{"className":93921,"style":41161},[59],[15,93923,93925,93928],{"className":93924},[59],[15,93926,33884],{"className":93927,"style":34038},[59,60],[15,93929,93931],{"className":93930},[281],[15,93932,93934],{"className":93933},[285],[15,93935,93937],{"className":93936},[290],[15,93938,93940],{"className":93939,"style":45032},[294],[15,93941,93942,93945],{"style":45035},[15,93943],{"className":93944,"style":303},[302],[15,93946,93948],{"className":93947},[307,308,309,310],[15,93949,2463],{"className":93950},[59,310],[15,93952,113],{"className":93953},[146],[15,93955,2463],{"className":93956},[59],[15,93958],{"className":93959,"style":2587},[157],[15,93961,4813],{"className":93962},[2591],[15,93964],{"className":93965,"style":2587},[157],[15,93967,93969,93972],{"className":93968},[59],[15,93970,33884],{"className":93971,"style":34038},[59,60],[15,93973,93975],{"className":93974},[281],[15,93976,93978],{"className":93977},[285],[15,93979,93981],{"className":93980},[290],[15,93982,93984],{"className":93983,"style":45032},[294],[15,93985,93986,93989],{"style":45035},[15,93987],{"className":93988,"style":303},[302],[15,93990,93992],{"className":93991},[307,308,309,310],[15,93993,2463],{"className":93994},[59,310],[15,93996,120],{"className":93997},[153],[15,93999,94000,94003],{"style":91972},[15,94001],{"className":94002,"style":14846},[302],[15,94004,94006],{"className":94005,"style":83628},[34443],[6323,94007,94008],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,94009],{"d":83635},[15,94011,318],{"className":94012},[317],[15,94014,94016],{"className":94015},[290],[15,94017,94019],{"className":94018,"style":91992},[294],[15,94020],{},[15,94022],{"className":94023,"style":158},[157],[15,94025,9952],{"className":94026},[162],[15,94028],{"className":94029,"style":158},[157],[15,94031,94033,94037],{"className":94032},[50],[15,94034],{"className":94035,"style":94036},[54],"height:1.04em;vertical-align:-0.0849em;",[15,94038,94040],{"className":94039},[59,34367],[15,94041,94043,94107],{"className":94042},[285,286],[15,94044,94046,94104],{"className":94045},[290],[15,94047,94050,94091],{"className":94048,"style":94049},[294],"height:0.9551em;",[15,94051,94053,94056],{"className":94052,"style":11863},[6307],[15,94054],{"className":94055,"style":461},[302],[15,94057,94059,94062],{"className":94058,"style":34387},[59],[15,94060,2463],{"className":94061},[59],[15,94063,94065,94068],{"className":94064},[59],[15,94066,33884],{"className":94067,"style":34038},[59,60],[15,94069,94071],{"className":94070},[281],[15,94072,94074],{"className":94073},[285],[15,94075,94077],{"className":94076},[290],[15,94078,94080],{"className":94079,"style":45032},[294],[15,94081,94082,94085],{"style":45035},[15,94083],{"className":94084,"style":303},[302],[15,94086,94088],{"className":94087},[307,308,309,310],[15,94089,2463],{"className":94090},[59,310],[15,94092,94094,94097],{"style":94093},"top:-2.9151em;",[15,94095],{"className":94096,"style":461},[302],[15,94098,94100],{"className":94099,"style":34444},[34443],[6323,94101,94102],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,94103],{"d":34451},[15,94105,318],{"className":94106},[317],[15,94108,94110],{"className":94109},[290],[15,94111,94114],{"className":94112,"style":94113},[294],"height:0.0849em;",[15,94115],{},"，TV 本身平凡。",[11,94118,94119,6494,94122,94454,94455,94458,94459,94510,94511,2745,94564,94891,94892,5645,95074,95206,95207,95397,95398,95608],{},[1225,94120,94121],{},"(b)（\"上去\"方向，需要条件）",[15,94123,94125,94195],{"className":94124,"translate":19},[18],[15,94126,94128],{"className":94127},[23],[25,94129,94130],{"xmlns":27},[29,94131,94132,94192],{},[32,94133,94134,94144,94146,94152,94154,94156,94158,94160,94162,94164,94166,94168,94174,94176,94182,94184,94186,94188,94190],{},[195,94135,94136,94138],{},[35,94137,199],{},[32,94139,94140,94142],{},[35,94141,5392],{},[35,94143,34850],{},[110,94145,113],{"stretchy":112},[195,94147,94148,94150],{},[35,94149,206],{},[35,94151,82296],{},[110,94153,551],{"separator":46},[35,94155,213],{},[110,94157,120],{"stretchy":112},[110,94159,1029],{},[115,94161,126],{},[1297,94163,4283],{},[110,94165,4286],{},[1297,94167,4283],{},[195,94169,94170,94172],{},[35,94171,199],{},[35,94173,37],{},[110,94175,113],{"stretchy":112},[195,94177,94178,94180],{},[35,94179,206],{},[35,94181,82296],{},[35,94183,210],{"mathvariant":209},[35,94185,213],{},[110,94187,120],{"stretchy":112},[110,94189,1029],{},[115,94191,126],{},[39,94193,94194],{"encoding":41},"D_{TV}(P_n,Q)\\to0\\ \\Longrightarrow\\ D_f(P_n\\|Q)\\to0",[15,94196,94198,94314,94338,94445],{"className":94197,"ariaHidden":46},[45],[15,94199,94201,94204,94250,94253,94293,94296,94299,94302,94305,94308,94311],{"className":94200},[50],[15,94202],{"className":94203,"style":139},[54],[15,94205,94207,94210],{"className":94206},[59],[15,94208,199],{"className":94209,"style":277},[59,60],[15,94211,94213],{"className":94212},[281],[15,94214,94216,94242],{"className":94215},[285,286],[15,94217,94219,94239],{"className":94218},[290],[15,94220,94222],{"className":94221,"style":379},[294],[15,94223,94224,94227],{"style":298},[15,94225],{"className":94226,"style":303},[302],[15,94228,94230],{"className":94229},[307,308,309,310],[15,94231,94233,94236],{"className":94232},[59,310],[15,94234,5392],{"className":94235,"style":334},[59,60,310],[15,94237,34850],{"className":94238,"style":2587},[59,60,310],[15,94240,318],{"className":94241},[317],[15,94243,94245],{"className":94244},[290],[15,94246,94248],{"className":94247,"style":7968},[294],[15,94249],{},[15,94251,113],{"className":94252},[146],[15,94254,94256,94259],{"className":94255},[59],[15,94257,206],{"className":94258,"style":334},[59,60],[15,94260,94262],{"className":94261},[281],[15,94263,94265,94285],{"className":94264},[285,286],[15,94266,94268,94282],{"className":94267},[290],[15,94269,94271],{"className":94270,"style":44929},[294],[15,94272,94273,94276],{"style":11136},[15,94274],{"className":94275,"style":303},[302],[15,94277,94279],{"className":94278},[307,308,309,310],[15,94280,82296],{"className":94281},[59,60,310],[15,94283,318],{"className":94284},[317],[15,94286,94288],{"className":94287},[290],[15,94289,94291],{"className":94290,"style":7968},[294],[15,94292],{},[15,94294,551],{"className":94295},[573],[15,94297],{"className":94298,"style":406},[157],[15,94300,213],{"className":94301},[59,60],[15,94303,120],{"className":94304},[153],[15,94306],{"className":94307,"style":158},[157],[15,94309,1029],{"className":94310},[162],[15,94312],{"className":94313,"style":158},[157],[15,94315,94317,94320,94323,94326,94329,94332,94335],{"className":94316},[50],[15,94318],{"className":94319,"style":92783},[54],[15,94321,126],{"className":94322},[59],[15,94324,4283],{"className":94325},[157],[15,94327],{"className":94328,"style":158},[157],[15,94330,4286],{"className":94331},[162],[15,94333,4283],{"className":94334},[157],[15,94336],{"className":94337,"style":158},[157],[15,94339,94341,94344,94384,94387,94427,94430,94433,94436,94439,94442],{"className":94340},[50],[15,94342],{"className":94343,"style":270},[54],[15,94345,94347,94350],{"className":94346},[59],[15,94348,199],{"className":94349,"style":277},[59,60],[15,94351,94353],{"className":94352},[281],[15,94354,94356,94376],{"className":94355},[285,286],[15,94357,94359,94373],{"className":94358},[290],[15,94360,94362],{"className":94361,"style":295},[294],[15,94363,94364,94367],{"style":298},[15,94365],{"className":94366,"style":303},[302],[15,94368,94370],{"className":94369},[307,308,309,310],[15,94371,37],{"className":94372,"style":61},[59,60,310],[15,94374,318],{"className":94375},[317],[15,94377,94379],{"className":94378},[290],[15,94380,94382],{"className":94381,"style":325},[294],[15,94383],{},[15,94385,113],{"className":94386},[146],[15,94388,94390,94393],{"className":94389},[59],[15,94391,206],{"className":94392,"style":334},[59,60],[15,94394,94396],{"className":94395},[281],[15,94397,94399,94419],{"className":94398},[285,286],[15,94400,94402,94416],{"className":94401},[290],[15,94403,94405],{"className":94404,"style":44929},[294],[15,94406,94407,94410],{"style":11136},[15,94408],{"className":94409,"style":303},[302],[15,94411,94413],{"className":94412},[307,308,309,310],[15,94414,82296],{"className":94415},[59,60,310],[15,94417,318],{"className":94418},[317],[15,94420,94422],{"className":94421},[290],[15,94423,94425],{"className":94424,"style":7968},[294],[15,94426],{},[15,94428,210],{"className":94429},[59],[15,94431,213],{"className":94432},[59,60],[15,94434,120],{"className":94435},[153],[15,94437],{"className":94438,"style":158},[157],[15,94440,1029],{"className":94441},[162],[15,94443],{"className":94444,"style":158},[157],[15,94446,94448,94451],{"className":94447},[50],[15,94449],{"className":94450,"style":172},[54],[15,94452,126],{"className":94453},[59]," 一般",[1225,94456,94457],{},"不成立","。反例：在 ",[15,94460,94462,94483],{"className":94461,"translate":19},[18],[15,94463,94465],{"className":94464},[23],[25,94466,94467],{"xmlns":27},[29,94468,94469,94481],{},[32,94470,94471,94473,94475,94477,94479],{},[110,94472,230],{"stretchy":112},[115,94474,126],{},[110,94476,551],{"separator":46},[115,94478,117],{},[110,94480,257],{"stretchy":112},[39,94482,36814],{"encoding":41},[15,94484,94486],{"className":94485,"ariaHidden":46},[45],[15,94487,94489,94492,94495,94498,94501,94504,94507],{"className":94488},[50],[15,94490],{"className":94491,"style":139},[54],[15,94493,230],{"className":94494},[146],[15,94496,126],{"className":94497},[59],[15,94499,551],{"className":94500},[573],[15,94502],{"className":94503,"style":406},[157],[15,94505,117],{"className":94506},[59],[15,94508,257],{"className":94509},[153]," 上取 ",[15,94512,94514,94533],{"className":94513,"translate":19},[18],[15,94515,94517],{"className":94516},[23],[25,94518,94519],{"xmlns":27},[29,94520,94521,94530],{},[32,94522,94523,94525,94528],{},[35,94524,11],{},[110,94526,94527],{},"≡",[115,94529,117],{},[39,94531,94532],{"encoding":41},"p\\equiv1",[15,94534,94536,94555],{"className":94535,"ariaHidden":46},[45],[15,94537,94539,94543,94546,94549,94552],{"className":94538},[50],[15,94540],{"className":94541,"style":94542},[54],"height:0.6582em;vertical-align:-0.1944em;",[15,94544,11],{"className":94545},[59,60],[15,94547],{"className":94548,"style":158},[157],[15,94550,94527],{"className":94551},[162],[15,94553],{"className":94554,"style":158},[157],[15,94556,94558,94561],{"className":94557},[50],[15,94559],{"className":94560,"style":172},[54],[15,94562,117],{"className":94563},[59],[15,94565,94567,94638],{"className":94566,"translate":19},[18],[15,94568,94570],{"className":94569},[23],[25,94571,94572],{"xmlns":27},[29,94573,94574,94635],{},[32,94575,94576,94582,94584,94586,94588,94590,94596,94598,94600,94602,94608,94610,94621,94623,94625,94627,94633],{},[195,94577,94578,94580],{},[35,94579,944],{},[35,94581,82296],{},[110,94583,123],{},[110,94585,113],{"stretchy":112},[115,94587,117],{},[110,94589,4813],{},[195,94591,94592,94594],{},[35,94593,15712],{},[35,94595,82296],{},[110,94597,120],{"stretchy":112},[35,94599,11],{},[110,94601,2470],{},[195,94603,94604,94606],{},[35,94605,15712],{},[35,94607,82296],{},[1297,94609,1299],{},[32,94611,94612,94615,94617,94619],{},[35,94613,94614],{"mathvariant":209},"U",[35,94616,82296],{"mathvariant":209},[35,94618,11963],{"mathvariant":209},[35,94620,37],{"mathvariant":209},[110,94622,230],{"stretchy":112},[115,94624,126],{},[110,94626,551],{"separator":46},[195,94628,94629,94631],{},[35,94630,38662],{},[35,94632,82296],{},[110,94634,257],{"stretchy":112},[39,94636,94637],{"encoding":41},"q_n=(1-\\delta_n)p+\\delta_n\\,\\mathrm{Unif}[0,\\varepsilon_n]",[15,94639,94641,94696,94717,94779],{"className":94640,"ariaHidden":46},[45],[15,94642,94644,94647,94687,94690,94693],{"className":94643},[50],[15,94645],{"className":94646,"style":2276},[54],[15,94648,94650,94653],{"className":94649},[59],[15,94651,944],{"className":94652,"style":981},[59,60],[15,94654,94656],{"className":94655},[281],[15,94657,94659,94679],{"className":94658},[285,286],[15,94660,94662,94676],{"className":94661},[290],[15,94663,94665],{"className":94664,"style":44929},[294],[15,94666,94667,94670],{"style":18843},[15,94668],{"className":94669,"style":303},[302],[15,94671,94673],{"className":94672},[307,308,309,310],[15,94674,82296],{"className":94675},[59,60,310],[15,94677,318],{"className":94678},[317],[15,94680,94682],{"className":94681},[290],[15,94683,94685],{"className":94684,"style":7968},[294],[15,94686],{},[15,94688],{"className":94689,"style":158},[157],[15,94691,123],{"className":94692},[162],[15,94694],{"className":94695,"style":158},[157],[15,94697,94699,94702,94705,94708,94711,94714],{"className":94698},[50],[15,94700],{"className":94701,"style":139},[54],[15,94703,113],{"className":94704},[146],[15,94706,117],{"className":94707},[59],[15,94709],{"className":94710,"style":2587},[157],[15,94712,4813],{"className":94713},[2591],[15,94715],{"className":94716,"style":2587},[157],[15,94718,94720,94723,94764,94767,94770,94773,94776],{"className":94719},[50],[15,94721],{"className":94722,"style":139},[54],[15,94724,94726,94729],{"className":94725},[59],[15,94727,15712],{"className":94728,"style":15761},[59,60],[15,94730,94732],{"className":94731},[281],[15,94733,94735,94756],{"className":94734},[285,286],[15,94736,94738,94753],{"className":94737},[290],[15,94739,94741],{"className":94740,"style":44929},[294],[15,94742,94744,94747],{"style":94743},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[15,94745],{"className":94746,"style":303},[302],[15,94748,94750],{"className":94749},[307,308,309,310],[15,94751,82296],{"className":94752},[59,60,310],[15,94754,318],{"className":94755},[317],[15,94757,94759],{"className":94758},[290],[15,94760,94762],{"className":94761,"style":7968},[294],[15,94763],{},[15,94765,120],{"className":94766},[153],[15,94768,11],{"className":94769},[59,60],[15,94771],{"className":94772,"style":2587},[157],[15,94774,2470],{"className":94775},[2591],[15,94777],{"className":94778,"style":2587},[157],[15,94780,94782,94785,94825,94828,94836,94839,94842,94845,94848,94888],{"className":94781},[50],[15,94783],{"className":94784,"style":139},[54],[15,94786,94788,94791],{"className":94787},[59],[15,94789,15712],{"className":94790,"style":15761},[59,60],[15,94792,94794],{"className":94793},[281],[15,94795,94797,94817],{"className":94796},[285,286],[15,94798,94800,94814],{"className":94799},[290],[15,94801,94803],{"className":94802,"style":44929},[294],[15,94804,94805,94808],{"style":94743},[15,94806],{"className":94807,"style":303},[302],[15,94809,94811],{"className":94810},[307,308,309,310],[15,94812,82296],{"className":94813},[59,60,310],[15,94815,318],{"className":94816},[317],[15,94818,94820],{"className":94819},[290],[15,94821,94823],{"className":94822,"style":7968},[294],[15,94824],{},[15,94826],{"className":94827,"style":406},[157],[15,94829,94831],{"className":94830},[59],[15,94832,94835],{"className":94833,"style":94834},[59,32662],"margin-right:0.0778em;","Unif",[15,94837,230],{"className":94838},[146],[15,94840,126],{"className":94841},[59],[15,94843,551],{"className":94844},[573],[15,94846],{"className":94847,"style":406},[157],[15,94849,94851,94854],{"className":94850},[59],[15,94852,38662],{"className":94853},[59,60],[15,94855,94857],{"className":94856},[281],[15,94858,94860,94880],{"className":94859},[285,286],[15,94861,94863,94877],{"className":94862},[290],[15,94864,94866],{"className":94865,"style":44929},[294],[15,94867,94868,94871],{"style":382},[15,94869],{"className":94870,"style":303},[302],[15,94872,94874],{"className":94873},[307,308,309,310],[15,94875,82296],{"className":94876},[59,60,310],[15,94878,318],{"className":94879},[317],[15,94881,94883],{"className":94882},[290],[15,94884,94886],{"className":94885,"style":7968},[294],[15,94887],{},[15,94889,257],{"className":94890},[153],"，取 ",[15,94893,94895,94930],{"className":94894,"translate":19},[18],[15,94896,94898],{"className":94897},[23],[25,94899,94900],{"xmlns":27},[29,94901,94902,94927],{},[32,94903,94904,94910,94912],{},[195,94905,94906,94908],{},[35,94907,15712],{},[35,94909,82296],{},[110,94911,123],{},[1255,94913,94914],{"scriptlevel":126,"displaystyle":112},[238,94915,94916,94918],{},[115,94917,117],{},[32,94919,94920,94923,94925],{},[35,94921,94922],{},"ln",[110,94924,4103],{},[35,94926,82296],{},[39,94928,94929],{"encoding":41},"\\delta_n=\\tfrac1{\\ln n}",[15,94931,94933,94988],{"className":94932,"ariaHidden":46},[45],[15,94934,94936,94939,94979,94982,94985],{"className":94935},[50],[15,94937],{"className":94938,"style":11474},[54],[15,94940,94942,94945],{"className":94941},[59],[15,94943,15712],{"className":94944,"style":15761},[59,60],[15,94946,94948],{"className":94947},[281],[15,94949,94951,94971],{"className":94950},[285,286],[15,94952,94954,94968],{"className":94953},[290],[15,94955,94957],{"className":94956,"style":44929},[294],[15,94958,94959,94962],{"style":94743},[15,94960],{"className":94961,"style":303},[302],[15,94963,94965],{"className":94964},[307,308,309,310],[15,94966,82296],{"className":94967},[59,60,310],[15,94969,318],{"className":94970},[317],[15,94972,94974],{"className":94973},[290],[15,94975,94977],{"className":94976,"style":7968},[294],[15,94978],{},[15,94980],{"className":94981,"style":158},[157],[15,94983,123],{"className":94984},[162],[15,94986],{"className":94987,"style":158},[157],[15,94989,94991,94994],{"className":94990},[50],[15,94992],{"className":94993,"style":2505},[54],[15,94995,94997,95000,95071],{"className":94996},[59],[15,94998],{"className":94999},[146,441],[15,95001,95003],{"className":95002},[238],[15,95004,95006,95063],{"className":95005},[285,286],[15,95007,95009,95060],{"className":95008},[290],[15,95010,95012,95038,95046],{"className":95011,"style":2524},[294],[15,95013,95014,95017],{"style":2527},[15,95015],{"className":95016,"style":461},[302],[15,95018,95020],{"className":95019},[307,308,309,310],[15,95021,95023,95032,95035],{"className":95022},[59,310],[15,95024,95026,95029],{"className":95025},[1484,310],[15,95027,47658],{"className":95028},[310],[15,95030,82296],{"className":95031},[310],[15,95033],{"className":95034,"style":42366},[157,310],[15,95036,82296],{"className":95037},[59,60,310],[15,95039,95040,95043],{"style":473},[15,95041],{"className":95042,"style":461},[302],[15,95044],{"className":95045,"style":481},[480],[15,95047,95048,95051],{"style":2550},[15,95049],{"className":95050,"style":461},[302],[15,95052,95054],{"className":95053},[307,308,309,310],[15,95055,95057],{"className":95056},[59,310],[15,95058,117],{"className":95059},[59,310],[15,95061,318],{"className":95062},[317],[15,95064,95066],{"className":95065},[290],[15,95067,95069],{"className":95068,"style":2572},[294],[15,95070],{},[15,95072],{"className":95073},[153,441],[15,95075,95077,95107],{"className":95076,"translate":19},[18],[15,95078,95080],{"className":95079},[23],[25,95081,95082],{"xmlns":27},[29,95083,95084,95104],{},[32,95085,95086,95092,95094],{},[195,95087,95088,95090],{},[35,95089,38662],{},[35,95091,82296],{},[110,95093,123],{},[6814,95095,95096,95098],{},[35,95097,7567],{},[32,95099,95100,95102],{},[110,95101,4813],{},[35,95103,82296],{},[39,95105,95106],{"encoding":41},"\\varepsilon_n=e^{-n}",[15,95108,95110,95165],{"className":95109,"ariaHidden":46},[45],[15,95111,95113,95116,95156,95159,95162],{"className":95112},[50],[15,95114],{"className":95115,"style":13374},[54],[15,95117,95119,95122],{"className":95118},[59],[15,95120,38662],{"className":95121},[59,60],[15,95123,95125],{"className":95124},[281],[15,95126,95128,95148],{"className":95127},[285,286],[15,95129,95131,95145],{"className":95130},[290],[15,95132,95134],{"className":95133,"style":44929},[294],[15,95135,95136,95139],{"style":382},[15,95137],{"className":95138,"style":303},[302],[15,95140,95142],{"className":95141},[307,308,309,310],[15,95143,82296],{"className":95144},[59,60,310],[15,95146,318],{"className":95147},[317],[15,95149,95151],{"className":95150},[290],[15,95152,95154],{"className":95153,"style":7968},[294],[15,95155],{},[15,95157],{"className":95158,"style":158},[157],[15,95160,123],{"className":95161},[162],[15,95163],{"className":95164,"style":158},[157],[15,95166,95168,95171],{"className":95167},[50],[15,95169],{"className":95170,"style":21009},[54],[15,95172,95174,95177],{"className":95173},[59],[15,95175,7567],{"className":95176},[59,60],[15,95178,95180],{"className":95179},[281],[15,95181,95183],{"className":95182},[285],[15,95184,95186],{"className":95185},[290],[15,95187,95189],{"className":95188,"style":21009},[294],[15,95190,95191,95194],{"style":6865},[15,95192],{"className":95193,"style":303},[302],[15,95195,95197],{"className":95196},[307,308,309,310],[15,95198,95200,95203],{"className":95199},[59,310],[15,95201,4813],{"className":95202},[59,310],[15,95204,82296],{"className":95205},[59,60,310],"。则 ",[15,95208,95210,95254],{"className":95209,"translate":19},[18],[15,95211,95213],{"className":95212},[23],[25,95214,95215],{"xmlns":27},[29,95216,95217,95251],{},[32,95218,95219,95225,95227,95233,95235,95237,95239,95241,95247,95249],{},[32,95220,95221,95223],{},[35,95222,5392],{"mathvariant":209},[35,95224,34850],{"mathvariant":209},[110,95226,113],{"stretchy":112},[195,95228,95229,95231],{},[35,95230,944],{},[35,95232,82296],{},[110,95234,551],{"separator":46},[35,95236,11],{},[110,95238,120],{"stretchy":112},[110,95240,32959],{},[195,95242,95243,95245],{},[35,95244,15712],{},[35,95246,82296],{},[110,95248,1029],{},[115,95250,126],{},[39,95252,95253],{"encoding":41},"\\mathrm{TV}(q_n,p)\\approx\\delta_n\\to0",[15,95255,95257,95333,95388],{"className":95256,"ariaHidden":46},[45],[15,95258,95260,95263,95269,95272,95312,95315,95318,95321,95324,95327,95330],{"className":95259},[50],[15,95261],{"className":95262,"style":139},[54],[15,95264,95266],{"className":95265},[59],[15,95267,86762],{"className":95268,"style":4157},[59,32662],[15,95270,113],{"className":95271},[146],[15,95273,95275,95278],{"className":95274},[59],[15,95276,944],{"className":95277,"style":981},[59,60],[15,95279,95281],{"className":95280},[281],[15,95282,95284,95304],{"className":95283},[285,286],[15,95285,95287,95301],{"className":95286},[290],[15,95288,95290],{"className":95289,"style":44929},[294],[15,95291,95292,95295],{"style":18843},[15,95293],{"className":95294,"style":303},[302],[15,95296,95298],{"className":95297},[307,308,309,310],[15,95299,82296],{"className":95300},[59,60,310],[15,95302,318],{"className":95303},[317],[15,95305,95307],{"className":95306},[290],[15,95308,95310],{"className":95309,"style":7968},[294],[15,95311],{},[15,95313,551],{"className":95314},[573],[15,95316],{"className":95317,"style":406},[157],[15,95319,11],{"className":95320},[59,60],[15,95322,120],{"className":95323},[153],[15,95325],{"className":95326,"style":158},[157],[15,95328,32959],{"className":95329},[162],[15,95331],{"className":95332,"style":158},[157],[15,95334,95336,95339,95379,95382,95385],{"className":95335},[50],[15,95337],{"className":95338,"style":11474},[54],[15,95340,95342,95345],{"className":95341},[59],[15,95343,15712],{"className":95344,"style":15761},[59,60],[15,95346,95348],{"className":95347},[281],[15,95349,95351,95371],{"className":95350},[285,286],[15,95352,95354,95368],{"className":95353},[290],[15,95355,95357],{"className":95356,"style":44929},[294],[15,95358,95359,95362],{"style":94743},[15,95360],{"className":95361,"style":303},[302],[15,95363,95365],{"className":95364},[307,308,309,310],[15,95366,82296],{"className":95367},[59,60,310],[15,95369,318],{"className":95370},[317],[15,95372,95374],{"className":95373},[290],[15,95375,95377],{"className":95376,"style":7968},[294],[15,95378],{},[15,95380],{"className":95381,"style":158},[157],[15,95383,1029],{"className":95384},[162],[15,95386],{"className":95387,"style":158},[157],[15,95389,95391,95394],{"className":95390},[50],[15,95392],{"className":95393,"style":172},[54],[15,95395,126],{"className":95396},[59],"，但 ",[15,95399,95401,95450],{"className":95400,"translate":19},[18],[15,95402,95404],{"className":95403},[23],[25,95405,95406],{"xmlns":27},[29,95407,95408,95447],{},[32,95409,95410,95416,95418,95424,95426,95428,95430,95433,95439,95441,95443,95445],{},[32,95411,95412,95414],{},[35,95413,10694],{"mathvariant":209},[35,95415,21893],{"mathvariant":209},[110,95417,113],{"stretchy":112},[195,95419,95420,95422],{},[35,95421,944],{},[35,95423,82296],{},[35,95425,210],{"mathvariant":209},[35,95427,11],{},[110,95429,120],{"stretchy":112},[110,95431,95432],{},"≳",[195,95434,95435,95437],{},[35,95436,15712],{},[35,95438,82296],{},[110,95440,3299],{},[35,95442,82296],{},[110,95444,1029],{},[35,95446,1024],{"mathvariant":209},[39,95448,95449],{"encoding":41},"\\mathrm{KL}(q_n\\|p)\\gtrsim \\delta_n\\cdot n\\to\\infty",[15,95451,95453,95526,95581,95599],{"className":95452,"ariaHidden":46},[45],[15,95454,95456,95459,95465,95468,95508,95511,95514,95517,95520,95523],{"className":95455},[50],[15,95457],{"className":95458,"style":139},[54],[15,95460,95462],{"className":95461},[59],[15,95463,32663],{"className":95464},[59,32662],[15,95466,113],{"className":95467},[146],[15,95469,95471,95474],{"className":95470},[59],[15,95472,944],{"className":95473,"style":981},[59,60],[15,95475,95477],{"className":95476},[281],[15,95478,95480,95500],{"className":95479},[285,286],[15,95481,95483,95497],{"className":95482},[290],[15,95484,95486],{"className":95485,"style":44929},[294],[15,95487,95488,95491],{"style":18843},[15,95489],{"className":95490,"style":303},[302],[15,95492,95494],{"className":95493},[307,308,309,310],[15,95495,82296],{"className":95496},[59,60,310],[15,95498,318],{"className":95499},[317],[15,95501,95503],{"className":95502},[290],[15,95504,95506],{"className":95505,"style":7968},[294],[15,95507],{},[15,95509,210],{"className":95510},[59],[15,95512,11],{"className":95513},[59,60],[15,95515,120],{"className":95516},[153],[15,95518],{"className":95519,"style":158},[157],[15,95521,95432],{"className":95522},[162,59794],[15,95524],{"className":95525,"style":158},[157],[15,95527,95529,95532,95572,95575,95578],{"className":95528},[50],[15,95530],{"className":95531,"style":11474},[54],[15,95533,95535,95538],{"className":95534},[59],[15,95536,15712],{"className":95537,"style":15761},[59,60],[15,95539,95541],{"className":95540},[281],[15,95542,95544,95564],{"className":95543},[285,286],[15,95545,95547,95561],{"className":95546},[290],[15,95548,95550],{"className":95549,"style":44929},[294],[15,95551,95552,95555],{"style":94743},[15,95553],{"className":95554,"style":303},[302],[15,95556,95558],{"className":95557},[307,308,309,310],[15,95559,82296],{"className":95560},[59,60,310],[15,95562,318],{"className":95563},[317],[15,95565,95567],{"className":95566},[290],[15,95568,95570],{"className":95569,"style":7968},[294],[15,95571],{},[15,95573],{"className":95574,"style":2587},[157],[15,95576,3299],{"className":95577},[2591],[15,95579],{"className":95580,"style":2587},[157],[15,95582,95584,95587,95590,95593,95596],{"className":95583},[50],[15,95585],{"className":95586,"style":2345},[54],[15,95588,82296],{"className":95589},[59,60],[15,95591],{"className":95592,"style":158},[157],[15,95594,1029],{"className":95595},[162],[15,95597],{"className":95598,"style":158},[157],[15,95600,95602,95605],{"className":95601},[50],[15,95603],{"className":95604,"style":2345},[54],[15,95606,1024],{"className":95607},[59],"。反例的机制很典型：TV 只控制\"总质量差\"，控制不了小测度集合上密度的巨大尖峰，而 KL 对小分母极其敏感——这正是 KL\u002Fχ² \"无界\"分歧的拓扑体现。",[11,95610,95611,95614,95615,95643,95644,60064,95710,95775,95776,23624],{},[1225,95612,95613],{},"(c)（有限字母表\u002F一致比值界下，全部等价）"," 若似然比一致有界（例如：",[15,95616,95618,95631],{"className":95617,"translate":19},[18],[15,95619,95621],{"className":95620},[23],[25,95622,95623],{"xmlns":27},[29,95624,95625,95629],{},[32,95626,95627],{},[35,95628,213],{},[39,95630,213],{"encoding":41},[15,95632,95634],{"className":95633,"ariaHidden":46},[45],[15,95635,95637,95640],{"className":95636},[50],[15,95638],{"className":95639,"style":566},[54],[15,95641,213],{"className":95642},[59,60]," 在有限字母表上且 ",[15,95645,95647,95671],{"className":95646,"translate":19},[18],[15,95648,95650],{"className":95649},[23],[25,95651,95652],{"xmlns":27},[29,95653,95654,95668],{},[32,95655,95656,95658,95660,95662,95664,95666],{},[35,95657,944],{},[110,95659,113],{"stretchy":112},[35,95661,774],{},[110,95663,120],{"stretchy":112},[110,95665,2903],{},[115,95667,126],{},[39,95669,95670],{"encoding":41},"q(x)>0",[15,95672,95674,95701],{"className":95673,"ariaHidden":46},[45],[15,95675,95677,95680,95683,95686,95689,95692,95695,95698],{"className":95676},[50],[15,95678],{"className":95679,"style":139},[54],[15,95681,944],{"className":95682,"style":981},[59,60],[15,95684,113],{"className":95685},[146],[15,95687,774],{"className":95688},[59,60],[15,95690,120],{"className":95691},[153],[15,95693],{"className":95694,"style":158},[157],[15,95696,2903],{"className":95697},[162],[15,95699],{"className":95700,"style":158},[157],[15,95702,95704,95707],{"className":95703},[50],[15,95705],{"className":95706,"style":172},[54],[15,95708,126],{"className":95709},[59],[15,95711,95713,95736],{"className":95712,"translate":19},[18],[15,95714,95716],{"className":95715},[23],[25,95717,95718],{"xmlns":27},[29,95719,95720,95733],{},[32,95721,95722,95724,95726,95729,95731],{},[35,95723,774],{},[110,95725,5909],{},[35,95727,95728],{"mathvariant":209},"supp",[110,95730,4103],{},[35,95732,206],{},[39,95734,95735],{"encoding":41},"x\\in\\operatorname{supp}P",[15,95737,95739,95757],{"className":95738,"ariaHidden":46},[45],[15,95740,95742,95745,95748,95751,95754],{"className":95741},[50],[15,95743],{"className":95744,"style":5924},[54],[15,95746,774],{"className":95747},[59,60],[15,95749],{"className":95750,"style":158},[157],[15,95752,5909],{"className":95753},[162],[15,95755],{"className":95756,"style":158},[157],[15,95758,95760,95763,95769,95772],{"className":95759},[50],[15,95761],{"className":95762,"style":566},[54],[15,95764,95766],{"className":95765},[1484],[15,95767,95728],{"className":95768},[59,32662],[15,95770],{"className":95771,"style":406},[157],[15,95773,206],{"className":95774,"style":334},[59,60],"——此时 ",[15,95777,95779,95815],{"className":95778,"translate":19},[18],[15,95780,95782],{"className":95781},[23],[25,95783,95784],{"xmlns":27},[29,95785,95786,95812],{},[32,95787,95788,95790,95792,95798,95800,95808,95810],{},[35,95789,769],{},[110,95791,123],{},[238,95793,95794,95796],{},[35,95795,11],{},[35,95797,944],{},[110,95799,9952],{},[195,95801,95802,95804,95806],{},[35,95803,769],{},[35,95805,52387],{},[110,95807,4103],{},[110,95809,7251],{},[35,95811,1024],{"mathvariant":209},[39,95813,95814],{"encoding":41},"t=\\frac{p}{q}\\le t_{\\max}\u003C\\infty",[15,95816,95818,95836,95919,95987],{"className":95817,"ariaHidden":46},[45],[15,95819,95821,95824,95827,95830,95833],{"className":95820},[50],[15,95822],{"className":95823,"style":5343},[54],[15,95825,769],{"className":95826},[59,60],[15,95828],{"className":95829,"style":158},[157],[15,95831,123],{"className":95832},[162],[15,95834],{"className":95835,"style":158},[157],[15,95837,95839,95842,95910,95913,95916],{"className":95838},[50],[15,95840],{"className":95841,"style":3084},[54],[15,95843,95845,95848,95907],{"className":95844},[59],[15,95846],{"className":95847},[146,441],[15,95849,95851],{"className":95850},[238],[15,95852,95854,95899],{"className":95853},[285,286],[15,95855,95857,95896],{"className":95856},[290],[15,95858,95860,95874,95882],{"className":95859,"style":3103},[294],[15,95861,95862,95865],{"style":2527},[15,95863],{"className":95864,"style":461},[302],[15,95866,95868],{"className":95867},[307,308,309,310],[15,95869,95871],{"className":95870},[59,310],[15,95872,944],{"className":95873,"style":981},[59,60,310],[15,95875,95876,95879],{"style":473},[15,95877],{"className":95878,"style":461},[302],[15,95880],{"className":95881,"style":481},[480],[15,95883,95884,95887],{"style":2853},[15,95885],{"className":95886,"style":461},[302],[15,95888,95890],{"className":95889},[307,308,309,310],[15,95891,95893],{"className":95892},[59,310],[15,95894,11],{"className":95895},[59,60,310],[15,95897,318],{"className":95898},[317],[15,95900,95902],{"className":95901},[290],[15,95903,95905],{"className":95904,"style":2739},[294],[15,95906],{},[15,95908],{"className":95909},[153,441],[15,95911],{"className":95912,"style":158},[157],[15,95914,9952],{"className":95915},[162],[15,95917],{"className":95918,"style":158},[157],[15,95920,95922,95926,95978,95981,95984],{"className":95921},[50],[15,95923],{"className":95924,"style":95925},[54],"height:0.7651em;vertical-align:-0.15em;",[15,95927,95929,95932],{"className":95928},[59],[15,95930,769],{"className":95931},[59,60],[15,95933,95935],{"className":95934},[281],[15,95936,95938,95970],{"className":95937},[285,286],[15,95939,95941,95967],{"className":95940},[290],[15,95942,95944],{"className":95943,"style":44929},[294],[15,95945,95946,95949],{"style":382},[15,95947],{"className":95948,"style":303},[302],[15,95950,95952],{"className":95951},[307,308,309,310],[15,95953,95955],{"className":95954},[59,310],[15,95956,95958,95961,95964],{"className":95957},[1484,310],[15,95959,26323],{"className":95960},[310],[15,95962,45180],{"className":95963},[310],[15,95965,774],{"className":95966},[310],[15,95968,318],{"className":95969},[317],[15,95971,95973],{"className":95972},[290],[15,95974,95976],{"className":95975,"style":7968},[294],[15,95977],{},[15,95979],{"className":95980,"style":158},[157],[15,95982,7251],{"className":95983},[162],[15,95985],{"className":95986,"style":158},[157],[15,95988,95990,95993],{"className":95989},[50],[15,95991],{"className":95992,"style":2345},[54],[15,95994,1024],{"className":95995},[59],[15,95997,95999],{"className":95998,"translate":19},[180],[15,96000,96002,96137],{"className":96001,"translate":19},[18],[15,96003,96005],{"className":96004},[23],[25,96006,96007],{"xmlns":27,"display":189},[29,96008,96009,96134],{},[1243,96010,96011,96082],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,96012,96013,96019],{},[1252,96014,96015],{},[1255,96016,96017],{"scriptlevel":126,"displaystyle":46},[32,96018],{},[1252,96020,96021],{},[1255,96022,96023],{"scriptlevel":126,"displaystyle":46},[32,96024,96025,96027,96033,96035,96041,96043,96045,96047,96049,96051,96053,96056,96058,96064,96066,96072,96074,96076,96078,96080],{},[32,96026],{},[195,96028,96029,96031],{},[35,96030,199],{},[35,96032,37],{},[110,96034,113],{"stretchy":112},[195,96036,96037,96039],{},[35,96038,206],{},[35,96040,82296],{},[35,96042,210],{"mathvariant":209},[35,96044,213],{},[110,96046,120],{"stretchy":112},[110,96048,1029],{},[115,96050,126],{},[1297,96052,15904],{},[110,96054,96055],{},"⟺",[1297,96057,15904],{},[32,96059,96060,96062],{},[35,96061,5392],{"mathvariant":209},[35,96063,34850],{"mathvariant":209},[110,96065,113],{"stretchy":112},[195,96067,96068,96070],{},[35,96069,206],{},[35,96071,82296],{},[110,96073,551],{"separator":46},[35,96075,213],{},[110,96077,120],{"stretchy":112},[110,96079,1029],{},[115,96081,126],{},[1249,96083,96084,96090],{},[1252,96085,96086],{},[1255,96087,96088],{"scriptlevel":126,"displaystyle":46},[32,96089],{},[1252,96091,96092],{},[1255,96093,96094],{"scriptlevel":126,"displaystyle":46},[32,96095,96096,96098,96100,96102,96104,96106,96116,96118,96124,96126,96128,96130,96132],{},[32,96097],{},[157,96099],{"width":3262},[1297,96101,15904],{},[110,96103,96055],{},[1297,96105,15904],{},[195,96107,96108,96110],{},[35,96109,199],{},[32,96111,96112,96114],{},[35,96113,10694],{},[35,96115,21893],{},[110,96117,113],{"stretchy":112},[195,96119,96120,96122],{},[35,96121,206],{},[35,96123,82296],{},[35,96125,210],{"mathvariant":209},[35,96127,213],{},[110,96129,120],{"stretchy":112},[110,96131,1029],{},[115,96133,126],{},[39,96135,96136],{"encoding":41},"\\begin{aligned}\n&D_f(P_n\\|Q)\\to0\n\\iff\\mathrm{TV}(P_n,Q)\\to0\\\\\n&\\qquad\\iff D_{KL}(P_n\\|Q)\\to0\n\\end{aligned}",[15,96138,96140],{"className":96139,"ariaHidden":46},[45],[15,96141,96143,96147],{"className":96142},[50],[15,96144],{"className":96145,"style":96146},[54],"height:2.7em;vertical-align:-1.1em;",[15,96148,96150],{"className":96149},[59],[15,96151,96153,96196],{"className":96152},[1243],[15,96154,96156],{"className":96155},[1360],[15,96157,96159,96187],{"className":96158},[285,286],[15,96160,96162,96184],{"className":96161},[290],[15,96163,96166,96176],{"className":96164,"style":96165},[294],"height:1.6em;",[15,96167,96169,96173],{"style":96168},"top:-3.6em;",[15,96170],{"className":96171,"style":96172},[302],"height:2.84em;",[15,96174],{"className":96175},[59],[15,96177,96178,96181],{"style":1903},[15,96179],{"className":96180,"style":96172},[302],[15,96182],{"className":96183},[59],[15,96185,318],{"className":96186},[317],[15,96188,96190],{"className":96189},[290],[15,96191,96194],{"className":96192,"style":96193},[294],"height:1.1em;",[15,96195],{},[15,96197,96199],{"className":96198},[1451],[15,96200,96202,96554],{"className":96201},[285,286],[15,96203,96205,96551],{"className":96204},[290],[15,96206,96208,96412],{"className":96207,"style":96165},[294],[15,96209,96211,96214],{"style":96210},"top:-3.76em;",[15,96212],{"className":96213,"style":461},[302],[15,96215,96217,96220,96260,96263,96303,96306,96309,96312,96315,96318,96321,96324,96327,96330,96333,96336,96339,96345,96348,96388,96391,96394,96397,96400,96403,96406,96409],{"className":96216},[59],[15,96218],{"className":96219},[59],[15,96221,96223,96226],{"className":96222},[59],[15,96224,199],{"className":96225,"style":277},[59,60],[15,96227,96229],{"className":96228},[281],[15,96230,96232,96252],{"className":96231},[285,286],[15,96233,96235,96249],{"className":96234},[290],[15,96236,96238],{"className":96237,"style":295},[294],[15,96239,96240,96243],{"style":298},[15,96241],{"className":96242,"style":303},[302],[15,96244,96246],{"className":96245},[307,308,309,310],[15,96247,37],{"className":96248,"style":61},[59,60,310],[15,96250,318],{"className":96251},[317],[15,96253,96255],{"className":96254},[290],[15,96256,96258],{"className":96257,"style":325},[294],[15,96259],{},[15,96261,113],{"className":96262},[146],[15,96264,96266,96269],{"className":96265},[59],[15,96267,206],{"className":96268,"style":334},[59,60],[15,96270,96272],{"className":96271},[281],[15,96273,96275,96295],{"className":96274},[285,286],[15,96276,96278,96292],{"className":96277},[290],[15,96279,96281],{"className":96280,"style":44929},[294],[15,96282,96283,96286],{"style":11136},[15,96284],{"className":96285,"style":303},[302],[15,96287,96289],{"className":96288},[307,308,309,310],[15,96290,82296],{"className":96291},[59,60,310],[15,96293,318],{"className":96294},[317],[15,96296,96298],{"className":96297},[290],[15,96299,96301],{"className":96300,"style":7968},[294],[15,96302],{},[15,96304,210],{"className":96305},[59],[15,96307,213],{"className":96308},[59,60],[15,96310,120],{"className":96311},[153],[15,96313],{"className":96314,"style":158},[157],[15,96316,1029],{"className":96317},[162],[15,96319],{"className":96320,"style":158},[157],[15,96322,126],{"className":96323},[59],[15,96325],{"className":96326,"style":158},[157],[15,96328],{"className":96329,"style":158},[157],[15,96331,96055],{"className":96332},[162],[15,96334],{"className":96335,"style":158},[157],[15,96337],{"className":96338,"style":158},[157],[15,96340,96342],{"className":96341},[59],[15,96343,86762],{"className":96344,"style":4157},[59,32662],[15,96346,113],{"className":96347},[146],[15,96349,96351,96354],{"className":96350},[59],[15,96352,206],{"className":96353,"style":334},[59,60],[15,96355,96357],{"className":96356},[281],[15,96358,96360,96380],{"className":96359},[285,286],[15,96361,96363,96377],{"className":96362},[290],[15,96364,96366],{"className":96365,"style":44929},[294],[15,96367,96368,96371],{"style":11136},[15,96369],{"className":96370,"style":303},[302],[15,96372,96374],{"className":96373},[307,308,309,310],[15,96375,82296],{"className":96376},[59,60,310],[15,96378,318],{"className":96379},[317],[15,96381,96383],{"className":96382},[290],[15,96384,96386],{"className":96385,"style":7968},[294],[15,96387],{},[15,96389,551],{"className":96390},[573],[15,96392],{"className":96393,"style":406},[157],[15,96395,213],{"className":96396},[59,60],[15,96398,120],{"className":96399},[153],[15,96401],{"className":96402,"style":158},[157],[15,96404,1029],{"className":96405},[162],[15,96407],{"className":96408,"style":158},[157],[15,96410,126],{"className":96411},[59],[15,96413,96414,96417],{"style":24736},[15,96415],{"className":96416,"style":461},[302],[15,96418,96420,96423,96426,96429,96432,96435,96438,96441,96487,96490,96530,96533,96536,96539,96542,96545,96548],{"className":96419},[59],[15,96421],{"className":96422},[59],[15,96424],{"className":96425,"style":3634},[157],[15,96427],{"className":96428,"style":158},[157],[15,96430],{"className":96431,"style":158},[157],[15,96433,96055],{"className":96434},[162],[15,96436],{"className":96437,"style":158},[157],[15,96439],{"className":96440,"style":158},[157],[15,96442,96444,96447],{"className":96443},[59],[15,96445,199],{"className":96446,"style":277},[59,60],[15,96448,96450],{"className":96449},[281],[15,96451,96453,96479],{"className":96452},[285,286],[15,96454,96456,96476],{"className":96455},[290],[15,96457,96459],{"className":96458,"style":379},[294],[15,96460,96461,96464],{"style":298},[15,96462],{"className":96463,"style":303},[302],[15,96465,96467],{"className":96466},[307,308,309,310],[15,96468,96470,96473],{"className":96469},[59,310],[15,96471,10694],{"className":96472,"style":10782},[59,60,310],[15,96474,21893],{"className":96475},[59,60,310],[15,96477,318],{"className":96478},[317],[15,96480,96482],{"className":96481},[290],[15,96483,96485],{"className":96484,"style":7968},[294],[15,96486],{},[15,96488,113],{"className":96489},[146],[15,96491,96493,96496],{"className":96492},[59],[15,96494,206],{"className":96495,"style":334},[59,60],[15,96497,96499],{"className":96498},[281],[15,96500,96502,96522],{"className":96501},[285,286],[15,96503,96505,96519],{"className":96504},[290],[15,96506,96508],{"className":96507,"style":44929},[294],[15,96509,96510,96513],{"style":11136},[15,96511],{"className":96512,"style":303},[302],[15,96514,96516],{"className":96515},[307,308,309,310],[15,96517,82296],{"className":96518},[59,60,310],[15,96520,318],{"className":96521},[317],[15,96523,96525],{"className":96524},[290],[15,96526,96528],{"className":96527,"style":7968},[294],[15,96529],{},[15,96531,210],{"className":96532},[59],[15,96534,213],{"className":96535},[59,60],[15,96537,120],{"className":96538},[153],[15,96540],{"className":96541,"style":158},[157],[15,96543,1029],{"className":96544},[162],[15,96546],{"className":96547,"style":158},[157],[15,96549,126],{"className":96550},[59],[15,96552,318],{"className":96553},[317],[15,96555,96557],{"className":96556},[290],[15,96558,96560],{"className":96559,"style":96193},[294],[15,96561],{},[11,96563,96564,96565,96593,96594,96741,96742,96939],{},"对一切上述 ",[15,96566,96568,96581],{"className":96567,"translate":19},[18],[15,96569,96571],{"className":96570},[23],[25,96572,96573],{"xmlns":27},[29,96574,96575,96579],{},[32,96576,96577],{},[35,96578,37],{},[39,96580,37],{"encoding":41},[15,96582,96584],{"className":96583,"ariaHidden":46},[45],[15,96585,96587,96590],{"className":96586},[50],[15,96588],{"className":96589,"style":55},[54],[15,96591,37],{"className":96592,"style":61},[59,60]," 同时成立（上界方向由 ",[15,96595,96597,96645],{"className":96596,"translate":19},[18],[15,96598,96600],{"className":96599},[23],[25,96601,96602],{"xmlns":27},[29,96603,96604,96642],{},[32,96605,96606,96608,96610,96612,96614,96616,96618,96620,96622,96624,96626,96628,96630,96632,96634,96636,96638,96640],{},[35,96607,4808],{"mathvariant":209},[35,96609,37],{},[110,96611,113],{"stretchy":112},[35,96613,769],{},[110,96615,120],{"stretchy":112},[110,96617,4813],{},[35,96619,37],{},[110,96621,113],{"stretchy":112},[115,96623,117],{},[110,96625,120],{"stretchy":112},[35,96627,4808],{"mathvariant":209},[110,96629,9952],{},[35,96631,39294],{},[35,96633,4808],{"mathvariant":209},[35,96635,769],{},[110,96637,4813],{},[115,96639,117],{},[35,96641,4808],{"mathvariant":209},[39,96643,96644],{"encoding":41},"|f(t)-f(1)|\\le C|t-1|",[15,96646,96648,96678,96708,96732],{"className":96647,"ariaHidden":46},[45],[15,96649,96651,96654,96657,96660,96663,96666,96669,96672,96675],{"className":96650},[50],[15,96652],{"className":96653,"style":139},[54],[15,96655,4808],{"className":96656},[59],[15,96658,37],{"className":96659,"style":61},[59,60],[15,96661,113],{"className":96662},[146],[15,96664,769],{"className":96665},[59,60],[15,96667,120],{"className":96668},[153],[15,96670],{"className":96671,"style":2587},[157],[15,96673,4813],{"className":96674},[2591],[15,96676],{"className":96677,"style":2587},[157],[15,96679,96681,96684,96687,96690,96693,96696,96699,96702,96705],{"className":96680},[50],[15,96682],{"className":96683,"style":139},[54],[15,96685,37],{"className":96686,"style":61},[59,60],[15,96688,113],{"className":96689},[146],[15,96691,117],{"className":96692},[59],[15,96694,120],{"className":96695},[153],[15,96697,4808],{"className":96698},[59],[15,96700],{"className":96701,"style":158},[157],[15,96703,9952],{"className":96704},[162],[15,96706],{"className":96707,"style":158},[157],[15,96709,96711,96714,96717,96720,96723,96726,96729],{"className":96710},[50],[15,96712],{"className":96713,"style":139},[54],[15,96715,39294],{"className":96716,"style":10782},[59,60],[15,96718,4808],{"className":96719},[59],[15,96721,769],{"className":96722},[59,60],[15,96724],{"className":96725,"style":2587},[157],[15,96727,4813],{"className":96728},[2591],[15,96730],{"className":96731,"style":2587},[157],[15,96733,96735,96738],{"className":96734},[50],[15,96736],{"className":96737,"style":139},[54],[15,96739,34679],{"className":96740},[59]," 于 ",[15,96743,96745,96789],{"className":96744,"translate":19},[18],[15,96746,96748],{"className":96747},[23],[25,96749,96750],{"xmlns":27},[29,96751,96752,96786],{},[32,96753,96754,96756,96758,96760,96762,96764,96772,96774,96776,96784],{},[35,96755,769],{},[110,96757,5909],{},[110,96759,230],{"stretchy":112},[115,96761,117],{},[35,96763,941],{"mathvariant":209},[195,96765,96766,96768,96770],{},[35,96767,769],{},[35,96769,51608],{},[110,96771,4103],{},[110,96773,551],{"separator":46},[1297,96775,1299],{},[195,96777,96778,96780,96782],{},[35,96779,769],{},[35,96781,52387],{},[110,96783,4103],{},[110,96785,257],{"stretchy":112},[39,96787,96788],{"encoding":41},"t\\in[1\u002Ft_{\\min},\\,t_{\\max}]",[15,96790,96792,96810],{"className":96791,"ariaHidden":46},[45],[15,96793,96795,96798,96801,96804,96807],{"className":96794},[50],[15,96796],{"className":96797,"style":7266},[54],[15,96799,769],{"className":96800},[59,60],[15,96802],{"className":96803,"style":158},[157],[15,96805,5909],{"className":96806},[162],[15,96808],{"className":96809,"style":158},[157],[15,96811,96813,96816,96819,96822,96875,96878,96881,96884,96936],{"className":96812},[50],[15,96814],{"className":96815,"style":139},[54],[15,96817,230],{"className":96818},[146],[15,96820,8589],{"className":96821},[59],[15,96823,96825,96828],{"className":96824},[59],[15,96826,769],{"className":96827},[59,60],[15,96829,96831],{"className":96830},[281],[15,96832,96834,96867],{"className":96833},[285,286],[15,96835,96837,96864],{"className":96836},[290],[15,96838,96841],{"className":96839,"style":96840},[294],"height:0.3175em;",[15,96842,96843,96846],{"style":382},[15,96844],{"className":96845,"style":303},[302],[15,96847,96849],{"className":96848},[307,308,309,310],[15,96850,96852],{"className":96851},[59,310],[15,96853,96855,96858,96861],{"className":96854},[1484,310],[15,96856,26323],{"className":96857},[310],[15,96859,11963],{"className":96860},[310],[15,96862,82296],{"className":96863},[310],[15,96865,318],{"className":96866},[317],[15,96868,96870],{"className":96869},[290],[15,96871,96873],{"className":96872,"style":7968},[294],[15,96874],{},[15,96876,551],{"className":96877},[573],[15,96879],{"className":96880,"style":406},[157],[15,96882],{"className":96883,"style":406},[157],[15,96885,96887,96890],{"className":96886},[59],[15,96888,769],{"className":96889},[59,60],[15,96891,96893],{"className":96892},[281],[15,96894,96896,96928],{"className":96895},[285,286],[15,96897,96899,96925],{"className":96898},[290],[15,96900,96902],{"className":96901,"style":44929},[294],[15,96903,96904,96907],{"style":382},[15,96905],{"className":96906,"style":303},[302],[15,96908,96910],{"className":96909},[307,308,309,310],[15,96911,96913],{"className":96912},[59,310],[15,96914,96916,96919,96922],{"className":96915},[1484,310],[15,96917,26323],{"className":96918},[310],[15,96920,45180],{"className":96921},[310],[15,96923,774],{"className":96924},[310],[15,96926,318],{"className":96927},[317],[15,96929,96931],{"className":96930},[290],[15,96932,96934],{"className":96933,"style":7968},[294],[15,96935],{},[15,96937,257],{"className":96938},[153]," 的一致 Lipschitz 性给出）。",[11,96941,96942,96943,96946],{},"也就是说，",[1225,96944,96945],{},"\"所有 f-散度诱导同一拓扑\"必须在有限\u002F紧设定或一致比值界下读","：此时它们都等价于全变差拓扑（也叫强拓扑），只是\"度量标尺\"不同；而在一般测度空间上，KL 型拓扑严格强于 TV 拓扑。这一分层对理解第 6 节 f-散度与 Wasserstein 的真正差异很重要：f-散度族的内部差异是\"强度\"差异，而它们与 Wasserstein 的差异是\"性质\"差异。",[2311,96948,96950],{"id":96949},"_48-一般不是度量","4.8 一般不是度量",[11,96952,96953],{},"f-散度一般不对称，也不满足三角不等式，因此通常不是距离度量。但某些特殊形式可以诱导出度量：",[10027,96955,96956,98468],{},[6665,96957,96958,96961,96962,97634,97637,97638,97666,97667,97740,97741,98001,98002,98407,98408,98467],{},[1225,96959,96960],{},"Hellinger 距离","是度量：",[15,96963,96965],{"className":96964,"translate":19},[180],[15,96966,96968,97072],{"className":96967,"translate":19},[18],[15,96969,96971],{"className":96970},[23],[25,96972,96973],{"xmlns":27,"display":189},[29,96974,96975,97069],{},[32,96976,96977,96983,96985,96987,96989,96991,96993,96995,97033,97035,97047,97049,97067],{},[195,96978,96979,96981],{},[35,96980,44560],{},[35,96982,33884],{},[110,96984,113],{"stretchy":112},[35,96986,206],{},[110,96988,551],{"separator":46},[35,96990,213],{},[110,96992,120],{"stretchy":112},[110,96994,123],{},[34339,96996,96997],{},[32,96998,96999,97007,97009,97011,97015,97017,97021,97027,97029,97031],{},[1255,97000,97001],{"scriptlevel":126,"displaystyle":112},[238,97002,97003,97005],{},[115,97004,117],{},[115,97006,2463],{},[110,97008,1287],{},[110,97010,113],{"stretchy":112},[34339,97012,97013],{},[35,97014,11],{},[110,97016,4813],{},[34339,97018,97019],{},[35,97020,944],{},[6814,97022,97023,97025],{},[110,97024,120],{"stretchy":112},[115,97026,2463],{},[1297,97028,1299],{},[35,97030,244],{},[35,97032,774],{},[110,97034,123],{},[34339,97036,97037],{},[32,97038,97039,97041,97043,97045],{},[115,97040,117],{},[110,97042,4813],{},[35,97044,39291],{},[35,97046,39294],{},[110,97048,123],{},[34339,97050,97051],{},[32,97052,97053,97055,97057,97059],{},[115,97054,2463],{},[110,97056,4813],{},[115,97058,2463],{},[7553,97060,97061,97063,97065],{},[35,97062,33884],{},[1297,97064,42137],{},[115,97066,2463],{},[35,97068,4375],{"mathvariant":209},[39,97070,97071],{"encoding":41},"\\rho_H(P,Q)\n=\\sqrt{\\tfrac12\\int(\\sqrt p-\\sqrt q)^2\\,dx}\n=\\sqrt{1-BC}\n=\\sqrt{2-2H^2_{\\text{Bhattacharyya}}}.",[15,97073,97075,97148,97420,97501],{"className":97074,"ariaHidden":46},[45],[15,97076,97078,97081,97121,97124,97127,97130,97133,97136,97139,97142,97145],{"className":97077},[50],[15,97079],{"className":97080,"style":139},[54],[15,97082,97084,97087],{"className":97083},[59],[15,97085,44560],{"className":97086},[59,60],[15,97088,97090],{"className":97089},[281],[15,97091,97093,97113],{"className":97092},[285,286],[15,97094,97096,97110],{"className":97095},[290],[15,97097,97099],{"className":97098,"style":379},[294],[15,97100,97101,97104],{"style":382},[15,97102],{"className":97103,"style":303},[302],[15,97105,97107],{"className":97106},[307,308,309,310],[15,97108,33884],{"className":97109,"style":34038},[59,60,310],[15,97111,318],{"className":97112},[317],[15,97114,97116],{"className":97115},[290],[15,97117,97119],{"className":97118,"style":7968},[294],[15,97120],{},[15,97122,113],{"className":97123},[146],[15,97125,206],{"className":97126,"style":334},[59,60],[15,97128,551],{"className":97129},[573],[15,97131],{"className":97132,"style":406},[157],[15,97134,213],{"className":97135},[59,60],[15,97137,120],{"className":97138},[153],[15,97140],{"className":97141,"style":158},[157],[15,97143,123],{"className":97144},[162],[15,97146],{"className":97147,"style":158},[157],[15,97149,97151,97155,97411,97414,97417],{"className":97150},[50],[15,97152],{"className":97153,"style":97154},[54],"height:3.04em;vertical-align:-1.1572em;",[15,97156,97158],{"className":97157},[59,34367],[15,97159,97161,97403],{"className":97160},[285,286],[15,97162,97164,97400],{"className":97163},[290],[15,97165,97167,97388],{"className":97166,"style":91111},[294],[15,97168,97170,97173],{"className":97169,"style":91115},[6307],[15,97171],{"className":97172,"style":91119},[302],[15,97174,97176,97244,97247,97250,97253,97297,97300,97303,97306,97350,97379,97382,97385],{"className":97175,"style":41161},[59],[15,97177,97179,97182,97241],{"className":97178},[59],[15,97180],{"className":97181},[146,441],[15,97183,97185],{"className":97184},[238],[15,97186,97188,97233],{"className":97187},[285,286],[15,97189,97191,97230],{"className":97190},[290],[15,97192,97194,97208,97216],{"className":97193,"style":2524},[294],[15,97195,97196,97199],{"style":2527},[15,97197],{"className":97198,"style":461},[302],[15,97200,97202],{"className":97201},[307,308,309,310],[15,97203,97205],{"className":97204},[59,310],[15,97206,2463],{"className":97207},[59,310],[15,97209,97210,97213],{"style":473},[15,97211],{"className":97212,"style":461},[302],[15,97214],{"className":97215,"style":481},[480],[15,97217,97218,97221],{"style":2550},[15,97219],{"className":97220,"style":461},[302],[15,97222,97224],{"className":97223},[307,308,309,310],[15,97225,97227],{"className":97226},[59,310],[15,97228,117],{"className":97229},[59,310],[15,97231,318],{"className":97232},[317],[15,97234,97236],{"className":97235},[290],[15,97237,97239],{"className":97238,"style":2572},[294],[15,97240],{},[15,97242],{"className":97243},[153,441],[15,97245],{"className":97246,"style":406},[157],[15,97248,1287],{"className":97249,"style":1487},[1484,1485,1486],[15,97251,113],{"className":97252},[146],[15,97254,97256],{"className":97255},[59,34367],[15,97257,97259,97289],{"className":97258},[285,286],[15,97260,97262,97286],{"className":97261},[290],[15,97263,97265,97274],{"className":97264,"style":6862},[294],[15,97266,97268,97271],{"className":97267,"style":11863},[6307],[15,97269],{"className":97270,"style":461},[302],[15,97272,11],{"className":97273,"style":34387},[59,60],[15,97275,97276,97279],{"style":41350},[15,97277],{"className":97278,"style":461},[302],[15,97280,97282],{"className":97281,"style":34444},[34443],[6323,97283,97284],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,97285],{"d":34451},[15,97287,318],{"className":97288},[317],[15,97290,97292],{"className":97291},[290],[15,97293,97295],{"className":97294,"style":41370},[294],[15,97296],{},[15,97298],{"className":97299,"style":2587},[157],[15,97301,4813],{"className":97302},[2591],[15,97304],{"className":97305,"style":2587},[157],[15,97307,97309],{"className":97308},[59,34367],[15,97310,97312,97342],{"className":97311},[285,286],[15,97313,97315,97339],{"className":97314},[290],[15,97316,97318,97327],{"className":97317,"style":6862},[294],[15,97319,97321,97324],{"className":97320,"style":11863},[6307],[15,97322],{"className":97323,"style":461},[302],[15,97325,944],{"className":97326,"style":39099},[59,60],[15,97328,97329,97332],{"style":41350},[15,97330],{"className":97331,"style":461},[302],[15,97333,97335],{"className":97334,"style":34444},[34443],[6323,97336,97337],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,97338],{"d":34451},[15,97340,318],{"className":97341},[317],[15,97343,97345],{"className":97344},[290],[15,97346,97348],{"className":97347,"style":41370},[294],[15,97349],{},[15,97351,97353,97356],{"className":97352},[153],[15,97354,120],{"className":97355},[153],[15,97357,97359],{"className":97358},[281],[15,97360,97362],{"className":97361},[285],[15,97363,97365],{"className":97364},[290],[15,97366,97368],{"className":97367,"style":45032},[294],[15,97369,97370,97373],{"style":45035},[15,97371],{"className":97372,"style":303},[302],[15,97374,97376],{"className":97375},[307,308,309,310],[15,97377,2463],{"className":97378},[59,310],[15,97380],{"className":97381,"style":406},[157],[15,97383,244],{"className":97384},[59,60],[15,97386,774],{"className":97387},[59,60],[15,97389,97390,97393],{"style":91257},[15,97391],{"className":97392,"style":91119},[302],[15,97394,97396],{"className":97395,"style":91264},[34443],[6323,97397,97398],{"xmlns":6325,"width":6326,"height":91267,"viewBox":91268,"preserveAspectRatio":6329},[6331,97399],{"d":91271},[15,97401,318],{"className":97402},[317],[15,97404,97406],{"className":97405},[290],[15,97407,97409],{"className":97408,"style":91281},[294],[15,97410],{},[15,97412],{"className":97413,"style":158},[157],[15,97415,123],{"className":97416},[162],[15,97418],{"className":97419,"style":158},[157],[15,97421,97423,97427,97492,97495,97498],{"className":97422},[50],[15,97424],{"className":97425,"style":97426},[54],"height:1.04em;vertical-align:-0.1061em;",[15,97428,97430],{"className":97429},[59,34367],[15,97431,97433,97483],{"className":97432},[285,286],[15,97434,97436,97480],{"className":97435},[290],[15,97437,97440,97467],{"className":97438,"style":97439},[294],"height:0.9339em;",[15,97441,97443,97446],{"className":97442,"style":11863},[6307],[15,97444],{"className":97445,"style":461},[302],[15,97447,97449,97452,97455,97458,97461,97464],{"className":97448,"style":34387},[59],[15,97450,117],{"className":97451},[59],[15,97453],{"className":97454,"style":2587},[157],[15,97456,4813],{"className":97457},[2591],[15,97459],{"className":97460,"style":2587},[157],[15,97462,39291],{"className":97463,"style":39387},[59,60],[15,97465,39294],{"className":97466,"style":10782},[59,60],[15,97468,97470,97473],{"style":97469},"top:-2.8939em;",[15,97471],{"className":97472,"style":461},[302],[15,97474,97476],{"className":97475,"style":34444},[34443],[6323,97477,97478],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,97479],{"d":34451},[15,97481,318],{"className":97482},[317],[15,97484,97486],{"className":97485},[290],[15,97487,97490],{"className":97488,"style":97489},[294],"height:0.1061em;",[15,97491],{},[15,97493],{"className":97494,"style":158},[157],[15,97496,123],{"className":97497},[162],[15,97499],{"className":97500,"style":158},[157],[15,97502,97504,97508,97631],{"className":97503},[50],[15,97505],{"className":97506,"style":97507},[54],"height:1.84em;vertical-align:-0.6269em;",[15,97509,97511],{"className":97510},[59,34367],[15,97512,97514,97622],{"className":97513},[285,286],[15,97515,97517,97619],{"className":97516},[290],[15,97518,97521,97606],{"className":97519,"style":97520},[294],"height:1.2131em;",[15,97522,97524,97527],{"className":97523,"style":82583},[6307],[15,97525],{"className":97526,"style":82587},[302],[15,97528,97530,97533,97536,97539,97542,97545],{"className":97529,"style":41161},[59],[15,97531,2463],{"className":97532},[59],[15,97534],{"className":97535,"style":2587},[157],[15,97537,4813],{"className":97538},[2591],[15,97540],{"className":97541,"style":2587},[157],[15,97543,2463],{"className":97544},[59],[15,97546,97548,97551],{"className":97547},[59],[15,97549,33884],{"className":97550,"style":34038},[59,60],[15,97552,97554],{"className":97553},[281],[15,97555,97557,97597],{"className":97556},[285,286],[15,97558,97560,97594],{"className":97559},[290],[15,97561,97564,97582],{"className":97562,"style":97563},[294],"height:0.7959em;",[15,97565,97567,97570],{"style":97566},"top:-2.3987em;margin-left:-0.0813em;margin-right:0.05em;",[15,97568],{"className":97569,"style":303},[302],[15,97571,97573],{"className":97572},[307,308,309,310],[15,97574,97576],{"className":97575},[59,310],[15,97577,97579],{"className":97578},[59,4598,310],[15,97580,42137],{"className":97581},[59,310],[15,97583,97585,97588],{"style":97584},"top:-3.0448em;margin-right:0.05em;",[15,97586],{"className":97587,"style":303},[302],[15,97589,97591],{"className":97590},[307,308,309,310],[15,97592,2463],{"className":97593},[59,310],[15,97595,318],{"className":97596},[317],[15,97598,97600],{"className":97599},[290],[15,97601,97604],{"className":97602,"style":97603},[294],"height:0.4374em;",[15,97605],{},[15,97607,97609,97612],{"style":97608},"top:-3.1731em;",[15,97610],{"className":97611,"style":82587},[302],[15,97613,97615],{"className":97614,"style":82729},[34443],[6323,97616,97617],{"xmlns":6325,"width":6326,"height":82732,"viewBox":82733,"preserveAspectRatio":6329},[6331,97618],{"d":82736},[15,97620,318],{"className":97621},[317],[15,97623,97625],{"className":97624},[290],[15,97626,97629],{"className":97627,"style":97628},[294],"height:0.6269em;",[15,97630],{},[15,97632,4375],{"className":97633},[59],[97635,97636],"br",{},"它有一个特别漂亮的几何解释：把分布 ",[15,97639,97641,97654],{"className":97640,"translate":19},[18],[15,97642,97644],{"className":97643},[23],[25,97645,97646],{"xmlns":27},[29,97647,97648,97652],{},[32,97649,97650],{},[35,97651,206],{},[39,97653,206],{"encoding":41},[15,97655,97657],{"className":97656,"ariaHidden":46},[45],[15,97658,97660,97663],{"className":97659},[50],[15,97661],{"className":97662,"style":664},[54],[15,97664,206],{"className":97665,"style":334},[59,60]," 映到单位球面上的点 ",[15,97668,97670,97686],{"className":97669,"translate":19},[18],[15,97671,97673],{"className":97672},[23],[25,97674,97675],{"xmlns":27},[29,97676,97677,97683],{},[32,97678,97679],{},[34339,97680,97681],{},[35,97682,11],{},[39,97684,97685],{"encoding":41},"\\sqrt p",[15,97687,97689],{"className":97688,"ariaHidden":46},[45],[15,97690,97692,97696],{"className":97691},[50],[15,97693],{"className":97694,"style":97695},[54],"height:1.04em;vertical-align:-0.3369em;",[15,97697,97699],{"className":97698},[59,34367],[15,97700,97702,97732],{"className":97701},[285,286],[15,97703,97705,97729],{"className":97704},[290],[15,97706,97708,97717],{"className":97707,"style":39027},[294],[15,97709,97711,97714],{"className":97710,"style":11863},[6307],[15,97712],{"className":97713,"style":461},[302],[15,97715,11],{"className":97716,"style":34387},[59,60],[15,97718,97719,97722],{"style":39039},[15,97720],{"className":97721,"style":461},[302],[15,97723,97725],{"className":97724,"style":34444},[34443],[6323,97726,97727],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,97728],{"d":34451},[15,97730,318],{"className":97731},[317],[15,97733,97735],{"className":97734},[290],[15,97736,97738],{"className":97737,"style":39059},[294],[15,97739],{},"（因 ",[15,97742,97744,97780],{"className":97743,"translate":19},[18],[15,97745,97747],{"className":97746},[23],[25,97748,97749],{"xmlns":27},[29,97750,97751,97777],{},[32,97752,97753,97755,97759,97767,97769,97771,97773,97775],{},[110,97754,210],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[34339,97756,97757],{},[35,97758,11],{},[7553,97760,97761,97763,97765],{},[110,97762,210],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[115,97764,2463],{},[115,97766,2463],{},[110,97768,123],{},[110,97770,1287],{},[35,97772,11],{},[110,97774,123],{},[115,97776,117],{},[39,97778,97779],{"encoding":41},"\\big\\lVert\\sqrt p\\big\\rVert_2^2=\\int p=1",[15,97781,97783,97968,97992],{"className":97782,"ariaHidden":46},[45],[15,97784,97786,97790,97827,97871,97959,97962,97965],{"className":97785},[50],[15,97787],{"className":97788,"style":97789},[54],"height:1.4537em;vertical-align:-0.3997em;",[15,97791,97793],{"className":97792},[59],[15,97794,97796],{"className":97795},[419,14829],[15,97797,97799,97819],{"className":97798},[285,286],[15,97800,97802,97816],{"className":97801},[290],[15,97803,97805],{"className":97804,"style":14839},[294],[15,97806,97807,97810],{"style":14842},[15,97808],{"className":97809,"style":14846},[302],[15,97811,97812],{"style":14849},[6323,97813,97814],{"xmlns":6325,"width":14852,"height":9450,"viewBox":14853},[6331,97815],{"d":14856},[15,97817,318],{"className":97818},[317],[15,97820,97822],{"className":97821},[290],[15,97823,97825],{"className":97824,"style":14866},[294],[15,97826],{},[15,97828,97830],{"className":97829},[59,34367],[15,97831,97833,97863],{"className":97832},[285,286],[15,97834,97836,97860],{"className":97835},[290],[15,97837,97839,97848],{"className":97838,"style":39027},[294],[15,97840,97842,97845],{"className":97841,"style":11863},[6307],[15,97843],{"className":97844,"style":461},[302],[15,97846,11],{"className":97847,"style":34387},[59,60],[15,97849,97850,97853],{"style":39039},[15,97851],{"className":97852,"style":461},[302],[15,97854,97856],{"className":97855,"style":34444},[34443],[6323,97857,97858],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,97859],{"d":34451},[15,97861,318],{"className":97862},[317],[15,97864,97866],{"className":97865},[290],[15,97867,97869],{"className":97868,"style":39059},[294],[15,97870],{},[15,97872,97874,97911],{"className":97873},[59],[15,97875,97877],{"className":97876},[59],[15,97878,97880],{"className":97879},[419,14829],[15,97881,97883,97903],{"className":97882},[285,286],[15,97884,97886,97900],{"className":97885},[290],[15,97887,97889],{"className":97888,"style":14839},[294],[15,97890,97891,97894],{"style":14842},[15,97892],{"className":97893,"style":14846},[302],[15,97895,97896],{"style":14849},[6323,97897,97898],{"xmlns":6325,"width":14852,"height":9450,"viewBox":14853},[6331,97899],{"d":14856},[15,97901,318],{"className":97902},[317],[15,97904,97906],{"className":97905},[290],[15,97907,97909],{"className":97908,"style":14866},[294],[15,97910],{},[15,97912,97914],{"className":97913},[281],[15,97915,97917,97950],{"className":97916},[285,286],[15,97918,97920,97947],{"className":97919},[290],[15,97921,97924,97936],{"className":97922,"style":97923},[294],"height:1.054em;",[15,97925,97927,97930],{"style":97926},"top:-2.3003em;margin-right:0.05em;",[15,97928],{"className":97929,"style":303},[302],[15,97931,97933],{"className":97932},[307,308,309,310],[15,97934,2463],{"className":97935},[59,310],[15,97937,97938,97941],{"style":51435},[15,97939],{"className":97940,"style":303},[302],[15,97942,97944],{"className":97943},[307,308,309,310],[15,97945,2463],{"className":97946},[59,310],[15,97948,318],{"className":97949},[317],[15,97951,97953],{"className":97952},[290],[15,97954,97957],{"className":97955,"style":97956},[294],"height:0.3997em;",[15,97958],{},[15,97960],{"className":97961,"style":158},[157],[15,97963,123],{"className":97964},[162],[15,97966],{"className":97967,"style":158},[157],[15,97969,97971,97974,97977,97980,97983,97986,97989],{"className":97970},[50],[15,97972],{"className":97973,"style":5612},[54],[15,97975,1287],{"className":97976,"style":5617},[1484,1485,5616],[15,97978],{"className":97979,"style":406},[157],[15,97981,11],{"className":97982},[59,60],[15,97984],{"className":97985,"style":158},[157],[15,97987,123],{"className":97988},[162],[15,97990],{"className":97991,"style":158},[157],[15,97993,97995,97998],{"className":97994},[50],[15,97996],{"className":97997,"style":172},[54],[15,97999,117],{"className":98000},[59],"），则 ",[15,98003,98005,98063],{"className":98004,"translate":19},[18],[15,98006,98008],{"className":98007},[23],[25,98009,98010],{"xmlns":27},[29,98011,98012,98060],{},[32,98013,98014,98020,98022,98024,98026,98028,98030,98032,98042,98044,98048,98050,98054],{},[195,98015,98016,98018],{},[35,98017,44560],{},[35,98019,33884],{},[110,98021,113],{"stretchy":112},[35,98023,206],{},[110,98025,551],{"separator":46},[35,98027,213],{},[110,98029,120],{"stretchy":112},[110,98031,123],{},[1255,98033,98034],{"scriptlevel":126,"displaystyle":112},[238,98035,98036,98038],{},[115,98037,117],{},[34339,98039,98040],{},[115,98041,2463],{},[110,98043,210],{"stretchy":112},[34339,98045,98046],{},[35,98047,11],{},[110,98049,4813],{},[34339,98051,98052],{},[35,98053,944],{},[195,98055,98056,98058],{},[110,98057,210],{"stretchy":112},[115,98059,2463],{},[39,98061,98062],{"encoding":41},"\\rho_H(P,Q)=\\tfrac{1}{\\sqrt2}\\lVert\\sqrt p-\\sqrt q\\rVert_2",[15,98064,98066,98139,98316],{"className":98065,"ariaHidden":46},[45],[15,98067,98069,98072,98112,98115,98118,98121,98124,98127,98130,98133,98136],{"className":98068},[50],[15,98070],{"className":98071,"style":139},[54],[15,98073,98075,98078],{"className":98074},[59],[15,98076,44560],{"className":98077},[59,60],[15,98079,98081],{"className":98080},[281],[15,98082,98084,98104],{"className":98083},[285,286],[15,98085,98087,98101],{"className":98086},[290],[15,98088,98090],{"className":98089,"style":379},[294],[15,98091,98092,98095],{"style":382},[15,98093],{"className":98094,"style":303},[302],[15,98096,98098],{"className":98097},[307,308,309,310],[15,98099,33884],{"className":98100,"style":34038},[59,60,310],[15,98102,318],{"className":98103},[317],[15,98105,98107],{"className":98106},[290],[15,98108,98110],{"className":98109,"style":7968},[294],[15,98111],{},[15,98113,113],{"className":98114},[146],[15,98116,206],{"className":98117,"style":334},[59,60],[15,98119,551],{"className":98120},[573],[15,98122],{"className":98123,"style":406},[157],[15,98125,213],{"className":98126},[59,60],[15,98128,120],{"className":98129},[153],[15,98131],{"className":98132,"style":158},[157],[15,98134,123],{"className":98135},[162],[15,98137],{"className":98138,"style":158},[157],[15,98140,98142,98146,98260,98263,98307,98310,98313],{"className":98141},[50],[15,98143],{"className":98144,"style":98145},[54],"height:1.3831em;vertical-align:-0.538em;",[15,98147,98149,98152,98257],{"className":98148},[59],[15,98150],{"className":98151},[146,441],[15,98153,98155],{"className":98154},[238],[15,98156,98158,98248],{"className":98157},[285,286],[15,98159,98161,98245],{"className":98160},[290],[15,98162,98164,98223,98231],{"className":98163,"style":2524},[294],[15,98165,98167,98170],{"style":98166},"top:-2.551em;",[15,98168],{"className":98169,"style":461},[302],[15,98171,98173],{"className":98172},[307,308,309,310],[15,98174,98176],{"className":98175},[59,310],[15,98177,98179],{"className":98178},[59,34367,310],[15,98180,98182,98214],{"className":98181},[285,286],[15,98183,98185,98211],{"className":98184},[290],[15,98186,98189,98198],{"className":98187,"style":98188},[294],"height:0.9128em;",[15,98190,98192,98195],{"className":98191,"style":11863},[6307],[15,98193],{"className":98194,"style":461},[302],[15,98196,2463],{"className":98197,"style":34387},[59,310],[15,98199,98201,98204],{"style":98200},"top:-2.8728em;",[15,98202],{"className":98203,"style":461},[302],[15,98205,98207],{"className":98206,"style":34444},[34443,310],[6323,98208,98209],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,98210],{"d":34451},[15,98212,318],{"className":98213},[317],[15,98215,98217],{"className":98216},[290],[15,98218,98221],{"className":98219,"style":98220},[294],"height:0.1272em;",[15,98222],{},[15,98224,98225,98228],{"style":473},[15,98226],{"className":98227,"style":461},[302],[15,98229],{"className":98230,"style":481},[480],[15,98232,98233,98236],{"style":2550},[15,98234],{"className":98235,"style":461},[302],[15,98237,98239],{"className":98238},[307,308,309,310],[15,98240,98242],{"className":98241},[59,310],[15,98243,117],{"className":98244},[59,310],[15,98246,318],{"className":98247},[317],[15,98249,98251],{"className":98250},[290],[15,98252,98255],{"className":98253,"style":98254},[294],"height:0.538em;",[15,98256],{},[15,98258],{"className":98259},[153,441],[15,98261,210],{"className":98262},[146],[15,98264,98266],{"className":98265},[59,34367],[15,98267,98269,98299],{"className":98268},[285,286],[15,98270,98272,98296],{"className":98271},[290],[15,98273,98275,98284],{"className":98274,"style":39027},[294],[15,98276,98278,98281],{"className":98277,"style":11863},[6307],[15,98279],{"className":98280,"style":461},[302],[15,98282,11],{"className":98283,"style":34387},[59,60],[15,98285,98286,98289],{"style":39039},[15,98287],{"className":98288,"style":461},[302],[15,98290,98292],{"className":98291,"style":34444},[34443],[6323,98293,98294],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,98295],{"d":34451},[15,98297,318],{"className":98298},[317],[15,98300,98302],{"className":98301},[290],[15,98303,98305],{"className":98304,"style":39059},[294],[15,98306],{},[15,98308],{"className":98309,"style":2587},[157],[15,98311,4813],{"className":98312},[2591],[15,98314],{"className":98315,"style":2587},[157],[15,98317,98319,98323,98367],{"className":98318},[50],[15,98320],{"className":98321,"style":98322},[54],"height:1.0869em;vertical-align:-0.3369em;",[15,98324,98326],{"className":98325},[59,34367],[15,98327,98329,98359],{"className":98328},[285,286],[15,98330,98332,98356],{"className":98331},[290],[15,98333,98335,98344],{"className":98334,"style":39027},[294],[15,98336,98338,98341],{"className":98337,"style":11863},[6307],[15,98339],{"className":98340,"style":461},[302],[15,98342,944],{"className":98343,"style":39099},[59,60],[15,98345,98346,98349],{"style":39039},[15,98347],{"className":98348,"style":461},[302],[15,98350,98352],{"className":98351,"style":34444},[34443],[6323,98353,98354],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,98355],{"d":34451},[15,98357,318],{"className":98358},[317],[15,98360,98362],{"className":98361},[290],[15,98363,98365],{"className":98364,"style":39059},[294],[15,98366],{},[15,98368,98370,98373],{"className":98369},[153],[15,98371,210],{"className":98372},[153],[15,98374,98376],{"className":98375},[281],[15,98377,98379,98399],{"className":98378},[285,286],[15,98380,98382,98396],{"className":98381},[290],[15,98383,98385],{"className":98384,"style":11133},[294],[15,98386,98387,98390],{"style":382},[15,98388],{"className":98389,"style":303},[302],[15,98391,98393],{"className":98392},[307,308,309,310],[15,98394,2463],{"className":98395},[59,310],[15,98397,318],{"className":98398},[317],[15,98400,98402],{"className":98401},[290],[15,98403,98405],{"className":98404,"style":7968},[294],[15,98406],{}," 就是单位球面上的欧氏距离——度量公理（对称、三角不等式）由 ",[15,98409,98411,98429],{"className":98410,"translate":19},[18],[15,98412,98414],{"className":98413},[23],[25,98415,98416],{"xmlns":27},[29,98417,98418,98426],{},[32,98419,98420],{},[6814,98421,98422,98424],{},[35,98423,21893],{},[115,98425,2463],{},[39,98427,98428],{"encoding":41},"L^2",[15,98430,98432],{"className":98431,"ariaHidden":46},[45],[15,98433,98435,98438],{"className":98434},[50],[15,98436],{"className":98437,"style":20028},[54],[15,98439,98441,98444],{"className":98440},[59],[15,98442,21893],{"className":98443},[59,60],[15,98445,98447],{"className":98446},[281],[15,98448,98450],{"className":98449},[285],[15,98451,98453],{"className":98452},[290],[15,98454,98456],{"className":98455,"style":20028},[294],[15,98457,98458,98461],{"style":6865},[15,98459],{"className":98460,"style":303},[302],[15,98462,98464],{"className":98463},[307,308,309,310],[15,98465,2463],{"className":98466},[59,310]," 距离直接继承，非退化由\"开平方是单射\"保证；",[6665,98469,98470,98786,98787,98866],{},[1225,98471,98472,98610,98611,98785],{},[15,98473,98475,98505],{"className":98474,"translate":19},[18],[15,98476,98478],{"className":98477},[23],[25,98479,98480],{"xmlns":27},[29,98481,98482,98502],{},[32,98483,98484],{},[34339,98485,98486],{},[32,98487,98488,98490,98492],{},[115,98489,2463],{},[1297,98491,1299],{},[195,98493,98494,98496],{},[35,98495,199],{},[32,98497,98498,98500],{},[35,98499,23743],{},[35,98501,25737],{},[39,98503,98504],{"encoding":41},"\\sqrt{2\\,D_{JS}}",[15,98506,98508],{"className":98507,"ariaHidden":46},[45],[15,98509,98511,98514],{"className":98510},[50],[15,98512],{"className":98513,"style":34363},[54],[15,98515,98517],{"className":98516},[59,34367],[15,98518,98520,98602],{"className":98519},[285,286],[15,98521,98523,98599],{"className":98522},[290],[15,98524,98526,98587],{"className":98525,"style":34377},[294],[15,98527,98529,98532],{"className":98528,"style":11863},[6307],[15,98530],{"className":98531,"style":461},[302],[15,98533,98535,98538,98541],{"className":98534,"style":34387},[59],[15,98536,2463],{"className":98537},[59],[15,98539],{"className":98540,"style":406},[157],[15,98542,98544,98547],{"className":98543},[59],[15,98545,199],{"className":98546,"style":277},[59,60],[15,98548,98550],{"className":98549},[281],[15,98551,98553,98579],{"className":98552},[285,286],[15,98554,98556,98576],{"className":98555},[290],[15,98557,98559],{"className":98558,"style":379},[294],[15,98560,98561,98564],{"style":298},[15,98562],{"className":98563,"style":303},[302],[15,98565,98567],{"className":98566},[307,308,309,310],[15,98568,98570,98573],{"className":98569},[59,310],[15,98571,23743],{"className":98572,"style":24153},[59,60,310],[15,98574,25737],{"className":98575,"style":25861},[59,60,310],[15,98577,318],{"className":98578},[317],[15,98580,98582],{"className":98581},[290],[15,98583,98585],{"className":98584,"style":7968},[294],[15,98586],{},[15,98588,98589,98592],{"style":34436},[15,98590],{"className":98591,"style":461},[302],[15,98593,98595],{"className":98594,"style":34444},[34443],[6323,98596,98597],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,98598],{"d":34451},[15,98600,318],{"className":98601},[317],[15,98603,98605],{"className":98604},[290],[15,98606,98608],{"className":98607,"style":34461},[294],[15,98609],{},"（等价地 ",[15,98612,98614,98642],{"className":98613,"translate":19},[18],[15,98615,98617],{"className":98616},[23],[25,98618,98619],{"xmlns":27},[29,98620,98621,98639],{},[32,98622,98623],{},[34339,98624,98625],{},[195,98626,98627,98629],{},[35,98628,199],{},[195,98630,98631,98633],{},[35,98632,37],{},[32,98634,98635,98637],{},[35,98636,23743],{},[35,98638,25737],{},[39,98640,98641],{"encoding":41},"\\sqrt{D_{f_{JS}}}",[15,98643,98645],{"className":98644,"ariaHidden":46},[45],[15,98646,98648,98652],{"className":98647},[50],[15,98649],{"className":98650,"style":98651},[54],"height:1.24em;vertical-align:-0.3564em;",[15,98653,98655],{"className":98654},[59,34367],[15,98656,98658,98776],{"className":98657},[285,286],[15,98659,98661,98773],{"className":98660},[290],[15,98662,98665,98760],{"className":98663,"style":98664},[294],"height:0.8836em;",[15,98666,98668,98671],{"className":98667,"style":83536},[6307],[15,98669],{"className":98670,"style":14846},[302],[15,98672,98674],{"className":98673,"style":41161},[59],[15,98675,98677,98680],{"className":98676},[59],[15,98678,199],{"className":98679,"style":277},[59,60],[15,98681,98683],{"className":98682},[281],[15,98684,98686,98752],{"className":98685},[285,286],[15,98687,98689,98749],{"className":98688},[290],[15,98690,98692],{"className":98691,"style":295},[294],[15,98693,98694,98697],{"style":298},[15,98695],{"className":98696,"style":303},[302],[15,98698,98700],{"className":98699},[307,308,309,310],[15,98701,98703],{"className":98702},[59,310],[15,98704,98706,98709],{"className":98705},[59,310],[15,98707,37],{"className":98708,"style":61},[59,60,310],[15,98710,98712],{"className":98711},[281],[15,98713,98715,98741],{"className":98714},[285,286],[15,98716,98718,98738],{"className":98717},[290],[15,98719,98721],{"className":98720,"style":6098},[294],[15,98722,98723,98726],{"style":30202},[15,98724],{"className":98725,"style":30206},[302],[15,98727,98729],{"className":98728},[307,30210,9674,310],[15,98730,98732,98735],{"className":98731},[59,310],[15,98733,23743],{"className":98734,"style":24153},[59,60,310],[15,98736,25737],{"className":98737,"style":25861},[59,60,310],[15,98739,318],{"className":98740},[317],[15,98742,98744],{"className":98743},[290],[15,98745,98747],{"className":98746,"style":30229},[294],[15,98748],{},[15,98750,318],{"className":98751},[317],[15,98753,98755],{"className":98754},[290],[15,98756,98758],{"className":98757,"style":325},[294],[15,98759],{},[15,98761,98763,98766],{"style":98762},"top:-2.8436em;",[15,98764],{"className":98765,"style":14846},[302],[15,98767,98769],{"className":98768,"style":83628},[34443],[6323,98770,98771],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,98772],{"d":83635},[15,98774,318],{"className":98775},[317],[15,98777,98779],{"className":98778},[290],[15,98780,98783],{"className":98781,"style":98782},[294],"height:0.3564em;",[15,98784],{}," 规范化后）是度量","（Endres–Schindelin 的结论），其证明用到了 ",[15,98788,98790,98811],{"className":98789,"translate":19},[18],[15,98791,98793],{"className":98792},[23],[25,98794,98795],{"xmlns":27},[29,98796,98797,98809],{},[32,98798,98799],{},[195,98800,98801,98803],{},[35,98802,37],{},[32,98804,98805,98807],{},[35,98806,23743],{},[35,98808,25737],{},[39,98810,30755],{"encoding":41},[15,98812,98814],{"className":98813,"ariaHidden":46},[45],[15,98815,98817,98820],{"className":98816},[50],[15,98818],{"className":98819,"style":55},[54],[15,98821,98823,98826],{"className":98822},[59],[15,98824,37],{"className":98825,"style":61},[59,60],[15,98827,98829],{"className":98828},[281],[15,98830,98832,98858],{"className":98831},[285,286],[15,98833,98835,98855],{"className":98834},[290],[15,98836,98838],{"className":98837,"style":379},[294],[15,98839,98840,98843],{"style":27509},[15,98841],{"className":98842,"style":303},[302],[15,98844,98846],{"className":98845},[307,308,309,310],[15,98847,98849,98852],{"className":98848},[59,310],[15,98850,23743],{"className":98851,"style":24153},[59,60,310],[15,98853,25737],{"className":98854,"style":25861},[59,60,310],[15,98856,318],{"className":98857},[317],[15,98859,98861],{"className":98860},[290],[15,98862,98864],{"className":98863,"style":7968},[294],[15,98865],{}," 对应生成元的\"负定型\"性质。",[11,98868,98869,98870,98986,98987,99067,99068,99096,99097,99125],{},"反过来，不对称显然排除度量；即使对称，",[15,98871,98873,98893],{"className":98872,"translate":19},[18],[15,98874,98876],{"className":98875},[23],[25,98877,98878],{"xmlns":27},[29,98879,98880,98890],{},[32,98881,98882],{},[34339,98883,98884],{},[195,98885,98886,98888],{},[35,98887,199],{},[35,98889,37],{},[39,98891,98892],{"encoding":41},"\\sqrt{D_f}",[15,98894,98896],{"className":98895,"ariaHidden":46},[45],[15,98897,98899,98902],{"className":98898},[50],[15,98900],{"className":98901,"style":98651},[54],[15,98903,98905],{"className":98904},[59,34367],[15,98906,98908,98978],{"className":98907},[285,286],[15,98909,98911,98975],{"className":98910},[290],[15,98912,98914,98963],{"className":98913,"style":98664},[294],[15,98915,98917,98920],{"className":98916,"style":83536},[6307],[15,98918],{"className":98919,"style":14846},[302],[15,98921,98923],{"className":98922,"style":41161},[59],[15,98924,98926,98929],{"className":98925},[59],[15,98927,199],{"className":98928,"style":277},[59,60],[15,98930,98932],{"className":98931},[281],[15,98933,98935,98955],{"className":98934},[285,286],[15,98936,98938,98952],{"className":98937},[290],[15,98939,98941],{"className":98940,"style":295},[294],[15,98942,98943,98946],{"style":298},[15,98944],{"className":98945,"style":303},[302],[15,98947,98949],{"className":98948},[307,308,309,310],[15,98950,37],{"className":98951,"style":61},[59,60,310],[15,98953,318],{"className":98954},[317],[15,98956,98958],{"className":98957},[290],[15,98959,98961],{"className":98960,"style":325},[294],[15,98962],{},[15,98964,98965,98968],{"style":98762},[15,98966],{"className":98967,"style":14846},[302],[15,98969,98971],{"className":98970,"style":83628},[34443],[6323,98972,98973],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,98974],{"d":83635},[15,98976,318],{"className":98977},[317],[15,98979,98981],{"className":98980},[290],[15,98982,98984],{"className":98983,"style":98782},[294],[15,98985],{}," 也不自动是度量。例如全变差 ",[15,98988,98990,99012],{"className":98989,"translate":19},[18],[15,98991,98993],{"className":98992},[23],[25,98994,98995],{"xmlns":27},[29,98996,98997,99009],{},[32,98998,98999],{},[195,99000,99001,99003],{},[35,99002,199],{},[32,99004,99005,99007],{},[35,99006,5392],{},[35,99008,34850],{},[39,99010,99011],{"encoding":41},"D_{TV}",[15,99013,99015],{"className":99014,"ariaHidden":46},[45],[15,99016,99018,99021],{"className":99017},[50],[15,99019],{"className":99020,"style":15961},[54],[15,99022,99024,99027],{"className":99023},[59],[15,99025,199],{"className":99026,"style":277},[59,60],[15,99028,99030],{"className":99029},[281],[15,99031,99033,99059],{"className":99032},[285,286],[15,99034,99036,99056],{"className":99035},[290],[15,99037,99039],{"className":99038,"style":379},[294],[15,99040,99041,99044],{"style":298},[15,99042],{"className":99043,"style":303},[302],[15,99045,99047],{"className":99046},[307,308,309,310],[15,99048,99050,99053],{"className":99049},[59,310],[15,99051,5392],{"className":99052,"style":334},[59,60,310],[15,99054,34850],{"className":99055,"style":2587},[59,60,310],[15,99057,318],{"className":99058},[317],[15,99060,99062],{"className":99061},[290],[15,99063,99065],{"className":99064,"style":7968},[294],[15,99066],{}," 本身就是度量，但若取某凸积 ",[15,99069,99071,99084],{"className":99070,"translate":19},[18],[15,99072,99074],{"className":99073},[23],[25,99075,99076],{"xmlns":27},[29,99077,99078,99082],{},[32,99079,99080],{},[35,99081,37],{},[39,99083,37],{"encoding":41},[15,99085,99087],{"className":99086,"ariaHidden":46},[45],[15,99088,99090,99093],{"className":99089},[50],[15,99091],{"className":99092,"style":55},[54],[15,99094,37],{"className":99095,"style":61},[59,60]," 的散度再做开方，三角不等式可能失效——这依赖 ",[15,99098,99100,99113],{"className":99099,"translate":19},[18],[15,99101,99103],{"className":99102},[23],[25,99104,99105],{"xmlns":27},[29,99106,99107,99111],{},[32,99108,99109],{},[35,99110,37],{},[39,99112,37],{"encoding":41},[15,99114,99116],{"className":99115,"ariaHidden":46},[45],[15,99117,99119,99122],{"className":99118},[50],[15,99120],{"className":99121,"style":55},[54],[15,99123,37],{"className":99124,"style":61},[59,60]," 是否落在\"负定（negative type）\"函数类中；不是自动成立的。",[11,99127,99128,99131,99132,99134,99135,99185,99186,99214,99215,99294],{},[1225,99129,99130],{},"与度量的对照结论："," f-散度的正确身份是",[1225,99133,52503],{},"（divergence）：非负、在 ",[15,99136,99138,99155],{"className":99137,"translate":19},[18],[15,99139,99141],{"className":99140},[23],[25,99142,99143],{"xmlns":27},[29,99144,99145,99153],{},[32,99146,99147,99149,99151],{},[35,99148,206],{},[110,99150,123],{},[35,99152,213],{},[39,99154,10271],{"encoding":41},[15,99156,99158,99176],{"className":99157,"ariaHidden":46},[45],[15,99159,99161,99164,99167,99170,99173],{"className":99160},[50],[15,99162],{"className":99163,"style":664},[54],[15,99165,206],{"className":99166,"style":334},[59,60],[15,99168],{"className":99169,"style":158},[157],[15,99171,123],{"className":99172},[162],[15,99174],{"className":99175,"style":158},[157],[15,99177,99179,99182],{"className":99178},[50],[15,99180],{"className":99181,"style":566},[54],[15,99183,213],{"className":99184},[59,60]," 处取零，但不要求对称与三角不等式。当我们需要真距离时（例如做收敛分析、中心化、 ",[15,99187,99189,99202],{"className":99188,"translate":19},[18],[15,99190,99192],{"className":99191},[23],[25,99193,99194],{"xmlns":27},[29,99195,99196,99200],{},[32,99197,99198],{},[35,99199,7564],{},[39,99201,7564],{"encoding":41},[15,99203,99205],{"className":99204,"ariaHidden":46},[45],[15,99206,99208,99211],{"className":99207},[50],[15,99209],{"className":99210,"style":12597},[54],[15,99212,7564],{"className":99213,"style":8267},[59,60],"-中心聚类），就从 f-散度族里挑那些 ",[15,99216,99218,99234],{"className":99217,"translate":19},[18],[15,99219,99221],{"className":99220},[23],[25,99222,99223],{"xmlns":27},[29,99224,99225,99231],{},[32,99226,99227],{},[34339,99228,99229],{},[110,99230,3299],{"lspace":1247,"rspace":1247},[39,99232,99233],{"encoding":41},"\\sqrt{\\cdot}",[15,99235,99237],{"className":99236,"ariaHidden":46},[45],[15,99238,99240,99244],{"className":99239},[50],[15,99241],{"className":99242,"style":99243},[54],"height:1.04em;vertical-align:-0.2328em;",[15,99245,99247],{"className":99246},[59,34367],[15,99248,99250,99285],{"className":99249},[285,286],[15,99251,99253,99282],{"className":99252},[290],[15,99254,99257,99269],{"className":99255,"style":99256},[294],"height:0.8072em;",[15,99258,99260,99263],{"className":99259,"style":11863},[6307],[15,99261],{"className":99262,"style":461},[302],[15,99264,99266],{"className":99265,"style":34387},[59],[15,99267,3299],{"className":99268},[59],[15,99270,99272,99275],{"style":99271},"top:-2.7672em;",[15,99273],{"className":99274,"style":461},[302],[15,99276,99278],{"className":99277,"style":34444},[34443],[6323,99279,99280],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,99281],{"d":34451},[15,99283,318],{"className":99284},[317],[15,99286,99288],{"className":99287},[290],[15,99289,99292],{"className":99290,"style":99291},[294],"height:0.2328em;",[15,99293],{}," 后成为度量的成员（Hellinger、JS、TV），或干脆换成真正的度量类（第 6 节的 IPM）。",[528,99296,99298],{"id":99297},"_5-变分表示与-f-gan","5. 变分表示与 f-GAN",[2311,99300,99302],{"id":99301},"_51-可训练目标","5.1 可训练目标",[11,99304,99305],{},"4.4 节给出精确对偶：",[15,99307,99309],{"className":99308,"translate":19},[180],[15,99310,99312,99406],{"className":99311,"translate":19},[18],[15,99313,99315],{"className":99314},[23],[25,99316,99317],{"xmlns":27,"display":189},[29,99318,99319,99403],{},[32,99320,99321,99327,99329,99331,99333,99335,99337,99339,99349,99351,99357,99359,99361,99363,99365,99367,99369,99371,99377,99379,99385,99387,99389,99391,99393,99395,99397,99399,99401],{},[195,99322,99323,99325],{},[35,99324,199],{},[35,99326,37],{},[110,99328,113],{"stretchy":112},[35,99330,206],{},[35,99332,210],{"mathvariant":209},[35,99334,213],{},[110,99336,120],{"stretchy":112},[110,99338,123],{},[6016,99340,99341,99347],{},[32,99342,99343,99345],{},[35,99344,35432],{},[110,99346,4103],{},[35,99348,4158],{},[110,99350,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,99352,99353,99355],{},[35,99354,223],{"mathvariant":222},[35,99356,206],{},[110,99358,230],{"stretchy":112},[35,99360,4158],{},[110,99362,113],{"stretchy":112},[35,99364,598],{},[110,99366,120],{"stretchy":112},[110,99368,257],{"stretchy":112},[110,99370,4813],{},[195,99372,99373,99375],{},[35,99374,223],{"mathvariant":222},[35,99376,213],{},[110,99378,230],{"stretchy":112},[6814,99380,99381,99383],{},[35,99382,37],{},[110,99384,7573],{},[110,99386,113],{"stretchy":112},[35,99388,4158],{},[110,99390,113],{"stretchy":112},[35,99392,598],{},[110,99394,120],{"stretchy":112},[110,99396,120],{"stretchy":112},[110,99398,257],{"stretchy":112},[110,99400,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,99402,4375],{"mathvariant":209},[39,99404,99405],{"encoding":41},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g(X)]\n-\\mathbb E_Q[f^*(g(X))]\\Big\\}.",[15,99407,99409,99479,99606],{"className":99408,"ariaHidden":46},[45],[15,99410,99412,99415,99455,99458,99461,99464,99467,99470,99473,99476],{"className":99411},[50],[15,99413],{"className":99414,"style":270},[54],[15,99416,99418,99421],{"className":99417},[59],[15,99419,199],{"className":99420,"style":277},[59,60],[15,99422,99424],{"className":99423},[281],[15,99425,99427,99447],{"className":99426},[285,286],[15,99428,99430,99444],{"className":99429},[290],[15,99431,99433],{"className":99432,"style":295},[294],[15,99434,99435,99438],{"style":298},[15,99436],{"className":99437,"style":303},[302],[15,99439,99441],{"className":99440},[307,308,309,310],[15,99442,37],{"className":99443,"style":61},[59,60,310],[15,99445,318],{"className":99446},[317],[15,99448,99450],{"className":99449},[290],[15,99451,99453],{"className":99452,"style":325},[294],[15,99454],{},[15,99456,113],{"className":99457},[146],[15,99459,206],{"className":99460,"style":334},[59,60],[15,99462,210],{"className":99463},[59],[15,99465,213],{"className":99466},[59,60],[15,99468,120],{"className":99469},[153],[15,99471],{"className":99472,"style":158},[157],[15,99474,123],{"className":99475},[162],[15,99477],{"className":99478,"style":158},[157],[15,99480,99482,99486,99533,99536,99542,99582,99585,99588,99591,99594,99597,99600,99603],{"className":99481},[50],[15,99483],{"className":99484,"style":99485},[54],"height:2.1805em;vertical-align:-1.0305em;",[15,99487,99489],{"className":99488},[1484,13716],[15,99490,99492,99525],{"className":99491},[285,286],[15,99493,99495,99522],{"className":99494},[290],[15,99496,99498,99512],{"className":99497,"style":2345},[294],[15,99499,99500,99503],{"style":61190},[15,99501],{"className":99502,"style":461},[302],[15,99504,99506],{"className":99505},[307,308,309,310],[15,99507,99509],{"className":99508},[59,310],[15,99510,4158],{"className":99511,"style":981},[59,60,310],[15,99513,99514,99517],{"style":11863},[15,99515],{"className":99516,"style":461},[302],[15,99518,99519],{},[15,99520,35432],{"className":99521},[1484],[15,99523,318],{"className":99524},[317],[15,99526,99528],{"className":99527},[290],[15,99529,99531],{"className":99530,"style":61222},[294],[15,99532],{},[15,99534],{"className":99535,"style":406},[157],[15,99537,99539],{"className":99538},[59],[15,99540,2898],{"className":99541},[419,3720],[15,99543,99545,99548],{"className":99544},[59],[15,99546,223],{"className":99547},[59,366],[15,99549,99551],{"className":99550},[281],[15,99552,99554,99574],{"className":99553},[285,286],[15,99555,99557,99571],{"className":99556},[290],[15,99558,99560],{"className":99559,"style":379},[294],[15,99561,99562,99565],{"style":382},[15,99563],{"className":99564,"style":303},[302],[15,99566,99568],{"className":99567},[307,308,309,310],[15,99569,206],{"className":99570,"style":334},[59,60,310],[15,99572,318],{"className":99573},[317],[15,99575,99577],{"className":99576},[290],[15,99578,99580],{"className":99579,"style":7968},[294],[15,99581],{},[15,99583,230],{"className":99584},[146],[15,99586,4158],{"className":99587,"style":981},[59,60],[15,99589,113],{"className":99590},[146],[15,99592,598],{"className":99593,"style":8887},[59,60],[15,99595,20390],{"className":99596},[153],[15,99598],{"className":99599,"style":2587},[157],[15,99601,4813],{"className":99602},[2591],[15,99604],{"className":99605,"style":2587},[157],[15,99607,99609,99612,99652,99655,99684,99687,99690,99693,99696,99700,99706],{"className":99608},[50],[15,99610],{"className":99611,"style":68117},[54],[15,99613,99615,99618],{"className":99614},[59],[15,99616,223],{"className":99617},[59,366],[15,99619,99621],{"className":99620},[281],[15,99622,99624,99644],{"className":99623},[285,286],[15,99625,99627,99641],{"className":99626},[290],[15,99628,99630],{"className":99629,"style":379},[294],[15,99631,99632,99635],{"style":382},[15,99633],{"className":99634,"style":303},[302],[15,99636,99638],{"className":99637},[307,308,309,310],[15,99639,213],{"className":99640},[59,60,310],[15,99642,318],{"className":99643},[317],[15,99645,99647],{"className":99646},[290],[15,99648,99650],{"className":99649,"style":325},[294],[15,99651],{},[15,99653,230],{"className":99654},[146],[15,99656,99658,99661],{"className":99657},[59],[15,99659,37],{"className":99660,"style":61},[59,60],[15,99662,99664],{"className":99663},[281],[15,99665,99667],{"className":99666},[285],[15,99668,99670],{"className":99669},[290],[15,99671,99673],{"className":99672,"style":8248},[294],[15,99674,99675,99678],{"style":8277},[15,99676],{"className":99677,"style":303},[302],[15,99679,99681],{"className":99680},[307,308,309,310],[15,99682,7573],{"className":99683},[2591,310],[15,99685,113],{"className":99686},[146],[15,99688,4158],{"className":99689,"style":981},[59,60],[15,99691,113],{"className":99692},[146],[15,99694,598],{"className":99695,"style":8887},[59,60],[15,99697,99699],{"className":99698},[153],"))]",[15,99701,99703],{"className":99702},[59],[15,99704,2908],{"className":99705},[419,3720],[15,99707,4375],{"className":99708},[59],[11,99710,68132,99711,99739,99740,99768,99769,99838,99839,99842,99843,99914],{},[15,99712,99714,99727],{"className":99713,"translate":19},[18],[15,99715,99717],{"className":99716},[23],[25,99718,99719],{"xmlns":27},[29,99720,99721,99725],{},[32,99722,99723],{},[35,99724,206],{},[39,99726,206],{"encoding":41},[15,99728,99730],{"className":99729,"ariaHidden":46},[45],[15,99731,99733,99736],{"className":99732},[50],[15,99734],{"className":99735,"style":664},[54],[15,99737,206],{"className":99738,"style":334},[59,60]," 是数据分布、",[15,99741,99743,99756],{"className":99742,"translate":19},[18],[15,99744,99746],{"className":99745},[23],[25,99747,99748],{"xmlns":27},[29,99749,99750,99754],{},[32,99751,99752],{},[35,99753,213],{},[39,99755,213],{"encoding":41},[15,99757,99759],{"className":99758,"ariaHidden":46},[45],[15,99760,99762,99765],{"className":99761},[50],[15,99763],{"className":99764,"style":566},[54],[15,99766,213],{"className":99767},[59,60]," 是生成分布时，右端可直接用两批样本做蒙特卡洛估计，得到 ",[15,99770,99772,99789],{"className":99771,"translate":19},[18],[15,99773,99775],{"className":99774},[23],[25,99776,99777],{"xmlns":27},[29,99778,99779,99787],{},[32,99780,99781],{},[195,99782,99783,99785],{},[35,99784,199],{},[35,99786,37],{},[39,99788,4022],{"encoding":41},[15,99790,99792],{"className":99791,"ariaHidden":46},[45],[15,99793,99795,99798],{"className":99794},[50],[15,99796],{"className":99797,"style":4032},[54],[15,99799,99801,99804],{"className":99800},[59],[15,99802,199],{"className":99803,"style":277},[59,60],[15,99805,99807],{"className":99806},[281],[15,99808,99810,99830],{"className":99809},[285,286],[15,99811,99813,99827],{"className":99812},[290],[15,99814,99816],{"className":99815,"style":295},[294],[15,99817,99818,99821],{"style":298},[15,99819],{"className":99820,"style":303},[302],[15,99822,99824],{"className":99823},[307,308,309,310],[15,99825,37],{"className":99826,"style":61},[59,60,310],[15,99828,318],{"className":99829},[317],[15,99831,99833],{"className":99832},[290],[15,99834,99836],{"className":99835,"style":325},[294],[15,99837],{}," 的一个",[1225,99840,99841],{},"下界","，并用一个网络 ",[15,99844,99846,99865],{"className":99845,"translate":19},[18],[15,99847,99849],{"className":99848},[23],[25,99850,99851],{"xmlns":27},[29,99852,99853,99862],{},[32,99854,99855],{},[195,99856,99857,99859],{},[35,99858,4158],{},[35,99860,99861],{},"ω",[39,99863,99864],{"encoding":41},"g_\\omega",[15,99866,99868],{"className":99867,"ariaHidden":46},[45],[15,99869,99871,99874],{"className":99870},[50],[15,99872],{"className":99873,"style":2276},[54],[15,99875,99877,99880],{"className":99876},[59],[15,99878,4158],{"className":99879,"style":981},[59,60],[15,99881,99883],{"className":99882},[281],[15,99884,99886,99906],{"className":99885},[285,286],[15,99887,99889,99903],{"className":99888},[290],[15,99890,99892],{"className":99891,"style":44929},[294],[15,99893,99894,99897],{"style":18843},[15,99895],{"className":99896,"style":303},[302],[15,99898,99900],{"className":99899},[307,308,309,310],[15,99901,99861],{"className":99902,"style":981},[59,60,310],[15,99904,318],{"className":99905},[317],[15,99907,99909],{"className":99908},[290],[15,99910,99912],{"className":99911,"style":7968},[294],[15,99913],{}," 逼近最优解。于是",[15,99916,99918],{"className":99917,"translate":19},[180],[15,99919,99921,100051],{"className":99920,"translate":19},[18],[15,99922,99924],{"className":99923},[23],[25,99925,99926],{"xmlns":27,"display":189},[29,99927,99928,100048],{},[32,99929,99930,99941,99943,99945,99947,99949,99951,99957,99959,99961,99967,99981,99987,99989,99995,99997,99999,100005,100020,100026,100028,100034,100036,100042,100044,100046],{},[195,99931,99932,99939],{},[11811,99933,99934,99936],{"accent":46},[35,99935,199],{},[110,99937,99938],{"stretchy":46},"^",[35,99940,37],{},[110,99942,113],{"stretchy":112},[35,99944,206],{},[35,99946,210],{"mathvariant":209},[35,99948,213],{},[110,99950,33875],{"separator":46},[195,99952,99953,99955],{},[35,99954,4158],{},[35,99956,99861],{},[110,99958,120],{"stretchy":112},[110,99960,123],{},[238,99962,99963,99965],{},[115,99964,117],{},[35,99966,82296],{},[48320,99968,99969,99971,99979],{},[110,99970,13461],{},[32,99972,99973,99975,99977],{},[35,99974,11963],{},[110,99976,123],{},[115,99978,117],{},[35,99980,82296],{},[195,99982,99983,99985],{},[35,99984,4158],{},[35,99986,99861],{},[110,99988,113],{"stretchy":112},[195,99990,99991,99993],{},[35,99992,774],{},[35,99994,11963],{},[110,99996,120],{"stretchy":112},[110,99998,4813],{},[238,100000,100001,100003],{},[115,100002,117],{},[35,100004,26323],{},[48320,100006,100007,100009,100018],{},[110,100008,13461],{},[32,100010,100011,100014,100016],{},[35,100012,100013],{},"j",[110,100015,123],{},[115,100017,117],{},[35,100019,26323],{},[6814,100021,100022,100024],{},[35,100023,37],{},[110,100025,7573],{},[110,100027,113],{"stretchy":112},[195,100029,100030,100032],{},[35,100031,4158],{},[35,100033,99861],{},[110,100035,113],{"stretchy":112},[195,100037,100038,100040],{},[35,100039,40237],{},[35,100041,100013],{},[110,100043,120],{"stretchy":112},[110,100045,120],{"stretchy":112},[35,100047,4375],{"mathvariant":209},[39,100049,100050],{"encoding":41},"\\widehat D_f(P\\|Q;g_\\omega)\n=\\frac1n\\sum_{i=1}^n g_\\omega(x_i)\n-\\frac1m\\sum_{j=1}^m f^*(g_\\omega(y_j)).",[15,100052,100054,100207,100443],{"className":100053,"ariaHidden":46},[45],[15,100055,100057,100061,100137,100140,100143,100146,100149,100152,100155,100195,100198,100201,100204],{"className":100056},[50],[15,100058],{"className":100059,"style":100060},[54],"height:1.2094em;vertical-align:-0.2861em;",[15,100062,100064,100103],{"className":100063},[59],[15,100065,100067],{"className":100066},[59,11851],[15,100068,100070],{"className":100069},[285],[15,100071,100073],{"className":100072},[290],[15,100074,100077,100085],{"className":100075,"style":100076},[294],"height:0.9233em;",[15,100078,100079,100082],{"style":11863},[15,100080],{"className":100081,"style":461},[302],[15,100083,199],{"className":100084,"style":277},[59,60],[15,100086,100089,100092],{"className":100087,"style":100088},[6307],"width:calc(100% - 0.1111em);margin-left:0.1111em;top:-3.6833em;",[15,100090],{"className":100091,"style":461},[302],[15,100093,100095],{"style":100094},"height:0.24em;",[6323,100096,100100],{"xmlns":6325,"width":75878,"height":100097,"viewBox":100098,"preserveAspectRatio":100099},"0.24em","0 0 1062 239","none",[6331,100101],{"d":100102},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[15,100104,100106],{"className":100105},[281],[15,100107,100109,100129],{"className":100108},[285,286],[15,100110,100112,100126],{"className":100111},[290],[15,100113,100115],{"className":100114,"style":295},[294],[15,100116,100117,100120],{"style":298},[15,100118],{"className":100119,"style":303},[302],[15,100121,100123],{"className":100122},[307,308,309,310],[15,100124,37],{"className":100125,"style":61},[59,60,310],[15,100127,318],{"className":100128},[317],[15,100130,100132],{"className":100131},[290],[15,100133,100135],{"className":100134,"style":325},[294],[15,100136],{},[15,100138,113],{"className":100139},[146],[15,100141,206],{"className":100142,"style":334},[59,60],[15,100144,210],{"className":100145},[59],[15,100147,213],{"className":100148},[59,60],[15,100150,33875],{"className":100151},[573],[15,100153],{"className":100154,"style":406},[157],[15,100156,100158,100161],{"className":100157},[59],[15,100159,4158],{"className":100160,"style":981},[59,60],[15,100162,100164],{"className":100163},[281],[15,100165,100167,100187],{"className":100166},[285,286],[15,100168,100170,100184],{"className":100169},[290],[15,100171,100173],{"className":100172,"style":44929},[294],[15,100174,100175,100178],{"style":18843},[15,100176],{"className":100177,"style":303},[302],[15,100179,100181],{"className":100180},[307,308,309,310],[15,100182,99861],{"className":100183,"style":981},[59,60,310],[15,100185,318],{"className":100186},[317],[15,100188,100190],{"className":100189},[290],[15,100191,100193],{"className":100192,"style":7968},[294],[15,100194],{},[15,100196,120],{"className":100197},[153],[15,100199],{"className":100200,"style":158},[157],[15,100202,123],{"className":100203},[162],[15,100205],{"className":100206,"style":158},[157],[15,100208,100210,100214,100276,100279,100345,100348,100388,100391,100431,100434,100437,100440],{"className":100209},[50],[15,100211],{"className":100212,"style":100213},[54],"height:2.9291em;vertical-align:-1.2777em;",[15,100215,100217,100220,100273],{"className":100216},[59],[15,100218],{"className":100219},[146,441],[15,100221,100223],{"className":100222},[238],[15,100224,100226,100265],{"className":100225},[285,286],[15,100227,100229,100262],{"className":100228},[290],[15,100230,100232,100243,100251],{"className":100231,"style":22889},[294],[15,100233,100234,100237],{"style":457},[15,100235],{"className":100236,"style":461},[302],[15,100238,100240],{"className":100239},[59],[15,100241,82296],{"className":100242},[59,60],[15,100244,100245,100248],{"style":473},[15,100246],{"className":100247,"style":461},[302],[15,100249],{"className":100250,"style":481},[480],[15,100252,100253,100256],{"style":484},[15,100254],{"className":100255,"style":461},[302],[15,100257,100259],{"className":100258},[59],[15,100260,117],{"className":100261},[59],[15,100263,318],{"className":100264},[317],[15,100266,100268],{"className":100267},[290],[15,100269,100271],{"className":100270,"style":3778},[294],[15,100272],{},[15,100274],{"className":100275},[153,441],[15,100277],{"className":100278,"style":406},[157],[15,100280,100282],{"className":100281},[1484,13716],[15,100283,100285,100337],{"className":100284},[285,286],[15,100286,100288,100334],{"className":100287},[290],[15,100289,100292,100312,100322],{"className":100290,"style":100291},[294],"height:1.6514em;",[15,100293,100294,100297],{"style":13729},[15,100295],{"className":100296,"style":13733},[302],[15,100298,100300],{"className":100299},[307,308,309,310],[15,100301,100303,100306,100309],{"className":100302},[59,310],[15,100304,11963],{"className":100305},[59,60,310],[15,100307,123],{"className":100308},[162,310],[15,100310,117],{"className":100311},[59,310],[15,100313,100314,100317],{"style":13742},[15,100315],{"className":100316,"style":13733},[302],[15,100318,100319],{},[15,100320,13461],{"className":100321},[1484,1485,1486],[15,100323,100325,100328],{"style":100324},"top:-4.3em;margin-left:0em;",[15,100326],{"className":100327,"style":13733},[302],[15,100329,100331],{"className":100330},[307,308,309,310],[15,100332,82296],{"className":100333},[59,60,310],[15,100335,318],{"className":100336},[317],[15,100338,100340],{"className":100339},[290],[15,100341,100343],{"className":100342,"style":13760},[294],[15,100344],{},[15,100346],{"className":100347,"style":406},[157],[15,100349,100351,100354],{"className":100350},[59],[15,100352,4158],{"className":100353,"style":981},[59,60],[15,100355,100357],{"className":100356},[281],[15,100358,100360,100380],{"className":100359},[285,286],[15,100361,100363,100377],{"className":100362},[290],[15,100364,100366],{"className":100365,"style":44929},[294],[15,100367,100368,100371],{"style":18843},[15,100369],{"className":100370,"style":303},[302],[15,100372,100374],{"className":100373},[307,308,309,310],[15,100375,99861],{"className":100376,"style":981},[59,60,310],[15,100378,318],{"className":100379},[317],[15,100381,100383],{"className":100382},[290],[15,100384,100386],{"className":100385,"style":7968},[294],[15,100387],{},[15,100389,113],{"className":100390},[146],[15,100392,100394,100397],{"className":100393},[59],[15,100395,774],{"className":100396},[59,60],[15,100398,100400],{"className":100399},[281],[15,100401,100403,100423],{"className":100402},[285,286],[15,100404,100406,100420],{"className":100405},[290],[15,100407,100409],{"className":100408,"style":12182},[294],[15,100410,100411,100414],{"style":382},[15,100412],{"className":100413,"style":303},[302],[15,100415,100417],{"className":100416},[307,308,309,310],[15,100418,11963],{"className":100419},[59,60,310],[15,100421,318],{"className":100422},[317],[15,100424,100426],{"className":100425},[290],[15,100427,100429],{"className":100428,"style":7968},[294],[15,100430],{},[15,100432,120],{"className":100433},[153],[15,100435],{"className":100436,"style":2587},[157],[15,100438,4813],{"className":100439},[2591],[15,100441],{"className":100442,"style":2587},[157],[15,100444,100446,100450,100512,100515,100581,100584,100613,100616,100656,100659,100699,100702],{"className":100445},[50],[15,100447],{"className":100448,"style":100449},[54],"height:3.0652em;vertical-align:-1.4138em;",[15,100451,100453,100456,100509],{"className":100452},[59],[15,100454],{"className":100455},[146,441],[15,100457,100459],{"className":100458},[238],[15,100460,100462,100501],{"className":100461},[285,286],[15,100463,100465,100498],{"className":100464},[290],[15,100466,100468,100479,100487],{"className":100467,"style":22889},[294],[15,100469,100470,100473],{"style":457},[15,100471],{"className":100472,"style":461},[302],[15,100474,100476],{"className":100475},[59],[15,100477,26323],{"className":100478},[59,60],[15,100480,100481,100484],{"style":473},[15,100482],{"className":100483,"style":461},[302],[15,100485],{"className":100486,"style":481},[480],[15,100488,100489,100492],{"style":484},[15,100490],{"className":100491,"style":461},[302],[15,100493,100495],{"className":100494},[59],[15,100496,117],{"className":100497},[59],[15,100499,318],{"className":100500},[317],[15,100502,100504],{"className":100503},[290],[15,100505,100507],{"className":100506,"style":3778},[294],[15,100508],{},[15,100510],{"className":100511},[153,441],[15,100513],{"className":100514,"style":406},[157],[15,100516,100518],{"className":100517},[1484,13716],[15,100519,100521,100572],{"className":100520},[285,286],[15,100522,100524,100569],{"className":100523},[290],[15,100525,100527,100548,100558],{"className":100526,"style":100291},[294],[15,100528,100529,100532],{"style":13729},[15,100530],{"className":100531,"style":13733},[302],[15,100533,100535],{"className":100534},[307,308,309,310],[15,100536,100538,100542,100545],{"className":100537},[59,310],[15,100539,100013],{"className":100540,"style":100541},[59,60,310],"margin-right:0.0572em;",[15,100543,123],{"className":100544},[162,310],[15,100546,117],{"className":100547},[59,310],[15,100549,100550,100553],{"style":13742},[15,100551],{"className":100552,"style":13733},[302],[15,100554,100555],{},[15,100556,13461],{"className":100557},[1484,1485,1486],[15,100559,100560,100563],{"style":100324},[15,100561],{"className":100562,"style":13733},[302],[15,100564,100566],{"className":100565},[307,308,309,310],[15,100567,26323],{"className":100568},[59,60,310],[15,100570,318],{"className":100571},[317],[15,100573,100575],{"className":100574},[290],[15,100576,100579],{"className":100577,"style":100578},[294],"height:1.4138em;",[15,100580],{},[15,100582],{"className":100583,"style":406},[157],[15,100585,100587,100590],{"className":100586},[59],[15,100588,37],{"className":100589,"style":61},[59,60],[15,100591,100593],{"className":100592},[281],[15,100594,100596],{"className":100595},[285],[15,100597,100599],{"className":100598},[290],[15,100600,100602],{"className":100601,"style":8248},[294],[15,100603,100604,100607],{"style":8277},[15,100605],{"className":100606,"style":303},[302],[15,100608,100610],{"className":100609},[307,308,309,310],[15,100611,7573],{"className":100612},[2591,310],[15,100614,113],{"className":100615},[146],[15,100617,100619,100622],{"className":100618},[59],[15,100620,4158],{"className":100621,"style":981},[59,60],[15,100623,100625],{"className":100624},[281],[15,100626,100628,100648],{"className":100627},[285,286],[15,100629,100631,100645],{"className":100630},[290],[15,100632,100634],{"className":100633,"style":44929},[294],[15,100635,100636,100639],{"style":18843},[15,100637],{"className":100638,"style":303},[302],[15,100640,100642],{"className":100641},[307,308,309,310],[15,100643,99861],{"className":100644,"style":981},[59,60,310],[15,100646,318],{"className":100647},[317],[15,100649,100651],{"className":100650},[290],[15,100652,100654],{"className":100653,"style":7968},[294],[15,100655],{},[15,100657,113],{"className":100658},[146],[15,100660,100662,100665],{"className":100661},[59],[15,100663,40237],{"className":100664,"style":981},[59,60],[15,100666,100668],{"className":100667},[281],[15,100669,100671,100691],{"className":100670},[285,286],[15,100672,100674,100688],{"className":100673},[290],[15,100675,100677],{"className":100676,"style":12182},[294],[15,100678,100679,100682],{"style":18843},[15,100680],{"className":100681,"style":303},[302],[15,100683,100685],{"className":100684},[307,308,309,310],[15,100686,100013],{"className":100687,"style":100541},[59,60,310],[15,100689,318],{"className":100690},[317],[15,100692,100694],{"className":100693},[290],[15,100695,100697],{"className":100696,"style":325},[294],[15,100698],{},[15,100700,19047],{"className":100701},[153],[15,100703,4375],{"className":100704},[59],[11,100706,14261,100707,100736,100737,100830],{},[15,100708,100710,100724],{"className":100709,"translate":19},[18],[15,100711,100713],{"className":100712},[23],[25,100714,100715],{"xmlns":27},[29,100716,100717,100721],{},[32,100718,100719],{},[35,100720,99861],{},[39,100722,100723],{"encoding":41},"\\omega",[15,100725,100727],{"className":100726,"ariaHidden":46},[45],[15,100728,100730,100733],{"className":100729},[50],[15,100731],{"className":100732,"style":2345},[54],[15,100734,99861],{"className":100735,"style":981},[59,60]," 极大化即得估计；把 ",[15,100738,100740,100763],{"className":100739,"translate":19},[18],[15,100741,100743],{"className":100742},[23],[25,100744,100745],{"xmlns":27},[29,100746,100747,100760],{},[32,100748,100749,100751,100753],{},[35,100750,213],{},[110,100752,123],{},[195,100754,100755,100757],{},[35,100756,213],{},[35,100758,100759],{},"θ",[39,100761,100762],{"encoding":41},"Q=Q_\\theta",[15,100764,100766,100784],{"className":100765,"ariaHidden":46},[45],[15,100767,100769,100772,100775,100778,100781],{"className":100768},[50],[15,100770],{"className":100771,"style":566},[54],[15,100773,213],{"className":100774},[59,60],[15,100776],{"className":100777,"style":158},[157],[15,100779,123],{"className":100780},[162],[15,100782],{"className":100783,"style":158},[157],[15,100785,100787,100790],{"className":100786},[50],[15,100788],{"className":100789,"style":566},[54],[15,100791,100793,100796],{"className":100792},[59],[15,100794,213],{"className":100795},[59,60],[15,100797,100799],{"className":100798},[281],[15,100800,100802,100822],{"className":100801},[285,286],[15,100803,100805,100819],{"className":100804},[290],[15,100806,100808],{"className":100807,"style":295},[294],[15,100809,100810,100813],{"style":382},[15,100811],{"className":100812,"style":303},[302],[15,100814,100816],{"className":100815},[307,308,309,310],[15,100817,100759],{"className":100818,"style":277},[59,60,310],[15,100820,318],{"className":100821},[317],[15,100823,100825],{"className":100824},[290],[15,100826,100828],{"className":100827,"style":7968},[294],[15,100829],{},"（生成器）同时放进去，就得到 f-GAN 的 minimax 目标：",[15,100832,100834],{"className":100833,"translate":19},[180],[15,100835,100837,100939],{"className":100836,"translate":19},[18],[15,100838,100840],{"className":100839},[23],[25,100841,100842],{"xmlns":27,"display":189},[29,100843,100844,100936],{},[32,100845,100846,100856,100858,100868,100870,100872,100878,100880,100886,100888,100890,100892,100894,100896,100906,100908,100914,100916,100922,100924,100926,100928,100930,100932,100934],{},[6016,100847,100848,100854],{},[32,100849,100850,100852],{},[35,100851,51608],{},[110,100853,4103],{},[35,100855,100759],{},[1297,100857,4283],{},[6016,100859,100860,100866],{},[32,100861,100862,100864],{},[35,100863,52387],{},[110,100865,4103],{},[35,100867,99861],{},[1297,100869,4283],{},[110,100871,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,100873,100874,100876],{},[35,100875,223],{"mathvariant":222},[35,100877,206],{},[110,100879,230],{"stretchy":112},[195,100881,100882,100884],{},[35,100883,4158],{},[35,100885,99861],{},[110,100887,113],{"stretchy":112},[35,100889,598],{},[110,100891,120],{"stretchy":112},[110,100893,257],{"stretchy":112},[110,100895,4813],{},[195,100897,100898,100900],{},[35,100899,223],{"mathvariant":222},[195,100901,100902,100904],{},[35,100903,213],{},[35,100905,100759],{},[110,100907,230],{"stretchy":112},[6814,100909,100910,100912],{},[35,100911,37],{},[110,100913,7573],{},[110,100915,113],{"stretchy":112},[195,100917,100918,100920],{},[35,100919,4158],{},[35,100921,99861],{},[110,100923,113],{"stretchy":112},[35,100925,598],{},[110,100927,120],{"stretchy":112},[110,100929,120],{"stretchy":112},[110,100931,257],{"stretchy":112},[110,100933,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,100935,4375],{"mathvariant":209},[39,100937,100938],{"encoding":41},"\\min_\\theta\\ \\max_\\omega\\\n\\Big\\{\\mathbb E_{P}[g_\\omega(X)]\n-\\mathbb E_{Q_\\theta}[f^*(g_\\omega(X))]\\Big\\}.",[15,100940,100942,101162],{"className":100941,"ariaHidden":46},[45],[15,100943,100945,100949,100994,100997,101000,101046,101049,101052,101058,101101,101104,101144,101147,101150,101153,101156,101159],{"className":100944},[50],[15,100946],{"className":100947,"style":100948},[54],"height:1.9021em;vertical-align:-0.7521em;",[15,100950,100952],{"className":100951},[1484,13716],[15,100953,100955,100985],{"className":100954},[285,286],[15,100956,100958,100982],{"className":100957},[290],[15,100959,100961,100972],{"className":100960,"style":51893},[294],[15,100962,100963,100966],{"style":51896},[15,100964],{"className":100965,"style":461},[302],[15,100967,100969],{"className":100968},[307,308,309,310],[15,100970,100759],{"className":100971,"style":277},[59,60,310],[15,100973,100974,100977],{"style":11863},[15,100975],{"className":100976,"style":461},[302],[15,100978,100979],{},[15,100980,51608],{"className":100981},[1484],[15,100983,318],{"className":100984},[317],[15,100986,100988],{"className":100987},[290],[15,100989,100992],{"className":100990,"style":100991},[294],"height:0.7521em;",[15,100993],{},[15,100995,4283],{"className":100996},[157],[15,100998],{"className":100999,"style":406},[157],[15,101001,101003],{"className":101002},[1484,13716],[15,101004,101006,101037],{"className":101005},[285,286],[15,101007,101009,101034],{"className":101008},[290],[15,101010,101012,101024],{"className":101011,"style":2345},[294],[15,101013,101015,101018],{"style":101014},"top:-2.4em;margin-left:0em;",[15,101016],{"className":101017,"style":461},[302],[15,101019,101021],{"className":101020},[307,308,309,310],[15,101022,99861],{"className":101023,"style":981},[59,60,310],[15,101025,101026,101029],{"style":11863},[15,101027],{"className":101028,"style":461},[302],[15,101030,101031],{},[15,101032,52387],{"className":101033},[1484],[15,101035,318],{"className":101036},[317],[15,101038,101040],{"className":101039},[290],[15,101041,101044],{"className":101042,"style":101043},[294],"height:0.7em;",[15,101045],{},[15,101047,4283],{"className":101048},[157],[15,101050],{"className":101051,"style":406},[157],[15,101053,101055],{"className":101054},[59],[15,101056,2898],{"className":101057},[419,3720],[15,101059,101061,101064],{"className":101060},[59],[15,101062,223],{"className":101063},[59,366],[15,101065,101067],{"className":101066},[281],[15,101068,101070,101093],{"className":101069},[285,286],[15,101071,101073,101090],{"className":101072},[290],[15,101074,101076],{"className":101075,"style":379},[294],[15,101077,101078,101081],{"style":382},[15,101079],{"className":101080,"style":303},[302],[15,101082,101084],{"className":101083},[307,308,309,310],[15,101085,101087],{"className":101086},[59,310],[15,101088,206],{"className":101089,"style":334},[59,60,310],[15,101091,318],{"className":101092},[317],[15,101094,101096],{"className":101095},[290],[15,101097,101099],{"className":101098,"style":7968},[294],[15,101100],{},[15,101102,230],{"className":101103},[146],[15,101105,101107,101110],{"className":101106},[59],[15,101108,4158],{"className":101109,"style":981},[59,60],[15,101111,101113],{"className":101112},[281],[15,101114,101116,101136],{"className":101115},[285,286],[15,101117,101119,101133],{"className":101118},[290],[15,101120,101122],{"className":101121,"style":44929},[294],[15,101123,101124,101127],{"style":18843},[15,101125],{"className":101126,"style":303},[302],[15,101128,101130],{"className":101129},[307,308,309,310],[15,101131,99861],{"className":101132,"style":981},[59,60,310],[15,101134,318],{"className":101135},[317],[15,101137,101139],{"className":101138},[290],[15,101140,101142],{"className":101141,"style":7968},[294],[15,101143],{},[15,101145,113],{"className":101146},[146],[15,101148,598],{"className":101149,"style":8887},[59,60],[15,101151,20390],{"className":101152},[153],[15,101154],{"className":101155,"style":2587},[157],[15,101157,4813],{"className":101158},[2591],[15,101160],{"className":101161,"style":2587},[157],[15,101163,101165,101168,101250,101253,101282,101285,101325,101328,101331,101334,101340],{"className":101164},[50],[15,101166],{"className":101167,"style":68117},[54],[15,101169,101171,101174],{"className":101170},[59],[15,101172,223],{"className":101173},[59,366],[15,101175,101177],{"className":101176},[281],[15,101178,101180,101242],{"className":101179},[285,286],[15,101181,101183,101239],{"className":101182},[290],[15,101184,101186],{"className":101185,"style":379},[294],[15,101187,101188,101191],{"style":382},[15,101189],{"className":101190,"style":303},[302],[15,101192,101194],{"className":101193},[307,308,309,310],[15,101195,101197],{"className":101196},[59,310],[15,101198,101200,101203],{"className":101199},[59,310],[15,101201,213],{"className":101202},[59,60,310],[15,101204,101206],{"className":101205},[281],[15,101207,101209,101230],{"className":101208},[285,286],[15,101210,101212,101227],{"className":101211},[290],[15,101213,101215],{"className":101214,"style":6098},[294],[15,101216,101218,101221],{"style":101217},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[15,101219],{"className":101220,"style":30206},[302],[15,101222,101224],{"className":101223},[307,30210,9674,310],[15,101225,100759],{"className":101226,"style":277},[59,60,310],[15,101228,318],{"className":101229},[317],[15,101231,101233],{"className":101232},[290],[15,101234,101237],{"className":101235,"style":101236},[294],"height:0.1512em;",[15,101238],{},[15,101240,318],{"className":101241},[317],[15,101243,101245],{"className":101244},[290],[15,101246,101248],{"className":101247,"style":325},[294],[15,101249],{},[15,101251,230],{"className":101252},[146],[15,101254,101256,101259],{"className":101255},[59],[15,101257,37],{"className":101258,"style":61},[59,60],[15,101260,101262],{"className":101261},[281],[15,101263,101265],{"className":101264},[285],[15,101266,101268],{"className":101267},[290],[15,101269,101271],{"className":101270,"style":8248},[294],[15,101272,101273,101276],{"style":8277},[15,101274],{"className":101275,"style":303},[302],[15,101277,101279],{"className":101278},[307,308,309,310],[15,101280,7573],{"className":101281},[2591,310],[15,101283,113],{"className":101284},[146],[15,101286,101288,101291],{"className":101287},[59],[15,101289,4158],{"className":101290,"style":981},[59,60],[15,101292,101294],{"className":101293},[281],[15,101295,101297,101317],{"className":101296},[285,286],[15,101298,101300,101314],{"className":101299},[290],[15,101301,101303],{"className":101302,"style":44929},[294],[15,101304,101305,101308],{"style":18843},[15,101306],{"className":101307,"style":303},[302],[15,101309,101311],{"className":101310},[307,308,309,310],[15,101312,99861],{"className":101313,"style":981},[59,60,310],[15,101315,318],{"className":101316},[317],[15,101318,101320],{"className":101319},[290],[15,101321,101323],{"className":101322,"style":7968},[294],[15,101324],{},[15,101326,113],{"className":101327},[146],[15,101329,598],{"className":101330,"style":8887},[59,60],[15,101332,99699],{"className":101333},[153],[15,101335,101337],{"className":101336},[59],[15,101338,2908],{"className":101339},[419,3720],[15,101341,4375],{"className":101342},[59],[2311,101344,101346],{"id":101345},"_52-最优判别器","5.2 最优判别器",[993,101348,101350,101424,101695],{"title":101349},"命题 5.1（最优判别器）",[11,101351,101352,101353,101394,101395,101423],{},"在 5.1 节的 minimax 目标中，固定 ",[15,101354,101356,101373],{"className":101355,"translate":19},[18],[15,101357,101359],{"className":101358},[23],[25,101360,101361],{"xmlns":27},[29,101362,101363,101371],{},[32,101364,101365,101367,101369],{},[35,101366,206],{},[110,101368,551],{"separator":46},[35,101370,213],{},[39,101372,556],{"encoding":41},[15,101374,101376],{"className":101375,"ariaHidden":46},[45],[15,101377,101379,101382,101385,101388,101391],{"className":101378},[50],[15,101380],{"className":101381,"style":566},[54],[15,101383,206],{"className":101384,"style":334},[59,60],[15,101386,551],{"className":101387},[573],[15,101389],{"className":101390,"style":406},[157],[15,101392,213],{"className":101393},[59,60]," 时内层对 ",[15,101396,101398,101411],{"className":101397,"translate":19},[18],[15,101399,101401],{"className":101400},[23],[25,101402,101403],{"xmlns":27},[29,101404,101405,101409],{},[32,101406,101407],{},[35,101408,4158],{},[39,101410,4158],{"encoding":41},[15,101412,101414],{"className":101413,"ariaHidden":46},[45],[15,101415,101417,101420],{"className":101416},[50],[15,101418],{"className":101419,"style":2276},[54],[15,101421,4158],{"className":101422,"style":981},[59,60]," 的最优解为",[15,101425,101427],{"className":101426,"translate":19},[180],[15,101428,101430,101494],{"className":101429,"translate":19},[18],[15,101431,101433],{"className":101432},[23],[25,101434,101435],{"xmlns":27,"display":189},[29,101436,101437,101491],{},[32,101438,101439,101445,101447,101449,101451,101453,101459,101461,101489],{},[6814,101440,101441,101443],{},[35,101442,4158],{},[110,101444,7573],{},[110,101446,113],{"stretchy":112},[35,101448,774],{},[110,101450,120],{"stretchy":112},[110,101452,123],{},[6814,101454,101455,101457],{},[35,101456,37],{},[110,101458,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[1297,101460,1304],{},[32,101462,101463,101465,101487],{},[110,101464,113],{"fence":46},[238,101466,101467,101477],{},[32,101468,101469,101471,101473,101475],{},[35,101470,11],{},[110,101472,113],{"stretchy":112},[35,101474,774],{},[110,101476,120],{"stretchy":112},[32,101478,101479,101481,101483,101485],{},[35,101480,944],{},[110,101482,113],{"stretchy":112},[35,101484,774],{},[110,101486,120],{"stretchy":112},[110,101488,120],{"fence":46},[110,101490,551],{"separator":46},[39,101492,101493],{"encoding":41},"g^*(x)=f'\\!\\left(\\frac{p(x)}{q(x)}\\right),",[15,101495,101497,101550],{"className":101496,"ariaHidden":46},[45],[15,101498,101500,101503,101532,101535,101538,101541,101544,101547],{"className":101499},[50],[15,101501],{"className":101502,"style":139},[54],[15,101504,101506,101509],{"className":101505},[59],[15,101507,4158],{"className":101508,"style":981},[59,60],[15,101510,101512],{"className":101511},[281],[15,101513,101515],{"className":101514},[285],[15,101516,101518],{"className":101517},[290],[15,101519,101521],{"className":101520,"style":8248},[294],[15,101522,101523,101526],{"style":8277},[15,101524],{"className":101525,"style":303},[302],[15,101527,101529],{"className":101528},[307,308,309,310],[15,101530,7573],{"className":101531},[2591,310],[15,101533,113],{"className":101534},[146],[15,101536,774],{"className":101537},[59,60],[15,101539,120],{"className":101540},[153],[15,101542],{"className":101543,"style":158},[157],[15,101545,123],{"className":101546},[162],[15,101548],{"className":101549,"style":158},[157],[15,101551,101553,101556,101588,101591,101594,101689,101692],{"className":101552},[50],[15,101554],{"className":101555,"style":359},[54],[15,101557,101559,101562],{"className":101558},[59],[15,101560,37],{"className":101561,"style":61},[59,60],[15,101563,101565],{"className":101564},[281],[15,101566,101568],{"className":101567},[285],[15,101569,101571],{"className":101570},[290],[15,101572,101574],{"className":101573,"style":28971},[294],[15,101575,101576,101579],{"style":8277},[15,101577],{"className":101578,"style":303},[302],[15,101580,101582],{"className":101581},[307,308,309,310],[15,101583,101585],{"className":101584},[59,310],[15,101586,6820],{"className":101587},[59,310],[15,101589],{"className":101590,"style":1512},[157],[15,101592],{"className":101593,"style":406},[157],[15,101595,101597,101603,101683],{"className":101596},[410],[15,101598,101600],{"className":101599,"style":415},[146,414],[15,101601,113],{"className":101602},[419,309],[15,101604,101606,101609,101680],{"className":101605},[59],[15,101607],{"className":101608},[146,441],[15,101610,101612],{"className":101611},[238],[15,101613,101615,101672],{"className":101614},[285,286],[15,101616,101618,101669],{"className":101617},[290],[15,101619,101621,101641,101649],{"className":101620,"style":1543},[294],[15,101622,101623,101626],{"style":457},[15,101624],{"className":101625,"style":461},[302],[15,101627,101629,101632,101635,101638],{"className":101628},[59],[15,101630,944],{"className":101631,"style":981},[59,60],[15,101633,113],{"className":101634},[146],[15,101636,774],{"className":101637},[59,60],[15,101639,120],{"className":101640},[153],[15,101642,101643,101646],{"style":473},[15,101644],{"className":101645,"style":461},[302],[15,101647],{"className":101648,"style":481},[480],[15,101650,101651,101654],{"style":484},[15,101652],{"className":101653,"style":461},[302],[15,101655,101657,101660,101663,101666],{"className":101656},[59],[15,101658,11],{"className":101659},[59,60],[15,101661,113],{"className":101662},[146],[15,101664,774],{"className":101665},[59,60],[15,101667,120],{"className":101668},[153],[15,101670,318],{"className":101671},[317],[15,101673,101675],{"className":101674},[290],[15,101676,101678],{"className":101677,"style":1601},[294],[15,101679],{},[15,101681],{"className":101682},[153,441],[15,101684,101686],{"className":101685,"style":415},[153,414],[15,101687,120],{"className":101688},[419,309],[15,101690],{"className":101691,"style":406},[157],[15,101693,551],{"className":101694},[573],[11,101696,101697,101698,101760],{},"即判别器学到的量是似然比经 ",[15,101699,101701,101719],{"className":101700,"translate":19},[18],[15,101702,101704],{"className":101703},[23],[25,101705,101706],{"xmlns":27},[29,101707,101708,101716],{},[32,101709,101710],{},[6814,101711,101712,101714],{},[35,101713,37],{},[110,101715,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[39,101717,101718],{"encoding":41},"f'",[15,101720,101722],{"className":101721,"ariaHidden":46},[45],[15,101723,101725,101728],{"className":101724},[50],[15,101726],{"className":101727,"style":64161},[54],[15,101729,101731,101734],{"className":101730},[59],[15,101732,37],{"className":101733,"style":61},[59,60],[15,101735,101737],{"className":101736},[281],[15,101738,101740],{"className":101739},[285],[15,101741,101743],{"className":101742},[290],[15,101744,101746],{"className":101745,"style":6862},[294],[15,101747,101748,101751],{"style":6865},[15,101749],{"className":101750,"style":303},[302],[15,101752,101754],{"className":101753},[307,308,309,310],[15,101755,101757],{"className":101756},[59,310],[15,101758,6820],{"className":101759},[59,310]," 之后的取值。",[11,101762,101763,101765,101766,101810,101811,101974,101975,102018],{},[1225,101764,55471],{}," 目标对 ",[15,101767,101769,101789],{"className":101768,"translate":19},[18],[15,101770,101772],{"className":101771},[23],[25,101773,101774],{"xmlns":27},[29,101775,101776,101786],{},[32,101777,101778,101780,101782,101784],{},[35,101779,4158],{},[110,101781,113],{"stretchy":112},[35,101783,774],{},[110,101785,120],{"stretchy":112},[39,101787,101788],{"encoding":41},"g(x)",[15,101790,101792],{"className":101791,"ariaHidden":46},[45],[15,101793,101795,101798,101801,101804,101807],{"className":101794},[50],[15,101796],{"className":101797,"style":139},[54],[15,101799,4158],{"className":101800,"style":981},[59,60],[15,101802,113],{"className":101803},[146],[15,101805,774],{"className":101806},[59,60],[15,101808,120],{"className":101809},[153]," 的逐点依赖是 ",[15,101812,101814,101870],{"className":101813,"translate":19},[18],[15,101815,101817],{"className":101816},[23],[25,101818,101819],{"xmlns":27},[29,101820,101821,101867],{},[32,101822,101823,101825,101827,101829,101831,101833,101835,101837,101839,101841,101843,101845,101847,101849,101855,101857,101859,101861,101863,101865],{},[35,101824,11],{},[110,101826,113],{"stretchy":112},[35,101828,774],{},[110,101830,120],{"stretchy":112},[35,101832,4158],{},[110,101834,113],{"stretchy":112},[35,101836,774],{},[110,101838,120],{"stretchy":112},[110,101840,4813],{},[35,101842,944],{},[110,101844,113],{"stretchy":112},[35,101846,774],{},[110,101848,120],{"stretchy":112},[6814,101850,101851,101853],{},[35,101852,37],{},[110,101854,7573],{},[110,101856,113],{"stretchy":112},[35,101858,4158],{},[110,101860,113],{"stretchy":112},[35,101862,774],{},[110,101864,120],{"stretchy":112},[110,101866,120],{"stretchy":112},[39,101868,101869],{"encoding":41},"p(x)g(x)-q(x)f^*(g(x))",[15,101871,101873,101912],{"className":101872,"ariaHidden":46},[45],[15,101874,101876,101879,101882,101885,101888,101891,101894,101897,101900,101903,101906,101909],{"className":101875},[50],[15,101877],{"className":101878,"style":139},[54],[15,101880,11],{"className":101881},[59,60],[15,101883,113],{"className":101884},[146],[15,101886,774],{"className":101887},[59,60],[15,101889,120],{"className":101890},[153],[15,101892,4158],{"className":101893,"style":981},[59,60],[15,101895,113],{"className":101896},[146],[15,101898,774],{"className":101899},[59,60],[15,101901,120],{"className":101902},[153],[15,101904],{"className":101905,"style":2587},[157],[15,101907,4813],{"className":101908},[2591],[15,101910],{"className":101911,"style":2587},[157],[15,101913,101915,101918,101921,101924,101927,101930,101959,101962,101965,101968,101971],{"className":101914},[50],[15,101916],{"className":101917,"style":139},[54],[15,101919,944],{"className":101920,"style":981},[59,60],[15,101922,113],{"className":101923},[146],[15,101925,774],{"className":101926},[59,60],[15,101928,120],{"className":101929},[153],[15,101931,101933,101936],{"className":101932},[59],[15,101934,37],{"className":101935,"style":61},[59,60],[15,101937,101939],{"className":101938},[281],[15,101940,101942],{"className":101941},[285],[15,101943,101945],{"className":101944},[290],[15,101946,101948],{"className":101947,"style":8499},[294],[15,101949,101950,101953],{"style":6865},[15,101951],{"className":101952,"style":303},[302],[15,101954,101956],{"className":101955},[307,308,309,310],[15,101957,7573],{"className":101958},[2591,310],[15,101960,113],{"className":101961},[146],[15,101963,4158],{"className":101964,"style":981},[59,60],[15,101966,113],{"className":101967},[146],[15,101969,774],{"className":101970},[59,60],[15,101972,19047],{"className":101973},[153],"，对 ",[15,101976,101978,101997],{"className":101977,"translate":19},[18],[15,101979,101981],{"className":101980},[23],[25,101982,101983],{"xmlns":27},[29,101984,101985,101995],{},[32,101986,101987,101989,101991,101993],{},[35,101988,4158],{},[110,101990,113],{"stretchy":112},[35,101992,774],{},[110,101994,120],{"stretchy":112},[39,101996,101788],{"encoding":41},[15,101998,102000],{"className":101999,"ariaHidden":46},[45],[15,102001,102003,102006,102009,102012,102015],{"className":102002},[50],[15,102004],{"className":102005,"style":139},[54],[15,102007,4158],{"className":102008,"style":981},[59,60],[15,102010,113],{"className":102011},[146],[15,102013,774],{"className":102014},[59,60],[15,102016,120],{"className":102017},[153]," 求导：",[15,102020,102022],{"className":102021,"translate":19},[180],[15,102023,102025,102145],{"className":102024,"translate":19},[18],[15,102026,102028],{"className":102027},[23],[25,102029,102030],{"xmlns":27,"display":189},[29,102031,102032,102142],{},[32,102033,102034,102036,102038,102040,102042,102044,102046,102048,102050,102052,102054,102064,102066,102068,102070,102072,102074,102076,102078,102080,102082,102084,102086,102096,102098,102104,102106,102108,102110,102112,102114,102136,102138,102140],{},[35,102035,11],{},[110,102037,113],{"stretchy":112},[35,102039,774],{},[110,102041,120],{"stretchy":112},[110,102043,4813],{},[35,102045,944],{},[110,102047,113],{"stretchy":112},[35,102049,774],{},[110,102051,120],{"stretchy":112},[1297,102053,1299],{},[6814,102055,102056,102058],{},[35,102057,37],{},[32,102059,102060,102062],{},[110,102061,7573],{},[110,102063,6820],{"mathvariant":209},[110,102065,113],{"stretchy":112},[35,102067,4158],{},[110,102069,113],{"stretchy":112},[35,102071,774],{},[110,102073,120],{"stretchy":112},[110,102075,120],{"stretchy":112},[110,102077,123],{},[115,102079,126],{},[1297,102081,4283],{},[110,102083,4286],{},[1297,102085,4283],{},[6814,102087,102088,102090],{},[35,102089,37],{},[32,102091,102092,102094],{},[110,102093,7573],{},[110,102095,6820],{"mathvariant":209},[110,102097,113],{"stretchy":112},[6814,102099,102100,102102],{},[35,102101,4158],{},[110,102103,7573],{},[110,102105,113],{"stretchy":112},[35,102107,774],{},[110,102109,120],{"stretchy":112},[110,102111,120],{"stretchy":112},[110,102113,123],{},[238,102115,102116,102126],{},[32,102117,102118,102120,102122,102124],{},[35,102119,11],{},[110,102121,113],{"stretchy":112},[35,102123,774],{},[110,102125,120],{"stretchy":112},[32,102127,102128,102130,102132,102134],{},[35,102129,944],{},[110,102131,113],{"stretchy":112},[35,102133,774],{},[110,102135,120],{"stretchy":112},[110,102137,123],{},[35,102139,769],{},[35,102141,4375],{"mathvariant":209},[39,102143,102144],{"encoding":41},"p(x)-q(x)\\,f^{*\\prime}(g(x))=0\n\\ \\Longrightarrow\\\nf^{*\\prime}(g^*(x))=\\frac{p(x)}{q(x)}=t .",[15,102146,102148,102175,102256,102280,102371,102467],{"className":102147,"ariaHidden":46},[45],[15,102149,102151,102154,102157,102160,102163,102166,102169,102172],{"className":102150},[50],[15,102152],{"className":102153,"style":139},[54],[15,102155,11],{"className":102156},[59,60],[15,102158,113],{"className":102159},[146],[15,102161,774],{"className":102162},[59,60],[15,102164,120],{"className":102165},[153],[15,102167],{"className":102168,"style":2587},[157],[15,102170,4813],{"className":102171},[2591],[15,102173],{"className":102174,"style":2587},[157],[15,102176,102178,102182,102185,102188,102191,102194,102197,102232,102235,102238,102241,102244,102247,102250,102253],{"className":102177},[50],[15,102179],{"className":102180,"style":102181},[54],"height:1.0519em;vertical-align:-0.25em;",[15,102183,944],{"className":102184,"style":981},[59,60],[15,102186,113],{"className":102187},[146],[15,102189,774],{"className":102190},[59,60],[15,102192,120],{"className":102193},[153],[15,102195],{"className":102196,"style":406},[157],[15,102198,102200,102203],{"className":102199},[59],[15,102201,37],{"className":102202,"style":61},[59,60],[15,102204,102206],{"className":102205},[281],[15,102207,102209],{"className":102208},[285],[15,102210,102212],{"className":102211},[290],[15,102213,102215],{"className":102214,"style":28971},[294],[15,102216,102217,102220],{"style":8277},[15,102218],{"className":102219,"style":303},[302],[15,102221,102223],{"className":102222},[307,308,309,310],[15,102224,102226,102229],{"className":102225},[59,310],[15,102227,7573],{"className":102228},[59,310],[15,102230,6820],{"className":102231},[59,310],[15,102233,113],{"className":102234},[146],[15,102236,4158],{"className":102237,"style":981},[59,60],[15,102239,113],{"className":102240},[146],[15,102242,774],{"className":102243},[59,60],[15,102245,19047],{"className":102246},[153],[15,102248],{"className":102249,"style":158},[157],[15,102251,123],{"className":102252},[162],[15,102254],{"className":102255,"style":158},[157],[15,102257,102259,102262,102265,102268,102271,102274,102277],{"className":102258},[50],[15,102260],{"className":102261,"style":92783},[54],[15,102263,126],{"className":102264},[59],[15,102266,4283],{"className":102267},[157],[15,102269],{"className":102270,"style":158},[157],[15,102272,4286],{"className":102273},[162],[15,102275,4283],{"className":102276},[157],[15,102278],{"className":102279,"style":158},[157],[15,102281,102283,102286,102321,102324,102353,102356,102359,102362,102365,102368],{"className":102282},[50],[15,102284],{"className":102285,"style":102181},[54],[15,102287,102289,102292],{"className":102288},[59],[15,102290,37],{"className":102291,"style":61},[59,60],[15,102293,102295],{"className":102294},[281],[15,102296,102298],{"className":102297},[285],[15,102299,102301],{"className":102300},[290],[15,102302,102304],{"className":102303,"style":28971},[294],[15,102305,102306,102309],{"style":8277},[15,102307],{"className":102308,"style":303},[302],[15,102310,102312],{"className":102311},[307,308,309,310],[15,102313,102315,102318],{"className":102314},[59,310],[15,102316,7573],{"className":102317},[59,310],[15,102319,6820],{"className":102320},[59,310],[15,102322,113],{"className":102323},[146],[15,102325,102327,102330],{"className":102326},[59],[15,102328,4158],{"className":102329,"style":981},[59,60],[15,102331,102333],{"className":102332},[281],[15,102334,102336],{"className":102335},[285],[15,102337,102339],{"className":102338},[290],[15,102340,102342],{"className":102341,"style":8248},[294],[15,102343,102344,102347],{"style":8277},[15,102345],{"className":102346,"style":303},[302],[15,102348,102350],{"className":102349},[307,308,309,310],[15,102351,7573],{"className":102352},[2591,310],[15,102354,113],{"className":102355},[146],[15,102357,774],{"className":102358},[59,60],[15,102360,19047],{"className":102361},[153],[15,102363],{"className":102364,"style":158},[157],[15,102366,123],{"className":102367},[162],[15,102369],{"className":102370,"style":158},[157],[15,102372,102374,102378,102458,102461,102464],{"className":102373},[50],[15,102375],{"className":102376,"style":102377},[54],"height:2.363em;vertical-align:-0.936em;",[15,102379,102381,102384,102455],{"className":102380},[59],[15,102382],{"className":102383},[146,441],[15,102385,102387],{"className":102386},[238],[15,102388,102390,102447],{"className":102389},[285,286],[15,102391,102393,102444],{"className":102392},[290],[15,102394,102396,102416,102424],{"className":102395,"style":1543},[294],[15,102397,102398,102401],{"style":457},[15,102399],{"className":102400,"style":461},[302],[15,102402,102404,102407,102410,102413],{"className":102403},[59],[15,102405,944],{"className":102406,"style":981},[59,60],[15,102408,113],{"className":102409},[146],[15,102411,774],{"className":102412},[59,60],[15,102414,120],{"className":102415},[153],[15,102417,102418,102421],{"style":473},[15,102419],{"className":102420,"style":461},[302],[15,102422],{"className":102423,"style":481},[480],[15,102425,102426,102429],{"style":484},[15,102427],{"className":102428,"style":461},[302],[15,102430,102432,102435,102438,102441],{"className":102431},[59],[15,102433,11],{"className":102434},[59,60],[15,102436,113],{"className":102437},[146],[15,102439,774],{"className":102440},[59,60],[15,102442,120],{"className":102443},[153],[15,102445,318],{"className":102446},[317],[15,102448,102450],{"className":102449},[290],[15,102451,102453],{"className":102452,"style":1601},[294],[15,102454],{},[15,102456],{"className":102457},[153,441],[15,102459],{"className":102460,"style":158},[157],[15,102462,123],{"className":102463},[162],[15,102465],{"className":102466,"style":158},[157],[15,102468,102470,102473,102476],{"className":102469},[50],[15,102471],{"className":102472,"style":5343},[54],[15,102474,769],{"className":102475},[59,60],[15,102477,4375],{"className":102478},[59],[11,102480,34092,102481,102688,102689,102845,102846,102904,102905,102999,103000,103003,103004,103073,103074,103155,103156,103184],{},[15,102482,102484,102530],{"className":102483,"translate":19},[18],[15,102485,102487],{"className":102486},[23],[25,102488,102489],{"xmlns":27},[29,102490,102491,102527],{},[32,102492,102493,102495,102501,102507,102509,102511,102517],{},[110,102494,113],{"stretchy":112},[6814,102496,102497,102499],{},[35,102498,37],{},[110,102500,7573],{},[6814,102502,102503,102505],{},[110,102504,120],{"stretchy":112},[110,102506,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,102508,123],{},[110,102510,113],{"stretchy":112},[6814,102512,102513,102515],{},[35,102514,37],{},[110,102516,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[6814,102518,102519,102521],{},[110,102520,120],{"stretchy":112},[32,102522,102523,102525],{},[110,102524,4813],{},[115,102526,117],{},[39,102528,102529],{"encoding":41},"(f^*)'=(f')^{-1}",[15,102531,102533,102612],{"className":102532,"ariaHidden":46},[45],[15,102534,102536,102539,102542,102571,102603,102606,102609],{"className":102535},[50],[15,102537],{"className":102538,"style":6843},[54],[15,102540,113],{"className":102541},[146],[15,102543,102545,102548],{"className":102544},[59],[15,102546,37],{"className":102547,"style":61},[59,60],[15,102549,102551],{"className":102550},[281],[15,102552,102554],{"className":102553},[285],[15,102555,102557],{"className":102556},[290],[15,102558,102560],{"className":102559,"style":8499},[294],[15,102561,102562,102565],{"style":6865},[15,102563],{"className":102564,"style":303},[302],[15,102566,102568],{"className":102567},[307,308,309,310],[15,102569,7573],{"className":102570},[2591,310],[15,102572,102574,102577],{"className":102573},[153],[15,102575,120],{"className":102576},[153],[15,102578,102580],{"className":102579},[281],[15,102581,102583],{"className":102582},[285],[15,102584,102586],{"className":102585},[290],[15,102587,102589],{"className":102588,"style":6862},[294],[15,102590,102591,102594],{"style":6865},[15,102592],{"className":102593,"style":303},[302],[15,102595,102597],{"className":102596},[307,308,309,310],[15,102598,102600],{"className":102599},[59,310],[15,102601,6820],{"className":102602},[59,310],[15,102604],{"className":102605,"style":158},[157],[15,102607,123],{"className":102608},[162],[15,102610],{"className":102611,"style":158},[157],[15,102613,102615,102618,102621,102653],{"className":102614},[50],[15,102616],{"className":102617,"style":20003},[54],[15,102619,113],{"className":102620},[146],[15,102622,102624,102627],{"className":102623},[59],[15,102625,37],{"className":102626,"style":61},[59,60],[15,102628,102630],{"className":102629},[281],[15,102631,102633],{"className":102632},[285],[15,102634,102636],{"className":102635},[290],[15,102637,102639],{"className":102638,"style":6862},[294],[15,102640,102641,102644],{"style":6865},[15,102642],{"className":102643,"style":303},[302],[15,102645,102647],{"className":102646},[307,308,309,310],[15,102648,102650],{"className":102649},[59,310],[15,102651,6820],{"className":102652},[59,310],[15,102654,102656,102659],{"className":102655},[153],[15,102657,120],{"className":102658},[153],[15,102660,102662],{"className":102661},[281],[15,102663,102665],{"className":102664},[285],[15,102666,102668],{"className":102667},[290],[15,102669,102671],{"className":102670,"style":20028},[294],[15,102672,102673,102676],{"style":6865},[15,102674],{"className":102675,"style":303},[302],[15,102677,102679],{"className":102678},[307,308,309,310],[15,102680,102682,102685],{"className":102681},[59,310],[15,102683,4813],{"className":102684},[59,310],[15,102686,117],{"className":102687},[59,310],"（Fenchel 的互逆关系），即得 ",[15,102690,102692,102736],{"className":102691,"translate":19},[18],[15,102693,102695],{"className":102694},[23],[25,102696,102697],{"xmlns":27},[29,102698,102699,102733],{},[32,102700,102701,102707,102709,102711,102713,102715,102721,102723,102725,102727,102729,102731],{},[6814,102702,102703,102705],{},[35,102704,4158],{},[110,102706,7573],{},[110,102708,113],{"stretchy":112},[35,102710,774],{},[110,102712,120],{"stretchy":112},[110,102714,123],{},[6814,102716,102717,102719],{},[35,102718,37],{},[110,102720,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,102722,113],{"stretchy":112},[35,102724,769],{},[110,102726,113],{"stretchy":112},[35,102728,774],{},[110,102730,120],{"stretchy":112},[110,102732,120],{"stretchy":112},[39,102734,102735],{"encoding":41},"g^*(x)=f'(t(x))",[15,102737,102739,102792],{"className":102738,"ariaHidden":46},[45],[15,102740,102742,102745,102774,102777,102780,102783,102786,102789],{"className":102741},[50],[15,102743],{"className":102744,"style":139},[54],[15,102746,102748,102751],{"className":102747},[59],[15,102749,4158],{"className":102750,"style":981},[59,60],[15,102752,102754],{"className":102753},[281],[15,102755,102757],{"className":102756},[285],[15,102758,102760],{"className":102759},[290],[15,102761,102763],{"className":102762,"style":8499},[294],[15,102764,102765,102768],{"style":6865},[15,102766],{"className":102767,"style":303},[302],[15,102769,102771],{"className":102770},[307,308,309,310],[15,102772,7573],{"className":102773},[2591,310],[15,102775,113],{"className":102776},[146],[15,102778,774],{"className":102779},[59,60],[15,102781,120],{"className":102782},[153],[15,102784],{"className":102785,"style":158},[157],[15,102787,123],{"className":102788},[162],[15,102790],{"className":102791,"style":158},[157],[15,102793,102795,102798,102830,102833,102836,102839,102842],{"className":102794},[50],[15,102796],{"className":102797,"style":6843},[54],[15,102799,102801,102804],{"className":102800},[59],[15,102802,37],{"className":102803,"style":61},[59,60],[15,102805,102807],{"className":102806},[281],[15,102808,102810],{"className":102809},[285],[15,102811,102813],{"className":102812},[290],[15,102814,102816],{"className":102815,"style":6862},[294],[15,102817,102818,102821],{"style":6865},[15,102819],{"className":102820,"style":303},[302],[15,102822,102824],{"className":102823},[307,308,309,310],[15,102825,102827],{"className":102826},[59,310],[15,102828,6820],{"className":102829},[59,310],[15,102831,113],{"className":102832},[146],[15,102834,769],{"className":102835},[59,60],[15,102837,113],{"className":102838},[146],[15,102840,774],{"className":102841},[59,60],[15,102843,19047],{"className":102844},[153],"。把 ",[15,102847,102849,102866],{"className":102848,"translate":19},[18],[15,102850,102852],{"className":102851},[23],[25,102853,102854],{"xmlns":27},[29,102855,102856,102864],{},[32,102857,102858],{},[6814,102859,102860,102862],{},[35,102861,4158],{},[110,102863,7573],{},[39,102865,64005],{"encoding":41},[15,102867,102869],{"className":102868,"ariaHidden":46},[45],[15,102870,102872,102875],{"className":102871},[50],[15,102873],{"className":102874,"style":64015},[54],[15,102876,102878,102881],{"className":102877},[59],[15,102879,4158],{"className":102880,"style":981},[59,60],[15,102882,102884],{"className":102883},[281],[15,102885,102887],{"className":102886},[285],[15,102888,102890],{"className":102889},[290],[15,102891,102893],{"className":102892,"style":8499},[294],[15,102894,102895,102898],{"style":6865},[15,102896],{"className":102897,"style":303},[302],[15,102899,102901],{"className":102900},[307,308,309,310],[15,102902,7573],{"className":102903},[2591,310]," 代回即得 ",[15,102906,102908,102935],{"className":102907,"translate":19},[18],[15,102909,102911],{"className":102910},[23],[25,102912,102913],{"xmlns":27},[29,102914,102915,102933],{},[32,102916,102917,102923,102925,102927,102929,102931],{},[195,102918,102919,102921],{},[35,102920,199],{},[35,102922,37],{},[110,102924,113],{"stretchy":112},[35,102926,206],{},[35,102928,210],{"mathvariant":209},[35,102930,213],{},[110,102932,120],{"stretchy":112},[39,102934,5239],{"encoding":41},[15,102936,102938],{"className":102937,"ariaHidden":46},[45],[15,102939,102941,102944,102984,102987,102990,102993,102996],{"className":102940},[50],[15,102942],{"className":102943,"style":270},[54],[15,102945,102947,102950],{"className":102946},[59],[15,102948,199],{"className":102949,"style":277},[59,60],[15,102951,102953],{"className":102952},[281],[15,102954,102956,102976],{"className":102955},[285,286],[15,102957,102959,102973],{"className":102958},[290],[15,102960,102962],{"className":102961,"style":295},[294],[15,102963,102964,102967],{"style":298},[15,102965],{"className":102966,"style":303},[302],[15,102968,102970],{"className":102969},[307,308,309,310],[15,102971,37],{"className":102972,"style":61},[59,60,310],[15,102974,318],{"className":102975},[317],[15,102977,102979],{"className":102978},[290],[15,102980,102982],{"className":102981,"style":325},[294],[15,102983],{},[15,102985,113],{"className":102986},[146],[15,102988,206],{"className":102989,"style":334},[59,60],[15,102991,210],{"className":102992},[59],[15,102994,213],{"className":102995},[59,60],[15,102997,120],{"className":102998},[153],"（这正是定理 4.1 所给的最优解）。",[1225,103001,103002],{},"实践含义："," 判别器网络 ",[15,103005,103007,103024],{"className":103006,"translate":19},[18],[15,103008,103010],{"className":103009},[23],[25,103011,103012],{"xmlns":27},[29,103013,103014,103022],{},[32,103015,103016],{},[195,103017,103018,103020],{},[35,103019,4158],{},[35,103021,99861],{},[39,103023,99864],{"encoding":41},[15,103025,103027],{"className":103026,"ariaHidden":46},[45],[15,103028,103030,103033],{"className":103029},[50],[15,103031],{"className":103032,"style":2276},[54],[15,103034,103036,103039],{"className":103035},[59],[15,103037,4158],{"className":103038,"style":981},[59,60],[15,103040,103042],{"className":103041},[281],[15,103043,103045,103065],{"className":103044},[285,286],[15,103046,103048,103062],{"className":103047},[290],[15,103049,103051],{"className":103050,"style":44929},[294],[15,103052,103053,103056],{"style":18843},[15,103054],{"className":103055,"style":303},[302],[15,103057,103059],{"className":103058},[307,308,309,310],[15,103060,99861],{"className":103061,"style":981},[59,60,310],[15,103063,318],{"className":103064},[317],[15,103066,103068],{"className":103067},[290],[15,103069,103071],{"className":103070,"style":7968},[294],[15,103072],{}," 学的是 ",[15,103075,103077,103102],{"className":103076,"translate":19},[18],[15,103078,103080],{"className":103079},[23],[25,103081,103082],{"xmlns":27},[29,103083,103084,103099],{},[32,103085,103086,103092,103094,103097],{},[6814,103087,103088,103090],{},[35,103089,37],{},[110,103091,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,103093,113],{"stretchy":112},[1297,103095,103096],{},"似然比",[110,103098,120],{"stretchy":112},[39,103100,103101],{"encoding":41},"f'(\\text{似然比})",[15,103103,103105],{"className":103104,"ariaHidden":46},[45],[15,103106,103108,103111,103143,103146,103152],{"className":103107},[50],[15,103109],{"className":103110,"style":6843},[54],[15,103112,103114,103117],{"className":103113},[59],[15,103115,37],{"className":103116,"style":61},[59,60],[15,103118,103120],{"className":103119},[281],[15,103121,103123],{"className":103122},[285],[15,103124,103126],{"className":103125},[290],[15,103127,103129],{"className":103128,"style":6862},[294],[15,103130,103131,103134],{"style":6865},[15,103132],{"className":103133,"style":303},[302],[15,103135,103137],{"className":103136},[307,308,309,310],[15,103138,103140],{"className":103139},[59,310],[15,103141,6820],{"className":103142},[59,310],[15,103144,113],{"className":103145},[146],[15,103147,103149],{"className":103148},[59,4598],[15,103150,103096],{"className":103151},[59,4602],[15,103153,120],{"className":103154},[153],"，而不是似然比本身；不同 ",[15,103157,103159,103172],{"className":103158,"translate":19},[18],[15,103160,103162],{"className":103161},[23],[25,103163,103164],{"xmlns":27},[29,103165,103166,103170],{},[32,103167,103168],{},[35,103169,37],{},[39,103171,37],{"encoding":41},[15,103173,103175],{"className":103174,"ariaHidden":46},[45],[15,103176,103178,103181],{"className":103177},[50],[15,103179],{"className":103180,"style":55},[54],[15,103182,37],{"className":103183,"style":61},[59,60]," 等价于对似然比做了不同的单调「整形」，因此决定了梯度的尺度与饱和方式。",[2311,103186,103188],{"id":103187},"_53-各散度的-gan-目标","5.3 各散度的 GAN 目标",[11,103190,103191,103192,9400],{},"取上表的 ",[15,103193,103195,103212],{"className":103194,"translate":19},[18],[15,103196,103198],{"className":103197},[23],[25,103199,103200],{"xmlns":27},[29,103201,103202,103210],{},[32,103203,103204],{},[6814,103205,103206,103208],{},[35,103207,37],{},[110,103209,7573],{},[39,103211,60708],{"encoding":41},[15,103213,103215],{"className":103214,"ariaHidden":46},[45],[15,103216,103218,103221],{"className":103217},[50],[15,103219],{"className":103220,"style":55},[54],[15,103222,103224,103227],{"className":103223},[59],[15,103225,37],{"className":103226,"style":61},[59,60],[15,103228,103230],{"className":103229},[281],[15,103231,103233],{"className":103232},[285],[15,103234,103236],{"className":103235},[290],[15,103237,103239],{"className":103238,"style":8499},[294],[15,103240,103241,103244],{"style":6865},[15,103242],{"className":103243,"style":303},[302],[15,103245,103247],{"className":103246},[307,308,309,310],[15,103248,7573],{"className":103249},[2591,310],[10027,103251,103252],{},[6665,103253,103254,15795,103256,45608],{},[1225,103255,32663],{},[15,103257,103259,103291],{"className":103258,"translate":19},[18],[15,103260,103262],{"className":103261},[23],[25,103263,103264],{"xmlns":27},[29,103265,103266,103288],{},[32,103267,103268,103274,103276],{},[6814,103269,103270,103272],{},[35,103271,37],{},[110,103273,7573],{},[110,103275,123],{},[6814,103277,103278,103280],{},[35,103279,7567],{},[32,103281,103282,103284,103286],{},[35,103283,40237],{},[110,103285,4813],{},[115,103287,117],{},[39,103289,103290],{"encoding":41},"f^*=e^{y-1}",[15,103292,103294,103338],{"className":103293,"ariaHidden":46},[45],[15,103295,103297,103300,103329,103332,103335],{"className":103296},[50],[15,103298],{"className":103299,"style":55},[54],[15,103301,103303,103306],{"className":103302},[59],[15,103304,37],{"className":103305,"style":61},[59,60],[15,103307,103309],{"className":103308},[281],[15,103310,103312],{"className":103311},[285],[15,103313,103315],{"className":103314},[290],[15,103316,103318],{"className":103317,"style":8499},[294],[15,103319,103320,103323],{"style":6865},[15,103321],{"className":103322,"style":303},[302],[15,103324,103326],{"className":103325},[307,308,309,310],[15,103327,7573],{"className":103328},[2591,310],[15,103330],{"className":103331,"style":158},[157],[15,103333,123],{"className":103334},[162],[15,103336],{"className":103337,"style":158},[157],[15,103339,103341,103344],{"className":103340},[50],[15,103342],{"className":103343,"style":20028},[54],[15,103345,103347,103350],{"className":103346},[59],[15,103348,7567],{"className":103349},[59,60],[15,103351,103353],{"className":103352},[281],[15,103354,103356],{"className":103355},[285],[15,103357,103359],{"className":103358},[290],[15,103360,103362],{"className":103361,"style":20028},[294],[15,103363,103364,103367],{"style":6865},[15,103365],{"className":103366,"style":303},[302],[15,103368,103370],{"className":103369},[307,308,309,310],[15,103371,103373,103376,103379],{"className":103372},[59,310],[15,103374,40237],{"className":103375,"style":981},[59,60,310],[15,103377,4813],{"className":103378},[2591,310],[15,103380,117],{"className":103381},[59,310],[15,103383,103385],{"className":103384,"translate":19},[180],[15,103386,103388,103474],{"className":103387,"translate":19},[18],[15,103389,103391],{"className":103390},[23],[25,103392,103393],{"xmlns":27,"display":189},[29,103394,103395,103471],{},[32,103396,103397,103407,103409,103411,103413,103415,103417,103419,103429,103431,103437,103439,103441,103443,103445,103451,103453,103465,103467,103469],{},[195,103398,103399,103401],{},[35,103400,199],{},[32,103402,103403,103405],{},[35,103404,10694],{},[35,103406,21893],{},[110,103408,113],{"stretchy":112},[35,103410,206],{},[35,103412,210],{"mathvariant":209},[35,103414,213],{},[110,103416,120],{"stretchy":112},[110,103418,123],{},[6016,103420,103421,103427],{},[32,103422,103423,103425],{},[35,103424,35432],{},[110,103426,4103],{},[35,103428,4158],{},[110,103430,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,103432,103433,103435],{},[35,103434,223],{"mathvariant":222},[35,103436,206],{},[110,103438,230],{"stretchy":112},[35,103440,4158],{},[110,103442,257],{"stretchy":112},[110,103444,4813],{},[195,103446,103447,103449],{},[35,103448,223],{"mathvariant":222},[35,103450,213],{},[110,103452,230],{"stretchy":112},[6814,103454,103455,103457],{},[35,103456,7567],{},[32,103458,103459,103461,103463],{},[35,103460,4158],{},[110,103462,4813],{},[115,103464,117],{},[110,103466,257],{"stretchy":112},[110,103468,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,103470,4375],{"mathvariant":209},[39,103472,103473],{"encoding":41},"D_{KL}(P\\|Q)\n=\\sup_g\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}]\\Big\\}.",[15,103475,103477,103553,103670],{"className":103476,"ariaHidden":46},[45],[15,103478,103480,103483,103529,103532,103535,103538,103541,103544,103547,103550],{"className":103479},[50],[15,103481],{"className":103482,"style":139},[54],[15,103484,103486,103489],{"className":103485},[59],[15,103487,199],{"className":103488,"style":277},[59,60],[15,103490,103492],{"className":103491},[281],[15,103493,103495,103521],{"className":103494},[285,286],[15,103496,103498,103518],{"className":103497},[290],[15,103499,103501],{"className":103500,"style":379},[294],[15,103502,103503,103506],{"style":298},[15,103504],{"className":103505,"style":303},[302],[15,103507,103509],{"className":103508},[307,308,309,310],[15,103510,103512,103515],{"className":103511},[59,310],[15,103513,10694],{"className":103514,"style":10782},[59,60,310],[15,103516,21893],{"className":103517},[59,60,310],[15,103519,318],{"className":103520},[317],[15,103522,103524],{"className":103523},[290],[15,103525,103527],{"className":103526,"style":7968},[294],[15,103528],{},[15,103530,113],{"className":103531},[146],[15,103533,206],{"className":103534,"style":334},[59,60],[15,103536,210],{"className":103537},[59],[15,103539,213],{"className":103540},[59,60],[15,103542,120],{"className":103543},[153],[15,103545],{"className":103546,"style":158},[157],[15,103548,123],{"className":103549},[162],[15,103551],{"className":103552,"style":158},[157],[15,103554,103556,103559,103603,103606,103612,103652,103655,103658,103661,103664,103667],{"className":103555},[50],[15,103557],{"className":103558,"style":99485},[54],[15,103560,103562],{"className":103561},[1484,13716],[15,103563,103565,103595],{"className":103564},[285,286],[15,103566,103568,103592],{"className":103567},[290],[15,103569,103571,103582],{"className":103570,"style":2345},[294],[15,103572,103573,103576],{"style":61190},[15,103574],{"className":103575,"style":461},[302],[15,103577,103579],{"className":103578},[307,308,309,310],[15,103580,4158],{"className":103581,"style":981},[59,60,310],[15,103583,103584,103587],{"style":11863},[15,103585],{"className":103586,"style":461},[302],[15,103588,103589],{},[15,103590,35432],{"className":103591},[1484],[15,103593,318],{"className":103594},[317],[15,103596,103598],{"className":103597},[290],[15,103599,103601],{"className":103600,"style":61222},[294],[15,103602],{},[15,103604],{"className":103605,"style":406},[157],[15,103607,103609],{"className":103608},[59],[15,103610,2898],{"className":103611},[419,3720],[15,103613,103615,103618],{"className":103614},[59],[15,103616,223],{"className":103617},[59,366],[15,103619,103621],{"className":103620},[281],[15,103622,103624,103644],{"className":103623},[285,286],[15,103625,103627,103641],{"className":103626},[290],[15,103628,103630],{"className":103629,"style":379},[294],[15,103631,103632,103635],{"style":382},[15,103633],{"className":103634,"style":303},[302],[15,103636,103638],{"className":103637},[307,308,309,310],[15,103639,206],{"className":103640,"style":334},[59,60,310],[15,103642,318],{"className":103643},[317],[15,103645,103647],{"className":103646},[290],[15,103648,103650],{"className":103649,"style":7968},[294],[15,103651],{},[15,103653,230],{"className":103654},[146],[15,103656,4158],{"className":103657,"style":981},[59,60],[15,103659,257],{"className":103660},[153],[15,103662],{"className":103663,"style":2587},[157],[15,103665,4813],{"className":103666},[2591],[15,103668],{"className":103669,"style":2587},[157],[15,103671,103673,103676,103716,103719,103757,103760,103766],{"className":103672},[50],[15,103674],{"className":103675,"style":68117},[54],[15,103677,103679,103682],{"className":103678},[59],[15,103680,223],{"className":103681},[59,366],[15,103683,103685],{"className":103684},[281],[15,103686,103688,103708],{"className":103687},[285,286],[15,103689,103691,103705],{"className":103690},[290],[15,103692,103694],{"className":103693,"style":379},[294],[15,103695,103696,103699],{"style":382},[15,103697],{"className":103698,"style":303},[302],[15,103700,103702],{"className":103701},[307,308,309,310],[15,103703,213],{"className":103704},[59,60,310],[15,103706,318],{"className":103707},[317],[15,103709,103711],{"className":103710},[290],[15,103712,103714],{"className":103713,"style":325},[294],[15,103715],{},[15,103717,230],{"className":103718},[146],[15,103720,103722,103725],{"className":103721},[59],[15,103723,7567],{"className":103724},[59,60],[15,103726,103728],{"className":103727},[281],[15,103729,103731],{"className":103730},[285],[15,103732,103734],{"className":103733},[290],[15,103735,103737],{"className":103736,"style":19735},[294],[15,103738,103739,103742],{"style":8277},[15,103740],{"className":103741,"style":303},[302],[15,103743,103745],{"className":103744},[307,308,309,310],[15,103746,103748,103751,103754],{"className":103747},[59,310],[15,103749,4158],{"className":103750,"style":981},[59,60,310],[15,103752,4813],{"className":103753},[2591,310],[15,103755,117],{"className":103756},[59,310],[15,103758,257],{"className":103759},[153],[15,103761,103763],{"className":103762},[59],[15,103764,2908],{"className":103765},[419,3720],[15,103767,4375],{"className":103768},[59],[11,103770,103771,103772,103980,103981,104054,104055,104087,104088,104116],{},"（这是「MINE-f」式下界。经典 Donsker–Varadhan 下界是 ",[15,103773,103775,103821],{"className":103774,"translate":19},[18],[15,103776,103778],{"className":103777},[23],[25,103779,103780],{"xmlns":27},[29,103781,103782,103818],{},[32,103783,103784,103790,103792,103794,103796,103798,103800,103802,103808,103810,103816],{},[195,103785,103786,103788],{},[35,103787,223],{"mathvariant":222},[35,103789,206],{},[110,103791,230],{"stretchy":112},[35,103793,4158],{},[110,103795,257],{"stretchy":112},[110,103797,4813],{},[35,103799,4100],{},[110,103801,4103],{},[195,103803,103804,103806],{},[35,103805,223],{"mathvariant":222},[35,103807,213],{},[110,103809,230],{"stretchy":112},[6814,103811,103812,103814],{},[35,103813,7567],{},[35,103815,4158],{},[110,103817,257],{"stretchy":112},[39,103819,103820],{"encoding":41},"\\mathbb E_P[g]-\\log\\mathbb E_Q[e^{g}]",[15,103822,103824,103888],{"className":103823,"ariaHidden":46},[45],[15,103825,103827,103830,103870,103873,103876,103879,103882,103885],{"className":103826},[50],[15,103828],{"className":103829,"style":139},[54],[15,103831,103833,103836],{"className":103832},[59],[15,103834,223],{"className":103835},[59,366],[15,103837,103839],{"className":103838},[281],[15,103840,103842,103862],{"className":103841},[285,286],[15,103843,103845,103859],{"className":103844},[290],[15,103846,103848],{"className":103847,"style":379},[294],[15,103849,103850,103853],{"style":382},[15,103851],{"className":103852,"style":303},[302],[15,103854,103856],{"className":103855},[307,308,309,310],[15,103857,206],{"className":103858,"style":334},[59,60,310],[15,103860,318],{"className":103861},[317],[15,103863,103865],{"className":103864},[290],[15,103866,103868],{"className":103867,"style":7968},[294],[15,103869],{},[15,103871,230],{"className":103872},[146],[15,103874,4158],{"className":103875,"style":981},[59,60],[15,103877,257],{"className":103878},[153],[15,103880],{"className":103881,"style":2587},[157],[15,103883,4813],{"className":103884},[2591],[15,103886],{"className":103887,"style":2587},[157],[15,103889,103891,103894,103899,103902,103942,103945,103977],{"className":103890},[50],[15,103892],{"className":103893,"style":270},[54],[15,103895,4154,103897],{"className":103896},[1484],[15,103898,4158],{"style":4157},[15,103900],{"className":103901,"style":406},[157],[15,103903,103905,103908],{"className":103904},[59],[15,103906,223],{"className":103907},[59,366],[15,103909,103911],{"className":103910},[281],[15,103912,103914,103934],{"className":103913},[285,286],[15,103915,103917,103931],{"className":103916},[290],[15,103918,103920],{"className":103919,"style":379},[294],[15,103921,103922,103925],{"style":382},[15,103923],{"className":103924,"style":303},[302],[15,103926,103928],{"className":103927},[307,308,309,310],[15,103929,213],{"className":103930},[59,60,310],[15,103932,318],{"className":103933},[317],[15,103935,103937],{"className":103936},[290],[15,103938,103940],{"className":103939,"style":325},[294],[15,103941],{},[15,103943,230],{"className":103944},[146],[15,103946,103948,103951],{"className":103947},[59],[15,103949,7567],{"className":103950},[59,60],[15,103952,103954],{"className":103953},[281],[15,103955,103957],{"className":103956},[285],[15,103958,103960],{"className":103959},[290],[15,103961,103963],{"className":103962,"style":50353},[294],[15,103964,103965,103968],{"style":6865},[15,103966],{"className":103967,"style":303},[302],[15,103969,103971],{"className":103970},[307,308,309,310],[15,103972,103974],{"className":103973},[59,310],[15,103975,4158],{"className":103976,"style":981},[59,60,310],[15,103978,257],{"className":103979},[153],"，二者同源但第二项不同：",[15,103982,103984,104007],{"className":103983,"translate":19},[18],[15,103985,103987],{"className":103986},[23],[25,103988,103989],{"xmlns":27},[29,103990,103991,104005],{},[32,103992,103993],{},[6814,103994,103995,103997],{},[35,103996,7567],{},[32,103998,103999,104001,104003],{},[35,104000,40237],{},[110,104002,4813],{},[115,104004,117],{},[39,104006,64902],{"encoding":41},[15,104008,104010],{"className":104009,"ariaHidden":46},[45],[15,104011,104013,104016],{"className":104012},[50],[15,104014],{"className":104015,"style":20028},[54],[15,104017,104019,104022],{"className":104018},[59],[15,104020,7567],{"className":104021},[59,60],[15,104023,104025],{"className":104024},[281],[15,104026,104028],{"className":104027},[285],[15,104029,104031],{"className":104030},[290],[15,104032,104034],{"className":104033,"style":20028},[294],[15,104035,104036,104039],{"style":6865},[15,104037],{"className":104038,"style":303},[302],[15,104040,104042],{"className":104041},[307,308,309,310],[15,104043,104045,104048,104051],{"className":104044},[59,310],[15,104046,40237],{"className":104047,"style":981},[59,60,310],[15,104049,4813],{"className":104050},[2591,310],[15,104052,117],{"className":104053},[59,310]," 是把 ",[15,104056,104058,104073],{"className":104057,"translate":19},[18],[15,104059,104061],{"className":104060},[23],[25,104062,104063],{"xmlns":27},[29,104064,104065,104071],{},[32,104066,104067,104069],{},[35,104068,4100],{},[110,104070,4103],{},[39,104072,21583],{"encoding":41},[15,104074,104076],{"className":104075,"ariaHidden":46},[45],[15,104077,104079,104082],{"className":104078},[50],[15,104080],{"className":104081,"style":55},[54],[15,104083,4154,104085],{"className":104084},[1484],[15,104086,4158],{"style":4157}," 移到最外层并做 ",[15,104089,104091,104104],{"className":104090,"translate":19},[18],[15,104092,104094],{"className":104093},[23],[25,104095,104096],{"xmlns":27},[29,104097,104098,104102],{},[32,104099,104100],{},[35,104101,37],{},[39,104103,37],{"encoding":41},[15,104105,104107],{"className":104106,"ariaHidden":46},[45],[15,104108,104110,104113],{"className":104109},[50],[15,104111],{"className":104112,"style":55},[54],[15,104114,37],{"className":104115,"style":61},[59,60],"-散度对偶后的结果。）",[10027,104118,104119,104345,104738,105169],{},[6665,104120,104121,104124,104125,49172,104158,104186,104187,104242,104243,104293,104294,104344],{},[1225,104122,104123],{},"反向 KL \u002F α-GAN","：把 α 从 ",[15,104126,104128,104143],{"className":104127,"translate":19},[18],[15,104129,104131],{"className":104130},[23],[25,104132,104133],{"xmlns":27},[29,104134,104135,104141],{},[32,104136,104137,104139],{},[110,104138,4813],{},[115,104140,117],{},[39,104142,49156],{"encoding":41},[15,104144,104146],{"className":104145,"ariaHidden":46},[45],[15,104147,104149,104152,104155],{"className":104148},[50],[15,104150],{"className":104151,"style":12578},[54],[15,104153,4813],{"className":104154},[59],[15,104156,117],{"className":104157},[59],[15,104159,104161,104174],{"className":104160,"translate":19},[18],[15,104162,104164],{"className":104163},[23],[25,104165,104166],{"xmlns":27},[29,104167,104168,104172],{},[32,104169,104170],{},[115,104171,117],{},[39,104173,117],{"encoding":41},[15,104175,104177],{"className":104176,"ariaHidden":46},[45],[15,104178,104180,104183],{"className":104179},[50],[15,104181],{"className":104182,"style":172},[54],[15,104184,117],{"className":104185},[59],"，散度从反向 KL（",[15,104188,104190,104209],{"className":104189,"translate":19},[18],[15,104191,104193],{"className":104192},[23],[25,104194,104195],{"xmlns":27},[29,104196,104197,104207],{},[32,104198,104199,104201,104203,104205],{},[35,104200,44754],{},[110,104202,1029],{},[110,104204,4813],{},[115,104206,117],{},[39,104208,49039],{"encoding":41},[15,104210,104212,104230],{"className":104211,"ariaHidden":46},[45],[15,104213,104215,104218,104221,104224,104227],{"className":104214},[50],[15,104216],{"className":104217,"style":2345},[54],[15,104219,44754],{"className":104220,"style":44784},[59,60],[15,104222],{"className":104223,"style":158},[157],[15,104225,1029],{"className":104226},[162],[15,104228],{"className":104229,"style":158},[157],[15,104231,104233,104236,104239],{"className":104232},[50],[15,104234],{"className":104235,"style":12578},[54],[15,104237,4813],{"className":104238},[59],[15,104240,117],{"className":104241},[59],"，zero-forcing、模式崩塌倾向）经 Hellinger 型对称散度（",[15,104244,104246,104263],{"className":104245,"translate":19},[18],[15,104247,104249],{"className":104248},[23],[25,104250,104251],{"xmlns":27},[29,104252,104253,104261],{},[32,104254,104255,104257,104259],{},[35,104256,44754],{},[110,104258,123],{},[115,104260,126],{},[39,104262,46488],{"encoding":41},[15,104264,104266,104284],{"className":104265,"ariaHidden":46},[45],[15,104267,104269,104272,104275,104278,104281],{"className":104268},[50],[15,104270],{"className":104271,"style":2345},[54],[15,104273,44754],{"className":104274,"style":44784},[59,60],[15,104276],{"className":104277,"style":158},[157],[15,104279,123],{"className":104280},[162],[15,104282],{"className":104283,"style":158},[157],[15,104285,104287,104290],{"className":104286},[50],[15,104288],{"className":104289,"style":172},[54],[15,104291,126],{"className":104292},[59],"）过渡到正向 KL（",[15,104295,104297,104314],{"className":104296,"translate":19},[18],[15,104298,104300],{"className":104299},[23],[25,104301,104302],{"xmlns":27},[29,104303,104304,104312],{},[32,104305,104306,104308,104310],{},[35,104307,44754],{},[110,104309,1029],{},[115,104311,117],{},[39,104313,47215],{"encoding":41},[15,104315,104317,104335],{"className":104316,"ariaHidden":46},[45],[15,104318,104320,104323,104326,104329,104332],{"className":104319},[50],[15,104321],{"className":104322,"style":2345},[54],[15,104324,44754],{"className":104325,"style":44784},[59,60],[15,104327],{"className":104328,"style":158},[157],[15,104330,1029],{"className":104331},[162],[15,104333],{"className":104334,"style":158},[157],[15,104336,104338,104341],{"className":104337},[50],[15,104339],{"className":104340,"style":172},[54],[15,104342,117],{"className":104343},[59],"，zero-avoiding、模式覆盖倾向），可以在\"崩塌—覆盖\"之间连续调节（见 3.6 节的两端极限）。",[6665,104346,104347,9400,104349,2745,104593,104733,104734,104737],{},[1225,104348,53124],{},[15,104350,104352,104402],{"className":104351,"translate":19},[18],[15,104353,104355],{"className":104354},[23],[25,104356,104357],{"xmlns":27},[29,104358,104359,104399],{},[32,104360,104361,104367,104369,104371,104377,104379,104381,104383,104385,104387,104397],{},[6814,104362,104363,104365],{},[35,104364,37],{},[110,104366,7573],{},[110,104368,123],{},[110,104370,4813],{},[238,104372,104373,104375],{},[115,104374,117],{},[115,104376,2463],{},[35,104378,4100],{},[110,104380,4103],{},[110,104382,113],{"stretchy":112},[115,104384,2463],{},[110,104386,4813],{},[6814,104388,104389,104391],{},[35,104390,7567],{},[32,104392,104393,104395],{},[115,104394,2463],{},[35,104396,40237],{},[110,104398,120],{"stretchy":112},[39,104400,104401],{"encoding":41},"f^*=-\\frac12\\log(2-e^{2y})",[15,104403,104405,104449,104549],{"className":104404,"ariaHidden":46},[45],[15,104406,104408,104411,104440,104443,104446],{"className":104407},[50],[15,104409],{"className":104410,"style":55},[54],[15,104412,104414,104417],{"className":104413},[59],[15,104415,37],{"className":104416,"style":61},[59,60],[15,104418,104420],{"className":104419},[281],[15,104421,104423],{"className":104422},[285],[15,104424,104426],{"className":104425},[290],[15,104427,104429],{"className":104428,"style":8499},[294],[15,104430,104431,104434],{"style":6865},[15,104432],{"className":104433,"style":303},[302],[15,104435,104437],{"className":104436},[307,308,309,310],[15,104438,7573],{"className":104439},[2591,310],[15,104441],{"className":104442,"style":158},[157],[15,104444,123],{"className":104445},[162],[15,104447],{"className":104448,"style":158},[157],[15,104450,104452,104455,104458,104526,104529,104534,104537,104540,104543,104546],{"className":104451},[50],[15,104453],{"className":104454,"style":2505},[54],[15,104456,4813],{"className":104457},[59],[15,104459,104461,104464,104523],{"className":104460},[59],[15,104462],{"className":104463},[146,441],[15,104465,104467],{"className":104466},[238],[15,104468,104470,104515],{"className":104469},[285,286],[15,104471,104473,104512],{"className":104472},[290],[15,104474,104476,104490,104498],{"className":104475,"style":2524},[294],[15,104477,104478,104481],{"style":2527},[15,104479],{"className":104480,"style":461},[302],[15,104482,104484],{"className":104483},[307,308,309,310],[15,104485,104487],{"className":104486},[59,310],[15,104488,2463],{"className":104489},[59,310],[15,104491,104492,104495],{"style":473},[15,104493],{"className":104494,"style":461},[302],[15,104496],{"className":104497,"style":481},[480],[15,104499,104500,104503],{"style":2550},[15,104501],{"className":104502,"style":461},[302],[15,104504,104506],{"className":104505},[307,308,309,310],[15,104507,104509],{"className":104508},[59,310],[15,104510,117],{"className":104511},[59,310],[15,104513,318],{"className":104514},[317],[15,104516,104518],{"className":104517},[290],[15,104519,104521],{"className":104520,"style":2572},[294],[15,104522],{},[15,104524],{"className":104525},[153,441],[15,104527],{"className":104528,"style":406},[157],[15,104530,4154,104532],{"className":104531},[1484],[15,104533,4158],{"style":4157},[15,104535,113],{"className":104536},[146],[15,104538,2463],{"className":104539},[59],[15,104541],{"className":104542,"style":2587},[157],[15,104544,4813],{"className":104545},[2591],[15,104547],{"className":104548,"style":2587},[157],[15,104550,104552,104555,104590],{"className":104551},[50],[15,104553],{"className":104554,"style":20003},[54],[15,104556,104558,104561],{"className":104557},[59],[15,104559,7567],{"className":104560},[59,60],[15,104562,104564],{"className":104563},[281],[15,104565,104567],{"className":104566},[285],[15,104568,104570],{"className":104569},[290],[15,104571,104573],{"className":104572,"style":20028},[294],[15,104574,104575,104578],{"style":6865},[15,104576],{"className":104577,"style":303},[302],[15,104579,104581],{"className":104580},[307,308,309,310],[15,104582,104584,104587],{"className":104583},[59,310],[15,104585,2463],{"className":104586},[59,310],[15,104588,40237],{"className":104589,"style":981},[59,60,310],[15,104591,120],{"className":104592},[153],[15,104594,104596,104623],{"className":104595,"translate":19},[18],[15,104597,104599],{"className":104598},[23],[25,104600,104601],{"xmlns":27},[29,104602,104603,104621],{},[32,104604,104605,104607,104609],{},[35,104606,40237],{},[110,104608,7251],{},[238,104610,104611,104619],{},[32,104612,104613,104615,104617],{},[35,104614,4100],{},[110,104616,4103],{},[115,104618,2463],{},[115,104620,2463],{},[39,104622,65743],{"encoding":41},[15,104624,104626,104644],{"className":104625,"ariaHidden":46},[45],[15,104627,104629,104632,104635,104638,104641],{"className":104628},[50],[15,104630],{"className":104631,"style":31692},[54],[15,104633,40237],{"className":104634,"style":981},[59,60],[15,104636],{"className":104637,"style":158},[157],[15,104639,7251],{"className":104640},[162],[15,104642],{"className":104643,"style":158},[157],[15,104645,104647,104650],{"className":104646},[50],[15,104648],{"className":104649,"style":65771},[54],[15,104651,104653,104656,104730],{"className":104652},[59],[15,104654],{"className":104655},[146,441],[15,104657,104659],{"className":104658},[238],[15,104660,104662,104722],{"className":104661},[285,286],[15,104663,104665,104719],{"className":104664},[290],[15,104666,104668,104682,104690],{"className":104667,"style":2825},[294],[15,104669,104670,104673],{"style":2527},[15,104671],{"className":104672,"style":461},[302],[15,104674,104676],{"className":104675},[307,308,309,310],[15,104677,104679],{"className":104678},[59,310],[15,104680,2463],{"className":104681},[59,310],[15,104683,104684,104687],{"style":473},[15,104685],{"className":104686,"style":461},[302],[15,104688],{"className":104689,"style":481},[480],[15,104691,104692,104695],{"style":2853},[15,104693],{"className":104694,"style":461},[302],[15,104696,104698],{"className":104697},[307,308,309,310],[15,104699,104701,104713,104716],{"className":104700},[59,310],[15,104702,104704,104707,104710],{"className":104703},[1484,310],[15,104705,47658],{"className":104706},[310],[15,104708,47662],{"className":104709},[310],[15,104711,4158],{"className":104712,"style":4157},[310],[15,104714],{"className":104715,"style":42366},[157,310],[15,104717,2463],{"className":104718},[59,310],[15,104720,318],{"className":104721},[317],[15,104723,104725],{"className":104724},[290],[15,104726,104728],{"className":104727,"style":2572},[294],[15,104729],{},[15,104731],{"className":104732},[153,441],"。代回即",[1225,104735,104736],{},"原始 GAN 的对抗目标","（见 5.4）。",[6665,104739,104740,9400,104801,104941,104942,105164,105165,105168],{},[1225,104741,104742,104800],{},[15,104743,104745,104762],{"className":104744,"translate":19},[18],[15,104746,104748],{"className":104747},[23],[25,104749,104750],{"xmlns":27},[29,104751,104752,104760],{},[32,104753,104754],{},[6814,104755,104756,104758],{},[35,104757,37449],{},[115,104759,2463],{},[39,104761,40394],{"encoding":41},[15,104763,104765],{"className":104764,"ariaHidden":46},[45],[15,104766,104768,104771],{"className":104767},[50],[15,104769],{"className":104770,"style":40404},[54],[15,104772,104774,104777],{"className":104773},[59],[15,104775,37449],{"className":104776},[59,60],[15,104778,104780],{"className":104779},[281],[15,104781,104783],{"className":104782},[285],[15,104784,104786],{"className":104785},[290],[15,104787,104789],{"className":104788,"style":20028},[294],[15,104790,104791,104794],{"style":6865},[15,104792],{"className":104793,"style":303},[302],[15,104795,104797],{"className":104796},[307,308,309,310],[15,104798,2463],{"className":104799},[59,310],"（LSGAN）",[15,104802,104804,104838],{"className":104803,"translate":19},[18],[15,104805,104807],{"className":104806},[23],[25,104808,104809],{"xmlns":27},[29,104810,104811,104835],{},[32,104812,104813,104819,104821,104823,104825,104831,104833],{},[6814,104814,104815,104817],{},[35,104816,37],{},[110,104818,7573],{},[110,104820,123],{},[35,104822,40237],{},[110,104824,2470],{},[6814,104826,104827,104829],{},[35,104828,40237],{},[115,104830,2463],{},[35,104832,941],{"mathvariant":209},[115,104834,38989],{},[39,104836,104837],{"encoding":41},"f^*=y+y^2\u002F4",[15,104839,104841,104885,104903],{"className":104840,"ariaHidden":46},[45],[15,104842,104844,104847,104876,104879,104882],{"className":104843},[50],[15,104845],{"className":104846,"style":55},[54],[15,104848,104850,104853],{"className":104849},[59],[15,104851,37],{"className":104852,"style":61},[59,60],[15,104854,104856],{"className":104855},[281],[15,104857,104859],{"className":104858},[285],[15,104860,104862],{"className":104861},[290],[15,104863,104865],{"className":104864,"style":8499},[294],[15,104866,104867,104870],{"style":6865},[15,104868],{"className":104869,"style":303},[302],[15,104871,104873],{"className":104872},[307,308,309,310],[15,104874,7573],{"className":104875},[2591,310],[15,104877],{"className":104878,"style":158},[157],[15,104880,123],{"className":104881},[162],[15,104883],{"className":104884,"style":158},[157],[15,104886,104888,104891,104894,104897,104900],{"className":104887},[50],[15,104889],{"className":104890,"style":40321},[54],[15,104892,40237],{"className":104893,"style":981},[59,60],[15,104895],{"className":104896,"style":2587},[157],[15,104898,2470],{"className":104899},[2591],[15,104901],{"className":104902,"style":2587},[157],[15,104904,104906,104909,104938],{"className":104905},[50],[15,104907],{"className":104908,"style":20003},[54],[15,104910,104912,104915],{"className":104911},[59],[15,104913,40237],{"className":104914,"style":981},[59,60],[15,104916,104918],{"className":104917},[281],[15,104919,104921],{"className":104920},[285],[15,104922,104924],{"className":104923},[290],[15,104925,104927],{"className":104926,"style":20028},[294],[15,104928,104929,104932],{"style":6865},[15,104930],{"className":104931,"style":303},[302],[15,104933,104935],{"className":104934},[307,308,309,310],[15,104936,2463],{"className":104937},[59,310],[15,104939,40372],{"className":104940},[59],"，目标变为 ",[15,104943,104945,104995],{"className":104944,"translate":19},[18],[15,104946,104948],{"className":104947},[23],[25,104949,104950],{"xmlns":27},[29,104951,104952,104992],{},[32,104953,104954,104960,104962,104964,104966,104968,104974,104976,104978,104980,104986,104988,104990],{},[195,104955,104956,104958],{},[35,104957,223],{"mathvariant":222},[35,104959,206],{},[110,104961,230],{"stretchy":112},[35,104963,4158],{},[110,104965,257],{"stretchy":112},[110,104967,4813],{},[195,104969,104970,104972],{},[35,104971,223],{"mathvariant":222},[35,104973,213],{},[110,104975,230],{"stretchy":112},[35,104977,4158],{},[110,104979,2470],{},[6814,104981,104982,104984],{},[35,104983,4158],{},[115,104985,2463],{},[35,104987,941],{"mathvariant":209},[115,104989,38989],{},[110,104991,257],{"stretchy":112},[39,104993,104994],{"encoding":41},"\\mathbb E_P[g]-\\mathbb E_Q[g+g^2\u002F4]",[15,104996,104998,105062,105123],{"className":104997,"ariaHidden":46},[45],[15,104999,105001,105004,105044,105047,105050,105053,105056,105059],{"className":105000},[50],[15,105002],{"className":105003,"style":139},[54],[15,105005,105007,105010],{"className":105006},[59],[15,105008,223],{"className":105009},[59,366],[15,105011,105013],{"className":105012},[281],[15,105014,105016,105036],{"className":105015},[285,286],[15,105017,105019,105033],{"className":105018},[290],[15,105020,105022],{"className":105021,"style":379},[294],[15,105023,105024,105027],{"style":382},[15,105025],{"className":105026,"style":303},[302],[15,105028,105030],{"className":105029},[307,308,309,310],[15,105031,206],{"className":105032,"style":334},[59,60,310],[15,105034,318],{"className":105035},[317],[15,105037,105039],{"className":105038},[290],[15,105040,105042],{"className":105041,"style":7968},[294],[15,105043],{},[15,105045,230],{"className":105046},[146],[15,105048,4158],{"className":105049,"style":981},[59,60],[15,105051,257],{"className":105052},[153],[15,105054],{"className":105055,"style":2587},[157],[15,105057,4813],{"className":105058},[2591],[15,105060],{"className":105061,"style":2587},[157],[15,105063,105065,105068,105108,105111,105114,105117,105120],{"className":105064},[50],[15,105066],{"className":105067,"style":270},[54],[15,105069,105071,105074],{"className":105070},[59],[15,105072,223],{"className":105073},[59,366],[15,105075,105077],{"className":105076},[281],[15,105078,105080,105100],{"className":105079},[285,286],[15,105081,105083,105097],{"className":105082},[290],[15,105084,105086],{"className":105085,"style":379},[294],[15,105087,105088,105091],{"style":382},[15,105089],{"className":105090,"style":303},[302],[15,105092,105094],{"className":105093},[307,308,309,310],[15,105095,213],{"className":105096},[59,60,310],[15,105098,318],{"className":105099},[317],[15,105101,105103],{"className":105102},[290],[15,105104,105106],{"className":105105,"style":325},[294],[15,105107],{},[15,105109,230],{"className":105110},[146],[15,105112,4158],{"className":105113,"style":981},[59,60],[15,105115],{"className":105116,"style":2587},[157],[15,105118,2470],{"className":105119},[2591],[15,105121],{"className":105122,"style":2587},[157],[15,105124,105126,105129,105158,105161],{"className":105125},[50],[15,105127],{"className":105128,"style":20003},[54],[15,105130,105132,105135],{"className":105131},[59],[15,105133,4158],{"className":105134,"style":981},[59,60],[15,105136,105138],{"className":105137},[281],[15,105139,105141],{"className":105140},[285],[15,105142,105144],{"className":105143},[290],[15,105145,105147],{"className":105146,"style":20028},[294],[15,105148,105149,105152],{"style":6865},[15,105150],{"className":105151,"style":303},[302],[15,105153,105155],{"className":105154},[307,308,309,310],[15,105156,2463],{"className":105157},[59,310],[15,105159,40372],{"className":105160},[59],[15,105162,257],{"className":105163},[153],"，即对判别器输出做",[1225,105166,105167],{},"最小二乘","回归，梯度不会像 sigmoid 那样饱和。",[6665,105170,105171,9400,105174,2745,105297,10180],{},[1225,105172,105173],{},"Hellinger²",[15,105175,105177,105211],{"className":105176,"translate":19},[18],[15,105178,105180],{"className":105179},[23],[25,105181,105182],{"xmlns":27},[29,105183,105184,105208],{},[32,105185,105186,105192,105194,105196,105198,105200,105202,105204,105206],{},[6814,105187,105188,105190],{},[35,105189,37],{},[110,105191,7573],{},[110,105193,123],{},[35,105195,40237],{},[35,105197,941],{"mathvariant":209},[110,105199,113],{"stretchy":112},[115,105201,117],{},[110,105203,4813],{},[35,105205,40237],{},[110,105207,120],{"stretchy":112},[39,105209,105210],{"encoding":41},"f^*=y\u002F(1-y)",[15,105212,105214,105258,105285],{"className":105213,"ariaHidden":46},[45],[15,105215,105217,105220,105249,105252,105255],{"className":105216},[50],[15,105218],{"className":105219,"style":55},[54],[15,105221,105223,105226],{"className":105222},[59],[15,105224,37],{"className":105225,"style":61},[59,60],[15,105227,105229],{"className":105228},[281],[15,105230,105232],{"className":105231},[285],[15,105233,105235],{"className":105234},[290],[15,105236,105238],{"className":105237,"style":8499},[294],[15,105239,105240,105243],{"style":6865},[15,105241],{"className":105242,"style":303},[302],[15,105244,105246],{"className":105245},[307,308,309,310],[15,105247,7573],{"className":105248},[2591,310],[15,105250],{"className":105251,"style":158},[157],[15,105253,123],{"className":105254},[162],[15,105256],{"className":105257,"style":158},[157],[15,105259,105261,105264,105267,105270,105273,105276,105279,105282],{"className":105260},[50],[15,105262],{"className":105263,"style":139},[54],[15,105265,40237],{"className":105266,"style":981},[59,60],[15,105268,941],{"className":105269},[59],[15,105271,113],{"className":105272},[146],[15,105274,117],{"className":105275},[59],[15,105277],{"className":105278,"style":2587},[157],[15,105280,4813],{"className":105281},[2591],[15,105283],{"className":105284,"style":2587},[157],[15,105286,105288,105291,105294],{"className":105287},[50],[15,105289],{"className":105290,"style":139},[54],[15,105292,40237],{"className":105293,"style":981},[59,60],[15,105295,120],{"className":105296},[153],[15,105298,105300,105317],{"className":105299,"translate":19},[18],[15,105301,105303],{"className":105302},[23],[25,105304,105305],{"xmlns":27},[29,105306,105307,105315],{},[32,105308,105309,105311,105313],{},[35,105310,40237],{},[110,105312,7251],{},[115,105314,117],{},[39,105316,66773],{"encoding":41},[15,105318,105320,105338],{"className":105319,"ariaHidden":46},[45],[15,105321,105323,105326,105329,105332,105335],{"className":105322},[50],[15,105324],{"className":105325,"style":31692},[54],[15,105327,40237],{"className":105328,"style":981},[59,60],[15,105330],{"className":105331,"style":158},[157],[15,105333,7251],{"className":105334},[162],[15,105336],{"className":105337,"style":158},[157],[15,105339,105341,105344],{"className":105340},[50],[15,105342],{"className":105343,"style":172},[54],[15,105345,117],{"className":105346},[59],[2311,105348,105350],{"id":105349},"_54-原始-gan-与-js-散度","5.4 原始 GAN 与 JS 散度",[11,105352,105353,105354,105536],{},"原始 GAN 的判别器输出经 sigmoid 得 ",[15,105355,105357,105409],{"className":105356,"translate":19},[18],[15,105358,105360],{"className":105359},[23],[25,105361,105362],{"xmlns":27},[29,105363,105364,105406],{},[32,105365,105366,105368,105370,105372,105374,105376,105378,105380,105382,105388,105390,105392,105394,105396,105398,105400,105402,105404],{},[35,105367,2332],{},[110,105369,113],{"stretchy":112},[35,105371,199],{},[110,105373,113],{"stretchy":112},[35,105375,774],{},[110,105377,120],{"stretchy":112},[110,105379,120],{"stretchy":112},[110,105381,123],{},[195,105383,105384,105386],{},[35,105385,199],{},[35,105387,7561],{},[110,105389,113],{"stretchy":112},[35,105391,774],{},[110,105393,120],{"stretchy":112},[110,105395,5909],{},[110,105397,113],{"stretchy":112},[115,105399,126],{},[110,105401,551],{"separator":46},[115,105403,117],{},[110,105405,120],{"stretchy":112},[39,105407,105408],{"encoding":41},"\\sigma(D(x))=D_{s}(x)\\in(0,1)",[15,105410,105412,105445,105512],{"className":105411,"ariaHidden":46},[45],[15,105413,105415,105418,105421,105424,105427,105430,105433,105436,105439,105442],{"className":105414},[50],[15,105416],{"className":105417,"style":139},[54],[15,105419,2332],{"className":105420,"style":981},[59,60],[15,105422,113],{"className":105423},[146],[15,105425,199],{"className":105426,"style":277},[59,60],[15,105428,113],{"className":105429},[146],[15,105431,774],{"className":105432},[59,60],[15,105434,19047],{"className":105435},[153],[15,105437],{"className":105438,"style":158},[157],[15,105440,123],{"className":105441},[162],[15,105443],{"className":105444,"style":158},[157],[15,105446,105448,105451,105494,105497,105500,105503,105506,105509],{"className":105447},[50],[15,105449],{"className":105450,"style":139},[54],[15,105452,105454,105457],{"className":105453},[59],[15,105455,199],{"className":105456,"style":277},[59,60],[15,105458,105460],{"className":105459},[281],[15,105461,105463,105486],{"className":105462},[285,286],[15,105464,105466,105483],{"className":105465},[290],[15,105467,105469],{"className":105468,"style":44929},[294],[15,105470,105471,105474],{"style":298},[15,105472],{"className":105473,"style":303},[302],[15,105475,105477],{"className":105476},[307,308,309,310],[15,105478,105480],{"className":105479},[59,310],[15,105481,7561],{"className":105482},[59,60,310],[15,105484,318],{"className":105485},[317],[15,105487,105489],{"className":105488},[290],[15,105490,105492],{"className":105491,"style":7968},[294],[15,105493],{},[15,105495,113],{"className":105496},[146],[15,105498,774],{"className":105499},[59,60],[15,105501,120],{"className":105502},[153],[15,105504],{"className":105505,"style":158},[157],[15,105507,5909],{"className":105508},[162],[15,105510],{"className":105511,"style":158},[157],[15,105513,105515,105518,105521,105524,105527,105530,105533],{"className":105514},[50],[15,105516],{"className":105517,"style":139},[54],[15,105519,113],{"className":105520},[146],[15,105522,126],{"className":105523},[59],[15,105525,551],{"className":105526},[573],[15,105528],{"className":105529,"style":406},[157],[15,105531,117],{"className":105532},[59],[15,105534,120],{"className":105535},[153],"，其目标等价于最小化 JS 散度下的对抗博弈。判别器写成 logit",[15,105538,105540],{"className":105539,"translate":19},[180],[15,105541,105543,105621],{"className":105542,"translate":19},[18],[15,105544,105546],{"className":105545},[23],[25,105547,105548],{"xmlns":27,"display":189},[29,105549,105550,105618],{},[32,105551,105552,105554,105556,105558,105560,105562,105564,105566,105572,105574,105576,105578,105580,105582,105584,105586,105588,105590,105596,105598,105600,105602,105604,105606,105608,105610,105616],{},[35,105553,4158],{},[110,105555,113],{"stretchy":112},[35,105557,774],{},[110,105559,120],{"stretchy":112},[110,105561,123],{},[35,105563,4100],{},[110,105565,4103],{},[195,105567,105568,105570],{},[35,105569,199],{},[35,105571,7561],{},[110,105573,113],{"stretchy":112},[35,105575,774],{},[110,105577,120],{"stretchy":112},[110,105579,4813],{},[35,105581,4100],{},[110,105583,4103],{},[110,105585,113],{"stretchy":112},[115,105587,117],{},[110,105589,4813],{},[195,105591,105592,105594],{},[35,105593,199],{},[35,105595,7561],{},[110,105597,113],{"stretchy":112},[35,105599,774],{},[110,105601,120],{"stretchy":112},[110,105603,120],{"stretchy":112},[110,105605,123],{},[35,105607,4100],{},[110,105609,4103],{},[238,105611,105612,105614],{},[35,105613,11],{},[35,105615,944],{},[110,105617,551],{"separator":46},[39,105619,105620],{"encoding":41},"g(x)=\\log D_s(x)-\\log(1-D_s(x))\n=\\log\\frac{p}{q},",[15,105622,105624,105651,105723,105749,105813],{"className":105623,"ariaHidden":46},[45],[15,105625,105627,105630,105633,105636,105639,105642,105645,105648],{"className":105626},[50],[15,105628],{"className":105629,"style":139},[54],[15,105631,4158],{"className":105632,"style":981},[59,60],[15,105634,113],{"className":105635},[146],[15,105637,774],{"className":105638},[59,60],[15,105640,120],{"className":105641},[153],[15,105643],{"className":105644,"style":158},[157],[15,105646,123],{"className":105647},[162],[15,105649],{"className":105650,"style":158},[157],[15,105652,105654,105657,105662,105665,105705,105708,105711,105714,105717,105720],{"className":105653},[50],[15,105655],{"className":105656,"style":139},[54],[15,105658,4154,105660],{"className":105659},[1484],[15,105661,4158],{"style":4157},[15,105663],{"className":105664,"style":406},[157],[15,105666,105668,105671],{"className":105667},[59],[15,105669,199],{"className":105670,"style":277},[59,60],[15,105672,105674],{"className":105673},[281],[15,105675,105677,105697],{"className":105676},[285,286],[15,105678,105680,105694],{"className":105679},[290],[15,105681,105683],{"className":105682,"style":44929},[294],[15,105684,105685,105688],{"style":298},[15,105686],{"className":105687,"style":303},[302],[15,105689,105691],{"className":105690},[307,308,309,310],[15,105692,7561],{"className":105693},[59,60,310],[15,105695,318],{"className":105696},[317],[15,105698,105700],{"className":105699},[290],[15,105701,105703],{"className":105702,"style":7968},[294],[15,105704],{},[15,105706,113],{"className":105707},[146],[15,105709,774],{"className":105710},[59,60],[15,105712,120],{"className":105713},[153],[15,105715],{"className":105716,"style":2587},[157],[15,105718,4813],{"className":105719},[2591],[15,105721],{"className":105722,"style":2587},[157],[15,105724,105726,105729,105734,105737,105740,105743,105746],{"className":105725},[50],[15,105727],{"className":105728,"style":139},[54],[15,105730,4154,105732],{"className":105731},[1484],[15,105733,4158],{"style":4157},[15,105735,113],{"className":105736},[146],[15,105738,117],{"className":105739},[59],[15,105741],{"className":105742,"style":2587},[157],[15,105744,4813],{"className":105745},[2591],[15,105747],{"className":105748,"style":2587},[157],[15,105750,105752,105755,105795,105798,105801,105804,105807,105810],{"className":105751},[50],[15,105753],{"className":105754,"style":139},[54],[15,105756,105758,105761],{"className":105757},[59],[15,105759,199],{"className":105760,"style":277},[59,60],[15,105762,105764],{"className":105763},[281],[15,105765,105767,105787],{"className":105766},[285,286],[15,105768,105770,105784],{"className":105769},[290],[15,105771,105773],{"className":105772,"style":44929},[294],[15,105774,105775,105778],{"style":298},[15,105776],{"className":105777,"style":303},[302],[15,105779,105781],{"className":105780},[307,308,309,310],[15,105782,7561],{"className":105783},[59,60,310],[15,105785,318],{"className":105786},[317],[15,105788,105790],{"className":105789},[290],[15,105791,105793],{"className":105792,"style":7968},[294],[15,105794],{},[15,105796,113],{"className":105797},[146],[15,105799,774],{"className":105800},[59,60],[15,105802,19047],{"className":105803},[153],[15,105805],{"className":105806,"style":158},[157],[15,105808,123],{"className":105809},[162],[15,105811],{"className":105812,"style":158},[157],[15,105814,105816,105819,105824,105827,105889],{"className":105815},[50],[15,105817],{"className":105818,"style":22010},[54],[15,105820,4154,105822],{"className":105821},[1484],[15,105823,4158],{"style":4157},[15,105825],{"className":105826,"style":406},[157],[15,105828,105830,105833,105886],{"className":105829},[59],[15,105831],{"className":105832},[146,441],[15,105834,105836],{"className":105835},[238],[15,105837,105839,105878],{"className":105838},[285,286],[15,105840,105842,105875],{"className":105841},[290],[15,105843,105845,105856,105864],{"className":105844,"style":3554},[294],[15,105846,105847,105850],{"style":457},[15,105848],{"className":105849,"style":461},[302],[15,105851,105853],{"className":105852},[59],[15,105854,944],{"className":105855,"style":981},[59,60],[15,105857,105858,105861],{"style":473},[15,105859],{"className":105860,"style":461},[302],[15,105862],{"className":105863,"style":481},[480],[15,105865,105866,105869],{"style":484},[15,105867],{"className":105868,"style":461},[302],[15,105870,105872],{"className":105871},[59],[15,105873,11],{"className":105874},[59,60],[15,105876,318],{"className":105877},[317],[15,105879,105881],{"className":105880},[290],[15,105882,105884],{"className":105883,"style":506},[294],[15,105885],{},[15,105887],{"className":105888},[153,441],[15,105890,551],{"className":105891},[573],[11,105893,105894],{},"它与 5.2 节的最优解",[15,105896,105898],{"className":105897,"translate":19},[180],[15,105899,105901,105983],{"className":105900,"translate":19},[18],[15,105902,105904],{"className":105903},[23],[25,105905,105906],{"xmlns":27,"display":189},[29,105907,105908,105980],{},[32,105909,105910,105922,105924,105926,105928,105930,105942,105944,105950,105952,105954,105960,105962,105964],{},[7553,105911,105912,105914,105920],{},[35,105913,4158],{},[32,105915,105916,105918],{},[35,105917,23743],{},[35,105919,25737],{},[110,105921,7573],{},[110,105923,113],{"stretchy":112},[35,105925,774],{},[110,105927,120],{"stretchy":112},[110,105929,123],{},[7553,105931,105932,105934,105940],{},[35,105933,37],{},[32,105935,105936,105938],{},[35,105937,23743],{},[35,105939,25737],{},[110,105941,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,105943,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[238,105945,105946,105948],{},[35,105947,11],{},[35,105949,944],{},[110,105951,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,105953,123],{},[238,105955,105956,105958],{},[115,105957,117],{},[115,105959,2463],{},[35,105961,4100],{},[110,105963,4103],{},[238,105965,105966,105972],{},[32,105967,105968,105970],{},[115,105969,2463],{},[35,105971,769],{},[32,105973,105974,105976,105978],{},[35,105975,769],{},[110,105977,2470],{},[115,105979,117],{},[39,105981,105982],{"encoding":41},"g_{JS}^*(x)=f_{JS}'\\Big(\\frac{p}{q}\\Big)\n=\\frac12\\log\\frac{2t}{t+1}",[15,105984,105986,106068,106217],{"className":105985,"ariaHidden":46},[45],[15,105987,105989,105992,106050,106053,106056,106059,106062,106065],{"className":105988},[50],[15,105990],{"className":105991,"style":139},[54],[15,105993,105995,105998],{"className":105994},[59],[15,105996,4158],{"className":105997,"style":981},[59,60],[15,105999,106001],{"className":106000},[281],[15,106002,106004,106042],{"className":106003},[285,286],[15,106005,106007,106039],{"className":106006},[290],[15,106008,106010,106028],{"className":106009,"style":8248},[294],[15,106011,106013,106016],{"style":106012},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[15,106014],{"className":106015,"style":303},[302],[15,106017,106019],{"className":106018},[307,308,309,310],[15,106020,106022,106025],{"className":106021},[59,310],[15,106023,23743],{"className":106024,"style":24153},[59,60,310],[15,106026,25737],{"className":106027,"style":25861},[59,60,310],[15,106029,106030,106033],{"style":8277},[15,106031],{"className":106032,"style":303},[302],[15,106034,106036],{"className":106035},[307,308,309,310],[15,106037,7573],{"className":106038},[2591,310],[15,106040,318],{"className":106041},[317],[15,106043,106045],{"className":106044},[290],[15,106046,106048],{"className":106047,"style":8299},[294],[15,106049],{},[15,106051,113],{"className":106052},[146],[15,106054,774],{"className":106055},[59,60],[15,106057,120],{"className":106058},[153],[15,106060],{"className":106061,"style":158},[157],[15,106063,123],{"className":106064},[162],[15,106066],{"className":106067,"style":158},[157],[15,106069,106071,106074,106134,106140,106202,106208,106211,106214],{"className":106070},[50],[15,106072],{"className":106073,"style":47965},[54],[15,106075,106077,106080],{"className":106076},[59],[15,106078,37],{"className":106079,"style":61},[59,60],[15,106081,106083],{"className":106082},[281],[15,106084,106086,106126],{"className":106085},[285,286],[15,106087,106089,106123],{"className":106088},[290],[15,106090,106092,106109],{"className":106091,"style":28971},[294],[15,106093,106094,106097],{"style":8251},[15,106095],{"className":106096,"style":303},[302],[15,106098,106100],{"className":106099},[307,308,309,310],[15,106101,106103,106106],{"className":106102},[59,310],[15,106104,23743],{"className":106105,"style":24153},[59,60,310],[15,106107,25737],{"className":106108,"style":25861},[59,60,310],[15,106110,106111,106114],{"style":8277},[15,106112],{"className":106113,"style":303},[302],[15,106115,106117],{"className":106116},[307,308,309,310],[15,106118,106120],{"className":106119},[59,310],[15,106121,6820],{"className":106122},[59,310],[15,106124,318],{"className":106125},[317],[15,106127,106129],{"className":106128},[290],[15,106130,106132],{"className":106131,"style":8299},[294],[15,106133],{},[15,106135,106137],{"className":106136},[59],[15,106138,113],{"className":106139},[419,3720],[15,106141,106143,106146,106199],{"className":106142},[59],[15,106144],{"className":106145},[146,441],[15,106147,106149],{"className":106148},[238],[15,106150,106152,106191],{"className":106151},[285,286],[15,106153,106155,106188],{"className":106154},[290],[15,106156,106158,106169,106177],{"className":106157,"style":3554},[294],[15,106159,106160,106163],{"style":457},[15,106161],{"className":106162,"style":461},[302],[15,106164,106166],{"className":106165},[59],[15,106167,944],{"className":106168,"style":981},[59,60],[15,106170,106171,106174],{"style":473},[15,106172],{"className":106173,"style":461},[302],[15,106175],{"className":106176,"style":481},[480],[15,106178,106179,106182],{"style":484},[15,106180],{"className":106181,"style":461},[302],[15,106183,106185],{"className":106184},[59],[15,106186,11],{"className":106187},[59,60],[15,106189,318],{"className":106190},[317],[15,106192,106194],{"className":106193},[290],[15,106195,106197],{"className":106196,"style":506},[294],[15,106198],{},[15,106200],{"className":106201},[153,441],[15,106203,106205],{"className":106204},[59],[15,106206,120],{"className":106207},[419,3720],[15,106209],{"className":106210,"style":158},[157],[15,106212,123],{"className":106213},[162],[15,106215],{"className":106216,"style":158},[157],[15,106218,106220,106223,106285,106288,106293,106296],{"className":106219},[50],[15,106221],{"className":106222,"style":26616},[54],[15,106224,106226,106229,106282],{"className":106225},[59],[15,106227],{"className":106228},[146,441],[15,106230,106232],{"className":106231},[238],[15,106233,106235,106274],{"className":106234},[285,286],[15,106236,106238,106271],{"className":106237},[290],[15,106239,106241,106252,106260],{"className":106240,"style":22889},[294],[15,106242,106243,106246],{"style":457},[15,106244],{"className":106245,"style":461},[302],[15,106247,106249],{"className":106248},[59],[15,106250,2463],{"className":106251},[59],[15,106253,106254,106257],{"style":473},[15,106255],{"className":106256,"style":461},[302],[15,106258],{"className":106259,"style":481},[480],[15,106261,106262,106265],{"style":484},[15,106263],{"className":106264,"style":461},[302],[15,106266,106268],{"className":106267},[59],[15,106269,117],{"className":106270},[59],[15,106272,318],{"className":106273},[317],[15,106275,106277],{"className":106276},[290],[15,106278,106280],{"className":106279,"style":3778},[294],[15,106281],{},[15,106283],{"className":106284},[153,441],[15,106286],{"className":106287,"style":406},[157],[15,106289,4154,106291],{"className":106290},[1484],[15,106292,4158],{"style":4157},[15,106294],{"className":106295,"style":406},[157],[15,106297,106299,106302,106370],{"className":106298},[59],[15,106300],{"className":106301},[146,441],[15,106303,106305],{"className":106304},[238],[15,106306,106308,106362],{"className":106307},[285,286],[15,106309,106311,106359],{"className":106310},[290],[15,106312,106314,106337,106345],{"className":106313,"style":22889},[294],[15,106315,106316,106319],{"style":457},[15,106317],{"className":106318,"style":461},[302],[15,106320,106322,106325,106328,106331,106334],{"className":106321},[59],[15,106323,769],{"className":106324},[59,60],[15,106326],{"className":106327,"style":2587},[157],[15,106329,2470],{"className":106330},[2591],[15,106332],{"className":106333,"style":2587},[157],[15,106335,117],{"className":106336},[59],[15,106338,106339,106342],{"style":473},[15,106340],{"className":106341,"style":461},[302],[15,106343],{"className":106344,"style":481},[480],[15,106346,106347,106350],{"style":484},[15,106348],{"className":106349,"style":461},[302],[15,106351,106353,106356],{"className":106352},[59],[15,106354,2463],{"className":106355},[59],[15,106357,769],{"className":106358},[59,60],[15,106360,318],{"className":106361},[317],[15,106363,106365],{"className":106364},[290],[15,106366,106368],{"className":106367,"style":17015},[294],[15,106369],{},[15,106371],{"className":106372},[153,441],[11,106374,106375,106376,106762],{},"通过重参数化 ",[15,106377,106379,106439],{"className":106378,"translate":19},[18],[15,106380,106382],{"className":106381},[23],[25,106383,106384],{"xmlns":27},[29,106385,106386,106436],{},[32,106387,106388,106396,106398,106422,106424],{},[7553,106389,106390,106392,106394],{},[35,106391,199],{},[35,106393,7561],{},[110,106395,7573],{},[110,106397,123],{},[238,106399,106400,106420],{},[6814,106401,106402,106404],{},[35,106403,7567],{},[32,106405,106406,106408],{},[115,106407,2463],{},[7553,106409,106410,106412,106418],{},[35,106411,4158],{},[32,106413,106414,106416],{},[35,106415,23743],{},[35,106417,25737],{},[110,106419,7573],{},[115,106421,2463],{},[110,106423,123],{},[238,106425,106426,106428],{},[35,106427,11],{},[32,106429,106430,106432,106434],{},[35,106431,11],{},[110,106433,2470],{},[35,106435,944],{},[39,106437,106438],{"encoding":41},"D_s^*=\\frac{e^{2g_{JS}^*}}{2}=\\frac{p}{p+q}",[15,106440,106442,106509,106682],{"className":106441,"ariaHidden":46},[45],[15,106443,106445,106449,106500,106503,106506],{"className":106444},[50],[15,106446],{"className":106447,"style":106448},[54],"height:0.9357em;vertical-align:-0.247em;",[15,106450,106452,106455],{"className":106451},[59],[15,106453,199],{"className":106454,"style":277},[59,60],[15,106456,106458],{"className":106457},[281],[15,106459,106461,106492],{"className":106460},[285,286],[15,106462,106464,106489],{"className":106463},[290],[15,106465,106467,106478],{"className":106466,"style":8499},[294],[15,106468,106469,106472],{"style":49572},[15,106470],{"className":106471,"style":303},[302],[15,106473,106475],{"className":106474},[307,308,309,310],[15,106476,7561],{"className":106477},[59,60,310],[15,106479,106480,106483],{"style":6865},[15,106481],{"className":106482,"style":303},[302],[15,106484,106486],{"className":106485},[307,308,309,310],[15,106487,7573],{"className":106488},[2591,310],[15,106490,318],{"className":106491},[317],[15,106493,106495],{"className":106494},[290],[15,106496,106498],{"className":106497,"style":8299},[294],[15,106499],{},[15,106501],{"className":106502,"style":158},[157],[15,106504,123],{"className":106505},[162],[15,106507],{"className":106508,"style":158},[157],[15,106510,106512,106516,106673,106676,106679],{"className":106511},[50],[15,106513],{"className":106514,"style":106515},[54],"height:1.4753em;vertical-align:-0.345em;",[15,106517,106519,106522,106670],{"className":106518},[59],[15,106520],{"className":106521},[146,441],[15,106523,106525],{"className":106524},[238],[15,106526,106528,106662],{"className":106527},[285,286],[15,106529,106531,106659],{"className":106530},[290],[15,106532,106535,106549,106557],{"className":106533,"style":106534},[294],"height:1.1303em;",[15,106536,106537,106540],{"style":2527},[15,106538],{"className":106539,"style":461},[302],[15,106541,106543],{"className":106542},[307,308,309,310],[15,106544,106546],{"className":106545},[59,310],[15,106547,2463],{"className":106548},[59,310],[15,106550,106551,106554],{"style":473},[15,106552],{"className":106553,"style":461},[302],[15,106555],{"className":106556,"style":481},[480],[15,106558,106559,106562],{"style":2550},[15,106560],{"className":106561,"style":461},[302],[15,106563,106565],{"className":106564},[307,308,309,310],[15,106566,106568],{"className":106567},[59,310],[15,106569,106571,106574],{"className":106570},[59,310],[15,106572,7567],{"className":106573},[59,60,310],[15,106575,106577],{"className":106576},[281],[15,106578,106580],{"className":106579},[285],[15,106581,106583],{"className":106582},[290],[15,106584,106587],{"className":106585,"style":106586},[294],"height:1.0519em;",[15,106588,106590,106594],{"style":106589},"top:-3.0519em;margin-right:0.0714em;",[15,106591],{"className":106592,"style":106593},[302],"height:2.6209em;",[15,106595,106597],{"className":106596},[307,30210,9674,310],[15,106598,106600,106603],{"className":106599},[59,310],[15,106601,2463],{"className":106602},[59,310],[15,106604,106606,106609],{"className":106605},[59,310],[15,106607,4158],{"className":106608,"style":981},[59,60,310],[15,106610,106612],{"className":106611},[281],[15,106613,106615,106650],{"className":106614},[285,286],[15,106616,106618,106647],{"className":106617},[290],[15,106619,106622,106638],{"className":106620,"style":106621},[294],"height:0.8693em;",[15,106623,106625,106629],{"style":106624},"top:-2.2427em;margin-left:-0.0359em;margin-right:0.1em;",[15,106626],{"className":106627,"style":106628},[302],"height:2.6833em;",[15,106630,106632,106635],{"className":106631},[59,310],[15,106633,23743],{"className":106634,"style":24153},[59,60,310],[15,106636,25737],{"className":106637,"style":25861},[59,60,310],[15,106639,106641,106644],{"style":106640},"top:-3.0873em;margin-right:0.1em;",[15,106642],{"className":106643,"style":106628},[302],[15,106645,7573],{"className":106646},[2591,310],[15,106648,318],{"className":106649},[317],[15,106651,106653],{"className":106652},[290],[15,106654,106657],{"className":106655,"style":106656},[294],"height:0.4406em;",[15,106658],{},[15,106660,318],{"className":106661},[317],[15,106663,106665],{"className":106664},[290],[15,106666,106668],{"className":106667,"style":2572},[294],[15,106669],{},[15,106671],{"className":106672},[153,441],[15,106674],{"className":106675,"style":158},[157],[15,106677,123],{"className":106678},[162],[15,106680],{"className":106681,"style":158},[157],[15,106683,106685,106688],{"className":106684},[50],[15,106686],{"className":106687,"style":3084},[54],[15,106689,106691,106694,106759],{"className":106690},[59],[15,106692],{"className":106693},[146,441],[15,106695,106697],{"className":106696},[238],[15,106698,106700,106751],{"className":106699},[285,286],[15,106701,106703,106748],{"className":106702},[290],[15,106704,106706,106726,106734],{"className":106705,"style":3103},[294],[15,106707,106708,106711],{"style":2527},[15,106709],{"className":106710,"style":461},[302],[15,106712,106714],{"className":106713},[307,308,309,310],[15,106715,106717,106720,106723],{"className":106716},[59,310],[15,106718,11],{"className":106719},[59,60,310],[15,106721,2470],{"className":106722},[2591,310],[15,106724,944],{"className":106725,"style":981},[59,60,310],[15,106727,106728,106731],{"style":473},[15,106729],{"className":106730,"style":461},[302],[15,106732],{"className":106733,"style":481},[480],[15,106735,106736,106739],{"style":2853},[15,106737],{"className":106738,"style":461},[302],[15,106740,106742],{"className":106741},[307,308,309,310],[15,106743,106745],{"className":106744},[59,310],[15,106746,11],{"className":106747},[59,60,310],[15,106749,318],{"className":106750},[317],[15,106752,106754],{"className":106753},[290],[15,106755,106757],{"className":106756,"style":2739},[294],[15,106758],{},[15,106760],{"className":106761},[153,441]," 相联系（常数平移在共轭表示中自由），故在最优判别器处可直接代入：",[15,106764,106766],{"className":106765,"translate":19},[180],[15,106767,106769,106876],{"className":106768,"translate":19},[18],[15,106770,106772],{"className":106771},[23],[25,106773,106774],{"xmlns":27,"display":189},[29,106775,106776,106873],{},[32,106777,106778,106784,106786,106788,106790,106796,106798,106800,106806,106808,106810,106812,106814,106816,106818,106824,106826,106828,106830,106832,106834,106844,106846,106862,106864,106866,106868,106870],{},[195,106779,106780,106782],{},[35,106781,223],{"mathvariant":222},[35,106783,206],{},[110,106785,230],{"stretchy":112},[35,106787,4100],{},[110,106789,4103],{},[195,106791,106792,106794],{},[35,106793,199],{},[35,106795,7561],{},[110,106797,257],{"stretchy":112},[110,106799,2470],{},[195,106801,106802,106804],{},[35,106803,223],{"mathvariant":222},[35,106805,213],{},[110,106807,230],{"stretchy":112},[35,106809,4100],{},[110,106811,4103],{},[110,106813,113],{"stretchy":112},[115,106815,117],{},[110,106817,4813],{},[195,106819,106820,106822],{},[35,106821,199],{},[35,106823,7561],{},[110,106825,120],{"stretchy":112},[110,106827,257],{"stretchy":112},[110,106829,123],{},[115,106831,2463],{},[1297,106833,1299],{},[195,106835,106836,106838],{},[35,106837,199],{},[32,106839,106840,106842],{},[35,106841,23743],{},[35,106843,25737],{},[1297,106845,1304],{},[32,106847,106848,106850,106852,106854,106856,106858,106860],{},[110,106849,113],{"fence":46},[35,106851,206],{},[1297,106853,4283],{},[110,106855,210],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[1297,106857,4283],{},[35,106859,213],{},[110,106861,120],{"fence":46},[110,106863,4813],{},[115,106865,2463],{},[35,106867,4100],{},[110,106869,4103],{},[115,106871,106872],{},"2.",[39,106874,106875],{"encoding":41},"\\mathbb E_P[\\log D_s]+\\mathbb E_Q[\\log(1-D_s)]\n=2\\,D_{JS}\\!\\left(P\\ \\Big\\|\\ Q\\right)-2\\log 2 .",[15,106877,106879,106988,107057,107115,107252],{"className":106878,"ariaHidden":46},[45],[15,106880,106882,106885,106925,106928,106933,106936,106976,106979,106982,106985],{"className":106881},[50],[15,106883],{"className":106884,"style":139},[54],[15,106886,106888,106891],{"className":106887},[59],[15,106889,223],{"className":106890},[59,366],[15,106892,106894],{"className":106893},[281],[15,106895,106897,106917],{"className":106896},[285,286],[15,106898,106900,106914],{"className":106899},[290],[15,106901,106903],{"className":106902,"style":379},[294],[15,106904,106905,106908],{"style":382},[15,106906],{"className":106907,"style":303},[302],[15,106909,106911],{"className":106910},[307,308,309,310],[15,106912,206],{"className":106913,"style":334},[59,60,310],[15,106915,318],{"className":106916},[317],[15,106918,106920],{"className":106919},[290],[15,106921,106923],{"className":106922,"style":7968},[294],[15,106924],{},[15,106926,230],{"className":106927},[146],[15,106929,4154,106931],{"className":106930},[1484],[15,106932,4158],{"style":4157},[15,106934],{"className":106935,"style":406},[157],[15,106937,106939,106942],{"className":106938},[59],[15,106940,199],{"className":106941,"style":277},[59,60],[15,106943,106945],{"className":106944},[281],[15,106946,106948,106968],{"className":106947},[285,286],[15,106949,106951,106965],{"className":106950},[290],[15,106952,106954],{"className":106953,"style":44929},[294],[15,106955,106956,106959],{"style":298},[15,106957],{"className":106958,"style":303},[302],[15,106960,106962],{"className":106961},[307,308,309,310],[15,106963,7561],{"className":106964},[59,60,310],[15,106966,318],{"className":106967},[317],[15,106969,106971],{"className":106970},[290],[15,106972,106974],{"className":106973,"style":7968},[294],[15,106975],{},[15,106977,257],{"className":106978},[153],[15,106980],{"className":106981,"style":2587},[157],[15,106983,2470],{"className":106984},[2591],[15,106986],{"className":106987,"style":2587},[157],[15,106989,106991,106994,107034,107037,107042,107045,107048,107051,107054],{"className":106990},[50],[15,106992],{"className":106993,"style":270},[54],[15,106995,106997,107000],{"className":106996},[59],[15,106998,223],{"className":106999},[59,366],[15,107001,107003],{"className":107002},[281],[15,107004,107006,107026],{"className":107005},[285,286],[15,107007,107009,107023],{"className":107008},[290],[15,107010,107012],{"className":107011,"style":379},[294],[15,107013,107014,107017],{"style":382},[15,107015],{"className":107016,"style":303},[302],[15,107018,107020],{"className":107019},[307,308,309,310],[15,107021,213],{"className":107022},[59,60,310],[15,107024,318],{"className":107025},[317],[15,107027,107029],{"className":107028},[290],[15,107030,107032],{"className":107031,"style":325},[294],[15,107033],{},[15,107035,230],{"className":107036},[146],[15,107038,4154,107040],{"className":107039},[1484],[15,107041,4158],{"style":4157},[15,107043,113],{"className":107044},[146],[15,107046,117],{"className":107047},[59],[15,107049],{"className":107050,"style":2587},[157],[15,107052,4813],{"className":107053},[2591],[15,107055],{"className":107056,"style":2587},[157],[15,107058,107060,107063,107103,107106,107109,107112],{"className":107059},[50],[15,107061],{"className":107062,"style":139},[54],[15,107064,107066,107069],{"className":107065},[59],[15,107067,199],{"className":107068,"style":277},[59,60],[15,107070,107072],{"className":107071},[281],[15,107073,107075,107095],{"className":107074},[285,286],[15,107076,107078,107092],{"className":107077},[290],[15,107079,107081],{"className":107080,"style":44929},[294],[15,107082,107083,107086],{"style":298},[15,107084],{"className":107085,"style":303},[302],[15,107087,107089],{"className":107088},[307,308,309,310],[15,107090,7561],{"className":107091},[59,60,310],[15,107093,318],{"className":107094},[317],[15,107096,107098],{"className":107097},[290],[15,107099,107101],{"className":107100,"style":7968},[294],[15,107102],{},[15,107104,20390],{"className":107105},[153],[15,107107],{"className":107108,"style":158},[157],[15,107110,123],{"className":107111},[162],[15,107113],{"className":107114,"style":158},[157],[15,107116,107118,107121,107124,107127,107173,107176,107179,107243,107246,107249],{"className":107117},[50],[15,107119],{"className":107120,"style":68117},[54],[15,107122,2463],{"className":107123},[59],[15,107125],{"className":107126,"style":406},[157],[15,107128,107130,107133],{"className":107129},[59],[15,107131,199],{"className":107132,"style":277},[59,60],[15,107134,107136],{"className":107135},[281],[15,107137,107139,107165],{"className":107138},[285,286],[15,107140,107142,107162],{"className":107141},[290],[15,107143,107145],{"className":107144,"style":379},[294],[15,107146,107147,107150],{"style":298},[15,107148],{"className":107149,"style":303},[302],[15,107151,107153],{"className":107152},[307,308,309,310],[15,107154,107156,107159],{"className":107155},[59,310],[15,107157,23743],{"className":107158,"style":24153},[59,60,310],[15,107160,25737],{"className":107161,"style":25861},[59,60,310],[15,107163,318],{"className":107164},[317],[15,107166,107168],{"className":107167},[290],[15,107169,107171],{"className":107170,"style":7968},[294],[15,107172],{},[15,107174],{"className":107175,"style":1512},[157],[15,107177],{"className":107178,"style":406},[157],[15,107180,107182,107188,107191,107194,107231,107234,107237],{"className":107181},[410],[15,107183,107185],{"className":107184,"style":415},[146,414],[15,107186,113],{"className":107187},[419,3720],[15,107189,206],{"className":107190,"style":334},[59,60],[15,107192,4283],{"className":107193},[157],[15,107195,107197],{"className":107196},[59],[15,107198,107200],{"className":107199},[419,14829],[15,107201,107203,107223],{"className":107202},[285,286],[15,107204,107206,107220],{"className":107205},[290],[15,107207,107209],{"className":107208,"style":85515},[294],[15,107210,107211,107214],{"style":73524},[15,107212],{"className":107213,"style":82587},[302],[15,107215,107216],{"style":85523},[6323,107217,107218],{"xmlns":6325,"width":14852,"height":17439,"viewBox":85526},[6331,107219],{"d":85529},[15,107221,318],{"className":107222},[317],[15,107224,107226],{"className":107225},[290],[15,107227,107229],{"className":107228,"style":85539},[294],[15,107230],{},[15,107232,4283],{"className":107233},[157],[15,107235,213],{"className":107236},[59,60],[15,107238,107240],{"className":107239,"style":415},[153,414],[15,107241,120],{"className":107242},[419,3720],[15,107244],{"className":107245,"style":2587},[157],[15,107247,4813],{"className":107248},[2591],[15,107250],{"className":107251,"style":2587},[157],[15,107253,107255,107258,107261,107264,107269,107272],{"className":107254},[50],[15,107256],{"className":107257,"style":55},[54],[15,107259,2463],{"className":107260},[59],[15,107262],{"className":107263,"style":406},[157],[15,107265,4154,107267],{"className":107266},[1484],[15,107268,4158],{"style":4157},[15,107270],{"className":107271,"style":406},[157],[15,107273,106872],{"className":107274},[59],[11,107276,107277,107278,32801],{},"推导：",[15,107279,107281,107339],{"className":107280,"translate":19},[18],[15,107282,107284],{"className":107283},[23],[25,107285,107286],{"xmlns":27},[29,107287,107288,107336],{},[32,107289,107290,107292,107294,107310,107312,107314,107316,107328,107330,107332,107334],{},[35,107291,4100],{},[110,107293,4103],{},[238,107295,107296,107302],{},[32,107297,107298,107300],{},[115,107299,2463],{},[35,107301,11],{},[32,107303,107304,107306,107308],{},[35,107305,11],{},[110,107307,2470],{},[35,107309,944],{},[110,107311,123],{},[35,107313,4100],{},[110,107315,4103],{},[238,107317,107318,107320],{},[35,107319,11],{},[32,107321,107322,107324,107326],{},[35,107323,11],{},[110,107325,2470],{},[35,107327,944],{},[110,107329,2470],{},[35,107331,4100],{},[110,107333,4103],{},[115,107335,2463],{},[39,107337,107338],{"encoding":41},"\\log\\frac{2p}{p+q}=\\log\\frac{p}{p+q}+\\log2",[15,107340,107342,107444,107541],{"className":107341,"ariaHidden":46},[45],[15,107343,107345,107349,107354,107357,107435,107438,107441],{"className":107344},[50],[15,107346],{"className":107347,"style":107348},[54],"height:1.3783em;vertical-align:-0.4811em;",[15,107350,4154,107352],{"className":107351},[1484],[15,107353,4158],{"style":4157},[15,107355],{"className":107356,"style":406},[157],[15,107358,107360,107363,107432],{"className":107359},[59],[15,107361],{"className":107362},[146,441],[15,107364,107366],{"className":107365},[238],[15,107367,107369,107424],{"className":107368},[285,286],[15,107370,107372,107421],{"className":107371},[290],[15,107373,107376,107396,107404],{"className":107374,"style":107375},[294],"height:0.8972em;",[15,107377,107378,107381],{"style":2527},[15,107379],{"className":107380,"style":461},[302],[15,107382,107384],{"className":107383},[307,308,309,310],[15,107385,107387,107390,107393],{"className":107386},[59,310],[15,107388,11],{"className":107389},[59,60,310],[15,107391,2470],{"className":107392},[2591,310],[15,107394,944],{"className":107395,"style":981},[59,60,310],[15,107397,107398,107401],{"style":473},[15,107399],{"className":107400,"style":461},[302],[15,107402],{"className":107403,"style":481},[480],[15,107405,107406,107409],{"style":2853},[15,107407],{"className":107408,"style":461},[302],[15,107410,107412],{"className":107411},[307,308,309,310],[15,107413,107415,107418],{"className":107414},[59,310],[15,107416,2463],{"className":107417},[59,310],[15,107419,11],{"className":107420},[59,60,310],[15,107422,318],{"className":107423},[317],[15,107425,107427],{"className":107426},[290],[15,107428,107430],{"className":107429,"style":2739},[294],[15,107431],{},[15,107433],{"className":107434},[153,441],[15,107436],{"className":107437,"style":158},[157],[15,107439,123],{"className":107440},[162],[15,107442],{"className":107443,"style":158},[157],[15,107445,107447,107450,107455,107458,107532,107535,107538],{"className":107446},[50],[15,107448],{"className":107449,"style":3084},[54],[15,107451,4154,107453],{"className":107452},[1484],[15,107454,4158],{"style":4157},[15,107456],{"className":107457,"style":406},[157],[15,107459,107461,107464,107529],{"className":107460},[59],[15,107462],{"className":107463},[146,441],[15,107465,107467],{"className":107466},[238],[15,107468,107470,107521],{"className":107469},[285,286],[15,107471,107473,107518],{"className":107472},[290],[15,107474,107476,107496,107504],{"className":107475,"style":3103},[294],[15,107477,107478,107481],{"style":2527},[15,107479],{"className":107480,"style":461},[302],[15,107482,107484],{"className":107483},[307,308,309,310],[15,107485,107487,107490,107493],{"className":107486},[59,310],[15,107488,11],{"className":107489},[59,60,310],[15,107491,2470],{"className":107492},[2591,310],[15,107494,944],{"className":107495,"style":981},[59,60,310],[15,107497,107498,107501],{"style":473},[15,107499],{"className":107500,"style":461},[302],[15,107502],{"className":107503,"style":481},[480],[15,107505,107506,107509],{"style":2853},[15,107507],{"className":107508,"style":461},[302],[15,107510,107512],{"className":107511},[307,308,309,310],[15,107513,107515],{"className":107514},[59,310],[15,107516,11],{"className":107517},[59,60,310],[15,107519,318],{"className":107520},[317],[15,107522,107524],{"className":107523},[290],[15,107525,107527],{"className":107526,"style":2739},[294],[15,107528],{},[15,107530],{"className":107531},[153,441],[15,107533],{"className":107534,"style":2587},[157],[15,107536,2470],{"className":107537},[2591],[15,107539],{"className":107540,"style":2587},[157],[15,107542,107544,107547,107552,107555],{"className":107543},[50],[15,107545],{"className":107546,"style":55},[54],[15,107548,4154,107550],{"className":107549},[1484],[15,107551,4158],{"style":4157},[15,107553],{"className":107554,"style":406},[157],[15,107556,2463],{"className":107557},[59],[15,107559,107561],{"className":107560,"translate":19},[180],[15,107562,107564,107656],{"className":107563,"translate":19},[18],[15,107565,107567],{"className":107566},[23],[25,107568,107569],{"xmlns":27,"display":189},[29,107570,107571,107653],{},[32,107572,107573,107579,107581,107583,107585,107587,107589,107591,107597,107599,107601,107603,107619,107621,107623,107629,107631,107633,107635,107641,107643,107645,107647,107649,107651],{},[32,107574,107575,107577],{},[35,107576,10694],{"mathvariant":209},[35,107578,21893],{"mathvariant":209},[110,107580,113],{"stretchy":112},[35,107582,206],{},[35,107584,210],{"mathvariant":209},[35,107586,25567],{},[110,107588,120],{"stretchy":112},[110,107590,123],{},[195,107592,107593,107595],{},[35,107594,223],{"mathvariant":222},[35,107596,206],{},[110,107598,230],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,107600,4100],{},[110,107602,4103],{},[238,107604,107605,107611],{},[32,107606,107607,107609],{},[115,107608,2463],{},[35,107610,11],{},[32,107612,107613,107615,107617],{},[35,107614,11],{},[110,107616,2470],{},[35,107618,944],{},[110,107620,257],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,107622,123],{},[195,107624,107625,107627],{},[35,107626,223],{"mathvariant":222},[35,107628,206],{},[110,107630,230],{"stretchy":112},[35,107632,4100],{},[110,107634,4103],{},[195,107636,107637,107639],{},[35,107638,199],{},[35,107640,7561],{},[110,107642,257],{"stretchy":112},[110,107644,2470],{},[35,107646,4100],{},[110,107648,4103],{},[115,107650,2463],{},[110,107652,551],{"separator":46},[39,107654,107655],{"encoding":41},"\\mathrm{KL}(P\\|M)\n=\\mathbb E_P\\Big[\\log\\frac{2p}{p+q}\\Big]\n=\\mathbb E_P[\\log D_s]+\\log2,",[15,107657,107659,107695,107850,107959],{"className":107658,"ariaHidden":46},[45],[15,107660,107662,107665,107671,107674,107677,107680,107683,107686,107689,107692],{"className":107661},[50],[15,107663],{"className":107664,"style":139},[54],[15,107666,107668],{"className":107667},[59],[15,107669,32663],{"className":107670},[59,32662],[15,107672,113],{"className":107673},[146],[15,107675,206],{"className":107676,"style":334},[59,60],[15,107678,210],{"className":107679},[59],[15,107681,25567],{"className":107682,"style":25601},[59,60],[15,107684,120],{"className":107685},[153],[15,107687],{"className":107688,"style":158},[157],[15,107690,123],{"className":107691},[162],[15,107693],{"className":107694,"style":158},[157],[15,107696,107698,107701,107741,107747,107750,107755,107758,107835,107841,107844,107847],{"className":107697},[50],[15,107699],{"className":107700,"style":31303},[54],[15,107702,107704,107707],{"className":107703},[59],[15,107705,223],{"className":107706},[59,366],[15,107708,107710],{"className":107709},[281],[15,107711,107713,107733],{"className":107712},[285,286],[15,107714,107716,107730],{"className":107715},[290],[15,107717,107719],{"className":107718,"style":379},[294],[15,107720,107721,107724],{"style":382},[15,107722],{"className":107723,"style":303},[302],[15,107725,107727],{"className":107726},[307,308,309,310],[15,107728,206],{"className":107729,"style":334},[59,60,310],[15,107731,318],{"className":107732},[317],[15,107734,107736],{"className":107735},[290],[15,107737,107739],{"className":107738,"style":7968},[294],[15,107740],{},[15,107742,107744],{"className":107743},[59],[15,107745,230],{"className":107746},[419,3720],[15,107748],{"className":107749,"style":406},[157],[15,107751,4154,107753],{"className":107752},[1484],[15,107754,4158],{"style":4157},[15,107756],{"className":107757,"style":406},[157],[15,107759,107761,107764,107832],{"className":107760},[59],[15,107762],{"className":107763},[146,441],[15,107765,107767],{"className":107766},[238],[15,107768,107770,107824],{"className":107769},[285,286],[15,107771,107773,107821],{"className":107772},[290],[15,107774,107776,107799,107807],{"className":107775,"style":22889},[294],[15,107777,107778,107781],{"style":457},[15,107779],{"className":107780,"style":461},[302],[15,107782,107784,107787,107790,107793,107796],{"className":107783},[59],[15,107785,11],{"className":107786},[59,60],[15,107788],{"className":107789,"style":2587},[157],[15,107791,2470],{"className":107792},[2591],[15,107794],{"className":107795,"style":2587},[157],[15,107797,944],{"className":107798,"style":981},[59,60],[15,107800,107801,107804],{"style":473},[15,107802],{"className":107803,"style":461},[302],[15,107805],{"className":107806,"style":481},[480],[15,107808,107809,107812],{"style":484},[15,107810],{"className":107811,"style":461},[302],[15,107813,107815,107818],{"className":107814},[59],[15,107816,2463],{"className":107817},[59],[15,107819,11],{"className":107820},[59,60],[15,107822,318],{"className":107823},[317],[15,107825,107827],{"className":107826},[290],[15,107828,107830],{"className":107829,"style":506},[294],[15,107831],{},[15,107833],{"className":107834},[153,441],[15,107836,107838],{"className":107837},[59],[15,107839,257],{"className":107840},[419,3720],[15,107842],{"className":107843,"style":158},[157],[15,107845,123],{"className":107846},[162],[15,107848],{"className":107849,"style":158},[157],[15,107851,107853,107856,107896,107899,107904,107907,107947,107950,107953,107956],{"className":107852},[50],[15,107854],{"className":107855,"style":139},[54],[15,107857,107859,107862],{"className":107858},[59],[15,107860,223],{"className":107861},[59,366],[15,107863,107865],{"className":107864},[281],[15,107866,107868,107888],{"className":107867},[285,286],[15,107869,107871,107885],{"className":107870},[290],[15,107872,107874],{"className":107873,"style":379},[294],[15,107875,107876,107879],{"style":382},[15,107877],{"className":107878,"style":303},[302],[15,107880,107882],{"className":107881},[307,308,309,310],[15,107883,206],{"className":107884,"style":334},[59,60,310],[15,107886,318],{"className":107887},[317],[15,107889,107891],{"className":107890},[290],[15,107892,107894],{"className":107893,"style":7968},[294],[15,107895],{},[15,107897,230],{"className":107898},[146],[15,107900,4154,107902],{"className":107901},[1484],[15,107903,4158],{"style":4157},[15,107905],{"className":107906,"style":406},[157],[15,107908,107910,107913],{"className":107909},[59],[15,107911,199],{"className":107912,"style":277},[59,60],[15,107914,107916],{"className":107915},[281],[15,107917,107919,107939],{"className":107918},[285,286],[15,107920,107922,107936],{"className":107921},[290],[15,107923,107925],{"className":107924,"style":44929},[294],[15,107926,107927,107930],{"style":298},[15,107928],{"className":107929,"style":303},[302],[15,107931,107933],{"className":107932},[307,308,309,310],[15,107934,7561],{"className":107935},[59,60,310],[15,107937,318],{"className":107938},[317],[15,107940,107942],{"className":107941},[290],[15,107943,107945],{"className":107944,"style":7968},[294],[15,107946],{},[15,107948,257],{"className":107949},[153],[15,107951],{"className":107952,"style":2587},[157],[15,107954,2470],{"className":107955},[2591],[15,107957],{"className":107958,"style":2587},[157],[15,107960,107962,107965,107970,107973,107976],{"className":107961},[50],[15,107963],{"className":107964,"style":55},[54],[15,107966,4154,107968],{"className":107967},[1484],[15,107969,4158],{"style":4157},[15,107971],{"className":107972,"style":406},[157],[15,107974,2463],{"className":107975},[59],[15,107977,551],{"className":107978},[573],[11,107980,14261,107981,108009,108010,108064,108065,108179,108180,108238],{},[15,107982,107984,107997],{"className":107983,"translate":19},[18],[15,107985,107987],{"className":107986},[23],[25,107988,107989],{"xmlns":27},[29,107990,107991,107995],{},[32,107992,107993],{},[35,107994,213],{},[39,107996,213],{"encoding":41},[15,107998,108000],{"className":107999,"ariaHidden":46},[45],[15,108001,108003,108006],{"className":108002},[50],[15,108004],{"className":108005,"style":566},[54],[15,108007,213],{"className":108008},[59,60]," 同理，两式相加即得。于是「最小化 JS」与「在最优判别器下最大化 GAN 目标」是同一件事，而常数 ",[15,108011,108013,108035],{"className":108012,"translate":19},[18],[15,108014,108016],{"className":108015},[23],[25,108017,108018],{"xmlns":27},[29,108019,108020,108032],{},[32,108021,108022,108024,108026,108028,108030],{},[110,108023,4813],{},[115,108025,2463],{},[35,108027,4100],{},[110,108029,4103],{},[115,108031,2463],{},[39,108033,108034],{"encoding":41},"-2\\log2",[15,108036,108038],{"className":108037,"ariaHidden":46},[45],[15,108039,108041,108044,108047,108050,108053,108058,108061],{"className":108040},[50],[15,108042],{"className":108043,"style":55},[54],[15,108045,4813],{"className":108046},[59],[15,108048,2463],{"className":108049},[59],[15,108051],{"className":108052,"style":406},[157],[15,108054,4154,108056],{"className":108055},[1484],[15,108057,4158],{"style":4157},[15,108059],{"className":108060,"style":406},[157],[15,108062,2463],{"className":108063},[59]," 与生成器无关。这解释了「GAN 训练不收敛」的来源：JS 有界，一旦支撑集几近不重叠，",[15,108066,108068,108098],{"className":108067,"translate":19},[18],[15,108069,108071],{"className":108070},[23],[25,108072,108073],{"xmlns":27},[29,108074,108075,108095],{},[32,108076,108077,108087,108089,108091,108093],{},[195,108078,108079,108081],{},[35,108080,199],{},[32,108082,108083,108085],{},[35,108084,23743],{},[35,108086,25737],{},[110,108088,1029],{},[35,108090,4100],{},[110,108092,4103],{},[115,108094,2463],{},[39,108096,108097],{"encoding":41},"D_{JS}\\to\\log2",[15,108099,108101,108162],{"className":108100,"ariaHidden":46},[45],[15,108102,108104,108107,108153,108156,108159],{"className":108103},[50],[15,108105],{"className":108106,"style":15961},[54],[15,108108,108110,108113],{"className":108109},[59],[15,108111,199],{"className":108112,"style":277},[59,60],[15,108114,108116],{"className":108115},[281],[15,108117,108119,108145],{"className":108118},[285,286],[15,108120,108122,108142],{"className":108121},[290],[15,108123,108125],{"className":108124,"style":379},[294],[15,108126,108127,108130],{"style":298},[15,108128],{"className":108129,"style":303},[302],[15,108131,108133],{"className":108132},[307,308,309,310],[15,108134,108136,108139],{"className":108135},[59,310],[15,108137,23743],{"className":108138,"style":24153},[59,60,310],[15,108140,25737],{"className":108141,"style":25861},[59,60,310],[15,108143,318],{"className":108144},[317],[15,108146,108148],{"className":108147},[290],[15,108149,108151],{"className":108150,"style":7968},[294],[15,108152],{},[15,108154],{"className":108155,"style":158},[157],[15,108157,1029],{"className":108158},[162],[15,108160],{"className":108161,"style":158},[157],[15,108163,108165,108168,108173,108176],{"className":108164},[50],[15,108166],{"className":108167,"style":55},[54],[15,108169,4154,108171],{"className":108170},[1484],[15,108172,4158],{"style":4157},[15,108174],{"className":108175,"style":406},[157],[15,108177,2463],{"className":108178},[59],"，判别器梯度饱和，生成器梯度消失。反过来，换成 LSGAN（",[15,108181,108183,108200],{"className":108182,"translate":19},[18],[15,108184,108186],{"className":108185},[23],[25,108187,108188],{"xmlns":27},[29,108189,108190,108198],{},[32,108191,108192],{},[6814,108193,108194,108196],{},[35,108195,37449],{},[115,108197,2463],{},[39,108199,40394],{"encoding":41},[15,108201,108203],{"className":108202,"ariaHidden":46},[45],[15,108204,108206,108209],{"className":108205},[50],[15,108207],{"className":108208,"style":40404},[54],[15,108210,108212,108215],{"className":108211},[59],[15,108213,37449],{"className":108214},[59,60],[15,108216,108218],{"className":108217},[281],[15,108219,108221],{"className":108220},[285],[15,108222,108224],{"className":108223},[290],[15,108225,108227],{"className":108226,"style":20028},[294],[15,108228,108229,108232],{"style":6865},[15,108230],{"className":108231,"style":303},[302],[15,108233,108235],{"className":108234},[307,308,309,310],[15,108236,2463],{"className":108237},[59,310],"）、Wasserstein（非 f-散度）或 α-GAN 就能改变这一点。",[2311,108240,108242],{"id":108241},"_55-估计性质","5.5 估计性质",[11,108244,108245],{},"用 5.1 的 Monte Carlo 下界做估计时：",[10027,108247,108248,108393,108548],{},[6665,108249,108250,108251,33825,108320,108322,108323,108392],{},"它是 ",[15,108252,108254,108271],{"className":108253,"translate":19},[18],[15,108255,108257],{"className":108256},[23],[25,108258,108259],{"xmlns":27},[29,108260,108261,108269],{},[32,108262,108263],{},[195,108264,108265,108267],{},[35,108266,199],{},[35,108268,37],{},[39,108270,4022],{"encoding":41},[15,108272,108274],{"className":108273,"ariaHidden":46},[45],[15,108275,108277,108280],{"className":108276},[50],[15,108278],{"className":108279,"style":4032},[54],[15,108281,108283,108286],{"className":108282},[59],[15,108284,199],{"className":108285,"style":277},[59,60],[15,108287,108289],{"className":108288},[281],[15,108290,108292,108312],{"className":108291},[285,286],[15,108293,108295,108309],{"className":108294},[290],[15,108296,108298],{"className":108297,"style":295},[294],[15,108299,108300,108303],{"style":298},[15,108301],{"className":108302,"style":303},[302],[15,108304,108306],{"className":108305},[307,308,309,310],[15,108307,37],{"className":108308,"style":61},[59,60,310],[15,108310,318],{"className":108311},[317],[15,108313,108315],{"className":108314},[290],[15,108316,108318],{"className":108317,"style":325},[294],[15,108319],{},[1225,108321,99841],{},"（偏差向下），且偏差来自 ",[15,108324,108326,108343],{"className":108325,"translate":19},[18],[15,108327,108329],{"className":108328},[23],[25,108330,108331],{"xmlns":27},[29,108332,108333,108341],{},[32,108334,108335],{},[195,108336,108337,108339],{},[35,108338,4158],{},[35,108340,99861],{},[39,108342,99864],{"encoding":41},[15,108344,108346],{"className":108345,"ariaHidden":46},[45],[15,108347,108349,108352],{"className":108348},[50],[15,108350],{"className":108351,"style":2276},[54],[15,108353,108355,108358],{"className":108354},[59],[15,108356,4158],{"className":108357,"style":981},[59,60],[15,108359,108361],{"className":108360},[281],[15,108362,108364,108384],{"className":108363},[285,286],[15,108365,108367,108381],{"className":108366},[290],[15,108368,108370],{"className":108369,"style":44929},[294],[15,108371,108372,108375],{"style":18843},[15,108373],{"className":108374,"style":303},[302],[15,108376,108378],{"className":108377},[307,308,309,310],[15,108379,99861],{"className":108380,"style":981},[59,60,310],[15,108382,318],{"className":108383},[317],[15,108385,108387],{"className":108386},[290],[15,108388,108390],{"className":108389,"style":7968},[294],[15,108391],{}," 未达到最优 + 样本有限；",[6665,108394,68132,108395,108425,108426,108484,108485,108547],{},[15,108396,108398,108413],{"className":108397,"translate":19},[18],[15,108399,108401],{"className":108400},[23],[25,108402,108403],{"xmlns":27},[29,108404,108405,108411],{},[32,108406,108407,108409],{},[35,108408,35432],{},[110,108410,4103],{},[39,108412,57147],{"encoding":41},[15,108414,108416],{"className":108415,"ariaHidden":46},[45],[15,108417,108419,108422],{"className":108418},[50],[15,108420],{"className":108421,"style":2276},[54],[15,108423,35432],{"className":108424},[1484]," 取到极值时，估计量方差随 ",[15,108427,108429,108446],{"className":108428,"translate":19},[18],[15,108430,108432],{"className":108431},[23],[25,108433,108434],{"xmlns":27},[29,108435,108436,108444],{},[32,108437,108438],{},[6814,108439,108440,108442],{},[35,108441,37],{},[110,108443,7573],{},[39,108445,60708],{"encoding":41},[15,108447,108449],{"className":108448,"ariaHidden":46},[45],[15,108450,108452,108455],{"className":108451},[50],[15,108453],{"className":108454,"style":55},[54],[15,108456,108458,108461],{"className":108457},[59],[15,108459,37],{"className":108460,"style":61},[59,60],[15,108462,108464],{"className":108463},[281],[15,108465,108467],{"className":108466},[285],[15,108468,108470],{"className":108469},[290],[15,108471,108473],{"className":108472,"style":8499},[294],[15,108474,108475,108478],{"style":6865},[15,108476],{"className":108477,"style":303},[302],[15,108479,108481],{"className":108480},[307,308,309,310],[15,108482,7573],{"className":108483},[2591,310]," 增长而增大（如 KL 的 ",[15,108486,108488,108506],{"className":108487,"translate":19},[18],[15,108489,108491],{"className":108490},[23],[25,108492,108493],{"xmlns":27},[29,108494,108495,108503],{},[32,108496,108497],{},[6814,108498,108499,108501],{},[35,108500,7567],{},[35,108502,4158],{},[39,108504,108505],{"encoding":41},"e^{g}",[15,108507,108509],{"className":108508,"ariaHidden":46},[45],[15,108510,108512,108515],{"className":108511},[50],[15,108513],{"className":108514,"style":50353},[54],[15,108516,108518,108521],{"className":108517},[59],[15,108519,7567],{"className":108520},[59,60],[15,108522,108524],{"className":108523},[281],[15,108525,108527],{"className":108526},[285],[15,108528,108530],{"className":108529},[290],[15,108531,108533],{"className":108532,"style":50353},[294],[15,108534,108535,108538],{"style":6865},[15,108536],{"className":108537,"style":303},[302],[15,108539,108541],{"className":108540},[307,308,309,310],[15,108542,108544],{"className":108543},[59,310],[15,108545,4158],{"className":108546,"style":981},[59,60,310]," 会重尾）；",[6665,108549,108550,108551,108579],{},"一个常用替代是「对称化」或「有界化」",[15,108552,108554,108567],{"className":108553,"translate":19},[18],[15,108555,108557],{"className":108556},[23],[25,108558,108559],{"xmlns":27},[29,108560,108561,108565],{},[32,108562,108563],{},[35,108564,37],{},[39,108566,37],{"encoding":41},[15,108568,108570],{"className":108569,"ariaHidden":46},[45],[15,108571,108573,108576],{"className":108572},[50],[15,108574],{"className":108575,"style":55},[54],[15,108577,37],{"className":108578,"style":61},[59,60],"（如 JS、TV），牺牲敏感性换取稳定梯度。这与第 6 节讨论的「有界\u002F无界」准确性—稳健性权衡是同一件事。",[528,108581,108583],{"id":108582},"_6-与其他散度的比较","6. 与其他散度的比较",[2311,108585,108587],{"id":108586},"_61-汇总","6.1 汇总",[52492,108589,108590,108720],{},[52495,108591,108592],{},[52498,108593,108594,108596,108641,108716,108718],{},[52501,108595,52503],{},[52501,108597,108598],{},[15,108599,108601,108620],{"className":108600,"translate":19},[18],[15,108602,108604],{"className":108603},[23],[25,108605,108606],{"xmlns":27},[29,108607,108608,108618],{},[32,108609,108610,108612,108614,108616],{},[35,108611,37],{},[110,108613,113],{"stretchy":112},[35,108615,769],{},[110,108617,120],{"stretchy":112},[39,108619,52528],{"encoding":41},[15,108621,108623],{"className":108622,"ariaHidden":46},[45],[15,108624,108626,108629,108632,108635,108638],{"className":108625},[50],[15,108627],{"className":108628,"style":139},[54],[15,108630,37],{"className":108631,"style":61},[59,60],[15,108633,113],{"className":108634},[146],[15,108636,769],{"className":108637},[59,60],[15,108639,120],{"className":108640},[153],[52501,108642,108643],{},[15,108644,108646,108669],{"className":108645,"translate":19},[18],[15,108647,108649],{"className":108648},[23],[25,108650,108651],{"xmlns":27},[29,108652,108653,108667],{},[32,108654,108655,108661,108663,108665],{},[6814,108656,108657,108659],{},[35,108658,37],{},[110,108660,7573],{},[110,108662,113],{"stretchy":112},[35,108664,40237],{},[110,108666,120],{"stretchy":112},[39,108668,64695],{"encoding":41},[15,108670,108672],{"className":108671,"ariaHidden":46},[45],[15,108673,108675,108678,108707,108710,108713],{"className":108674},[50],[15,108676],{"className":108677,"style":139},[54],[15,108679,108681,108684],{"className":108680},[59],[15,108682,37],{"className":108683,"style":61},[59,60],[15,108685,108687],{"className":108686},[281],[15,108688,108690],{"className":108689},[285],[15,108691,108693],{"className":108692},[290],[15,108694,108696],{"className":108695,"style":8499},[294],[15,108697,108698,108701],{"style":6865},[15,108699],{"className":108700,"style":303},[302],[15,108702,108704],{"className":108703},[307,308,309,310],[15,108705,7573],{"className":108706},[2591,310],[15,108708,113],{"className":108709},[146],[15,108711,40237],{"className":108712,"style":981},[59,60],[15,108714,120],{"className":108715},[153],[52501,108717,29686],{},[52501,108719,52554],{},[52590,108721,108722,108855,108995,109485,109789,110098,110515,110826],{},[52498,108723,108724,108726,108776,108851,108853],{},[52595,108725,32663],{},[52595,108727,108728],{},[15,108729,108731,108750],{"className":108730,"translate":19},[18],[15,108732,108734],{"className":108733},[23],[25,108735,108736],{"xmlns":27},[29,108737,108738,108748],{},[32,108739,108740,108742,108744,108746],{},[35,108741,769],{},[35,108743,4100],{},[110,108745,4103],{},[35,108747,769],{},[39,108749,52726],{"encoding":41},[15,108751,108753],{"className":108752,"ariaHidden":46},[45],[15,108754,108756,108759,108762,108765,108770,108773],{"className":108755},[50],[15,108757],{"className":108758,"style":55},[54],[15,108760,769],{"className":108761},[59,60],[15,108763],{"className":108764,"style":406},[157],[15,108766,4154,108768],{"className":108767},[1484],[15,108769,4158],{"style":4157},[15,108771],{"className":108772,"style":406},[157],[15,108774,769],{"className":108775},[59,60],[52595,108777,108778],{},[15,108779,108781,108804],{"className":108780,"translate":19},[18],[15,108782,108784],{"className":108783},[23],[25,108785,108786],{"xmlns":27},[29,108787,108788,108802],{},[32,108789,108790],{},[6814,108791,108792,108794],{},[35,108793,7567],{},[32,108795,108796,108798,108800],{},[35,108797,40237],{},[110,108799,4813],{},[115,108801,117],{},[39,108803,64902],{"encoding":41},[15,108805,108807],{"className":108806,"ariaHidden":46},[45],[15,108808,108810,108813],{"className":108809},[50],[15,108811],{"className":108812,"style":20028},[54],[15,108814,108816,108819],{"className":108815},[59],[15,108817,7567],{"className":108818},[59,60],[15,108820,108822],{"className":108821},[281],[15,108823,108825],{"className":108824},[285],[15,108826,108828],{"className":108827},[290],[15,108829,108831],{"className":108830,"style":20028},[294],[15,108832,108833,108836],{"style":6865},[15,108834],{"className":108835,"style":303},[302],[15,108837,108839],{"className":108838},[307,308,309,310],[15,108840,108842,108845,108848],{"className":108841},[59,310],[15,108843,40237],{"className":108844,"style":981},[59,60,310],[15,108846,4813],{"className":108847},[2591,310],[15,108849,117],{"className":108850},[59,310],[52595,108852,52755],{},[52595,108854,52755],{},[52498,108856,108857,108860,108910,108991,108993],{},[52595,108858,108859],{},"反向 KL",[52595,108861,108862],{},[15,108863,108865,108884],{"className":108864,"translate":19},[18],[15,108866,108868],{"className":108867},[23],[25,108869,108870],{"xmlns":27},[29,108871,108872,108882],{},[32,108873,108874,108876,108878,108880],{},[110,108875,4813],{},[35,108877,4100],{},[110,108879,4103],{},[35,108881,769],{},[39,108883,52926],{"encoding":41},[15,108885,108887],{"className":108886,"ariaHidden":46},[45],[15,108888,108890,108893,108896,108899,108904,108907],{"className":108889},[50],[15,108891],{"className":108892,"style":55},[54],[15,108894,4813],{"className":108895},[59],[15,108897],{"className":108898,"style":406},[157],[15,108900,4154,108902],{"className":108901},[1484],[15,108903,4158],{"style":4157},[15,108905],{"className":108906,"style":406},[157],[15,108908,769],{"className":108909},[59,60],[52595,108911,108912],{},[15,108913,108915,108944],{"className":108914,"translate":19},[18],[15,108916,108918],{"className":108917},[23],[25,108919,108920],{"xmlns":27},[29,108921,108922,108942],{},[32,108923,108924,108926,108928,108930,108932,108934,108936,108938,108940],{},[110,108925,4813],{},[115,108927,117],{},[110,108929,4813],{},[35,108931,4100],{},[110,108933,4103],{},[110,108935,113],{"stretchy":112},[110,108937,4813],{},[35,108939,40237],{},[110,108941,120],{"stretchy":112},[39,108943,65071],{"encoding":41},[15,108945,108947,108968],{"className":108946,"ariaHidden":46},[45],[15,108948,108950,108953,108956,108959,108962,108965],{"className":108949},[50],[15,108951],{"className":108952,"style":12578},[54],[15,108954,4813],{"className":108955},[59],[15,108957,117],{"className":108958},[59],[15,108960],{"className":108961,"style":2587},[157],[15,108963,4813],{"className":108964},[2591],[15,108966],{"className":108967,"style":2587},[157],[15,108969,108971,108974,108979,108982,108985,108988],{"className":108970},[50],[15,108972],{"className":108973,"style":139},[54],[15,108975,4154,108977],{"className":108976},[1484],[15,108978,4158],{"style":4157},[15,108980,113],{"className":108981},[146],[15,108983,4813],{"className":108984},[59],[15,108986,40237],{"className":108987,"style":981},[59,60],[15,108989,120],{"className":108990},[153],[52595,108992,52755],{},[52595,108994,52755],{},[52498,108996,108997,108999,109288,109481,109483],{},[52595,108998,53124],{},[52595,109000,109001],{},[15,109002,109004,109061],{"className":109003,"translate":19},[18],[15,109005,109007],{"className":109006},[23],[25,109008,109009],{"xmlns":27},[29,109010,109011,109059],{},[32,109012,109013,109019,109021,109023,109025,109027,109029,109031,109033,109035,109037,109039,109041,109043,109045,109057],{},[238,109014,109015,109017],{},[115,109016,117],{},[115,109018,2463],{},[110,109020,230],{"stretchy":112},[35,109022,769],{},[35,109024,4100],{},[110,109026,4103],{},[35,109028,769],{},[110,109030,4813],{},[110,109032,113],{"stretchy":112},[35,109034,769],{},[110,109036,2470],{},[115,109038,117],{},[110,109040,120],{"stretchy":112},[35,109042,4100],{},[110,109044,4103],{},[238,109046,109047,109055],{},[32,109048,109049,109051,109053],{},[35,109050,769],{},[110,109052,2470],{},[115,109054,117],{},[115,109056,2463],{},[110,109058,257],{"stretchy":112},[39,109060,53187],{"encoding":41},[15,109062,109064,109167,109188],{"className":109063,"ariaHidden":46},[45],[15,109065,109067,109070,109138,109141,109144,109147,109152,109155,109158,109161,109164],{"className":109066},[50],[15,109068],{"className":109069,"style":2505},[54],[15,109071,109073,109076,109135],{"className":109072},[59],[15,109074],{"className":109075},[146,441],[15,109077,109079],{"className":109078},[238],[15,109080,109082,109127],{"className":109081},[285,286],[15,109083,109085,109124],{"className":109084},[290],[15,109086,109088,109102,109110],{"className":109087,"style":2524},[294],[15,109089,109090,109093],{"style":2527},[15,109091],{"className":109092,"style":461},[302],[15,109094,109096],{"className":109095},[307,308,309,310],[15,109097,109099],{"className":109098},[59,310],[15,109100,2463],{"className":109101},[59,310],[15,109103,109104,109107],{"style":473},[15,109105],{"className":109106,"style":461},[302],[15,109108],{"className":109109,"style":481},[480],[15,109111,109112,109115],{"style":2550},[15,109113],{"className":109114,"style":461},[302],[15,109116,109118],{"className":109117},[307,308,309,310],[15,109119,109121],{"className":109120},[59,310],[15,109122,117],{"className":109123},[59,310],[15,109125,318],{"className":109126},[317],[15,109128,109130],{"className":109129},[290],[15,109131,109133],{"className":109132,"style":2572},[294],[15,109134],{},[15,109136],{"className":109137},[153,441],[15,109139,230],{"className":109140},[146],[15,109142,769],{"className":109143},[59,60],[15,109145],{"className":109146,"style":406},[157],[15,109148,4154,109150],{"className":109149},[1484],[15,109151,4158],{"style":4157},[15,109153],{"className":109154,"style":406},[157],[15,109156,769],{"className":109157},[59,60],[15,109159],{"className":109160,"style":2587},[157],[15,109162,4813],{"className":109163},[2591],[15,109165],{"className":109166,"style":2587},[157],[15,109168,109170,109173,109176,109179,109182,109185],{"className":109169},[50],[15,109171],{"className":109172,"style":139},[54],[15,109174,113],{"className":109175},[146],[15,109177,769],{"className":109178},[59,60],[15,109180],{"className":109181,"style":2587},[157],[15,109183,2470],{"className":109184},[2591],[15,109186],{"className":109187,"style":2587},[157],[15,109189,109191,109194,109197,109200,109203,109208,109211,109285],{"className":109190},[50],[15,109192],{"className":109193,"style":2505},[54],[15,109195,117],{"className":109196},[59],[15,109198,120],{"className":109199},[153],[15,109201],{"className":109202,"style":406},[157],[15,109204,4154,109206],{"className":109205},[1484],[15,109207,4158],{"style":4157},[15,109209],{"className":109210,"style":406},[157],[15,109212,109214,109217,109282],{"className":109213},[59],[15,109215],{"className":109216},[146,441],[15,109218,109220],{"className":109219},[238],[15,109221,109223,109274],{"className":109222},[285,286],[15,109224,109226,109271],{"className":109225},[290],[15,109227,109229,109243,109251],{"className":109228,"style":2524},[294],[15,109230,109231,109234],{"style":2527},[15,109232],{"className":109233,"style":461},[302],[15,109235,109237],{"className":109236},[307,308,309,310],[15,109238,109240],{"className":109239},[59,310],[15,109241,2463],{"className":109242},[59,310],[15,109244,109245,109248],{"style":473},[15,109246],{"className":109247,"style":461},[302],[15,109249],{"className":109250,"style":481},[480],[15,109252,109253,109256],{"style":2550},[15,109254],{"className":109255,"style":461},[302],[15,109257,109259],{"className":109258},[307,308,309,310],[15,109260,109262,109265,109268],{"className":109261},[59,310],[15,109263,769],{"className":109264},[59,60,310],[15,109266,2470],{"className":109267},[2591,310],[15,109269,117],{"className":109270},[59,310],[15,109272,318],{"className":109273},[317],[15,109275,109277],{"className":109276},[290],[15,109278,109280],{"className":109279,"style":2572},[294],[15,109281],{},[15,109283],{"className":109284},[153,441],[15,109286,257],{"className":109287},[153],[52595,109289,109290],{},[15,109291,109293,109334],{"className":109292,"translate":19},[18],[15,109294,109296],{"className":109295},[23],[25,109297,109298],{"xmlns":27},[29,109299,109300,109332],{},[32,109301,109302,109304,109310,109312,109314,109316,109318,109320,109330],{},[110,109303,4813],{},[238,109305,109306,109308],{},[115,109307,117],{},[115,109309,2463],{},[35,109311,4100],{},[110,109313,4103],{},[110,109315,113],{"stretchy":112},[115,109317,2463],{},[110,109319,4813],{},[6814,109321,109322,109324],{},[35,109323,7567],{},[32,109325,109326,109328],{},[115,109327,2463],{},[35,109329,40237],{},[110,109331,120],{"stretchy":112},[39,109333,65563],{"encoding":41},[15,109335,109337,109437],{"className":109336,"ariaHidden":46},[45],[15,109338,109340,109343,109346,109414,109417,109422,109425,109428,109431,109434],{"className":109339},[50],[15,109341],{"className":109342,"style":2505},[54],[15,109344,4813],{"className":109345},[59],[15,109347,109349,109352,109411],{"className":109348},[59],[15,109350],{"className":109351},[146,441],[15,109353,109355],{"className":109354},[238],[15,109356,109358,109403],{"className":109357},[285,286],[15,109359,109361,109400],{"className":109360},[290],[15,109362,109364,109378,109386],{"className":109363,"style":2524},[294],[15,109365,109366,109369],{"style":2527},[15,109367],{"className":109368,"style":461},[302],[15,109370,109372],{"className":109371},[307,308,309,310],[15,109373,109375],{"className":109374},[59,310],[15,109376,2463],{"className":109377},[59,310],[15,109379,109380,109383],{"style":473},[15,109381],{"className":109382,"style":461},[302],[15,109384],{"className":109385,"style":481},[480],[15,109387,109388,109391],{"style":2550},[15,109389],{"className":109390,"style":461},[302],[15,109392,109394],{"className":109393},[307,308,309,310],[15,109395,109397],{"className":109396},[59,310],[15,109398,117],{"className":109399},[59,310],[15,109401,318],{"className":109402},[317],[15,109404,109406],{"className":109405},[290],[15,109407,109409],{"className":109408,"style":2572},[294],[15,109410],{},[15,109412],{"className":109413},[153,441],[15,109415],{"className":109416,"style":406},[157],[15,109418,4154,109420],{"className":109419},[1484],[15,109421,4158],{"style":4157},[15,109423,113],{"className":109424},[146],[15,109426,2463],{"className":109427},[59],[15,109429],{"className":109430,"style":2587},[157],[15,109432,4813],{"className":109433},[2591],[15,109435],{"className":109436,"style":2587},[157],[15,109438,109440,109443,109478],{"className":109439},[50],[15,109441],{"className":109442,"style":20003},[54],[15,109444,109446,109449],{"className":109445},[59],[15,109447,7567],{"className":109448},[59,60],[15,109450,109452],{"className":109451},[281],[15,109453,109455],{"className":109454},[285],[15,109456,109458],{"className":109457},[290],[15,109459,109461],{"className":109460,"style":20028},[294],[15,109462,109463,109466],{"style":6865},[15,109464],{"className":109465,"style":303},[302],[15,109467,109469],{"className":109468},[307,308,309,310],[15,109470,109472,109475],{"className":109471},[59,310],[15,109473,2463],{"className":109474},[59,310],[15,109476,40237],{"className":109477,"style":981},[59,60,310],[15,109479,120],{"className":109480},[153],[52595,109482,53082],{},[52595,109484,53082],{},[52498,109486,109487,109490,109626,109785,109787],{},[52595,109488,109489],{},"全变差",[52595,109491,109492],{},[15,109493,109495,109522],{"className":109494,"translate":19},[18],[15,109496,109498],{"className":109497},[23],[25,109499,109500],{"xmlns":27},[29,109501,109502,109520],{},[32,109503,109504,109510,109512,109514,109516,109518],{},[238,109505,109506,109508],{},[115,109507,117],{},[115,109509,2463],{},[110,109511,4808],{"stretchy":112},[35,109513,769],{},[110,109515,4813],{},[115,109517,117],{},[110,109519,4808],{"stretchy":112},[39,109521,53555],{"encoding":41},[15,109523,109525,109614],{"className":109524,"ariaHidden":46},[45],[15,109526,109528,109531,109599,109602,109605,109608,109611],{"className":109527},[50],[15,109529],{"className":109530,"style":2505},[54],[15,109532,109534,109537,109596],{"className":109533},[59],[15,109535],{"className":109536},[146,441],[15,109538,109540],{"className":109539},[238],[15,109541,109543,109588],{"className":109542},[285,286],[15,109544,109546,109585],{"className":109545},[290],[15,109547,109549,109563,109571],{"className":109548,"style":2524},[294],[15,109550,109551,109554],{"style":2527},[15,109552],{"className":109553,"style":461},[302],[15,109555,109557],{"className":109556},[307,308,309,310],[15,109558,109560],{"className":109559},[59,310],[15,109561,2463],{"className":109562},[59,310],[15,109564,109565,109568],{"style":473},[15,109566],{"className":109567,"style":461},[302],[15,109569],{"className":109570,"style":481},[480],[15,109572,109573,109576],{"style":2550},[15,109574],{"className":109575,"style":461},[302],[15,109577,109579],{"className":109578},[307,308,309,310],[15,109580,109582],{"className":109581},[59,310],[15,109583,117],{"className":109584},[59,310],[15,109586,318],{"className":109587},[317],[15,109589,109591],{"className":109590},[290],[15,109592,109594],{"className":109593,"style":2572},[294],[15,109595],{},[15,109597],{"className":109598},[153,441],[15,109600,4808],{"className":109601},[146],[15,109603,769],{"className":109604},[59,60],[15,109606],{"className":109607,"style":2587},[157],[15,109609,4813],{"className":109610},[2591],[15,109612],{"className":109613,"style":2587},[157],[15,109615,109617,109620,109623],{"className":109616},[50],[15,109618],{"className":109619,"style":139},[54],[15,109621,117],{"className":109622},[59],[15,109624,4808],{"className":109625},[153],[52595,109627,109628,15795,109656,53475],{},[15,109629,109631,109644],{"className":109630,"translate":19},[18],[15,109632,109634],{"className":109633},[23],[25,109635,109636],{"xmlns":27},[29,109637,109638,109642],{},[32,109639,109640],{},[35,109641,40237],{},[39,109643,40237],{"encoding":41},[15,109645,109647],{"className":109646,"ariaHidden":46},[45],[15,109648,109650,109653],{"className":109649},[50],[15,109651],{"className":109652,"style":2276},[54],[15,109654,40237],{"className":109655,"style":981},[59,60],[15,109657,109659,109684],{"className":109658,"translate":19},[18],[15,109660,109662],{"className":109661},[23],[25,109663,109664],{"xmlns":27},[29,109665,109666,109682],{},[32,109667,109668,109670,109672,109674,109676],{},[110,109669,4808],{"stretchy":112},[35,109671,40237],{},[110,109673,4808],{"stretchy":112},[110,109675,9952],{},[238,109677,109678,109680],{},[115,109679,117],{},[115,109681,2463],{},[39,109683,66057],{"encoding":41},[15,109685,109687,109711],{"className":109686,"ariaHidden":46},[45],[15,109688,109690,109693,109696,109699,109702,109705,109708],{"className":109689},[50],[15,109691],{"className":109692,"style":139},[54],[15,109694,4808],{"className":109695},[146],[15,109697,40237],{"className":109698,"style":981},[59,60],[15,109700,4808],{"className":109701},[153],[15,109703],{"className":109704,"style":158},[157],[15,109706,9952],{"className":109707},[162],[15,109709],{"className":109710,"style":158},[157],[15,109712,109714,109717],{"className":109713},[50],[15,109715],{"className":109716,"style":2505},[54],[15,109718,109720,109723,109782],{"className":109719},[59],[15,109721],{"className":109722},[146,441],[15,109724,109726],{"className":109725},[238],[15,109727,109729,109774],{"className":109728},[285,286],[15,109730,109732,109771],{"className":109731},[290],[15,109733,109735,109749,109757],{"className":109734,"style":2524},[294],[15,109736,109737,109740],{"style":2527},[15,109738],{"className":109739,"style":461},[302],[15,109741,109743],{"className":109742},[307,308,309,310],[15,109744,109746],{"className":109745},[59,310],[15,109747,2463],{"className":109748},[59,310],[15,109750,109751,109754],{"style":473},[15,109752],{"className":109753,"style":461},[302],[15,109755],{"className":109756,"style":481},[480],[15,109758,109759,109762],{"style":2550},[15,109760],{"className":109761,"style":461},[302],[15,109763,109765],{"className":109764},[307,308,309,310],[15,109766,109768],{"className":109767},[59,310],[15,109769,117],{"className":109770},[59,310],[15,109772,318],{"className":109773},[317],[15,109775,109777],{"className":109776},[290],[15,109778,109780],{"className":109779,"style":2572},[294],[15,109781],{},[15,109783],{"className":109784},[153,441],[52595,109786,53082],{},[52595,109788,53082],{},[52498,109790,109791,109851,109943,110094,110096],{},[52595,109792,53741,109793],{},[15,109794,109796,109813],{"className":109795,"translate":19},[18],[15,109797,109799],{"className":109798},[23],[25,109800,109801],{"xmlns":27},[29,109802,109803,109811],{},[32,109804,109805],{},[6814,109806,109807,109809],{},[35,109808,37449],{},[115,109810,2463],{},[39,109812,40394],{"encoding":41},[15,109814,109816],{"className":109815,"ariaHidden":46},[45],[15,109817,109819,109822],{"className":109818},[50],[15,109820],{"className":109821,"style":40404},[54],[15,109823,109825,109828],{"className":109824},[59],[15,109826,37449],{"className":109827},[59,60],[15,109829,109831],{"className":109830},[281],[15,109832,109834],{"className":109833},[285],[15,109835,109837],{"className":109836},[290],[15,109838,109840],{"className":109839,"style":20028},[294],[15,109841,109842,109845],{"style":6865},[15,109843],{"className":109844,"style":303},[302],[15,109846,109848],{"className":109847},[307,308,309,310],[15,109849,2463],{"className":109850},[59,310],[52595,109852,109853],{},[15,109854,109856,109881],{"className":109855,"translate":19},[18],[15,109857,109859],{"className":109858},[23],[25,109860,109861],{"xmlns":27},[29,109862,109863,109879],{},[32,109864,109865,109867,109869,109871,109873],{},[110,109866,113],{"stretchy":112},[35,109868,769],{},[110,109870,4813],{},[115,109872,117],{},[6814,109874,109875,109877],{},[110,109876,120],{"stretchy":112},[115,109878,2463],{},[39,109880,53830],{"encoding":41},[15,109882,109884,109905],{"className":109883,"ariaHidden":46},[45],[15,109885,109887,109890,109893,109896,109899,109902],{"className":109886},[50],[15,109888],{"className":109889,"style":139},[54],[15,109891,113],{"className":109892},[146],[15,109894,769],{"className":109895},[59,60],[15,109897],{"className":109898,"style":2587},[157],[15,109900,4813],{"className":109901},[2591],[15,109903],{"className":109904,"style":2587},[157],[15,109906,109908,109911,109914],{"className":109907},[50],[15,109909],{"className":109910,"style":20003},[54],[15,109912,117],{"className":109913},[59],[15,109915,109917,109920],{"className":109916},[153],[15,109918,120],{"className":109919},[153],[15,109921,109923],{"className":109922},[281],[15,109924,109926],{"className":109925},[285],[15,109927,109929],{"className":109928},[290],[15,109930,109932],{"className":109931,"style":20028},[294],[15,109933,109934,109937],{"style":6865},[15,109935],{"className":109936,"style":303},[302],[15,109938,109940],{"className":109939},[307,308,309,310],[15,109941,2463],{"className":109942},[59,310],[52595,109944,109945],{},[15,109946,109948,109973],{"className":109947,"translate":19},[18],[15,109949,109951],{"className":109950},[23],[25,109952,109953],{"xmlns":27},[29,109954,109955,109971],{},[32,109956,109957,109959,109961],{},[35,109958,40237],{},[110,109960,2470],{},[238,109962,109963,109969],{},[6814,109964,109965,109967],{},[35,109966,40237],{},[115,109968,2463],{},[115,109970,38989],{},[39,109972,66344],{"encoding":41},[15,109974,109976,109994],{"className":109975,"ariaHidden":46},[45],[15,109977,109979,109982,109985,109988,109991],{"className":109978},[50],[15,109980],{"className":109981,"style":40321},[54],[15,109983,40237],{"className":109984,"style":981},[59,60],[15,109986],{"className":109987,"style":2587},[157],[15,109989,2470],{"className":109990},[2591],[15,109992],{"className":109993,"style":2587},[157],[15,109995,109997,110000],{"className":109996},[50],[15,109998],{"className":109999,"style":66372},[54],[15,110001,110003,110006,110091],{"className":110002},[59],[15,110004],{"className":110005},[146,441],[15,110007,110009],{"className":110008},[238],[15,110010,110012,110083],{"className":110011},[285,286],[15,110013,110015,110080],{"className":110014},[290],[15,110016,110018,110032,110040],{"className":110017,"style":66391},[294],[15,110019,110020,110023],{"style":2527},[15,110021],{"className":110022,"style":461},[302],[15,110024,110026],{"className":110025},[307,308,309,310],[15,110027,110029],{"className":110028},[59,310],[15,110030,38989],{"className":110031},[59,310],[15,110033,110034,110037],{"style":473},[15,110035],{"className":110036,"style":461},[302],[15,110038],{"className":110039,"style":481},[480],[15,110041,110042,110045],{"style":2853},[15,110043],{"className":110044,"style":461},[302],[15,110046,110048],{"className":110047},[307,308,309,310],[15,110049,110051],{"className":110050},[59,310],[15,110052,110054,110057],{"className":110053},[59,310],[15,110055,40237],{"className":110056,"style":981},[59,60,310],[15,110058,110060],{"className":110059},[281],[15,110061,110063],{"className":110062},[285],[15,110064,110066],{"className":110065},[290],[15,110067,110069],{"className":110068,"style":38512},[294],[15,110070,110071,110074],{"style":38515},[15,110072],{"className":110073,"style":30206},[302],[15,110075,110077],{"className":110076},[307,30210,9674,310],[15,110078,2463],{"className":110079},[59,310],[15,110081,318],{"className":110082},[317],[15,110084,110086],{"className":110085},[290],[15,110087,110089],{"className":110088,"style":2572},[294],[15,110090],{},[15,110092],{"className":110093},[153,441],[52595,110095,52755],{},[52595,110097,52755],{},[52498,110099,110100,110184,110335,110511,110513],{},[52595,110101,53936,110102],{},[15,110103,110105,110124],{"className":110104,"translate":19},[18],[15,110106,110108],{"className":110107},[23],[25,110109,110110],{"xmlns":27},[29,110111,110112,110122],{},[32,110113,110114],{},[7553,110115,110116,110118,110120],{},[35,110117,37449],{},[35,110119,38284],{},[115,110121,2463],{},[39,110123,53959],{"encoding":41},[15,110125,110127],{"className":110126,"ariaHidden":46},[45],[15,110128,110130,110133],{"className":110129},[50],[15,110131],{"className":110132,"style":38339},[54],[15,110134,110136,110139],{"className":110135},[59],[15,110137,37449],{"className":110138},[59,60],[15,110140,110142],{"className":110141},[281],[15,110143,110145,110176],{"className":110144},[285,286],[15,110146,110148,110173],{"className":110147},[290],[15,110149,110151,110162],{"className":110150,"style":20028},[294],[15,110152,110153,110156],{"style":38360},[15,110154],{"className":110155,"style":303},[302],[15,110157,110159],{"className":110158},[307,308,309,310],[15,110160,38284],{"className":110161,"style":25601},[59,60,310],[15,110163,110164,110167],{"style":6865},[15,110165],{"className":110166,"style":303},[302],[15,110168,110170],{"className":110169},[307,308,309,310],[15,110171,2463],{"className":110172},[59,310],[15,110174,318],{"className":110175},[317],[15,110177,110179],{"className":110178},[290],[15,110180,110182],{"className":110181,"style":38390},[294],[15,110183],{},[52595,110185,110186],{},[15,110187,110189,110220],{"className":110188,"translate":19},[18],[15,110190,110192],{"className":110191},[23],[25,110193,110194],{"xmlns":27},[29,110195,110196,110218],{},[32,110197,110198],{},[238,110199,110200,110216],{},[32,110201,110202,110204,110206,110208,110210],{},[110,110203,113],{"stretchy":112},[35,110205,769],{},[110,110207,4813],{},[115,110209,117],{},[6814,110211,110212,110214],{},[110,110213,120],{"stretchy":112},[115,110215,2463],{},[35,110217,769],{},[39,110219,54056],{"encoding":41},[15,110221,110223],{"className":110222,"ariaHidden":46},[45],[15,110224,110226,110229],{"className":110225},[50],[15,110227],{"className":110228,"style":54066},[54],[15,110230,110232,110235,110332],{"className":110231},[59],[15,110233],{"className":110234},[146,441],[15,110236,110238],{"className":110237},[238],[15,110239,110241,110324],{"className":110240},[285,286],[15,110242,110244,110321],{"className":110243},[290],[15,110245,110247,110261,110269],{"className":110246,"style":38448},[294],[15,110248,110249,110252],{"style":2527},[15,110250],{"className":110251,"style":461},[302],[15,110253,110255],{"className":110254},[307,308,309,310],[15,110256,110258],{"className":110257},[59,310],[15,110259,769],{"className":110260},[59,60,310],[15,110262,110263,110266],{"style":473},[15,110264],{"className":110265,"style":461},[302],[15,110267],{"className":110268,"style":481},[480],[15,110270,110271,110274],{"style":26418},[15,110272],{"className":110273,"style":461},[302],[15,110275,110277],{"className":110276},[307,308,309,310],[15,110278,110280,110283,110286,110289,110292],{"className":110279},[59,310],[15,110281,113],{"className":110282},[146,310],[15,110284,769],{"className":110285},[59,60,310],[15,110287,4813],{"className":110288},[2591,310],[15,110290,117],{"className":110291},[59,310],[15,110293,110295,110298],{"className":110294},[153,310],[15,110296,120],{"className":110297},[153,310],[15,110299,110301],{"className":110300},[281],[15,110302,110304],{"className":110303},[285],[15,110305,110307],{"className":110306},[290],[15,110308,110310],{"className":110309,"style":38512},[294],[15,110311,110312,110315],{"style":38515},[15,110313],{"className":110314,"style":30206},[302],[15,110316,110318],{"className":110317},[307,30210,9674,310],[15,110319,2463],{"className":110320},[59,310],[15,110322,318],{"className":110323},[317],[15,110325,110327],{"className":110326},[290],[15,110328,110330],{"className":110329,"style":2572},[294],[15,110331],{},[15,110333],{"className":110334},[153,441],[52595,110336,110337,15795,110461,53475],{},[15,110338,110340,110368],{"className":110339,"translate":19},[18],[15,110341,110343],{"className":110342},[23],[25,110344,110345],{"xmlns":27},[29,110346,110347,110365],{},[32,110348,110349,110351,110353,110355],{},[115,110350,2463],{},[110,110352,4813],{},[115,110354,2463],{},[34339,110356,110357],{},[32,110358,110359,110361,110363],{},[115,110360,117],{},[110,110362,4813],{},[35,110364,40237],{},[39,110366,110367],{"encoding":41},"2-2\\sqrt{1-y}",[15,110369,110371,110389],{"className":110370,"ariaHidden":46},[45],[15,110372,110374,110377,110380,110383,110386],{"className":110373},[50],[15,110375],{"className":110376,"style":12578},[54],[15,110378,2463],{"className":110379},[59],[15,110381],{"className":110382,"style":2587},[157],[15,110384,4813],{"className":110385},[2591],[15,110387],{"className":110388,"style":2587},[157],[15,110390,110392,110396,110399],{"className":110391},[50],[15,110393],{"className":110394,"style":110395},[54],"height:1.04em;vertical-align:-0.23em;",[15,110397,2463],{"className":110398},[59],[15,110400,110402],{"className":110401},[59,34367],[15,110403,110405,110452],{"className":110404},[285,286],[15,110406,110408,110449],{"className":110407},[290],[15,110409,110412,110436],{"className":110410,"style":110411},[294],"height:0.81em;",[15,110413,110415,110418],{"className":110414,"style":11863},[6307],[15,110416],{"className":110417,"style":461},[302],[15,110419,110421,110424,110427,110430,110433],{"className":110420,"style":34387},[59],[15,110422,117],{"className":110423},[59],[15,110425],{"className":110426,"style":2587},[157],[15,110428,4813],{"className":110429},[2591],[15,110431],{"className":110432,"style":2587},[157],[15,110434,40237],{"className":110435,"style":981},[59,60],[15,110437,110439,110442],{"style":110438},"top:-2.77em;",[15,110440],{"className":110441,"style":461},[302],[15,110443,110445],{"className":110444,"style":34444},[34443],[6323,110446,110447],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,110448],{"d":34451},[15,110450,318],{"className":110451},[317],[15,110453,110455],{"className":110454},[290],[15,110456,110459],{"className":110457,"style":110458},[294],"height:0.23em;",[15,110460],{},[15,110462,110464,110481],{"className":110463,"translate":19},[18],[15,110465,110467],{"className":110466},[23],[25,110468,110469],{"xmlns":27},[29,110470,110471,110479],{},[32,110472,110473,110475,110477],{},[35,110474,40237],{},[110,110476,7251],{},[115,110478,117],{},[39,110480,66773],{"encoding":41},[15,110482,110484,110502],{"className":110483,"ariaHidden":46},[45],[15,110485,110487,110490,110493,110496,110499],{"className":110486},[50],[15,110488],{"className":110489,"style":31692},[54],[15,110491,40237],{"className":110492,"style":981},[59,60],[15,110494],{"className":110495,"style":158},[157],[15,110497,7251],{"className":110498},[162],[15,110500],{"className":110501,"style":158},[157],[15,110503,110505,110508],{"className":110504},[50],[15,110506],{"className":110507,"style":172},[54],[15,110509,117],{"className":110510},[59],[52595,110512,52755],{},[52595,110514,52755],{},[52498,110516,110517,110576,110711,110822,110824],{},[52595,110518,54216,110519],{},[15,110520,110522,110539],{"className":110521,"translate":19},[18],[15,110523,110525],{"className":110524},[23],[25,110526,110527],{"xmlns":27},[29,110528,110529,110537],{},[32,110530,110531],{},[6814,110532,110533,110535],{},[32,110534],{},[115,110536,2463],{},[39,110538,44269],{"encoding":41},[15,110540,110542],{"className":110541,"ariaHidden":46},[45],[15,110543,110545,110548],{"className":110544},[50],[15,110546],{"className":110547,"style":20028},[54],[15,110549,110551,110553],{"className":110550},[59],[15,110552],{},[15,110554,110556],{"className":110555},[281],[15,110557,110559],{"className":110558},[285],[15,110560,110562],{"className":110561},[290],[15,110563,110565],{"className":110564,"style":20028},[294],[15,110566,110567,110570],{"style":6865},[15,110568],{"className":110569,"style":303},[302],[15,110571,110573],{"className":110572},[307,308,309,310],[15,110574,2463],{"className":110575},[59,310],[52595,110577,110578],{},[15,110579,110581,110608],{"className":110580,"translate":19},[18],[15,110582,110584],{"className":110583},[23],[25,110585,110586],{"xmlns":27},[29,110587,110588,110606],{},[32,110589,110590,110592,110596,110598,110600],{},[110,110591,113],{"stretchy":112},[34339,110593,110594],{},[35,110595,769],{},[110,110597,4813],{},[115,110599,117],{},[6814,110601,110602,110604],{},[110,110603,120],{"stretchy":112},[115,110605,2463],{},[39,110607,54307],{"encoding":41},[15,110609,110611,110673],{"className":110610,"ariaHidden":46},[45],[15,110612,110614,110617,110620,110664,110667,110670],{"className":110613},[50],[15,110615],{"className":110616,"style":42667},[54],[15,110618,113],{"className":110619},[146],[15,110621,110623],{"className":110622},[59,34367],[15,110624,110626,110656],{"className":110625},[285,286],[15,110627,110629,110653],{"className":110628},[290],[15,110630,110632,110641],{"className":110631,"style":42683},[294],[15,110633,110635,110638],{"className":110634,"style":11863},[6307],[15,110636],{"className":110637,"style":461},[302],[15,110639,769],{"className":110640,"style":34387},[59,60],[15,110642,110643,110646],{"style":42695},[15,110644],{"className":110645,"style":461},[302],[15,110647,110649],{"className":110648,"style":34444},[34443],[6323,110650,110651],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,110652],{"d":34451},[15,110654,318],{"className":110655},[317],[15,110657,110659],{"className":110658},[290],[15,110660,110662],{"className":110661,"style":42715},[294],[15,110663],{},[15,110665],{"className":110666,"style":2587},[157],[15,110668,4813],{"className":110669},[2591],[15,110671],{"className":110672,"style":2587},[157],[15,110674,110676,110679,110682],{"className":110675},[50],[15,110677],{"className":110678,"style":20003},[54],[15,110680,117],{"className":110681},[59],[15,110683,110685,110688],{"className":110684},[153],[15,110686,120],{"className":110687},[153],[15,110689,110691],{"className":110690},[281],[15,110692,110694],{"className":110693},[285],[15,110695,110697],{"className":110696},[290],[15,110698,110700],{"className":110699,"style":20028},[294],[15,110701,110702,110705],{"style":6865},[15,110703],{"className":110704,"style":303},[302],[15,110706,110708],{"className":110707},[307,308,309,310],[15,110709,2463],{"className":110710},[59,310],[52595,110712,110713],{},[15,110714,110716,110739],{"className":110715,"translate":19},[18],[15,110717,110719],{"className":110718},[23],[25,110720,110721],{"xmlns":27},[29,110722,110723,110737],{},[32,110724,110725],{},[238,110726,110727,110729],{},[35,110728,40237],{},[32,110730,110731,110733,110735],{},[115,110732,117],{},[110,110734,4813],{},[35,110736,40237],{},[39,110738,66667],{"encoding":41},[15,110740,110742],{"className":110741,"ariaHidden":46},[45],[15,110743,110745,110748],{"className":110744},[50],[15,110746],{"className":110747,"style":3084},[54],[15,110749,110751,110754,110819],{"className":110750},[59],[15,110752],{"className":110753},[146,441],[15,110755,110757],{"className":110756},[238],[15,110758,110760,110811],{"className":110759},[285,286],[15,110761,110763,110808],{"className":110762},[290],[15,110764,110766,110786,110794],{"className":110765,"style":3103},[294],[15,110767,110768,110771],{"style":2527},[15,110769],{"className":110770,"style":461},[302],[15,110772,110774],{"className":110773},[307,308,309,310],[15,110775,110777,110780,110783],{"className":110776},[59,310],[15,110778,117],{"className":110779},[59,310],[15,110781,4813],{"className":110782},[2591,310],[15,110784,40237],{"className":110785,"style":981},[59,60,310],[15,110787,110788,110791],{"style":473},[15,110789],{"className":110790,"style":461},[302],[15,110792],{"className":110793,"style":481},[480],[15,110795,110796,110799],{"style":2853},[15,110797],{"className":110798,"style":461},[302],[15,110800,110802],{"className":110801},[307,308,309,310],[15,110803,110805],{"className":110804},[59,310],[15,110806,40237],{"className":110807,"style":981},[59,60,310],[15,110809,318],{"className":110810},[317],[15,110812,110814],{"className":110813},[290],[15,110815,110817],{"className":110816,"style":2739},[294],[15,110818],{},[15,110820],{"className":110821},[153,441],[52595,110823,53082],{},[52595,110825,53082],{},[52498,110827,110828,110830,111070,111544,111546],{},[52595,110829,45990],{},[52595,110831,110832],{},[15,110833,110835,110890],{"className":110834,"translate":19},[18],[15,110836,110838],{"className":110837},[23],[25,110839,110840],{"xmlns":27},[29,110841,110842,110888],{},[32,110843,110844,110860,110862,110864,110866,110886],{},[238,110845,110846,110848],{},[115,110847,38989],{},[32,110849,110850,110852,110854],{},[115,110851,117],{},[110,110853,4813],{},[6814,110855,110856,110858],{},[35,110857,44754],{},[115,110859,2463],{},[110,110861,113],{"stretchy":112},[115,110863,117],{},[110,110865,4813],{},[6814,110867,110868,110870],{},[35,110869,769],{},[32,110871,110872,110874,110876,110878,110880,110882,110884],{},[110,110873,113],{"stretchy":112},[115,110875,117],{},[110,110877,2470],{},[35,110879,44754],{},[110,110881,120],{"stretchy":112},[35,110883,941],{"mathvariant":209},[115,110885,2463],{},[110,110887,120],{"stretchy":112},[39,110889,54631],{"encoding":41},[15,110891,110893,111014],{"className":110892,"ariaHidden":46},[45],[15,110894,110896,110899,110999,111002,111005,111008,111011],{"className":110895},[50],[15,110897],{"className":110898,"style":45405},[54],[15,110900,110902,110905,110996],{"className":110901},[59],[15,110903],{"className":110904},[146,441],[15,110906,110908],{"className":110907},[238],[15,110909,110911,110988],{"className":110910},[285,286],[15,110912,110914,110985],{"className":110913},[290],[15,110915,110917,110963,110971],{"className":110916,"style":2524},[294],[15,110918,110919,110922],{"style":2527},[15,110920],{"className":110921,"style":461},[302],[15,110923,110925],{"className":110924},[307,308,309,310],[15,110926,110928,110931,110934],{"className":110927},[59,310],[15,110929,117],{"className":110930},[59,310],[15,110932,4813],{"className":110933},[2591,310],[15,110935,110937,110940],{"className":110936},[59,310],[15,110938,44754],{"className":110939,"style":44784},[59,60,310],[15,110941,110943],{"className":110942},[281],[15,110944,110946],{"className":110945},[285],[15,110947,110949],{"className":110948},[290],[15,110950,110952],{"className":110951,"style":45459},[294],[15,110953,110954,110957],{"style":45462},[15,110955],{"className":110956,"style":30206},[302],[15,110958,110960],{"className":110959},[307,30210,9674,310],[15,110961,2463],{"className":110962},[59,310],[15,110964,110965,110968],{"style":473},[15,110966],{"className":110967,"style":461},[302],[15,110969],{"className":110970,"style":481},[480],[15,110972,110973,110976],{"style":2550},[15,110974],{"className":110975,"style":461},[302],[15,110977,110979],{"className":110978},[307,308,309,310],[15,110980,110982],{"className":110981},[59,310],[15,110983,38989],{"className":110984},[59,310],[15,110986,318],{"className":110987},[317],[15,110989,110991],{"className":110990},[290],[15,110992,110994],{"className":110993,"style":16429},[294],[15,110995],{},[15,110997],{"className":110998},[153,441],[15,111000,113],{"className":111001},[146],[15,111003,117],{"className":111004},[59],[15,111006],{"className":111007,"style":2587},[157],[15,111009,4813],{"className":111010},[2591],[15,111012],{"className":111013,"style":2587},[157],[15,111015,111017,111020,111067],{"className":111016},[50],[15,111018],{"className":111019,"style":54762},[54],[15,111021,111023,111026],{"className":111022},[59],[15,111024,769],{"className":111025},[59,60],[15,111027,111029],{"className":111028},[281],[15,111030,111032],{"className":111031},[285],[15,111033,111035],{"className":111034},[290],[15,111036,111038],{"className":111037,"style":54781},[294],[15,111039,111040,111043],{"style":6865},[15,111041],{"className":111042,"style":303},[302],[15,111044,111046],{"className":111045},[307,308,309,310],[15,111047,111049,111052,111055,111058,111061,111064],{"className":111048},[59,310],[15,111050,113],{"className":111051},[146,310],[15,111053,117],{"className":111054},[59,310],[15,111056,2470],{"className":111057},[2591,310],[15,111059,44754],{"className":111060,"style":44784},[59,60,310],[15,111062,120],{"className":111063},[153,310],[15,111065,45150],{"className":111066},[59,310],[15,111068,120],{"className":111069},[153],[52595,111071,111072,2745,111494],{},[15,111073,111075,111151],{"className":111074,"translate":19},[18],[15,111076,111078],{"className":111077},[23],[25,111079,111080],{"xmlns":27},[29,111081,111082,111148],{},[32,111083,111084,111090,111092,111094,111096,111098,111100,111102,111104,111106,111108,111110,111112,111132,111134,111146],{},[238,111085,111086,111088],{},[115,111087,117],{},[35,111089,45180],{},[110,111091,230],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,111093,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,111095,113],{"stretchy":112},[115,111097,117],{},[110,111099,4813],{},[35,111101,45180],{},[110,111103,120],{"stretchy":112},[110,111105,113],{"stretchy":112},[110,111107,4813],{},[35,111109,40237],{},[110,111111,120],{"stretchy":112},[6814,111113,111114,111116],{},[110,111115,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[32,111117,111118,111120],{},[110,111119,4813],{},[238,111121,111122,111124],{},[35,111123,45180],{},[32,111125,111126,111128,111130],{},[115,111127,117],{},[110,111129,4813],{},[35,111131,45180],{},[110,111133,4813],{},[238,111135,111136,111138],{},[115,111137,117],{},[32,111139,111140,111142,111144],{},[115,111141,117],{},[110,111143,4813],{},[35,111145,45180],{},[110,111147,257],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[39,111149,111150],{"encoding":41},"\\frac{1}{a}\\big[\\big((1-a)(-y)\\big)^{-\\frac{a}{1-a}}-\\frac{1}{1-a}\\big]",[15,111152,111154,111255,111407],{"className":111153,"ariaHidden":46},[45],[15,111155,111157,111160,111228,111234,111240,111243,111246,111249,111252],{"className":111156},[50],[15,111158],{"className":111159,"style":20563},[54],[15,111161,111163,111166,111225],{"className":111162},[59],[15,111164],{"className":111165},[146,441],[15,111167,111169],{"className":111168},[238],[15,111170,111172,111217],{"className":111171},[285,286],[15,111173,111175,111214],{"className":111174},[290],[15,111176,111178,111192,111200],{"className":111177,"style":2524},[294],[15,111179,111180,111183],{"style":2527},[15,111181],{"className":111182,"style":461},[302],[15,111184,111186],{"className":111185},[307,308,309,310],[15,111187,111189],{"className":111188},[59,310],[15,111190,45180],{"className":111191},[59,60,310],[15,111193,111194,111197],{"style":473},[15,111195],{"className":111196,"style":461},[302],[15,111198],{"className":111199,"style":481},[480],[15,111201,111202,111205],{"style":2550},[15,111203],{"className":111204,"style":461},[302],[15,111206,111208],{"className":111207},[307,308,309,310],[15,111209,111211],{"className":111210},[59,310],[15,111212,117],{"className":111213},[59,310],[15,111215,318],{"className":111216},[317],[15,111218,111220],{"className":111219},[290],[15,111221,111223],{"className":111222,"style":2572},[294],[15,111224],{},[15,111226],{"className":111227},[153,441],[15,111229,111231],{"className":111230},[59],[15,111232,230],{"className":111233},[419,9674],[15,111235,111237],{"className":111236},[59],[15,111238,113],{"className":111239},[419,9674],[15,111241,113],{"className":111242},[146],[15,111244,117],{"className":111245},[59],[15,111247],{"className":111248,"style":2587},[157],[15,111250,4813],{"className":111251},[2591],[15,111253],{"className":111254,"style":2587},[157],[15,111256,111258,111262,111265,111268,111271,111274,111277,111280,111398,111401,111404],{"className":111257},[50],[15,111259],{"className":111260,"style":111261},[54],"height:1.437em;vertical-align:-0.35em;",[15,111263,45180],{"className":111264},[59,60],[15,111266,120],{"className":111267},[153],[15,111269,113],{"className":111270},[146],[15,111272,4813],{"className":111273},[59],[15,111275,40237],{"className":111276,"style":981},[59,60],[15,111278,120],{"className":111279},[153],[15,111281,111283,111289],{"className":111282},[59],[15,111284,111286],{"className":111285},[59],[15,111287,120],{"className":111288},[419,9674],[15,111290,111292],{"className":111291},[281],[15,111293,111295],{"className":111294},[285],[15,111296,111298],{"className":111297},[290],[15,111299,111302],{"className":111300,"style":111301},[294],"height:1.087em;",[15,111303,111305,111308],{"style":111304},"top:-3.6029em;margin-right:0.05em;",[15,111306],{"className":111307,"style":461},[302],[15,111309,111311],{"className":111310},[307,308,309,310],[15,111312,111314,111317],{"className":111313},[59,310],[15,111315,4813],{"className":111316},[59,310],[15,111318,111320,111324,111395],{"className":111319},[59,310],[15,111321],{"className":111322},[146,441,307,30210,111323],"size6",[15,111325,111327],{"className":111326},[238],[15,111328,111330,111386],{"className":111329},[285,286],[15,111331,111333,111383],{"className":111332},[290],[15,111334,111337,111358,111368],{"className":111335,"style":111336},[294],"height:0.6915em;",[15,111338,111340,111343],{"style":111339},"top:-2.656em;",[15,111341],{"className":111342,"style":461},[302],[15,111344,111346],{"className":111345},[307,30210,9674,310],[15,111347,111349,111352,111355],{"className":111348},[59,310],[15,111350,117],{"className":111351},[59,310],[15,111353,4813],{"className":111354},[2591,310],[15,111356,45180],{"className":111357},[59,60,310],[15,111359,111361,111364],{"style":111360},"top:-3.2255em;",[15,111362],{"className":111363,"style":461},[302],[15,111365],{"className":111366,"style":111367},[480,310],"border-bottom-width:0.049em;",[15,111369,111371,111374],{"style":111370},"top:-3.384em;",[15,111372],{"className":111373,"style":461},[302],[15,111375,111377],{"className":111376},[307,30210,9674,310],[15,111378,111380],{"className":111379},[59,310],[15,111381,45180],{"className":111382},[59,60,310],[15,111384,318],{"className":111385},[317],[15,111387,111389],{"className":111388},[290],[15,111390,111393],{"className":111391,"style":111392},[294],"height:0.4035em;",[15,111394],{},[15,111396],{"className":111397},[153,441,307,30210,111323],[15,111399],{"className":111400,"style":2587},[157],[15,111402,4813],{"className":111403},[2591],[15,111405],{"className":111406,"style":2587},[157],[15,111408,111410,111414,111488],{"className":111409},[50],[15,111411],{"className":111412,"style":111413},[54],"height:1.2533em;vertical-align:-0.4033em;",[15,111415,111417,111420,111485],{"className":111416},[59],[15,111418],{"className":111419},[146,441],[15,111421,111423],{"className":111422},[238],[15,111424,111426,111477],{"className":111425},[285,286],[15,111427,111429,111474],{"className":111428},[290],[15,111430,111432,111452,111460],{"className":111431,"style":2524},[294],[15,111433,111434,111437],{"style":2527},[15,111435],{"className":111436,"style":461},[302],[15,111438,111440],{"className":111439},[307,308,309,310],[15,111441,111443,111446,111449],{"className":111442},[59,310],[15,111444,117],{"className":111445},[59,310],[15,111447,4813],{"className":111448},[2591,310],[15,111450,45180],{"className":111451},[59,60,310],[15,111453,111454,111457],{"style":473},[15,111455],{"className":111456,"style":461},[302],[15,111458],{"className":111459,"style":481},[480],[15,111461,111462,111465],{"style":2550},[15,111463],{"className":111464,"style":461},[302],[15,111466,111468],{"className":111467},[307,308,309,310],[15,111469,111471],{"className":111470},[59,310],[15,111472,117],{"className":111473},[59,310],[15,111475,318],{"className":111476},[317],[15,111478,111480],{"className":111479},[290],[15,111481,111483],{"className":111482,"style":16429},[294],[15,111484],{},[15,111486],{"className":111487},[153,441],[15,111489,111491],{"className":111490},[59],[15,111492,257],{"className":111493},[419,9674],[15,111495,111497,111514],{"className":111496,"translate":19},[18],[15,111498,111500],{"className":111499},[23],[25,111501,111502],{"xmlns":27},[29,111503,111504,111512],{},[32,111505,111506,111508,111510],{},[35,111507,40237],{},[110,111509,7251],{},[115,111511,126],{},[39,111513,65141],{"encoding":41},[15,111515,111517,111535],{"className":111516,"ariaHidden":46},[45],[15,111518,111520,111523,111526,111529,111532],{"className":111519},[50],[15,111521],{"className":111522,"style":31692},[54],[15,111524,40237],{"className":111525,"style":981},[59,60],[15,111527],{"className":111528,"style":158},[157],[15,111530,7251],{"className":111531},[162],[15,111533],{"className":111534,"style":158},[157],[15,111536,111538,111541],{"className":111537},[50],[15,111539],{"className":111540,"style":172},[54],[15,111542,126],{"className":111543},[59],[52595,111545,52755],{},[52595,111547,52755],{},[11,111549,111550,111551,2745,111873,112184,112185,93622,112379,15795,112561,112611,112612,113155,113156,113332,113333,67114,113681,93622,113882,15795,114125,114175,114176,88307,114296,2745,114346,114477,114478,114606],{},"（Neyman 一行的验证：",[15,111552,111554,111612],{"className":111553,"translate":19},[18],[15,111555,111557],{"className":111556},[23],[25,111558,111559],{"xmlns":27},[29,111560,111561,111609],{},[32,111562,111563,111565,111567,111569,111571,111573,111593,111595,111597,111599,111601,111603],{},[35,111564,37],{},[110,111566,113],{"stretchy":112},[35,111568,769],{},[110,111570,120],{"stretchy":112},[110,111572,123],{},[238,111574,111575,111591],{},[32,111576,111577,111579,111581,111583,111585],{},[110,111578,113],{"stretchy":112},[35,111580,769],{},[110,111582,4813],{},[115,111584,117],{},[6814,111586,111587,111589],{},[110,111588,120],{"stretchy":112},[115,111590,2463],{},[35,111592,769],{},[110,111594,123],{},[35,111596,769],{},[110,111598,4813],{},[115,111600,2463],{},[110,111602,2470],{},[238,111604,111605,111607],{},[115,111606,117],{},[35,111608,769],{},[39,111610,111611],{"encoding":41},"f(t)=\\frac{(t-1)^2}{t}=t-2+\\frac1t",[15,111613,111615,111642,111763,111781,111799],{"className":111614,"ariaHidden":46},[45],[15,111616,111618,111621,111624,111627,111630,111633,111636,111639],{"className":111617},[50],[15,111619],{"className":111620,"style":139},[54],[15,111622,37],{"className":111623,"style":61},[59,60],[15,111625,113],{"className":111626},[146],[15,111628,769],{"className":111629},[59,60],[15,111631,120],{"className":111632},[153],[15,111634],{"className":111635,"style":158},[157],[15,111637,123],{"className":111638},[162],[15,111640],{"className":111641,"style":158},[157],[15,111643,111645,111648,111754,111757,111760],{"className":111644},[50],[15,111646],{"className":111647,"style":54066},[54],[15,111649,111651,111654,111751],{"className":111650},[59],[15,111652],{"className":111653},[146,441],[15,111655,111657],{"className":111656},[238],[15,111658,111660,111743],{"className":111659},[285,286],[15,111661,111663,111740],{"className":111662},[290],[15,111664,111666,111680,111688],{"className":111665,"style":38448},[294],[15,111667,111668,111671],{"style":2527},[15,111669],{"className":111670,"style":461},[302],[15,111672,111674],{"className":111673},[307,308,309,310],[15,111675,111677],{"className":111676},[59,310],[15,111678,769],{"className":111679},[59,60,310],[15,111681,111682,111685],{"style":473},[15,111683],{"className":111684,"style":461},[302],[15,111686],{"className":111687,"style":481},[480],[15,111689,111690,111693],{"style":26418},[15,111691],{"className":111692,"style":461},[302],[15,111694,111696],{"className":111695},[307,308,309,310],[15,111697,111699,111702,111705,111708,111711],{"className":111698},[59,310],[15,111700,113],{"className":111701},[146,310],[15,111703,769],{"className":111704},[59,60,310],[15,111706,4813],{"className":111707},[2591,310],[15,111709,117],{"className":111710},[59,310],[15,111712,111714,111717],{"className":111713},[153,310],[15,111715,120],{"className":111716},[153,310],[15,111718,111720],{"className":111719},[281],[15,111721,111723],{"className":111722},[285],[15,111724,111726],{"className":111725},[290],[15,111727,111729],{"className":111728,"style":38512},[294],[15,111730,111731,111734],{"style":38515},[15,111732],{"className":111733,"style":30206},[302],[15,111735,111737],{"className":111736},[307,30210,9674,310],[15,111738,2463],{"className":111739},[59,310],[15,111741,318],{"className":111742},[317],[15,111744,111746],{"className":111745},[290],[15,111747,111749],{"className":111748,"style":2572},[294],[15,111750],{},[15,111752],{"className":111753},[153,441],[15,111755],{"className":111756,"style":158},[157],[15,111758,123],{"className":111759},[162],[15,111761],{"className":111762,"style":158},[157],[15,111764,111766,111769,111772,111775,111778],{"className":111765},[50],[15,111767],{"className":111768,"style":67618},[54],[15,111770,769],{"className":111771},[59,60],[15,111773],{"className":111774,"style":2587},[157],[15,111776,4813],{"className":111777},[2591],[15,111779],{"className":111780,"style":2587},[157],[15,111782,111784,111787,111790,111793,111796],{"className":111783},[50],[15,111785],{"className":111786,"style":12578},[54],[15,111788,2463],{"className":111789},[59],[15,111791],{"className":111792,"style":2587},[157],[15,111794,2470],{"className":111795},[2591],[15,111797],{"className":111798,"style":2587},[157],[15,111800,111802,111805],{"className":111801},[50],[15,111803],{"className":111804,"style":2505},[54],[15,111806,111808,111811,111870],{"className":111807},[59],[15,111809],{"className":111810},[146,441],[15,111812,111814],{"className":111813},[238],[15,111815,111817,111862],{"className":111816},[285,286],[15,111818,111820,111859],{"className":111819},[290],[15,111821,111823,111837,111845],{"className":111822,"style":2524},[294],[15,111824,111825,111828],{"style":2527},[15,111826],{"className":111827,"style":461},[302],[15,111829,111831],{"className":111830},[307,308,309,310],[15,111832,111834],{"className":111833},[59,310],[15,111835,769],{"className":111836},[59,60,310],[15,111838,111839,111842],{"style":473},[15,111840],{"className":111841,"style":461},[302],[15,111843],{"className":111844,"style":481},[480],[15,111846,111847,111850],{"style":2550},[15,111848],{"className":111849,"style":461},[302],[15,111851,111853],{"className":111852},[307,308,309,310],[15,111854,111856],{"className":111855},[59,310],[15,111857,117],{"className":111858},[59,310],[15,111860,318],{"className":111861},[317],[15,111863,111865],{"className":111864},[290],[15,111866,111868],{"className":111867,"style":2572},[294],[15,111869],{},[15,111871],{"className":111872},[153,441],[15,111874,111876,111942],{"className":111875,"translate":19},[18],[15,111877,111879],{"className":111878},[23],[25,111880,111881],{"xmlns":27},[29,111882,111883,111939],{},[32,111884,111885,111891,111893,111895,111897,111899,111915,111917,111919,111921,111923,111925,111927,111929,111931,111937],{},[6814,111886,111887,111889],{},[35,111888,37],{},[110,111890,7573],{},[110,111892,113],{"stretchy":112},[35,111894,40237],{},[110,111896,120],{"stretchy":112},[110,111898,123],{},[195,111900,111901,111907],{},[32,111902,111903,111905],{},[35,111904,35432],{},[110,111906,4103],{},[32,111908,111909,111911,111913],{},[35,111910,769],{},[110,111912,2903],{},[115,111914,126],{},[110,111916,2898],{"stretchy":112},[35,111918,40237],{},[35,111920,769],{},[110,111922,4813],{},[35,111924,769],{},[110,111926,2470],{},[115,111928,2463],{},[110,111930,4813],{},[238,111932,111933,111935],{},[115,111934,117],{},[35,111936,769],{},[110,111938,2908],{"stretchy":112},[39,111940,111941],{"encoding":41},"f^*(y)=\\sup_{t>0}\\{yt-t+2-\\frac1t\\}",[15,111943,111945,111998,112071,112089,112107],{"className":111944,"ariaHidden":46},[45],[15,111946,111948,111951,111980,111983,111986,111989,111992,111995],{"className":111947},[50],[15,111949],{"className":111950,"style":139},[54],[15,111952,111954,111957],{"className":111953},[59],[15,111955,37],{"className":111956,"style":61},[59,60],[15,111958,111960],{"className":111959},[281],[15,111961,111963],{"className":111962},[285],[15,111964,111966],{"className":111965},[290],[15,111967,111969],{"className":111968,"style":8499},[294],[15,111970,111971,111974],{"style":6865},[15,111972],{"className":111973,"style":303},[302],[15,111975,111977],{"className":111976},[307,308,309,310],[15,111978,7573],{"className":111979},[2591,310],[15,111981,113],{"className":111982},[146],[15,111984,40237],{"className":111985,"style":981},[59,60],[15,111987,120],{"className":111988},[153],[15,111990],{"className":111991,"style":158},[157],[15,111993,123],{"className":111994},[162],[15,111996],{"className":111997,"style":158},[157],[15,111999,112001,112004,112053,112056,112059,112062,112065,112068],{"className":112000},[50],[15,112002],{"className":112003,"style":35556},[54],[15,112005,112007,112010],{"className":112006},[1484],[15,112008,35432],{"className":112009},[1484],[15,112011,112013],{"className":112012},[281],[15,112014,112016,112045],{"className":112015},[285,286],[15,112017,112019,112042],{"className":112018},[290],[15,112020,112022],{"className":112021,"style":71650},[294],[15,112023,112024,112027],{"style":35578},[15,112025],{"className":112026,"style":303},[302],[15,112028,112030],{"className":112029},[307,308,309,310],[15,112031,112033,112036,112039],{"className":112032},[59,310],[15,112034,769],{"className":112035},[59,60,310],[15,112037,2903],{"className":112038},[162,310],[15,112040,126],{"className":112041},[59,310],[15,112043,318],{"className":112044},[317],[15,112046,112048],{"className":112047},[290],[15,112049,112051],{"className":112050,"style":35606},[294],[15,112052],{},[15,112054,2898],{"className":112055},[146],[15,112057,40237],{"className":112058,"style":981},[59,60],[15,112060,769],{"className":112061},[59,60],[15,112063],{"className":112064,"style":2587},[157],[15,112066,4813],{"className":112067},[2591],[15,112069],{"className":112070,"style":2587},[157],[15,112072,112074,112077,112080,112083,112086],{"className":112073},[50],[15,112075],{"className":112076,"style":67618},[54],[15,112078,769],{"className":112079},[59,60],[15,112081],{"className":112082,"style":2587},[157],[15,112084,2470],{"className":112085},[2591],[15,112087],{"className":112088,"style":2587},[157],[15,112090,112092,112095,112098,112101,112104],{"className":112091},[50],[15,112093],{"className":112094,"style":12578},[54],[15,112096,2463],{"className":112097},[59],[15,112099],{"className":112100,"style":2587},[157],[15,112102,4813],{"className":112103},[2591],[15,112105],{"className":112106,"style":2587},[157],[15,112108,112110,112113,112181],{"className":112109},[50],[15,112111],{"className":112112,"style":2505},[54],[15,112114,112116,112119,112178],{"className":112115},[59],[15,112117],{"className":112118},[146,441],[15,112120,112122],{"className":112121},[238],[15,112123,112125,112170],{"className":112124},[285,286],[15,112126,112128,112167],{"className":112127},[290],[15,112129,112131,112145,112153],{"className":112130,"style":2524},[294],[15,112132,112133,112136],{"style":2527},[15,112134],{"className":112135,"style":461},[302],[15,112137,112139],{"className":112138},[307,308,309,310],[15,112140,112142],{"className":112141},[59,310],[15,112143,769],{"className":112144},[59,60,310],[15,112146,112147,112150],{"style":473},[15,112148],{"className":112149,"style":461},[302],[15,112151],{"className":112152,"style":481},[480],[15,112154,112155,112158],{"style":2550},[15,112156],{"className":112157,"style":461},[302],[15,112159,112161],{"className":112160},[307,308,309,310],[15,112162,112164],{"className":112163},[59,310],[15,112165,117],{"className":112166},[59,310],[15,112168,318],{"className":112169},[317],[15,112171,112173],{"className":112172},[290],[15,112174,112176],{"className":112175,"style":2572},[294],[15,112177],{},[15,112179],{"className":112180},[153,441],[15,112182,2908],{"className":112183},[153],"，驻点条件 ",[15,112186,112188,112222],{"className":112187,"translate":19},[18],[15,112189,112191],{"className":112190},[23],[25,112192,112193],{"xmlns":27},[29,112194,112195,112219],{},[32,112196,112197,112199,112201,112203,112205,112215,112217],{},[35,112198,40237],{},[110,112200,4813],{},[115,112202,117],{},[110,112204,2470],{},[238,112206,112207,112209],{},[115,112208,117],{},[6814,112210,112211,112213],{},[35,112212,769],{},[115,112214,2463],{},[110,112216,123],{},[115,112218,126],{},[39,112220,112221],{"encoding":41},"y-1+\\frac1{t^2}=0",[15,112223,112225,112243,112261,112370],{"className":112224,"ariaHidden":46},[45],[15,112226,112228,112231,112234,112237,112240],{"className":112227},[50],[15,112229],{"className":112230,"style":40321},[54],[15,112232,40237],{"className":112233,"style":981},[59,60],[15,112235],{"className":112236,"style":2587},[157],[15,112238,4813],{"className":112239},[2591],[15,112241],{"className":112242,"style":2587},[157],[15,112244,112246,112249,112252,112255,112258],{"className":112245},[50],[15,112247],{"className":112248,"style":12578},[54],[15,112250,117],{"className":112251},[59],[15,112253],{"className":112254,"style":2587},[157],[15,112256,2470],{"className":112257},[2591],[15,112259],{"className":112260,"style":2587},[157],[15,112262,112264,112267,112361,112364,112367],{"className":112263},[50],[15,112265],{"className":112266,"style":2505},[54],[15,112268,112270,112273,112358],{"className":112269},[59],[15,112271],{"className":112272},[146,441],[15,112274,112276],{"className":112275},[238],[15,112277,112279,112350],{"className":112278},[285,286],[15,112280,112282,112347],{"className":112281},[290],[15,112283,112285,112325,112333],{"className":112284,"style":2524},[294],[15,112286,112287,112290],{"style":2527},[15,112288],{"className":112289,"style":461},[302],[15,112291,112293],{"className":112292},[307,308,309,310],[15,112294,112296],{"className":112295},[59,310],[15,112297,112299,112302],{"className":112298},[59,310],[15,112300,769],{"className":112301},[59,60,310],[15,112303,112305],{"className":112304},[281],[15,112306,112308],{"className":112307},[285],[15,112309,112311],{"className":112310},[290],[15,112312,112314],{"className":112313,"style":45459},[294],[15,112315,112316,112319],{"style":45462},[15,112317],{"className":112318,"style":30206},[302],[15,112320,112322],{"className":112321},[307,30210,9674,310],[15,112323,2463],{"className":112324},[59,310],[15,112326,112327,112330],{"style":473},[15,112328],{"className":112329,"style":461},[302],[15,112331],{"className":112332,"style":481},[480],[15,112334,112335,112338],{"style":2550},[15,112336],{"className":112337,"style":461},[302],[15,112339,112341],{"className":112340},[307,308,309,310],[15,112342,112344],{"className":112343},[59,310],[15,112345,117],{"className":112346},[59,310],[15,112348,318],{"className":112349},[317],[15,112351,112353],{"className":112352},[290],[15,112354,112356],{"className":112355,"style":2572},[294],[15,112357],{},[15,112359],{"className":112360},[153,441],[15,112362],{"className":112363,"style":158},[157],[15,112365,123],{"className":112366},[162],[15,112368],{"className":112369,"style":158},[157],[15,112371,112373,112376],{"className":112372},[50],[15,112374],{"className":112375,"style":172},[54],[15,112377,126],{"className":112378},[59],[15,112380,112382,112412],{"className":112381,"translate":19},[18],[15,112383,112385],{"className":112384},[23],[25,112386,112387],{"xmlns":27},[29,112388,112389,112409],{},[32,112390,112391,112393,112395],{},[35,112392,769],{},[110,112394,123],{},[238,112396,112397,112399],{},[115,112398,117],{},[34339,112400,112401],{},[32,112402,112403,112405,112407],{},[115,112404,117],{},[110,112406,4813],{},[35,112408,40237],{},[39,112410,112411],{"encoding":41},"t=\\frac{1}{\\sqrt{1-y}}",[15,112413,112415,112433],{"className":112414,"ariaHidden":46},[45],[15,112416,112418,112421,112424,112427,112430],{"className":112417},[50],[15,112419],{"className":112420,"style":5343},[54],[15,112422,769],{"className":112423},[59,60],[15,112425],{"className":112426,"style":158},[157],[15,112428,123],{"className":112429},[162],[15,112431],{"className":112432,"style":158},[157],[15,112434,112436,112439],{"className":112435},[50],[15,112437],{"className":112438,"style":98145},[54],[15,112440,112442,112445,112558],{"className":112441},[59],[15,112443],{"className":112444},[146,441],[15,112446,112448],{"className":112447},[238],[15,112449,112451,112550],{"className":112450},[285,286],[15,112452,112454,112547],{"className":112453},[290],[15,112455,112457,112525,112533],{"className":112456,"style":2524},[294],[15,112458,112460,112463],{"style":112459},"top:-2.6191em;",[15,112461],{"className":112462,"style":461},[302],[15,112464,112466],{"className":112465},[307,308,309,310],[15,112467,112469],{"className":112468},[59,310],[15,112470,112472],{"className":112471},[59,34367,310],[15,112473,112475,112516],{"className":112474},[285,286],[15,112476,112478,112513],{"className":112477},[290],[15,112479,112482,112500],{"className":112480,"style":112481},[294],"height:0.8156em;",[15,112483,112485,112488],{"className":112484,"style":11863},[6307],[15,112486],{"className":112487,"style":461},[302],[15,112489,112491,112494,112497],{"className":112490,"style":34387},[59,310],[15,112492,117],{"className":112493},[59,310],[15,112495,4813],{"className":112496},[2591,310],[15,112498,40237],{"className":112499,"style":981},[59,60,310],[15,112501,112503,112506],{"style":112502},"top:-2.7756em;",[15,112504],{"className":112505,"style":461},[302],[15,112507,112509],{"className":112508,"style":34444},[34443,310],[6323,112510,112511],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,112512],{"d":34451},[15,112514,318],{"className":112515},[317],[15,112517,112519],{"className":112518},[290],[15,112520,112523],{"className":112521,"style":112522},[294],"height:0.2244em;",[15,112524],{},[15,112526,112527,112530],{"style":473},[15,112528],{"className":112529,"style":461},[302],[15,112531],{"className":112532,"style":481},[480],[15,112534,112535,112538],{"style":2550},[15,112536],{"className":112537,"style":461},[302],[15,112539,112541],{"className":112540},[307,308,309,310],[15,112542,112544],{"className":112543},[59,310],[15,112545,117],{"className":112546},[59,310],[15,112548,318],{"className":112549},[317],[15,112551,112553],{"className":112552},[290],[15,112554,112556],{"className":112555,"style":98254},[294],[15,112557],{},[15,112559],{"className":112560},[153,441],[15,112562,112564,112581],{"className":112563,"translate":19},[18],[15,112565,112567],{"className":112566},[23],[25,112568,112569],{"xmlns":27},[29,112570,112571,112579],{},[32,112572,112573,112575,112577],{},[35,112574,40237],{},[110,112576,7251],{},[115,112578,117],{},[39,112580,66773],{"encoding":41},[15,112582,112584,112602],{"className":112583,"ariaHidden":46},[45],[15,112585,112587,112590,112593,112596,112599],{"className":112586},[50],[15,112588],{"className":112589,"style":31692},[54],[15,112591,40237],{"className":112592,"style":981},[59,60],[15,112594],{"className":112595,"style":158},[157],[15,112597,7251],{"className":112598},[162],[15,112600],{"className":112601,"style":158},[157],[15,112603,112605,112608],{"className":112604},[50],[15,112606],{"className":112607,"style":172},[54],[15,112609,117],{"className":112610},[59],"），代回得 ",[15,112613,112615,112707],{"className":112614,"translate":19},[18],[15,112616,112618],{"className":112617},[23],[25,112619,112620],{"xmlns":27},[29,112621,112622,112704],{},[32,112623,112624,112630,112632,112634,112636,112638,112640,112642,112644,112646,112648,112650,112656,112658,112660,112670,112672,112674,112676,112686,112688,112690,112692,112694],{},[6814,112625,112626,112628],{},[35,112627,37],{},[110,112629,7573],{},[110,112631,123],{},[35,112633,769],{},[110,112635,113],{"stretchy":112},[35,112637,40237],{},[110,112639,4813],{},[115,112641,117],{},[110,112643,120],{"stretchy":112},[110,112645,2470],{},[115,112647,2463],{},[110,112649,4813],{},[238,112651,112652,112654],{},[115,112653,117],{},[35,112655,769],{},[110,112657,123],{},[110,112659,4813],{},[34339,112661,112662],{},[32,112663,112664,112666,112668],{},[115,112665,117],{},[110,112667,4813],{},[35,112669,40237],{},[110,112671,2470],{},[115,112673,2463],{},[110,112675,4813],{},[34339,112677,112678],{},[32,112679,112680,112682,112684],{},[115,112681,117],{},[110,112683,4813],{},[35,112685,40237],{},[110,112687,123],{},[115,112689,2463],{},[110,112691,4813],{},[115,112693,2463],{},[34339,112695,112696],{},[32,112697,112698,112700,112702],{},[115,112699,117],{},[110,112701,4813],{},[35,112703,40237],{},[39,112705,112706],{"encoding":41},"f^*=t(y-1)+2-\\frac1t=-\\sqrt{1-y}+2-\\sqrt{1-y}=2-2\\sqrt{1-y}",[15,112708,112710,112754,112778,112799,112817,112900,112977,112995,113069,113087],{"className":112709,"ariaHidden":46},[45],[15,112711,112713,112716,112745,112748,112751],{"className":112712},[50],[15,112714],{"className":112715,"style":55},[54],[15,112717,112719,112722],{"className":112718},[59],[15,112720,37],{"className":112721,"style":61},[59,60],[15,112723,112725],{"className":112724},[281],[15,112726,112728],{"className":112727},[285],[15,112729,112731],{"className":112730},[290],[15,112732,112734],{"className":112733,"style":8499},[294],[15,112735,112736,112739],{"style":6865},[15,112737],{"className":112738,"style":303},[302],[15,112740,112742],{"className":112741},[307,308,309,310],[15,112743,7573],{"className":112744},[2591,310],[15,112746],{"className":112747,"style":158},[157],[15,112749,123],{"className":112750},[162],[15,112752],{"className":112753,"style":158},[157],[15,112755,112757,112760,112763,112766,112769,112772,112775],{"className":112756},[50],[15,112758],{"className":112759,"style":139},[54],[15,112761,769],{"className":112762},[59,60],[15,112764,113],{"className":112765},[146],[15,112767,40237],{"className":112768,"style":981},[59,60],[15,112770],{"className":112771,"style":2587},[157],[15,112773,4813],{"className":112774},[2591],[15,112776],{"className":112777,"style":2587},[157],[15,112779,112781,112784,112787,112790,112793,112796],{"className":112780},[50],[15,112782],{"className":112783,"style":139},[54],[15,112785,117],{"className":112786},[59],[15,112788,120],{"className":112789},[153],[15,112791],{"className":112792,"style":2587},[157],[15,112794,2470],{"className":112795},[2591],[15,112797],{"className":112798,"style":2587},[157],[15,112800,112802,112805,112808,112811,112814],{"className":112801},[50],[15,112803],{"className":112804,"style":12578},[54],[15,112806,2463],{"className":112807},[59],[15,112809],{"className":112810,"style":2587},[157],[15,112812,4813],{"className":112813},[2591],[15,112815],{"className":112816,"style":2587},[157],[15,112818,112820,112823,112891,112894,112897],{"className":112819},[50],[15,112821],{"className":112822,"style":2505},[54],[15,112824,112826,112829,112888],{"className":112825},[59],[15,112827],{"className":112828},[146,441],[15,112830,112832],{"className":112831},[238],[15,112833,112835,112880],{"className":112834},[285,286],[15,112836,112838,112877],{"className":112837},[290],[15,112839,112841,112855,112863],{"className":112840,"style":2524},[294],[15,112842,112843,112846],{"style":2527},[15,112844],{"className":112845,"style":461},[302],[15,112847,112849],{"className":112848},[307,308,309,310],[15,112850,112852],{"className":112851},[59,310],[15,112853,769],{"className":112854},[59,60,310],[15,112856,112857,112860],{"style":473},[15,112858],{"className":112859,"style":461},[302],[15,112861],{"className":112862,"style":481},[480],[15,112864,112865,112868],{"style":2550},[15,112866],{"className":112867,"style":461},[302],[15,112869,112871],{"className":112870},[307,308,309,310],[15,112872,112874],{"className":112873},[59,310],[15,112875,117],{"className":112876},[59,310],[15,112878,318],{"className":112879},[317],[15,112881,112883],{"className":112882},[290],[15,112884,112886],{"className":112885,"style":2572},[294],[15,112887],{},[15,112889],{"className":112890},[153,441],[15,112892],{"className":112893,"style":158},[157],[15,112895,123],{"className":112896},[162],[15,112898],{"className":112899,"style":158},[157],[15,112901,112903,112906,112909,112968,112971,112974],{"className":112902},[50],[15,112904],{"className":112905,"style":110395},[54],[15,112907,4813],{"className":112908},[59],[15,112910,112912],{"className":112911},[59,34367],[15,112913,112915,112960],{"className":112914},[285,286],[15,112916,112918,112957],{"className":112917},[290],[15,112919,112921,112945],{"className":112920,"style":110411},[294],[15,112922,112924,112927],{"className":112923,"style":11863},[6307],[15,112925],{"className":112926,"style":461},[302],[15,112928,112930,112933,112936,112939,112942],{"className":112929,"style":34387},[59],[15,112931,117],{"className":112932},[59],[15,112934],{"className":112935,"style":2587},[157],[15,112937,4813],{"className":112938},[2591],[15,112940],{"className":112941,"style":2587},[157],[15,112943,40237],{"className":112944,"style":981},[59,60],[15,112946,112947,112950],{"style":110438},[15,112948],{"className":112949,"style":461},[302],[15,112951,112953],{"className":112952,"style":34444},[34443],[6323,112954,112955],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,112956],{"d":34451},[15,112958,318],{"className":112959},[317],[15,112961,112963],{"className":112962},[290],[15,112964,112966],{"className":112965,"style":110458},[294],[15,112967],{},[15,112969],{"className":112970,"style":2587},[157],[15,112972,2470],{"className":112973},[2591],[15,112975],{"className":112976,"style":2587},[157],[15,112978,112980,112983,112986,112989,112992],{"className":112979},[50],[15,112981],{"className":112982,"style":12578},[54],[15,112984,2463],{"className":112985},[59],[15,112987],{"className":112988,"style":2587},[157],[15,112990,4813],{"className":112991},[2591],[15,112993],{"className":112994,"style":2587},[157],[15,112996,112998,113001,113060,113063,113066],{"className":112997},[50],[15,112999],{"className":113000,"style":110395},[54],[15,113002,113004],{"className":113003},[59,34367],[15,113005,113007,113052],{"className":113006},[285,286],[15,113008,113010,113049],{"className":113009},[290],[15,113011,113013,113037],{"className":113012,"style":110411},[294],[15,113014,113016,113019],{"className":113015,"style":11863},[6307],[15,113017],{"className":113018,"style":461},[302],[15,113020,113022,113025,113028,113031,113034],{"className":113021,"style":34387},[59],[15,113023,117],{"className":113024},[59],[15,113026],{"className":113027,"style":2587},[157],[15,113029,4813],{"className":113030},[2591],[15,113032],{"className":113033,"style":2587},[157],[15,113035,40237],{"className":113036,"style":981},[59,60],[15,113038,113039,113042],{"style":110438},[15,113040],{"className":113041,"style":461},[302],[15,113043,113045],{"className":113044,"style":34444},[34443],[6323,113046,113047],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,113048],{"d":34451},[15,113050,318],{"className":113051},[317],[15,113053,113055],{"className":113054},[290],[15,113056,113058],{"className":113057,"style":110458},[294],[15,113059],{},[15,113061],{"className":113062,"style":158},[157],[15,113064,123],{"className":113065},[162],[15,113067],{"className":113068,"style":158},[157],[15,113070,113072,113075,113078,113081,113084],{"className":113071},[50],[15,113073],{"className":113074,"style":12578},[54],[15,113076,2463],{"className":113077},[59],[15,113079],{"className":113080,"style":2587},[157],[15,113082,4813],{"className":113083},[2591],[15,113085],{"className":113086,"style":2587},[157],[15,113088,113090,113093,113096],{"className":113089},[50],[15,113091],{"className":113092,"style":110395},[54],[15,113094,2463],{"className":113095},[59],[15,113097,113099],{"className":113098},[59,34367],[15,113100,113102,113147],{"className":113101},[285,286],[15,113103,113105,113144],{"className":113104},[290],[15,113106,113108,113132],{"className":113107,"style":110411},[294],[15,113109,113111,113114],{"className":113110,"style":11863},[6307],[15,113112],{"className":113113,"style":461},[302],[15,113115,113117,113120,113123,113126,113129],{"className":113116,"style":34387},[59],[15,113118,117],{"className":113119},[59],[15,113121],{"className":113122,"style":2587},[157],[15,113124,4813],{"className":113125},[2591],[15,113127],{"className":113128,"style":2587},[157],[15,113130,40237],{"className":113131,"style":981},[59,60],[15,113133,113134,113137],{"style":110438},[15,113135],{"className":113136,"style":461},[302],[15,113138,113140],{"className":113139,"style":34444},[34443],[6323,113141,113142],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,113143],{"d":34451},[15,113145,318],{"className":113146},[317],[15,113148,113150],{"className":113149},[290],[15,113151,113153],{"className":113152,"style":110458},[294],[15,113154],{},"。α 一行取 ",[15,113157,113159,113198],{"className":113158,"translate":19},[18],[15,113160,113162],{"className":113161},[23],[25,113163,113164],{"xmlns":27},[29,113165,113166,113196],{},[32,113167,113168,113170,113172,113184,113186,113188,113190,113192,113194],{},[35,113169,45180],{},[110,113171,123],{},[238,113173,113174,113182],{},[32,113175,113176,113178,113180],{},[115,113177,117],{},[110,113179,2470],{},[35,113181,44754],{},[115,113183,2463],{},[110,113185,5909],{},[110,113187,113],{"stretchy":112},[115,113189,126],{},[110,113191,551],{"separator":46},[115,113193,117],{},[110,113195,120],{"stretchy":112},[39,113197,45209],{"encoding":41},[15,113199,113201,113219,113308],{"className":113200,"ariaHidden":46},[45],[15,113202,113204,113207,113210,113213,113216],{"className":113203},[50],[15,113205],{"className":113206,"style":2345},[54],[15,113208,45180],{"className":113209},[59,60],[15,113211],{"className":113212,"style":158},[157],[15,113214,123],{"className":113215},[162],[15,113217],{"className":113218,"style":158},[157],[15,113220,113222,113225,113299,113302,113305],{"className":113221},[50],[15,113223],{"className":113224,"style":2505},[54],[15,113226,113228,113231,113296],{"className":113227},[59],[15,113229],{"className":113230},[146,441],[15,113232,113234],{"className":113233},[238],[15,113235,113237,113288],{"className":113236},[285,286],[15,113238,113240,113285],{"className":113239},[290],[15,113241,113243,113257,113265],{"className":113242,"style":2524},[294],[15,113244,113245,113248],{"style":2527},[15,113246],{"className":113247,"style":461},[302],[15,113249,113251],{"className":113250},[307,308,309,310],[15,113252,113254],{"className":113253},[59,310],[15,113255,2463],{"className":113256},[59,310],[15,113258,113259,113262],{"style":473},[15,113260],{"className":113261,"style":461},[302],[15,113263],{"className":113264,"style":481},[480],[15,113266,113267,113270],{"style":2550},[15,113268],{"className":113269,"style":461},[302],[15,113271,113273],{"className":113272},[307,308,309,310],[15,113274,113276,113279,113282],{"className":113275},[59,310],[15,113277,117],{"className":113278},[59,310],[15,113280,2470],{"className":113281},[2591,310],[15,113283,44754],{"className":113284,"style":44784},[59,60,310],[15,113286,318],{"className":113287},[317],[15,113289,113291],{"className":113290},[290],[15,113292,113294],{"className":113293,"style":2572},[294],[15,113295],{},[15,113297],{"className":113298},[153,441],[15,113300],{"className":113301,"style":158},[157],[15,113303,5909],{"className":113304},[162],[15,113306],{"className":113307,"style":158},[157],[15,113309,113311,113314,113317,113320,113323,113326,113329],{"className":113310},[50],[15,113312],{"className":113313,"style":139},[54],[15,113315,113],{"className":113316},[146],[15,113318,126],{"className":113319},[59],[15,113321,551],{"className":113322},[573],[15,113324],{"className":113325,"style":406},[157],[15,113327,117],{"className":113328},[59],[15,113330,120],{"className":113331},[153],"，验证：",[15,113334,113336,113412],{"className":113335,"translate":19},[18],[15,113337,113339],{"className":113338},[23],[25,113340,113341],{"xmlns":27},[29,113342,113343,113409],{},[32,113344,113345,113353,113355,113357,113359,113361,113371,113373,113375,113377,113379,113407],{},[7553,113346,113347,113349,113351],{},[35,113348,37],{},[35,113350,44754],{},[110,113352,7573],{},[110,113354,113],{"stretchy":112},[35,113356,40237],{},[110,113358,120],{"stretchy":112},[110,113360,123],{},[195,113362,113363,113369],{},[32,113364,113365,113367],{},[35,113366,35432],{},[110,113368,4103],{},[35,113370,769],{},[110,113372,2898],{"stretchy":112},[35,113374,769],{},[35,113376,40237],{},[110,113378,4813],{},[238,113380,113381,113393],{},[32,113382,113383,113385,113387],{},[115,113384,117],{},[110,113386,4813],{},[6814,113388,113389,113391],{},[35,113390,769],{},[35,113392,45180],{},[32,113394,113395,113397,113399,113401,113403,113405],{},[35,113396,45180],{},[110,113398,113],{"stretchy":112},[115,113400,117],{},[110,113402,4813],{},[35,113404,45180],{},[110,113406,120],{"stretchy":112},[110,113408,2908],{"stretchy":112},[39,113410,113411],{"encoding":41},"f_\\alpha^*(y)=\\sup_t\\{ty-\\frac{1-t^a}{a(1-a)}\\}",[15,113413,113415,113490,113554],{"className":113414,"ariaHidden":46},[45],[15,113416,113418,113421,113472,113475,113478,113481,113484,113487],{"className":113417},[50],[15,113419],{"className":113420,"style":139},[54],[15,113422,113424,113427],{"className":113423},[59],[15,113425,37],{"className":113426,"style":61},[59,60],[15,113428,113430],{"className":113429},[281],[15,113431,113433,113464],{"className":113432},[285,286],[15,113434,113436,113461],{"className":113435},[290],[15,113437,113439,113450],{"className":113438,"style":8499},[294],[15,113440,113441,113444],{"style":8251},[15,113442],{"className":113443,"style":303},[302],[15,113445,113447],{"className":113446},[307,308,309,310],[15,113448,44754],{"className":113449,"style":44784},[59,60,310],[15,113451,113452,113455],{"style":6865},[15,113453],{"className":113454,"style":303},[302],[15,113456,113458],{"className":113457},[307,308,309,310],[15,113459,7573],{"className":113460},[2591,310],[15,113462,318],{"className":113463},[317],[15,113465,113467],{"className":113466},[290],[15,113468,113470],{"className":113469,"style":8299},[294],[15,113471],{},[15,113473,113],{"className":113474},[146],[15,113476,40237],{"className":113477,"style":981},[59,60],[15,113479,120],{"className":113480},[153],[15,113482],{"className":113483,"style":158},[157],[15,113485,123],{"className":113486},[162],[15,113488],{"className":113489,"style":158},[157],[15,113491,113493,113496,113536,113539,113542,113545,113548,113551],{"className":113492},[50],[15,113494],{"className":113495,"style":139},[54],[15,113497,113499,113502],{"className":113498},[1484],[15,113500,35432],{"className":113501},[1484],[15,113503,113505],{"className":113504},[281],[15,113506,113508,113528],{"className":113507},[285,286],[15,113509,113511,113525],{"className":113510},[290],[15,113512,113514],{"className":113513,"style":67011},[294],[15,113515,113516,113519],{"style":35578},[15,113517],{"className":113518,"style":303},[302],[15,113520,113522],{"className":113521},[307,308,309,310],[15,113523,769],{"className":113524},[59,60,310],[15,113526,318],{"className":113527},[317],[15,113529,113531],{"className":113530},[290],[15,113532,113534],{"className":113533,"style":37020},[294],[15,113535],{},[15,113537,2898],{"className":113538},[146],[15,113540,769],{"className":113541},[59,60],[15,113543,40237],{"className":113544,"style":981},[59,60],[15,113546],{"className":113547,"style":2587},[157],[15,113549,4813],{"className":113550},[2591],[15,113552],{"className":113553,"style":2587},[157],[15,113555,113557,113561,113678],{"className":113556},[50],[15,113558],{"className":113559,"style":113560},[54],"height:1.431em;vertical-align:-0.52em;",[15,113562,113564,113567,113675],{"className":113563},[59],[15,113565],{"className":113566},[146,441],[15,113568,113570],{"className":113569},[238],[15,113571,113573,113667],{"className":113572},[285,286],[15,113574,113576,113664],{"className":113575},[290],[15,113577,113580,113609,113617],{"className":113578,"style":113579},[294],"height:0.911em;",[15,113581,113582,113585],{"style":2527},[15,113583],{"className":113584,"style":461},[302],[15,113586,113588],{"className":113587},[307,308,309,310],[15,113589,113591,113594,113597,113600,113603,113606],{"className":113590},[59,310],[15,113592,45180],{"className":113593},[59,60,310],[15,113595,113],{"className":113596},[146,310],[15,113598,117],{"className":113599},[59,310],[15,113601,4813],{"className":113602},[2591,310],[15,113604,45180],{"className":113605},[59,60,310],[15,113607,120],{"className":113608},[153,310],[15,113610,113611,113614],{"style":473},[15,113612],{"className":113613,"style":461},[302],[15,113615],{"className":113616,"style":481},[480],[15,113618,113619,113622],{"style":2550},[15,113620],{"className":113621,"style":461},[302],[15,113623,113625],{"className":113624},[307,308,309,310],[15,113626,113628,113631,113634],{"className":113627},[59,310],[15,113629,117],{"className":113630},[59,310],[15,113632,4813],{"className":113633},[2591,310],[15,113635,113637,113640],{"className":113636},[59,310],[15,113638,769],{"className":113639},[59,60,310],[15,113641,113643],{"className":113642},[281],[15,113644,113646],{"className":113645},[285],[15,113647,113649],{"className":113648},[290],[15,113650,113653],{"className":113651,"style":113652},[294],"height:0.7385em;",[15,113654,113655,113658],{"style":38515},[15,113656],{"className":113657,"style":30206},[302],[15,113659,113661],{"className":113660},[307,30210,9674,310],[15,113662,45180],{"className":113663},[59,60,310],[15,113665,318],{"className":113666},[317],[15,113668,113670],{"className":113669},[290],[15,113671,113673],{"className":113672,"style":45602},[294],[15,113674],{},[15,113676],{"className":113677},[153,441],[15,113679,2908],{"className":113680},[153],[15,113682,113684,113726],{"className":113683,"translate":19},[18],[15,113685,113687],{"className":113686},[23],[25,113688,113689],{"xmlns":27},[29,113690,113691,113723],{},[32,113692,113693,113695,113697,113719,113721],{},[35,113694,40237],{},[110,113696,2470],{},[238,113698,113699,113711],{},[6814,113700,113701,113703],{},[35,113702,769],{},[32,113704,113705,113707,113709],{},[35,113706,45180],{},[110,113708,4813],{},[115,113710,117],{},[32,113712,113713,113715,113717],{},[115,113714,117],{},[110,113716,4813],{},[35,113718,45180],{},[110,113720,123],{},[115,113722,126],{},[39,113724,113725],{"encoding":41},"y+\\frac{t^{a-1}}{1-a}=0",[15,113727,113729,113747,113873],{"className":113728,"ariaHidden":46},[45],[15,113730,113732,113735,113738,113741,113744],{"className":113731},[50],[15,113733],{"className":113734,"style":40321},[54],[15,113736,40237],{"className":113737,"style":981},[59,60],[15,113739],{"className":113740,"style":2587},[157],[15,113742,2470],{"className":113743},[2591],[15,113745],{"className":113746,"style":2587},[157],[15,113748,113750,113754,113864,113867,113870],{"className":113749},[50],[15,113751],{"className":113752,"style":113753},[54],"height:1.4213em;vertical-align:-0.4033em;",[15,113755,113757,113760,113861],{"className":113756},[59],[15,113758],{"className":113759},[146,441],[15,113761,113763],{"className":113762},[238],[15,113764,113766,113853],{"className":113765},[285,286],[15,113767,113769,113850],{"className":113768},[290],[15,113770,113773,113793,113801],{"className":113771,"style":113772},[294],"height:1.0179em;",[15,113774,113775,113778],{"style":2527},[15,113776],{"className":113777,"style":461},[302],[15,113779,113781],{"className":113780},[307,308,309,310],[15,113782,113784,113787,113790],{"className":113783},[59,310],[15,113785,117],{"className":113786},[59,310],[15,113788,4813],{"className":113789},[2591,310],[15,113791,45180],{"className":113792},[59,60,310],[15,113794,113795,113798],{"style":473},[15,113796],{"className":113797,"style":461},[302],[15,113799],{"className":113800,"style":481},[480],[15,113802,113803,113806],{"style":2550},[15,113804],{"className":113805,"style":461},[302],[15,113807,113809],{"className":113808},[307,308,309,310],[15,113810,113812],{"className":113811},[59,310],[15,113813,113815,113818],{"className":113814},[59,310],[15,113816,769],{"className":113817},[59,60,310],[15,113819,113821],{"className":113820},[281],[15,113822,113824],{"className":113823},[285],[15,113825,113827],{"className":113826},[290],[15,113828,113830],{"className":113829,"style":38512},[294],[15,113831,113832,113835],{"style":38515},[15,113833],{"className":113834,"style":30206},[302],[15,113836,113838],{"className":113837},[307,30210,9674,310],[15,113839,113841,113844,113847],{"className":113840},[59,310],[15,113842,45180],{"className":113843},[59,60,310],[15,113845,4813],{"className":113846},[2591,310],[15,113848,117],{"className":113849},[59,310],[15,113851,318],{"className":113852},[317],[15,113854,113856],{"className":113855},[290],[15,113857,113859],{"className":113858,"style":16429},[294],[15,113860],{},[15,113862],{"className":113863},[153,441],[15,113865],{"className":113866,"style":158},[157],[15,113868,123],{"className":113869},[162],[15,113871],{"className":113872,"style":158},[157],[15,113874,113876,113879],{"className":113875},[50],[15,113877],{"className":113878,"style":172},[54],[15,113880,126],{"className":113881},[59],[15,113883,113885,113941],{"className":113884,"translate":19},[18],[15,113886,113888],{"className":113887},[23],[25,113889,113890],{"xmlns":27},[29,113891,113892,113938],{},[32,113893,113894,113896,113898,113900,113902,113904,113906,113908,113910,113912,113914,113916,113918],{},[35,113895,769],{},[110,113897,123],{},[110,113899,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,113901,113],{"stretchy":112},[115,113903,117],{},[110,113905,4813],{},[35,113907,45180],{},[110,113909,120],{"stretchy":112},[110,113911,113],{"stretchy":112},[110,113913,4813],{},[35,113915,40237],{},[110,113917,120],{"stretchy":112},[6814,113919,113920,113922],{},[110,113921,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[32,113923,113924,113926],{},[110,113925,4813],{},[238,113927,113928,113930],{},[115,113929,117],{},[32,113931,113932,113934,113936],{},[115,113933,117],{},[110,113935,4813],{},[35,113937,45180],{},[39,113939,113940],{"encoding":41},"t=\\big((1-a)(-y)\\big)^{-\\frac{1}{1-a}}",[15,113942,113944,113962,113989],{"className":113943,"ariaHidden":46},[45],[15,113945,113947,113950,113953,113956,113959],{"className":113946},[50],[15,113948],{"className":113949,"style":5343},[54],[15,113951,769],{"className":113952},[59,60],[15,113954],{"className":113955,"style":158},[157],[15,113957,123],{"className":113958},[162],[15,113960],{"className":113961,"style":158},[157],[15,113963,113965,113968,113974,113977,113980,113983,113986],{"className":113964},[50],[15,113966],{"className":113967,"style":20563},[54],[15,113969,113971],{"className":113970},[59],[15,113972,113],{"className":113973},[419,9674],[15,113975,113],{"className":113976},[146],[15,113978,117],{"className":113979},[59],[15,113981],{"className":113982,"style":2587},[157],[15,113984,4813],{"className":113985},[2591],[15,113987],{"className":113988,"style":2587},[157],[15,113990,113992,113996,113999,114002,114005,114008,114011,114014],{"className":113991},[50],[15,113993],{"className":113994,"style":113995},[54],"height:1.5439em;vertical-align:-0.35em;",[15,113997,45180],{"className":113998},[59,60],[15,114000,120],{"className":114001},[153],[15,114003,113],{"className":114004},[146],[15,114006,4813],{"className":114007},[59],[15,114009,40237],{"className":114010,"style":981},[59,60],[15,114012,120],{"className":114013},[153],[15,114015,114017,114023],{"className":114016},[59],[15,114018,114020],{"className":114019},[59],[15,114021,120],{"className":114022},[419,9674],[15,114024,114026],{"className":114025},[281],[15,114027,114029],{"className":114028},[285],[15,114030,114032],{"className":114031},[290],[15,114033,114036],{"className":114034,"style":114035},[294],"height:1.1939em;",[15,114037,114038,114041],{"style":111304},[15,114039],{"className":114040,"style":461},[302],[15,114042,114044],{"className":114043},[307,308,309,310],[15,114045,114047,114050],{"className":114046},[59,310],[15,114048,4813],{"className":114049},[59,310],[15,114051,114053,114056,114122],{"className":114052},[59,310],[15,114054],{"className":114055},[146,441,307,30210,111323],[15,114057,114059],{"className":114058},[238],[15,114060,114062,114114],{"className":114061},[285,286],[15,114063,114065,114111],{"className":114064},[290],[15,114066,114069,114089,114097],{"className":114067,"style":114068},[294],"height:0.8443em;",[15,114070,114071,114074],{"style":111339},[15,114072],{"className":114073,"style":461},[302],[15,114075,114077],{"className":114076},[307,30210,9674,310],[15,114078,114080,114083,114086],{"className":114079},[59,310],[15,114081,117],{"className":114082},[59,310],[15,114084,4813],{"className":114085},[2591,310],[15,114087,45180],{"className":114088},[59,60,310],[15,114090,114091,114094],{"style":111360},[15,114092],{"className":114093,"style":461},[302],[15,114095],{"className":114096,"style":111367},[480,310],[15,114098,114099,114102],{"style":111370},[15,114100],{"className":114101,"style":461},[302],[15,114103,114105],{"className":114104},[307,30210,9674,310],[15,114106,114108],{"className":114107},[59,310],[15,114109,117],{"className":114110},[59,310],[15,114112,318],{"className":114113},[317],[15,114115,114117],{"className":114116},[290],[15,114118,114120],{"className":114119,"style":111392},[294],[15,114121],{},[15,114123],{"className":114124},[153,441,307,30210,111323],[15,114126,114128,114145],{"className":114127,"translate":19},[18],[15,114129,114131],{"className":114130},[23],[25,114132,114133],{"xmlns":27},[29,114134,114135,114143],{},[32,114136,114137,114139,114141],{},[35,114138,40237],{},[110,114140,7251],{},[115,114142,126],{},[39,114144,65141],{"encoding":41},[15,114146,114148,114166],{"className":114147,"ariaHidden":46},[45],[15,114149,114151,114154,114157,114160,114163],{"className":114150},[50],[15,114152],{"className":114153,"style":31692},[54],[15,114155,40237],{"className":114156,"style":981},[59,60],[15,114158],{"className":114159,"style":158},[157],[15,114161,7251],{"className":114162},[162],[15,114164],{"className":114165,"style":158},[157],[15,114167,114169,114172],{"className":114168},[50],[15,114170],{"className":114171,"style":172},[54],[15,114173,126],{"className":114174},[59],"），代回即得上式；",[15,114177,114179,114201],{"className":114178,"translate":19},[18],[15,114180,114182],{"className":114181},[23],[25,114183,114184],{"xmlns":27},[29,114185,114186,114198],{},[32,114187,114188,114190,114192],{},[35,114189,45180],{},[110,114191,123],{},[238,114193,114194,114196],{},[115,114195,117],{},[115,114197,2463],{},[39,114199,114200],{"encoding":41},"a=\\frac12",[15,114202,114204,114222],{"className":114203,"ariaHidden":46},[45],[15,114205,114207,114210,114213,114216,114219],{"className":114206},[50],[15,114208],{"className":114209,"style":2345},[54],[15,114211,45180],{"className":114212},[59,60],[15,114214],{"className":114215,"style":158},[157],[15,114217,123],{"className":114218},[162],[15,114220],{"className":114221,"style":158},[157],[15,114223,114225,114228],{"className":114224},[50],[15,114226],{"className":114227,"style":2505},[54],[15,114229,114231,114234,114293],{"className":114230},[59],[15,114232],{"className":114233},[146,441],[15,114235,114237],{"className":114236},[238],[15,114238,114240,114285],{"className":114239},[285,286],[15,114241,114243,114282],{"className":114242},[290],[15,114244,114246,114260,114268],{"className":114245,"style":2524},[294],[15,114247,114248,114251],{"style":2527},[15,114249],{"className":114250,"style":461},[302],[15,114252,114254],{"className":114253},[307,308,309,310],[15,114255,114257],{"className":114256},[59,310],[15,114258,2463],{"className":114259},[59,310],[15,114261,114262,114265],{"style":473},[15,114263],{"className":114264,"style":461},[302],[15,114266],{"className":114267,"style":481},[480],[15,114269,114270,114273],{"style":2550},[15,114271],{"className":114272,"style":461},[302],[15,114274,114276],{"className":114275},[307,308,309,310],[15,114277,114279],{"className":114278},[59,310],[15,114280,117],{"className":114281},[59,310],[15,114283,318],{"className":114284},[317],[15,114286,114288],{"className":114287},[290],[15,114289,114291],{"className":114290,"style":2572},[294],[15,114292],{},[15,114294],{"className":114295},[153,441],[15,114297,114299,114316],{"className":114298,"translate":19},[18],[15,114300,114302],{"className":114301},[23],[25,114303,114304],{"xmlns":27},[29,114305,114306,114314],{},[32,114307,114308,114310,114312],{},[35,114309,44754],{},[110,114311,123],{},[115,114313,126],{},[39,114315,46488],{"encoding":41},[15,114317,114319,114337],{"className":114318,"ariaHidden":46},[45],[15,114320,114322,114325,114328,114331,114334],{"className":114321},[50],[15,114323],{"className":114324,"style":2345},[54],[15,114326,44754],{"className":114327,"style":44784},[59,60],[15,114329],{"className":114330,"style":158},[157],[15,114332,123],{"className":114333},[162],[15,114335],{"className":114336,"style":158},[157],[15,114338,114340,114343],{"className":114339},[50],[15,114341],{"className":114342,"style":172},[54],[15,114344,126],{"className":114345},[59],[15,114347,114349,114379],{"className":114348,"translate":19},[18],[15,114350,114352],{"className":114351},[23],[25,114353,114354],{"xmlns":27},[29,114355,114356,114376],{},[32,114357,114358,114360,114362,114364,114366,114368,114370,114374],{},[35,114359,37],{},[110,114361,123],{},[115,114363,38989],{},[110,114365,113],{"stretchy":112},[115,114367,117],{},[110,114369,4813],{},[34339,114371,114372],{},[35,114373,769],{},[110,114375,120],{"stretchy":112},[39,114377,114378],{"encoding":41},"f=4(1-\\sqrt t)",[15,114380,114382,114400,114424],{"className":114381,"ariaHidden":46},[45],[15,114383,114385,114388,114391,114394,114397],{"className":114384},[50],[15,114386],{"className":114387,"style":55},[54],[15,114389,37],{"className":114390,"style":61},[59,60],[15,114392],{"className":114393,"style":158},[157],[15,114395,123],{"className":114396},[162],[15,114398],{"className":114399,"style":158},[157],[15,114401,114403,114406,114409,114412,114415,114418,114421],{"className":114402},[50],[15,114404],{"className":114405,"style":139},[54],[15,114407,38989],{"className":114408},[59],[15,114410,113],{"className":114411},[146],[15,114413,117],{"className":114414},[59],[15,114416],{"className":114417,"style":2587},[157],[15,114419,4813],{"className":114420},[2591],[15,114422],{"className":114423,"style":2587},[157],[15,114425,114427,114430,114474],{"className":114426},[50],[15,114428],{"className":114429,"style":42667},[54],[15,114431,114433],{"className":114432},[59,34367],[15,114434,114436,114466],{"className":114435},[285,286],[15,114437,114439,114463],{"className":114438},[290],[15,114440,114442,114451],{"className":114441,"style":42683},[294],[15,114443,114445,114448],{"className":114444,"style":11863},[6307],[15,114446],{"className":114447,"style":461},[302],[15,114449,769],{"className":114450,"style":34387},[59,60],[15,114452,114453,114456],{"style":42695},[15,114454],{"className":114455,"style":461},[302],[15,114457,114459],{"className":114458,"style":34444},[34443],[6323,114460,114461],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,114462],{"d":34451},[15,114464,318],{"className":114465},[317],[15,114467,114469],{"className":114468},[290],[15,114470,114472],{"className":114471,"style":42715},[294],[15,114473],{},[15,114475,120],{"className":114476},[153],"）时公式给出 ",[15,114479,114481,114507],{"className":114480,"translate":19},[18],[15,114482,114484],{"className":114483},[23],[25,114485,114486],{"xmlns":27},[29,114487,114488,114504],{},[32,114489,114490,114500,114502],{},[238,114491,114492,114494],{},[115,114493,38989],{},[32,114495,114496,114498],{},[110,114497,4813],{},[35,114499,40237],{},[110,114501,4813],{},[115,114503,38989],{},[39,114505,114506],{"encoding":41},"\\frac{4}{-y}-4",[15,114508,114510,114597],{"className":114509,"ariaHidden":46},[45],[15,114511,114513,114517,114588,114591,114594],{"className":114512},[50],[15,114514],{"className":114515,"style":114516},[54],"height:1.3262em;vertical-align:-0.4811em;",[15,114518,114520,114523,114585],{"className":114519},[59],[15,114521],{"className":114522},[146,441],[15,114524,114526],{"className":114525},[238],[15,114527,114529,114577],{"className":114528},[285,286],[15,114530,114532,114574],{"className":114531},[290],[15,114533,114535,114552,114560],{"className":114534,"style":2524},[294],[15,114536,114537,114540],{"style":2527},[15,114538],{"className":114539,"style":461},[302],[15,114541,114543],{"className":114542},[307,308,309,310],[15,114544,114546,114549],{"className":114545},[59,310],[15,114547,4813],{"className":114548},[59,310],[15,114550,40237],{"className":114551,"style":981},[59,60,310],[15,114553,114554,114557],{"style":473},[15,114555],{"className":114556,"style":461},[302],[15,114558],{"className":114559,"style":481},[480],[15,114561,114562,114565],{"style":2550},[15,114563],{"className":114564,"style":461},[302],[15,114566,114568],{"className":114567},[307,308,309,310],[15,114569,114571],{"className":114570},[59,310],[15,114572,38989],{"className":114573},[59,310],[15,114575,318],{"className":114576},[317],[15,114578,114580],{"className":114579},[290],[15,114581,114583],{"className":114582,"style":2739},[294],[15,114584],{},[15,114586],{"className":114587},[153,441],[15,114589],{"className":114590,"style":2587},[157],[15,114592,4813],{"className":114593},[2591],[15,114595],{"className":114596,"style":2587},[157],[15,114598,114600,114603],{"className":114599},[50],[15,114601],{"className":114602,"style":172},[54],[15,114604,38989],{"className":114605},[59],"，可与直接展开互相验证。）",[11,114608,114609],{},"可见，f-散度族统一了「不对称\u002F对称」「有界\u002F无界」的多种散度。",[2311,114611,114613],{"id":114612},"_62-积分概率度量ipm","6.2 积分概率度量（IPM）",[11,114615,114616,114617,114666],{},"f-散度只依赖似然比 ",[15,114618,114620,114642],{"className":114619,"translate":19},[18],[15,114621,114623],{"className":114622},[23],[25,114624,114625],{"xmlns":27},[29,114626,114627,114639],{},[32,114628,114629,114631,114633,114635,114637],{},[35,114630,244],{},[35,114632,206],{},[35,114634,941],{"mathvariant":209},[35,114636,244],{},[35,114638,213],{},[39,114640,114641],{"encoding":41},"dP\u002FdQ",[15,114643,114645],{"className":114644,"ariaHidden":46},[45],[15,114646,114648,114651,114654,114657,114660,114663],{"className":114647},[50],[15,114649],{"className":114650,"style":139},[54],[15,114652,244],{"className":114653},[59,60],[15,114655,206],{"className":114656,"style":334},[59,60],[15,114658,941],{"className":114659},[59],[15,114661,244],{"className":114662},[59,60],[15,114664,213],{"className":114665},[59,60],"，因此把两个分布同时「搬到别处」值不变。这带来一个根本局限：",[15,114668,114670],{"className":114669,"translate":19},[180],[15,114671,114673,114728],{"className":114672,"translate":19},[18],[15,114674,114676],{"className":114675},[23],[25,114677,114678],{"xmlns":27,"display":189},[29,114679,114680,114725],{},[32,114681,114682,114684,114686,114688,114690,114692,114694,114697,114699,114701,114707,114709,114711,114713,114715,114721,114723],{},[1297,114683,4338],{},[35,114685,206],{},[110,114687,33547],{},[35,114689,213],{},[1297,114691,4283],{},[110,114693,113],{"stretchy":112},[1297,114695,114696],{},"支撑集不重叠，如 ",[35,114698,206],{},[110,114700,123],{},[195,114702,114703,114705],{},[35,114704,15712],{},[115,114706,126],{},[110,114708,551],{"separator":46},[1297,114710,4283],{},[35,114712,213],{},[110,114714,123],{},[195,114716,114717,114719],{},[35,114718,15712],{},[115,114720,117],{},[110,114722,120],{"stretchy":112},[110,114724,551],{"separator":46},[39,114726,114727],{"encoding":41},"\\text{若 } P\\perp Q\\\n(\\text{支撑集不重叠，如 } P=\\delta_0,\\ Q=\\delta_1),",[15,114729,114731,114758,114795,114862],{"className":114730,"ariaHidden":46},[45],[15,114732,114734,114737,114746,114749,114752,114755],{"className":114733},[50],[15,114735],{"className":114736,"style":12597},[54],[15,114738,114740,114743],{"className":114739},[59,4598],[15,114741,4649],{"className":114742},[59,4602],[15,114744,4283],{"className":114745},[59],[15,114747,206],{"className":114748,"style":334},[59,60],[15,114750],{"className":114751,"style":158},[157],[15,114753,33547],{"className":114754},[162],[15,114756],{"className":114757,"style":158},[157],[15,114759,114761,114764,114767,114770,114773,114783,114786,114789,114792],{"className":114760},[50],[15,114762],{"className":114763,"style":139},[54],[15,114765,213],{"className":114766},[59,60],[15,114768,4283],{"className":114769},[157],[15,114771,113],{"className":114772},[146],[15,114774,114776,114780],{"className":114775},[59,4598],[15,114777,114779],{"className":114778},[59,4602],"支撑集不重叠，如",[15,114781,4283],{"className":114782},[59],[15,114784,206],{"className":114785,"style":334},[59,60],[15,114787],{"className":114788,"style":158},[157],[15,114790,123],{"className":114791},[162],[15,114793],{"className":114794,"style":158},[157],[15,114796,114798,114801,114841,114844,114847,114850,114853,114856,114859],{"className":114797},[50],[15,114799],{"className":114800,"style":55},[54],[15,114802,114804,114807],{"className":114803},[59],[15,114805,15712],{"className":114806,"style":15761},[59,60],[15,114808,114810],{"className":114809},[281],[15,114811,114813,114833],{"className":114812},[285,286],[15,114814,114816,114830],{"className":114815},[290],[15,114817,114819],{"className":114818,"style":11133},[294],[15,114820,114821,114824],{"style":94743},[15,114822],{"className":114823,"style":303},[302],[15,114825,114827],{"className":114826},[307,308,309,310],[15,114828,126],{"className":114829},[59,310],[15,114831,318],{"className":114832},[317],[15,114834,114836],{"className":114835},[290],[15,114837,114839],{"className":114838,"style":7968},[294],[15,114840],{},[15,114842,551],{"className":114843},[573],[15,114845,4283],{"className":114846},[157],[15,114848],{"className":114849,"style":406},[157],[15,114851,213],{"className":114852},[59,60],[15,114854],{"className":114855,"style":158},[157],[15,114857,123],{"className":114858},[162],[15,114860],{"className":114861,"style":158},[157],[15,114863,114865,114868,114908,114911],{"className":114864},[50],[15,114866],{"className":114867,"style":139},[54],[15,114869,114871,114874],{"className":114870},[59],[15,114872,15712],{"className":114873,"style":15761},[59,60],[15,114875,114877],{"className":114876},[281],[15,114878,114880,114900],{"className":114879},[285,286],[15,114881,114883,114897],{"className":114882},[290],[15,114884,114886],{"className":114885,"style":11133},[294],[15,114887,114888,114891],{"style":94743},[15,114889],{"className":114890,"style":303},[302],[15,114892,114894],{"className":114893},[307,308,309,310],[15,114895,117],{"className":114896},[59,310],[15,114898,318],{"className":114899},[317],[15,114901,114903],{"className":114902},[290],[15,114904,114906],{"className":114905,"style":7968},[294],[15,114907],{},[15,114909,120],{"className":114910},[153],[15,114912,551],{"className":114913},[573],[15,114915,114917],{"className":114916,"translate":19},[180],[15,114918,114920,114970],{"className":114919,"translate":19},[18],[15,114921,114923],{"className":114922},[23],[25,114924,114925],{"xmlns":27,"display":189},[29,114926,114927,114967],{},[32,114928,114929,114939,114941,114943,114945,114947,114949,114951,114961,114963,114965],{},[195,114930,114931,114933],{},[35,114932,199],{},[32,114934,114935,114937],{},[35,114936,23743],{},[35,114938,25737],{},[110,114940,123],{},[35,114942,4100],{},[110,114944,4103],{},[115,114946,2463],{},[110,114948,551],{"separator":46},[157,114950],{"width":4315},[195,114952,114953,114955],{},[35,114954,199],{},[32,114956,114957,114959],{},[35,114958,5392],{},[35,114960,34850],{},[110,114962,123],{},[115,114964,117],{},[110,114966,551],{"separator":46},[39,114968,114969],{"encoding":41},"D_{JS}=\\log2,\\quad D_{TV}=1,",[15,114971,114973,115034,115115],{"className":114972,"ariaHidden":46},[45],[15,114974,114976,114979,115025,115028,115031],{"className":114975},[50],[15,114977],{"className":114978,"style":15961},[54],[15,114980,114982,114985],{"className":114981},[59],[15,114983,199],{"className":114984,"style":277},[59,60],[15,114986,114988],{"className":114987},[281],[15,114989,114991,115017],{"className":114990},[285,286],[15,114992,114994,115014],{"className":114993},[290],[15,114995,114997],{"className":114996,"style":379},[294],[15,114998,114999,115002],{"style":298},[15,115000],{"className":115001,"style":303},[302],[15,115003,115005],{"className":115004},[307,308,309,310],[15,115006,115008,115011],{"className":115007},[59,310],[15,115009,23743],{"className":115010,"style":24153},[59,60,310],[15,115012,25737],{"className":115013,"style":25861},[59,60,310],[15,115015,318],{"className":115016},[317],[15,115018,115020],{"className":115019},[290],[15,115021,115023],{"className":115022,"style":7968},[294],[15,115024],{},[15,115026],{"className":115027,"style":158},[157],[15,115029,123],{"className":115030},[162],[15,115032],{"className":115033,"style":158},[157],[15,115035,115037,115040,115045,115048,115051,115054,115057,115060,115106,115109,115112],{"className":115036},[50],[15,115038],{"className":115039,"style":55},[54],[15,115041,4154,115043],{"className":115042},[1484],[15,115044,4158],{"style":4157},[15,115046],{"className":115047,"style":406},[157],[15,115049,2463],{"className":115050},[59],[15,115052,551],{"className":115053},[573],[15,115055],{"className":115056,"style":87968},[157],[15,115058],{"className":115059,"style":406},[157],[15,115061,115063,115066],{"className":115062},[59],[15,115064,199],{"className":115065,"style":277},[59,60],[15,115067,115069],{"className":115068},[281],[15,115070,115072,115098],{"className":115071},[285,286],[15,115073,115075,115095],{"className":115074},[290],[15,115076,115078],{"className":115077,"style":379},[294],[15,115079,115080,115083],{"style":298},[15,115081],{"className":115082,"style":303},[302],[15,115084,115086],{"className":115085},[307,308,309,310],[15,115087,115089,115092],{"className":115088},[59,310],[15,115090,5392],{"className":115091,"style":334},[59,60,310],[15,115093,34850],{"className":115094,"style":2587},[59,60,310],[15,115096,318],{"className":115097},[317],[15,115099,115101],{"className":115100},[290],[15,115102,115104],{"className":115103,"style":7968},[294],[15,115105],{},[15,115107],{"className":115108,"style":158},[157],[15,115110,123],{"className":115111},[162],[15,115113],{"className":115114,"style":158},[157],[15,115116,115118,115121,115124],{"className":115117},[50],[15,115119],{"className":115120,"style":9358},[54],[15,115122,117],{"className":115123},[59],[15,115125,551],{"className":115126},[573],[11,115128,115129,115130,115133,115134,115198,115199,115249,115250,9400],{},"也就是说，f-散度在支撑分离时",[1225,115131,115132],{},"饱和到常数上界，对生成器参数的微小改动失去梯度","：因为被积分的量 ",[15,115135,115137,115165],{"className":115136,"translate":19},[18],[15,115138,115140],{"className":115139},[23],[25,115141,115142],{"xmlns":27},[29,115143,115144,115162],{},[32,115145,115146,115148,115150,115152,115154,115156,115158,115160],{},[35,115147,944],{},[1297,115149,1299],{},[35,115151,37],{},[110,115153,113],{"stretchy":112},[35,115155,11],{},[35,115157,941],{"mathvariant":209},[35,115159,944],{},[110,115161,120],{"stretchy":112},[39,115163,115164],{"encoding":41},"q\\,f(p\u002Fq)",[15,115166,115168],{"className":115167,"ariaHidden":46},[45],[15,115169,115171,115174,115177,115180,115183,115186,115189,115192,115195],{"className":115170},[50],[15,115172],{"className":115173,"style":139},[54],[15,115175,944],{"className":115176,"style":981},[59,60],[15,115178],{"className":115179,"style":406},[157],[15,115181,37],{"className":115182,"style":61},[59,60],[15,115184,113],{"className":115185},[146],[15,115187,11],{"className":115188},[59,60],[15,115190,941],{"className":115191},[59],[15,115193,944],{"className":115194,"style":981},[59,60],[15,115196,120],{"className":115197},[153]," 只在 ",[15,115200,115202,115219],{"className":115201,"translate":19},[18],[15,115203,115205],{"className":115204},[23],[25,115206,115207],{"xmlns":27},[29,115208,115209,115217],{},[32,115210,115211,115213,115215],{},[35,115212,944],{},[110,115214,2903],{},[115,115216,126],{},[39,115218,31682],{"encoding":41},[15,115220,115222,115240],{"className":115221,"ariaHidden":46},[45],[15,115223,115225,115228,115231,115234,115237],{"className":115224},[50],[15,115226],{"className":115227,"style":31692},[54],[15,115229,944],{"className":115230,"style":981},[59,60],[15,115232],{"className":115233,"style":158},[157],[15,115235,2903],{"className":115236},[162],[15,115238],{"className":115239,"style":158},[157],[15,115241,115243,115246],{"className":115242},[50],[15,115244],{"className":115245,"style":172},[54],[15,115247,126],{"className":115248},[59]," 处有定义，当两个支撑几乎不重叠时，极小化散度的博弈只剩\"常数项 − 常数项\"，梯度信息全部丢失（这正是原 GAN 训练崩溃的理论根源）。Wasserstein 距离与 MMD 属于另一族——",[1225,115251,115252],{},"积分概率度量",[15,115254,115256],{"className":115255,"translate":19},[180],[15,115257,115259,115334],{"className":115258,"translate":19},[18],[15,115260,115262],{"className":115261},[23],[25,115263,115264],{"xmlns":27,"display":189},[29,115265,115266,115331],{},[32,115267,115268,115275,115277,115279,115281,115283,115285,115287,115303,115305,115307,115309,115311,115313,115315,115317,115319,115321,115323,115325,115327,115329],{},[195,115269,115270,115273],{},[1297,115271,115272],{},"IPM",[35,115274,36883],{"mathvariant":597},[110,115276,113],{"stretchy":112},[35,115278,206],{},[110,115280,551],{"separator":46},[35,115282,213],{},[110,115284,120],{"stretchy":112},[110,115286,123],{},[6016,115288,115289,115295],{},[32,115290,115291,115293],{},[35,115292,35432],{},[110,115294,4103],{},[32,115296,115297,115299,115301],{},[35,115298,38665],{},[110,115300,5909],{},[35,115302,36883],{"mathvariant":597},[110,115304,4808],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,115306,1287],{},[35,115308,38665],{},[1297,115310,1299],{},[35,115312,244],{},[35,115314,206],{},[110,115316,4813],{},[110,115318,1287],{},[35,115320,38665],{},[1297,115322,1299],{},[35,115324,244],{},[35,115326,213],{},[110,115328,4808],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[35,115330,4375],{"mathvariant":209},[39,115332,115333],{"encoding":41},"\\text{IPM}_{\\mathcal F}(P,Q)\n=\\sup_{h\\in\\mathcal F}\\Big|\\int h\\,dP\n-\\int h\\,dQ\\Big| .",[15,115335,115337,115417,115550],{"className":115336,"ariaHidden":46},[45],[15,115338,115340,115343,115390,115393,115396,115399,115402,115405,115408,115411,115414],{"className":115339},[50],[15,115341],{"className":115342,"style":139},[54],[15,115344,115346,115352],{"className":115345},[59],[15,115347,115349],{"className":115348},[59,4598],[15,115350,115272],{"className":115351},[59],[15,115353,115355],{"className":115354},[281],[15,115356,115358,115382],{"className":115357},[285,286],[15,115359,115361,115379],{"className":115360},[290],[15,115362,115364],{"className":115363,"style":379},[294],[15,115365,115366,115369],{"style":52446},[15,115367],{"className":115368,"style":303},[302],[15,115370,115372],{"className":115371},[307,308,309,310],[15,115373,115375],{"className":115374},[59,310],[15,115376,36883],{"className":115377,"style":115378},[59,624,310],"margin-right:0.0993em;",[15,115380,318],{"className":115381},[317],[15,115383,115385],{"className":115384},[290],[15,115386,115388],{"className":115387,"style":7968},[294],[15,115389],{},[15,115391,113],{"className":115392},[146],[15,115394,206],{"className":115395,"style":334},[59,60],[15,115397,551],{"className":115398},[573],[15,115400],{"className":115401,"style":406},[157],[15,115403,213],{"className":115404},[59,60],[15,115406,120],{"className":115407},[153],[15,115409],{"className":115410,"style":158},[157],[15,115412,123],{"className":115413},[162],[15,115415],{"className":115416,"style":158},[157],[15,115418,115420,115424,115477,115480,115520,115523,115526,115529,115532,115535,115538,115541,115544,115547],{"className":115419},[50],[15,115421],{"className":115422,"style":115423},[54],"height:2.3339em;vertical-align:-0.9739em;",[15,115425,115427],{"className":115426},[1484,13716],[15,115428,115430,115469],{"className":115429},[285,286],[15,115431,115433,115466],{"className":115432},[290],[15,115434,115436,115456],{"className":115435,"style":2345},[294],[15,115437,115438,115441],{"style":51706},[15,115439],{"className":115440,"style":461},[302],[15,115442,115444],{"className":115443},[307,308,309,310],[15,115445,115447,115450,115453],{"className":115446},[59,310],[15,115448,38665],{"className":115449},[59,60,310],[15,115451,5909],{"className":115452},[162,310],[15,115454,36883],{"className":115455,"style":115378},[59,624,310],[15,115457,115458,115461],{"style":11863},[15,115459],{"className":115460,"style":461},[302],[15,115462,115463],{},[15,115464,35432],{"className":115465},[1484],[15,115467,318],{"className":115468},[317],[15,115470,115472],{"className":115471},[290],[15,115473,115475],{"className":115474,"style":51750},[294],[15,115476],{},[15,115478],{"className":115479,"style":406},[157],[15,115481,115483],{"className":115482},[59],[15,115484,115486],{"className":115485},[419,14829],[15,115487,115489,115512],{"className":115488},[285,286],[15,115490,115492,115509],{"className":115491},[290],[15,115493,115495],{"className":115494,"style":85515},[294],[15,115496,115497,115500],{"style":73524},[15,115498],{"className":115499,"style":82587},[302],[15,115501,115503],{"style":115502},"width:0.333em;height:1.8em;",[6323,115504,115506],{"xmlns":6325,"width":35051,"height":17439,"viewBox":115505},"0 0 333 1800",[6331,115507],{"d":115508},"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",[15,115510,318],{"className":115511},[317],[15,115513,115515],{"className":115514},[290],[15,115516,115518],{"className":115517,"style":85539},[294],[15,115519],{},[15,115521],{"className":115522,"style":406},[157],[15,115524,1287],{"className":115525,"style":1487},[1484,1485,1486],[15,115527],{"className":115528,"style":406},[157],[15,115530,38665],{"className":115531},[59,60],[15,115533],{"className":115534,"style":406},[157],[15,115536,244],{"className":115537},[59,60],[15,115539,206],{"className":115540,"style":334},[59,60],[15,115542],{"className":115543,"style":2587},[157],[15,115545,4813],{"className":115546},[2591],[15,115548],{"className":115549,"style":2587},[157],[15,115551,115553,115556,115559,115562,115565,115568,115571,115574,115611],{"className":115552},[50],[15,115554],{"className":115555,"style":5777},[54],[15,115557,1287],{"className":115558,"style":1487},[1484,1485,1486],[15,115560],{"className":115561,"style":406},[157],[15,115563,38665],{"className":115564},[59,60],[15,115566],{"className":115567,"style":406},[157],[15,115569,244],{"className":115570},[59,60],[15,115572,213],{"className":115573},[59,60],[15,115575,115577],{"className":115576},[59],[15,115578,115580],{"className":115579},[419,14829],[15,115581,115583,115603],{"className":115582},[285,286],[15,115584,115586,115600],{"className":115585},[290],[15,115587,115589],{"className":115588,"style":85515},[294],[15,115590,115591,115594],{"style":73524},[15,115592],{"className":115593,"style":82587},[302],[15,115595,115596],{"style":115502},[6323,115597,115598],{"xmlns":6325,"width":35051,"height":17439,"viewBox":115505},[6331,115599],{"d":115508},[15,115601,318],{"className":115602},[317],[15,115604,115606],{"className":115605},[290],[15,115607,115609],{"className":115608,"style":85539},[294],[15,115610],{},[15,115612,4375],{"className":115613},[59],[11,115615,115616,115617,115646,115647,115698,115699,115728,115729,115779,115780,115808,115809,115859,115860,115888],{},"它们比较的是「在函数类 ",[15,115618,115620,115634],{"className":115619,"translate":19},[18],[15,115621,115623],{"className":115622},[23],[25,115624,115625],{"xmlns":27},[29,115626,115627,115631],{},[32,115628,115629],{},[35,115630,36883],{"mathvariant":597},[39,115632,115633],{"encoding":41},"\\mathcal F",[15,115635,115637],{"className":115636,"ariaHidden":46},[45],[15,115638,115640,115643],{"className":115639},[50],[15,115641],{"className":115642,"style":664},[54],[15,115644,36883],{"className":115645,"style":115378},[59,624]," 上积分的差」，而不是似然比，因此利用了样本空间的度量\u002F几何结构。KS 距离（",[15,115648,115650,115668],{"className":115649,"translate":19},[18],[15,115651,115653],{"className":115652},[23],[25,115654,115655],{"xmlns":27},[29,115656,115657,115665],{},[32,115658,115659,115661,115663],{},[35,115660,36883],{"mathvariant":597},[110,115662,123],{},[110,115664,2898],{"stretchy":112},[39,115666,115667],{"encoding":41},"\\mathcal F=\\{",[15,115669,115671,115689],{"className":115670,"ariaHidden":46},[45],[15,115672,115674,115677,115680,115683,115686],{"className":115673},[50],[15,115675],{"className":115676,"style":664},[54],[15,115678,36883],{"className":115679,"style":115378},[59,624],[15,115681],{"className":115682,"style":158},[157],[15,115684,123],{"className":115685},[162],[15,115687],{"className":115688,"style":158},[157],[15,115690,115692,115695],{"className":115691},[50],[15,115693],{"className":115694,"style":139},[54],[15,115696,2898],{"className":115697},[146],"一维区间指示函数",[15,115700,115702,115716],{"className":115701,"translate":19},[18],[15,115703,115705],{"className":115704},[23],[25,115706,115707],{"xmlns":27},[29,115708,115709,115713],{},[32,115710,115711],{},[110,115712,2908],{"stretchy":112},[39,115714,115715],{"encoding":41},"\\}",[15,115717,115719],{"className":115718,"ariaHidden":46},[45],[15,115720,115722,115725],{"className":115721},[50],[15,115723],{"className":115724,"style":139},[54],[15,115726,2908],{"className":115727},[153],"）、Wasserstein（",[15,115730,115732,115749],{"className":115731,"translate":19},[18],[15,115733,115735],{"className":115734},[23],[25,115736,115737],{"xmlns":27},[29,115738,115739,115747],{},[32,115740,115741,115743,115745],{},[35,115742,36883],{"mathvariant":597},[110,115744,123],{},[110,115746,2898],{"stretchy":112},[39,115748,115667],{"encoding":41},[15,115750,115752,115770],{"className":115751,"ariaHidden":46},[45],[15,115753,115755,115758,115761,115764,115767],{"className":115754},[50],[15,115756],{"className":115757,"style":664},[54],[15,115759,36883],{"className":115760,"style":115378},[59,624],[15,115762],{"className":115763,"style":158},[157],[15,115765,123],{"className":115766},[162],[15,115768],{"className":115769,"style":158},[157],[15,115771,115773,115776],{"className":115772},[50],[15,115774],{"className":115775,"style":139},[54],[15,115777,2898],{"className":115778},[146],"1-Lipschitz 函数",[15,115781,115783,115796],{"className":115782,"translate":19},[18],[15,115784,115786],{"className":115785},[23],[25,115787,115788],{"xmlns":27},[29,115789,115790,115794],{},[32,115791,115792],{},[110,115793,2908],{"stretchy":112},[39,115795,115715],{"encoding":41},[15,115797,115799],{"className":115798,"ariaHidden":46},[45],[15,115800,115802,115805],{"className":115801},[50],[15,115803],{"className":115804,"style":139},[54],[15,115806,2908],{"className":115807},[153],"）、MMD（",[15,115810,115812,115829],{"className":115811,"translate":19},[18],[15,115813,115815],{"className":115814},[23],[25,115816,115817],{"xmlns":27},[29,115818,115819,115827],{},[32,115820,115821,115823,115825],{},[35,115822,36883],{"mathvariant":597},[110,115824,123],{},[110,115826,2898],{"stretchy":112},[39,115828,115667],{"encoding":41},[15,115830,115832,115850],{"className":115831,"ariaHidden":46},[45],[15,115833,115835,115838,115841,115844,115847],{"className":115834},[50],[15,115836],{"className":115837,"style":664},[54],[15,115839,36883],{"className":115840,"style":115378},[59,624],[15,115842],{"className":115843,"style":158},[157],[15,115845,123],{"className":115846},[162],[15,115848],{"className":115849,"style":158},[157],[15,115851,115853,115856],{"className":115852},[50],[15,115854],{"className":115855,"style":139},[54],[15,115857,2898],{"className":115858},[146],"RKHS 单位球",[15,115861,115863,115876],{"className":115862,"translate":19},[18],[15,115864,115866],{"className":115865},[23],[25,115867,115868],{"xmlns":27},[29,115869,115870,115874],{},[32,115871,115872],{},[110,115873,2908],{"stretchy":112},[39,115875,115715],{"encoding":41},[15,115877,115879],{"className":115878,"ariaHidden":46},[45],[15,115880,115882,115885],{"className":115881},[50],[15,115883],{"className":115884,"style":139},[54],[15,115886,2908],{"className":115887},[153],"）都是 IPM。上面对 f-散度的变分表示其实是「带惩罚的 IPM」：",[15,115890,115892],{"className":115891,"translate":19},[180],[15,115893,115895,115977],{"className":115894,"translate":19},[18],[15,115896,115898],{"className":115897},[23],[25,115899,115900],{"xmlns":27,"display":189},[29,115901,115902,115974],{},[32,115903,115904,115910,115912,115914,115916,115918,115920,115922,115932,115934,115940,115942,115944,115946,115948,115954,115956,115962,115964,115966,115968,115970,115972],{},[195,115905,115906,115908],{},[35,115907,199],{},[35,115909,37],{},[110,115911,113],{"stretchy":112},[35,115913,206],{},[35,115915,210],{"mathvariant":209},[35,115917,213],{},[110,115919,120],{"stretchy":112},[110,115921,123],{},[6016,115923,115924,115930],{},[32,115925,115926,115928],{},[35,115927,35432],{},[110,115929,4103],{},[35,115931,4158],{},[110,115933,2898],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[195,115935,115936,115938],{},[35,115937,223],{"mathvariant":222},[35,115939,206],{},[110,115941,230],{"stretchy":112},[35,115943,4158],{},[110,115945,257],{"stretchy":112},[110,115947,4813],{},[195,115949,115950,115952],{},[35,115951,223],{"mathvariant":222},[35,115953,213],{},[110,115955,230],{"stretchy":112},[6814,115957,115958,115960],{},[35,115959,37],{},[110,115961,7573],{},[110,115963,113],{"stretchy":112},[35,115965,4158],{},[110,115967,120],{"stretchy":112},[110,115969,257],{"stretchy":112},[110,115971,2908],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,115973,551],{"separator":46},[39,115975,115976],{"encoding":41},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\Big\\},",[15,115978,115980,116050,116170],{"className":115979,"ariaHidden":46},[45],[15,115981,115983,115986,116026,116029,116032,116035,116038,116041,116044,116047],{"className":115982},[50],[15,115984],{"className":115985,"style":270},[54],[15,115987,115989,115992],{"className":115988},[59],[15,115990,199],{"className":115991,"style":277},[59,60],[15,115993,115995],{"className":115994},[281],[15,115996,115998,116018],{"className":115997},[285,286],[15,115999,116001,116015],{"className":116000},[290],[15,116002,116004],{"className":116003,"style":295},[294],[15,116005,116006,116009],{"style":298},[15,116007],{"className":116008,"style":303},[302],[15,116010,116012],{"className":116011},[307,308,309,310],[15,116013,37],{"className":116014,"style":61},[59,60,310],[15,116016,318],{"className":116017},[317],[15,116019,116021],{"className":116020},[290],[15,116022,116024],{"className":116023,"style":325},[294],[15,116025],{},[15,116027,113],{"className":116028},[146],[15,116030,206],{"className":116031,"style":334},[59,60],[15,116033,210],{"className":116034},[59],[15,116036,213],{"className":116037},[59,60],[15,116039,120],{"className":116040},[153],[15,116042],{"className":116043,"style":158},[157],[15,116045,123],{"className":116046},[162],[15,116048],{"className":116049,"style":158},[157],[15,116051,116053,116056,116103,116106,116112,116152,116155,116158,116161,116164,116167],{"className":116052},[50],[15,116054],{"className":116055,"style":99485},[54],[15,116057,116059],{"className":116058},[1484,13716],[15,116060,116062,116095],{"className":116061},[285,286],[15,116063,116065,116092],{"className":116064},[290],[15,116066,116068,116082],{"className":116067,"style":2345},[294],[15,116069,116070,116073],{"style":61190},[15,116071],{"className":116072,"style":461},[302],[15,116074,116076],{"className":116075},[307,308,309,310],[15,116077,116079],{"className":116078},[59,310],[15,116080,4158],{"className":116081,"style":981},[59,60,310],[15,116083,116084,116087],{"style":11863},[15,116085],{"className":116086,"style":461},[302],[15,116088,116089],{},[15,116090,35432],{"className":116091},[1484],[15,116093,318],{"className":116094},[317],[15,116096,116098],{"className":116097},[290],[15,116099,116101],{"className":116100,"style":61222},[294],[15,116102],{},[15,116104],{"className":116105,"style":406},[157],[15,116107,116109],{"className":116108},[59],[15,116110,2898],{"className":116111},[419,3720],[15,116113,116115,116118],{"className":116114},[59],[15,116116,223],{"className":116117},[59,366],[15,116119,116121],{"className":116120},[281],[15,116122,116124,116144],{"className":116123},[285,286],[15,116125,116127,116141],{"className":116126},[290],[15,116128,116130],{"className":116129,"style":379},[294],[15,116131,116132,116135],{"style":382},[15,116133],{"className":116134,"style":303},[302],[15,116136,116138],{"className":116137},[307,308,309,310],[15,116139,206],{"className":116140,"style":334},[59,60,310],[15,116142,318],{"className":116143},[317],[15,116145,116147],{"className":116146},[290],[15,116148,116150],{"className":116149,"style":7968},[294],[15,116151],{},[15,116153,230],{"className":116154},[146],[15,116156,4158],{"className":116157,"style":981},[59,60],[15,116159,257],{"className":116160},[153],[15,116162],{"className":116163,"style":2587},[157],[15,116165,4813],{"className":116166},[2591],[15,116168],{"className":116169,"style":2587},[157],[15,116171,116173,116176,116216,116219,116248,116251,116254,116257,116263],{"className":116172},[50],[15,116174],{"className":116175,"style":68117},[54],[15,116177,116179,116182],{"className":116178},[59],[15,116180,223],{"className":116181},[59,366],[15,116183,116185],{"className":116184},[281],[15,116186,116188,116208],{"className":116187},[285,286],[15,116189,116191,116205],{"className":116190},[290],[15,116192,116194],{"className":116193,"style":379},[294],[15,116195,116196,116199],{"style":382},[15,116197],{"className":116198,"style":303},[302],[15,116200,116202],{"className":116201},[307,308,309,310],[15,116203,213],{"className":116204},[59,60,310],[15,116206,318],{"className":116207},[317],[15,116209,116211],{"className":116210},[290],[15,116212,116214],{"className":116213,"style":325},[294],[15,116215],{},[15,116217,230],{"className":116218},[146],[15,116220,116222,116225],{"className":116221},[59],[15,116223,37],{"className":116224,"style":61},[59,60],[15,116226,116228],{"className":116227},[281],[15,116229,116231],{"className":116230},[285],[15,116232,116234],{"className":116233},[290],[15,116235,116237],{"className":116236,"style":8248},[294],[15,116238,116239,116242],{"style":8277},[15,116240],{"className":116241,"style":303},[302],[15,116243,116245],{"className":116244},[307,308,309,310],[15,116246,7573],{"className":116247},[2591,310],[15,116249,113],{"className":116250},[146],[15,116252,4158],{"className":116253,"style":981},[59,60],[15,116255,20390],{"className":116256},[153],[15,116258,116260],{"className":116259},[59],[15,116261,2908],{"className":116262},[419,3720],[15,116264,551],{"className":116265},[573],[11,116267,116268,116269,116343,116344,116386],{},"它的被估计量是 ",[15,116270,116272,116296],{"className":116271,"translate":19},[18],[15,116273,116275],{"className":116274},[23],[25,116276,116277],{"xmlns":27},[29,116278,116279,116293],{},[32,116280,116281,116287,116289,116291],{},[6814,116282,116283,116285],{},[35,116284,37],{},[110,116286,7573],{},[110,116288,113],{"stretchy":112},[35,116290,4158],{},[110,116292,120],{"stretchy":112},[39,116294,116295],{"encoding":41},"f^*(g)",[15,116297,116299],{"className":116298,"ariaHidden":46},[45],[15,116300,116302,116305,116334,116337,116340],{"className":116301},[50],[15,116303],{"className":116304,"style":139},[54],[15,116306,116308,116311],{"className":116307},[59],[15,116309,37],{"className":116310,"style":61},[59,60],[15,116312,116314],{"className":116313},[281],[15,116315,116317],{"className":116316},[285],[15,116318,116320],{"className":116319},[290],[15,116321,116323],{"className":116322,"style":8499},[294],[15,116324,116325,116328],{"style":6865},[15,116326],{"className":116327,"style":303},[302],[15,116329,116331],{"className":116330},[307,308,309,310],[15,116332,7573],{"className":116333},[2591,310],[15,116335,113],{"className":116336},[146],[15,116338,4158],{"className":116339,"style":981},[59,60],[15,116341,120],{"className":116342},[153],"，而不是 ",[15,116345,116347,116365],{"className":116346,"translate":19},[18],[15,116348,116350],{"className":116349},[23],[25,116351,116352],{"xmlns":27},[29,116353,116354,116362],{},[32,116355,116356,116358,116360],{},[35,116357,4808],{"mathvariant":209},[110,116359,3299],{"lspace":1247,"rspace":1247},[35,116361,4808],{"mathvariant":209},[39,116363,116364],{"encoding":41},"|{\\cdot}|",[15,116366,116368],{"className":116367,"ariaHidden":46},[45],[15,116369,116371,116374,116377,116383],{"className":116370},[50],[15,116372],{"className":116373,"style":139},[54],[15,116375,4808],{"className":116376},[59],[15,116378,116380],{"className":116379},[59],[15,116381,3299],{"className":116382},[59],[15,116384,4808],{"className":116385},[59],"，所以是「非对称 IPM」。",[11,116388,116389,116391],{},[1225,116390,6493],{}," Wasserstein\u002FMMD 不是 f-散度，也不能写成 f-散度；它们的关键区别在于是否利用几何、是否在支撑分离时仍给梯度、以及是否满足数据处理不等式（Wasserstein 一般不满足数据处理不等式，因为传输方案可以随条件分布\"重新安排\"质量；MMD 由核特征映射的条件期望是收缩算子，沿核的具体结构可证其满足数据处理不等式）。",[2311,116393,116395],{"id":116394},"_63-支撑不重叠的极限","6.3 支撑不重叠的极限",[52492,116397,116398,116478],{},[52495,116399,116400],{},[52498,116401,116402,116405,116407,116409,116411,116413,116473,116475],{},[52501,116403,116404],{},"情形",[52501,116406,32663],{},[52501,116408,108859],{},[52501,116410,53124],{},[52501,116412,86762],{},[52501,116414,116415],{},[15,116416,116418,116435],{"className":116417,"translate":19},[18],[15,116419,116421],{"className":116420},[23],[25,116422,116423],{"xmlns":27},[29,116424,116425,116433],{},[32,116426,116427],{},[6814,116428,116429,116431],{},[35,116430,37449],{},[115,116432,2463],{},[39,116434,40394],{"encoding":41},[15,116436,116438],{"className":116437,"ariaHidden":46},[45],[15,116439,116441,116444],{"className":116440},[50],[15,116442],{"className":116443,"style":40404},[54],[15,116445,116447,116450],{"className":116446},[59],[15,116448,37449],{"className":116449},[59,60],[15,116451,116453],{"className":116452},[281],[15,116454,116456],{"className":116455},[285],[15,116457,116459],{"className":116458},[290],[15,116460,116462],{"className":116461,"style":20028},[294],[15,116463,116464,116467],{"style":6865},[15,116465],{"className":116466,"style":303},[302],[15,116468,116470],{"className":116469},[307,308,309,310],[15,116471,2463],{"className":116472},[59,310],[52501,116474,105173],{},[52501,116476,116477],{},"Wasserstein",[52590,116479,116480,116890],{},[52498,116481,116482,116653,116688,116723,116765,116795,116830,116860],{},[52595,116483,116484,116652],{},[15,116485,116487,116521],{"className":116486,"translate":19},[18],[15,116488,116490],{"className":116489},[23],[25,116491,116492],{"xmlns":27},[29,116493,116494,116518],{},[32,116495,116496,116498,116500,116506,116508,116510,116512],{},[35,116497,206],{},[110,116499,123],{},[195,116501,116502,116504],{},[35,116503,15712],{},[115,116505,126],{},[110,116507,551],{"separator":46},[35,116509,213],{},[110,116511,123],{},[195,116513,116514,116516],{},[35,116515,15712],{},[115,116517,117],{},[39,116519,116520],{"encoding":41},"P=\\delta_0,Q=\\delta_1",[15,116522,116524,116542,116606],{"className":116523,"ariaHidden":46},[45],[15,116525,116527,116530,116533,116536,116539],{"className":116526},[50],[15,116528],{"className":116529,"style":664},[54],[15,116531,206],{"className":116532,"style":334},[59,60],[15,116534],{"className":116535,"style":158},[157],[15,116537,123],{"className":116538},[162],[15,116540],{"className":116541,"style":158},[157],[15,116543,116545,116548,116588,116591,116594,116597,116600,116603],{"className":116544},[50],[15,116546],{"className":116547,"style":55},[54],[15,116549,116551,116554],{"className":116550},[59],[15,116552,15712],{"className":116553,"style":15761},[59,60],[15,116555,116557],{"className":116556},[281],[15,116558,116560,116580],{"className":116559},[285,286],[15,116561,116563,116577],{"className":116562},[290],[15,116564,116566],{"className":116565,"style":11133},[294],[15,116567,116568,116571],{"style":94743},[15,116569],{"className":116570,"style":303},[302],[15,116572,116574],{"className":116573},[307,308,309,310],[15,116575,126],{"className":116576},[59,310],[15,116578,318],{"className":116579},[317],[15,116581,116583],{"className":116582},[290],[15,116584,116586],{"className":116585,"style":7968},[294],[15,116587],{},[15,116589,551],{"className":116590},[573],[15,116592],{"className":116593,"style":406},[157],[15,116595,213],{"className":116596},[59,60],[15,116598],{"className":116599,"style":158},[157],[15,116601,123],{"className":116602},[162],[15,116604],{"className":116605,"style":158},[157],[15,116607,116609,116612],{"className":116608},[50],[15,116610],{"className":116611,"style":11474},[54],[15,116613,116615,116618],{"className":116614},[59],[15,116616,15712],{"className":116617,"style":15761},[59,60],[15,116619,116621],{"className":116620},[281],[15,116622,116624,116644],{"className":116623},[285,286],[15,116625,116627,116641],{"className":116626},[290],[15,116628,116630],{"className":116629,"style":11133},[294],[15,116631,116632,116635],{"style":94743},[15,116633],{"className":116634,"style":303},[302],[15,116636,116638],{"className":116637},[307,308,309,310],[15,116639,117],{"className":116640},[59,310],[15,116642,318],{"className":116643},[317],[15,116645,116647],{"className":116646},[290],[15,116648,116650],{"className":116649,"style":7968},[294],[15,116651],{},"（约）",[52595,116654,116655],{},[15,116656,116658,116673],{"className":116657,"translate":19},[18],[15,116659,116661],{"className":116660},[23],[25,116662,116663],{"xmlns":27},[29,116664,116665,116671],{},[32,116666,116667,116669],{},[110,116668,2470],{},[35,116670,1024],{"mathvariant":209},[39,116672,4241],{"encoding":41},[15,116674,116676],{"className":116675,"ariaHidden":46},[45],[15,116677,116679,116682,116685],{"className":116678},[50],[15,116680],{"className":116681,"style":4251},[54],[15,116683,2470],{"className":116684},[59],[15,116686,1024],{"className":116687},[59],[52595,116689,116690],{},[15,116691,116693,116708],{"className":116692,"translate":19},[18],[15,116694,116696],{"className":116695},[23],[25,116697,116698],{"xmlns":27},[29,116699,116700,116706],{},[32,116701,116702,116704],{},[110,116703,2470],{},[35,116705,1024],{"mathvariant":209},[39,116707,4241],{"encoding":41},[15,116709,116711],{"className":116710,"ariaHidden":46},[45],[15,116712,116714,116717,116720],{"className":116713},[50],[15,116715],{"className":116716,"style":4251},[54],[15,116718,2470],{"className":116719},[59],[15,116721,1024],{"className":116722},[59],[52595,116724,116725],{},[15,116726,116728,116745],{"className":116727,"translate":19},[18],[15,116729,116731],{"className":116730},[23],[25,116732,116733],{"xmlns":27},[29,116734,116735,116743],{},[32,116736,116737,116739,116741],{},[35,116738,4100],{},[110,116740,4103],{},[115,116742,2463],{},[39,116744,34485],{"encoding":41},[15,116746,116748],{"className":116747,"ariaHidden":46},[45],[15,116749,116751,116754,116759,116762],{"className":116750},[50],[15,116752],{"className":116753,"style":55},[54],[15,116755,4154,116757],{"className":116756},[1484],[15,116758,4158],{"style":4157},[15,116760],{"className":116761,"style":406},[157],[15,116763,2463],{"className":116764},[59],[52595,116766,116767],{},[15,116768,116770,116783],{"className":116769,"translate":19},[18],[15,116771,116773],{"className":116772},[23],[25,116774,116775],{"xmlns":27},[29,116776,116777,116781],{},[32,116778,116779],{},[115,116780,117],{},[39,116782,117],{"encoding":41},[15,116784,116786],{"className":116785,"ariaHidden":46},[45],[15,116787,116789,116792],{"className":116788},[50],[15,116790],{"className":116791,"style":172},[54],[15,116793,117],{"className":116794},[59],[52595,116796,116797],{},[15,116798,116800,116815],{"className":116799,"translate":19},[18],[15,116801,116803],{"className":116802},[23],[25,116804,116805],{"xmlns":27},[29,116806,116807,116813],{},[32,116808,116809,116811],{},[110,116810,2470],{},[35,116812,1024],{"mathvariant":209},[39,116814,4241],{"encoding":41},[15,116816,116818],{"className":116817,"ariaHidden":46},[45],[15,116819,116821,116824,116827],{"className":116820},[50],[15,116822],{"className":116823,"style":4251},[54],[15,116825,2470],{"className":116826},[59],[15,116828,1024],{"className":116829},[59],[52595,116831,116832],{},[15,116833,116835,116848],{"className":116834,"translate":19},[18],[15,116836,116838],{"className":116837},[23],[25,116839,116840],{"xmlns":27},[29,116841,116842,116846],{},[32,116843,116844],{},[115,116845,2463],{},[39,116847,2463],{"encoding":41},[15,116849,116851],{"className":116850,"ariaHidden":46},[45],[15,116852,116854,116857],{"className":116853},[50],[15,116855],{"className":116856,"style":172},[54],[15,116858,2463],{"className":116859},[59],[52595,116861,116862],{},[15,116863,116865,116878],{"className":116864,"translate":19},[18],[15,116866,116868],{"className":116867},[23],[25,116869,116870],{"xmlns":27},[29,116871,116872,116876],{},[32,116873,116874],{},[115,116875,117],{},[39,116877,117],{"encoding":41},[15,116879,116881],{"className":116880,"ariaHidden":46},[45],[15,116882,116884,116887],{"className":116883},[50],[15,116885],{"className":116886,"style":172},[54],[15,116888,117],{"className":116889},[59],[52498,116891,116892,117037,117083,117127,117185,117230,117343,117388],{},[52595,116893,116894],{},[15,116895,116897,116944],{"className":116896,"translate":19},[18],[15,116898,116900],{"className":116899},[23],[25,116901,116902],{"xmlns":27},[29,116903,116904,116941],{},[32,116905,116906,116908,116910,116912,116914,116916,116918,116920,116922,116924,116926,116928,116930,116932,116935,116937,116939],{},[35,116907,206],{},[110,116909,123],{},[35,116911,38284],{},[110,116913,113],{"stretchy":112},[115,116915,126],{},[110,116917,551],{"separator":46},[115,116919,117],{},[110,116921,120],{"stretchy":112},[110,116923,551],{"separator":46},[35,116925,213],{},[110,116927,123],{},[35,116929,38284],{},[110,116931,113],{"stretchy":112},[115,116933,116934],{},"100",[110,116936,551],{"separator":46},[115,116938,117],{},[110,116940,120],{"stretchy":112},[39,116942,116943],{"encoding":41},"P=N(0,1),Q=N(100,1)",[15,116945,116947,116965,117010],{"className":116946,"ariaHidden":46},[45],[15,116948,116950,116953,116956,116959,116962],{"className":116949},[50],[15,116951],{"className":116952,"style":664},[54],[15,116954,206],{"className":116955,"style":334},[59,60],[15,116957],{"className":116958,"style":158},[157],[15,116960,123],{"className":116961},[162],[15,116963],{"className":116964,"style":158},[157],[15,116966,116968,116971,116974,116977,116980,116983,116986,116989,116992,116995,116998,117001,117004,117007],{"className":116967},[50],[15,116969],{"className":116970,"style":139},[54],[15,116972,38284],{"className":116973,"style":25601},[59,60],[15,116975,113],{"className":116976},[146],[15,116978,126],{"className":116979},[59],[15,116981,551],{"className":116982},[573],[15,116984],{"className":116985,"style":406},[157],[15,116987,117],{"className":116988},[59],[15,116990,120],{"className":116991},[153],[15,116993,551],{"className":116994},[573],[15,116996],{"className":116997,"style":406},[157],[15,116999,213],{"className":117000},[59,60],[15,117002],{"className":117003,"style":158},[157],[15,117005,123],{"className":117006},[162],[15,117008],{"className":117009,"style":158},[157],[15,117011,117013,117016,117019,117022,117025,117028,117031,117034],{"className":117012},[50],[15,117014],{"className":117015,"style":139},[54],[15,117017,38284],{"className":117018,"style":25601},[59,60],[15,117020,113],{"className":117021},[146],[15,117023,116934],{"className":117024},[59],[15,117026,551],{"className":117027},[573],[15,117029],{"className":117030,"style":406},[157],[15,117032,117],{"className":117033},[59],[15,117035,120],{"className":117036},[153],[52595,117038,117039],{},[15,117040,117042,117059],{"className":117041,"translate":19},[18],[15,117043,117045],{"className":117044},[23],[25,117046,117047],{"xmlns":27},[29,117048,117049,117056],{},[32,117050,117051,117053],{},[110,117052,123],{},[115,117054,117055],{},"5000",[39,117057,117058],{"encoding":41},"=5000",[15,117060,117062,117074],{"className":117061,"ariaHidden":46},[45],[15,117063,117065,117068,117071],{"className":117064},[50],[15,117066],{"className":117067,"style":11003},[54],[15,117069,123],{"className":117070},[162],[15,117072],{"className":117073,"style":158},[157],[15,117075,117077,117080],{"className":117076},[50],[15,117078],{"className":117079,"style":172},[54],[15,117081,117055],{"className":117082},[59],[52595,117084,117085],{},[15,117086,117088,117103],{"className":117087,"translate":19},[18],[15,117089,117091],{"className":117090},[23],[25,117092,117093],{"xmlns":27},[29,117094,117095,117101],{},[32,117096,117097,117099],{},[110,117098,123],{},[115,117100,117055],{},[39,117102,117058],{"encoding":41},[15,117104,117106,117118],{"className":117105,"ariaHidden":46},[45],[15,117107,117109,117112,117115],{"className":117108},[50],[15,117110],{"className":117111,"style":11003},[54],[15,117113,123],{"className":117114},[162],[15,117116],{"className":117117,"style":158},[157],[15,117119,117121,117124],{"className":117120},[50],[15,117122],{"className":117123,"style":172},[54],[15,117125,117055],{"className":117126},[59],[52595,117128,117129],{},[15,117130,117132,117152],{"className":117131,"translate":19},[18],[15,117133,117135],{"className":117134},[23],[25,117136,117137],{"xmlns":27},[29,117138,117139,117149],{},[32,117140,117141,117143,117145,117147],{},[110,117142,32959],{},[35,117144,4100],{},[110,117146,4103],{},[115,117148,2463],{},[39,117150,117151],{"encoding":41},"\\approx\\log2",[15,117153,117155,117168],{"className":117154,"ariaHidden":46},[45],[15,117156,117158,117162,117165],{"className":117157},[50],[15,117159],{"className":117160,"style":117161},[54],"height:0.4831em;",[15,117163,32959],{"className":117164},[162],[15,117166],{"className":117167,"style":158},[157],[15,117169,117171,117174,117179,117182],{"className":117170},[50],[15,117172],{"className":117173,"style":55},[54],[15,117175,4154,117177],{"className":117176},[1484],[15,117178,4158],{"style":4157},[15,117180],{"className":117181,"style":406},[157],[15,117183,2463],{"className":117184},[59],[52595,117186,117187],{},[15,117188,117190,117206],{"className":117189,"translate":19},[18],[15,117191,117193],{"className":117192},[23],[25,117194,117195],{"xmlns":27},[29,117196,117197,117203],{},[32,117198,117199,117201],{},[110,117200,32959],{},[115,117202,117],{},[39,117204,117205],{"encoding":41},"\\approx1",[15,117207,117209,117221],{"className":117208,"ariaHidden":46},[45],[15,117210,117212,117215,117218],{"className":117211},[50],[15,117213],{"className":117214,"style":117161},[54],[15,117216,32959],{"className":117217},[162],[15,117219],{"className":117220,"style":158},[157],[15,117222,117224,117227],{"className":117223},[50],[15,117225],{"className":117226,"style":172},[54],[15,117228,117],{"className":117229},[59],[52595,117231,117232],{},[15,117233,117235,117260],{"className":117234,"translate":19},[18],[15,117236,117238],{"className":117237},[23],[25,117239,117240],{"xmlns":27},[29,117241,117242,117257],{},[32,117243,117244,117246],{},[110,117245,32959],{},[6814,117247,117248,117250],{},[35,117249,7567],{},[6814,117251,117252,117255],{},[115,117253,117254],{},"10",[115,117256,38989],{},[39,117258,117259],{"encoding":41},"\\approx e^{10^4}",[15,117261,117263,117275],{"className":117262,"ariaHidden":46},[45],[15,117264,117266,117269,117272],{"className":117265},[50],[15,117267],{"className":117268,"style":117161},[54],[15,117270,32959],{"className":117271},[162],[15,117273],{"className":117274,"style":158},[157],[15,117276,117278,117282],{"className":117277},[50],[15,117279],{"className":117280,"style":117281},[54],"height:0.9869em;",[15,117283,117285,117288],{"className":117284},[59],[15,117286,7567],{"className":117287},[59,60],[15,117289,117291],{"className":117290},[281],[15,117292,117294],{"className":117293},[285],[15,117295,117297],{"className":117296},[290],[15,117298,117300],{"className":117299,"style":117281},[294],[15,117301,117302,117305],{"style":6865},[15,117303],{"className":117304,"style":303},[302],[15,117306,117308],{"className":117307},[307,308,309,310],[15,117309,117311,117314],{"className":117310},[59,310],[15,117312,117],{"className":117313},[59,310],[15,117315,117317,117320],{"className":117316},[59,310],[15,117318,126],{"className":117319},[59,310],[15,117321,117323],{"className":117322},[281],[15,117324,117326],{"className":117325},[285],[15,117327,117329],{"className":117328},[290],[15,117330,117332],{"className":117331,"style":38512},[294],[15,117333,117334,117337],{"style":38515},[15,117335],{"className":117336,"style":30206},[302],[15,117338,117340],{"className":117339},[307,30210,9674,310],[15,117341,38989],{"className":117342},[59,310],[52595,117344,117345],{},[15,117346,117348,117364],{"className":117347,"translate":19},[18],[15,117349,117351],{"className":117350},[23],[25,117352,117353],{"xmlns":27},[29,117354,117355,117361],{},[32,117356,117357,117359],{},[110,117358,32959],{},[115,117360,2463],{},[39,117362,117363],{"encoding":41},"\\approx2",[15,117365,117367,117379],{"className":117366,"ariaHidden":46},[45],[15,117368,117370,117373,117376],{"className":117369},[50],[15,117371],{"className":117372,"style":117161},[54],[15,117374,32959],{"className":117375},[162],[15,117377],{"className":117378,"style":158},[157],[15,117380,117382,117385],{"className":117381},[50],[15,117383],{"className":117384,"style":172},[54],[15,117386,2463],{"className":117387},[59],[52595,117389,117390],{},[15,117391,117393,117409],{"className":117392,"translate":19},[18],[15,117394,117396],{"className":117395},[23],[25,117397,117398],{"xmlns":27},[29,117399,117400,117406],{},[32,117401,117402,117404],{},[110,117403,123],{},[115,117405,116934],{},[39,117407,117408],{"encoding":41},"=100",[15,117410,117412,117424],{"className":117411,"ariaHidden":46},[45],[15,117413,117415,117418,117421],{"className":117414},[50],[15,117416],{"className":117417,"style":11003},[54],[15,117419,123],{"className":117420},[162],[15,117422],{"className":117423,"style":158},[157],[15,117425,117427,117430],{"className":117426},[50],[15,117428],{"className":117429,"style":172},[54],[15,117431,116934],{"className":117432},[59],[11,117434,117435],{},"f-散度在第二行全部「饱和到下界\u002F上界」，而 Wasserstein 随距离线性增长——这正是词嵌入、最优传输、Wasserstein GAN 的动机。",[528,117437,117439],{"id":117438},"_7-机器学习应用","7. 机器学习应用",[11,117441,117442],{},"f-散度族之所以重要，是因为：",[6662,117444,117445,117451,117461,117496],{},[6665,117446,117447,117450],{},[1225,117448,117449],{},"统一框架","：许多生成模型的目标函数可以写成 f-散度。",[6665,117452,117453,117456,117457,117460],{},[1225,117454,117455],{},"变分估计","：通过凸共轭，可以用神经网络估计 f-散度，这就是 ",[1225,117458,117459],{},"f-GAN"," 的核心思想。",[6665,117462,117463,117466,117467,117495],{},[1225,117464,117465],{},"灵活选择","：不同 ",[15,117468,117470,117483],{"className":117469,"translate":19},[18],[15,117471,117473],{"className":117472},[23],[25,117474,117475],{"xmlns":27},[29,117476,117477,117481],{},[32,117478,117479],{},[35,117480,37],{},[39,117482,37],{"encoding":41},[15,117484,117486],{"className":117485,"ariaHidden":46},[45],[15,117487,117489,117492],{"className":117488},[50],[15,117490],{"className":117491,"style":55},[54],[15,117493,37],{"className":117494,"style":61},[59,60]," 对应不同训练性质。例如 JS 有界但可能梯度消失，KL 无界但敏感。",[6665,117497,117498,117501],{},[1225,117499,117500],{},"理论分析","：数据处理不等式、凸性、对偶表示等为收敛性和泛化分析提供工具。",[11,117503,117504],{},"下面把这几条落到具体场景。",[2311,117506,117508],{"id":117507},"_71-f-gan","7.1 f-GAN",[11,117510,117511,117512,117640,117641,117669,117670,117698],{},"见第 5 节。核心是：",[15,117513,117515,117547],{"className":117514,"translate":19},[18],[15,117516,117518],{"className":117517},[23],[25,117519,117520],{"xmlns":27},[29,117521,117522,117544],{},[32,117523,117524,117534],{},[195,117525,117526,117532],{},[32,117527,117528,117530],{},[35,117529,51608],{},[110,117531,4103],{},[35,117533,100759],{},[195,117535,117536,117542],{},[32,117537,117538,117540],{},[35,117539,52387],{},[110,117541,4103],{},[35,117543,99861],{},[39,117545,117546],{"encoding":41},"\\min_\\theta\\max_\\omega",[15,117548,117550],{"className":117549,"ariaHidden":46},[45],[15,117551,117553,117557,117597,117600],{"className":117552},[50],[15,117554],{"className":117555,"style":117556},[54],"height:0.8179em;vertical-align:-0.15em;",[15,117558,117560,117563],{"className":117559},[1484],[15,117561,51608],{"className":117562},[1484],[15,117564,117566],{"className":117565},[281],[15,117567,117569,117589],{"className":117568},[285,286],[15,117570,117572,117586],{"className":117571},[290],[15,117573,117575],{"className":117574,"style":295},[294],[15,117576,117577,117580],{"style":52446},[15,117578],{"className":117579,"style":303},[302],[15,117581,117583],{"className":117582},[307,308,309,310],[15,117584,100759],{"className":117585,"style":277},[59,60,310],[15,117587,318],{"className":117588},[317],[15,117590,117592],{"className":117591},[290],[15,117593,117595],{"className":117594,"style":7968},[294],[15,117596],{},[15,117598],{"className":117599,"style":406},[157],[15,117601,117603,117606],{"className":117602},[1484],[15,117604,52387],{"className":117605},[1484],[15,117607,117609],{"className":117608},[281],[15,117610,117612,117632],{"className":117611},[285,286],[15,117613,117615,117629],{"className":117614},[290],[15,117616,117618],{"className":117617,"style":44929},[294],[15,117619,117620,117623],{"style":52446},[15,117621],{"className":117622,"style":303},[302],[15,117624,117626],{"className":117625},[307,308,309,310],[15,117627,99861],{"className":117628,"style":981},[59,60,310],[15,117630,318],{"className":117631},[317],[15,117633,117635],{"className":117634},[290],[15,117636,117638],{"className":117637,"style":7968},[294],[15,117639],{}," 的对抗目标 = 对 ",[15,117642,117644,117657],{"className":117643,"translate":19},[18],[15,117645,117647],{"className":117646},[23],[25,117648,117649],{"xmlns":27},[29,117650,117651,117655],{},[32,117652,117653],{},[35,117654,37],{},[39,117656,37],{"encoding":41},[15,117658,117660],{"className":117659,"ariaHidden":46},[45],[15,117661,117663,117666],{"className":117662},[50],[15,117664],{"className":117665,"style":55},[54],[15,117667,37],{"className":117668,"style":61},[59,60]," 做对偶后的 f-散度估计。选择 ",[15,117671,117673,117686],{"className":117672,"translate":19},[18],[15,117674,117676],{"className":117675},[23],[25,117677,117678],{"xmlns":27},[29,117679,117680,117684],{},[32,117681,117682],{},[35,117683,37],{},[39,117685,37],{"encoding":41},[15,117687,117689],{"className":117688,"ariaHidden":46},[45],[15,117690,117692,117695],{"className":117691},[50],[15,117693],{"className":117694,"style":55},[54],[15,117696,37],{"className":117697,"style":61},[59,60]," 就是选择「用哪种散度训练生成器」，这直接决定模式崩塌、梯度消失与训练稳定性的权衡。",[2311,117700,117702],{"id":117701},"_72-变分推断与-elbo","7.2 变分推断与 ELBO",[11,117704,117705],{},"变分推断里最大化证据下界",[15,117707,117709],{"className":117708,"translate":19},[180],[15,117710,117712,117871],{"className":117711,"translate":19},[18],[15,117713,117715],{"className":117714},[23],[25,117716,117717],{"xmlns":27,"display":189},[29,117718,117719,117868],{},[1243,117720,117721,117798],{"rowspacing":1245,"columnalign":1246,"columnspacing":1247},[1249,117722,117723,117737],{},[1252,117724,117725],{},[1255,117726,117727],{"scriptlevel":126,"displaystyle":46},[32,117728,117729,117731,117733,117735],{},[35,117730,21893],{"mathvariant":597},[110,117732,113],{"stretchy":112},[35,117734,944],{},[110,117736,120],{"stretchy":112},[1252,117738,117739],{},[1255,117740,117741],{"scriptlevel":126,"displaystyle":46},[32,117742,117743,117745,117747,117753,117755,117757,117759,117761,117763,117765,117767,117770,117772,117774,117776,117782,117784,117786,117788,117790,117792,117794,117796],{},[32,117744],{},[110,117746,123],{},[195,117748,117749,117751],{},[35,117750,223],{"mathvariant":222},[35,117752,944],{},[110,117754,230],{"stretchy":112},[35,117756,4100],{},[110,117758,4103],{},[35,117760,11],{},[110,117762,113],{"stretchy":112},[35,117764,774],{},[110,117766,551],{"separator":46},[35,117768,117769],{},"z",[110,117771,120],{"stretchy":112},[110,117773,257],{"stretchy":112},[110,117775,4813],{},[195,117777,117778,117780],{},[35,117779,223],{"mathvariant":222},[35,117781,944],{},[110,117783,230],{"stretchy":112},[35,117785,4100],{},[110,117787,4103],{},[35,117789,944],{},[110,117791,113],{"stretchy":112},[35,117793,117769],{},[110,117795,120],{"stretchy":112},[110,117797,257],{"stretchy":112},[1249,117799,117800,117806],{},[1252,117801,117802],{},[1255,117803,117804],{"scriptlevel":126,"displaystyle":46},[32,117805],{},[1252,117807,117808],{},[1255,117809,117810],{"scriptlevel":126,"displaystyle":46},[32,117811,117812,117814,117816,117818,117820,117822,117824,117826,117828,117830,117836,117838,117840,117842,117844,117846,117848,117850,117852,117854,117856,117858,117860,117862,117864,117866],{},[32,117813],{},[110,117815,123],{},[35,117817,4100],{},[110,117819,4103],{},[35,117821,11],{},[110,117823,113],{"stretchy":112},[35,117825,774],{},[110,117827,120],{"stretchy":112},[110,117829,4813],{},[32,117831,117832,117834],{},[35,117833,10694],{"mathvariant":209},[35,117835,21893],{"mathvariant":209},[110,117837,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,117839,944],{},[110,117841,113],{"stretchy":112},[35,117843,117769],{},[110,117845,120],{"stretchy":112},[1297,117847,1299],{},[35,117849,210],{"mathvariant":209},[1297,117851,1299],{},[35,117853,11],{},[110,117855,113],{"stretchy":112},[35,117857,117769],{},[35,117859,4808],{"mathvariant":209},[35,117861,774],{},[110,117863,120],{"stretchy":112},[110,117865,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,117867,551],{"separator":46},[39,117869,117870],{"encoding":41},"\\begin{aligned}\n\\mathcal L(q)\n&=\\mathbb E_q[\\log p(x,z)]\n-\\mathbb E_q[\\log q(z)]\\\\\n&=\\log p(x)\n-\\mathrm{KL}\\big(q(z)\\,\\|\\,p(z|x)\\big),\n\\end{aligned}",[15,117872,117874],{"className":117873,"ariaHidden":46},[45],[15,117875,117877,117880],{"className":117876},[50],[15,117878],{"className":117879,"style":14586},[54],[15,117881,117883],{"className":117882},[59],[15,117884,117886,117938],{"className":117885},[1243],[15,117887,117889],{"className":117888},[1360],[15,117890,117892,117930],{"className":117891},[285,286],[15,117893,117895,117927],{"className":117894},[290],[15,117896,117898,117919],{"className":117897,"style":14605},[294],[15,117899,117901,117904],{"style":117900},"top:-3.765em;",[15,117902],{"className":117903,"style":461},[302],[15,117905,117907,117910,117913,117916],{"className":117906},[59],[15,117908,21893],{"className":117909},[59,624],[15,117911,113],{"className":117912},[146],[15,117914,944],{"className":117915,"style":981},[59,60],[15,117917,120],{"className":117918},[153],[15,117920,117921,117924],{"style":14993},[15,117922],{"className":117923,"style":461},[302],[15,117925],{"className":117926},[59],[15,117928,318],{"className":117929},[317],[15,117931,117933],{"className":117932},[290],[15,117934,117936],{"className":117935,"style":14634},[294],[15,117937],{},[15,117939,117941],{"className":117940},[1451],[15,117942,117944,118227],{"className":117943},[285,286],[15,117945,117947,118224],{"className":117946},[290],[15,117948,117950,118115],{"className":117949,"style":14605},[294],[15,117951,117952,117955],{"style":117900},[15,117953],{"className":117954,"style":461},[302],[15,117956,117958,117961,117964,117967,117970,118010,118013,118018,118021,118024,118027,118030,118033,118036,118040,118043,118046,118049,118052,118092,118095,118100,118103,118106,118109,118112],{"className":117957},[59],[15,117959],{"className":117960},[59],[15,117962],{"className":117963,"style":158},[157],[15,117965,123],{"className":117966},[162],[15,117968],{"className":117969,"style":158},[157],[15,117971,117973,117976],{"className":117972},[59],[15,117974,223],{"className":117975},[59,366],[15,117977,117979],{"className":117978},[281],[15,117980,117982,118002],{"className":117981},[285,286],[15,117983,117985,117999],{"className":117984},[290],[15,117986,117988],{"className":117987,"style":44929},[294],[15,117989,117990,117993],{"style":382},[15,117991],{"className":117992,"style":303},[302],[15,117994,117996],{"className":117995},[307,308,309,310],[15,117997,944],{"className":117998,"style":981},[59,60,310],[15,118000,318],{"className":118001},[317],[15,118003,118005],{"className":118004},[290],[15,118006,118008],{"className":118007,"style":325},[294],[15,118009],{},[15,118011,230],{"className":118012},[146],[15,118014,4154,118016],{"className":118015},[1484],[15,118017,4158],{"style":4157},[15,118019],{"className":118020,"style":406},[157],[15,118022,11],{"className":118023},[59,60],[15,118025,113],{"className":118026},[146],[15,118028,774],{"className":118029},[59,60],[15,118031,551],{"className":118032},[573],[15,118034],{"className":118035,"style":406},[157],[15,118037,117769],{"className":118038,"style":118039},[59,60],"margin-right:0.044em;",[15,118041,20390],{"className":118042},[153],[15,118044],{"className":118045,"style":2587},[157],[15,118047,4813],{"className":118048},[2591],[15,118050],{"className":118051,"style":2587},[157],[15,118053,118055,118058],{"className":118054},[59],[15,118056,223],{"className":118057},[59,366],[15,118059,118061],{"className":118060},[281],[15,118062,118064,118084],{"className":118063},[285,286],[15,118065,118067,118081],{"className":118066},[290],[15,118068,118070],{"className":118069,"style":44929},[294],[15,118071,118072,118075],{"style":382},[15,118073],{"className":118074,"style":303},[302],[15,118076,118078],{"className":118077},[307,308,309,310],[15,118079,944],{"className":118080,"style":981},[59,60,310],[15,118082,318],{"className":118083},[317],[15,118085,118087],{"className":118086},[290],[15,118088,118090],{"className":118089,"style":325},[294],[15,118091],{},[15,118093,230],{"className":118094},[146],[15,118096,4154,118098],{"className":118097},[1484],[15,118099,4158],{"style":4157},[15,118101],{"className":118102,"style":406},[157],[15,118104,944],{"className":118105,"style":981},[59,60],[15,118107,113],{"className":118108},[146],[15,118110,117769],{"className":118111,"style":118039},[59,60],[15,118113,20390],{"className":118114},[153],[15,118116,118117,118120],{"style":14993},[15,118118],{"className":118119,"style":461},[302],[15,118121,118123,118126,118129,118132,118135,118140,118143,118146,118149,118152,118155,118158,118161,118164,118170,118176,118179,118182,118185,118188,118191,118194,118197,118200,118203,118206,118209,118212,118215,118221],{"className":118122},[59],[15,118124],{"className":118125},[59],[15,118127],{"className":118128,"style":158},[157],[15,118130,123],{"className":118131},[162],[15,118133],{"className":118134,"style":158},[157],[15,118136,4154,118138],{"className":118137},[1484],[15,118139,4158],{"style":4157},[15,118141],{"className":118142,"style":406},[157],[15,118144,11],{"className":118145},[59,60],[15,118147,113],{"className":118148},[146],[15,118150,774],{"className":118151},[59,60],[15,118153,120],{"className":118154},[153],[15,118156],{"className":118157,"style":2587},[157],[15,118159,4813],{"className":118160},[2591],[15,118162],{"className":118163,"style":2587},[157],[15,118165,118167],{"className":118166},[59],[15,118168,32663],{"className":118169},[59,32662],[15,118171,118173],{"className":118172},[59],[15,118174,113],{"className":118175},[419,9674],[15,118177,944],{"className":118178,"style":981},[59,60],[15,118180,113],{"className":118181},[146],[15,118183,117769],{"className":118184,"style":118039},[59,60],[15,118186,120],{"className":118187},[153],[15,118189],{"className":118190,"style":406},[157],[15,118192,210],{"className":118193},[59],[15,118195],{"className":118196,"style":406},[157],[15,118198,11],{"className":118199},[59,60],[15,118201,113],{"className":118202},[146],[15,118204,117769],{"className":118205,"style":118039},[59,60],[15,118207,4808],{"className":118208},[59],[15,118210,774],{"className":118211},[59,60],[15,118213,120],{"className":118214},[153],[15,118216,118218],{"className":118217},[59],[15,118219,120],{"className":118220},[419,9674],[15,118222,551],{"className":118223},[573],[15,118225,318],{"className":118226},[317],[15,118228,118230],{"className":118229},[290],[15,118231,118233],{"className":118232,"style":14634},[294],[15,118234],{},[11,118236,2250,118237,118298,118299,118370,118371,118472,118473,118501,118502,118560,118561,118589],{},[15,118238,118240,118268],{"className":118239,"translate":19},[18],[15,118241,118243],{"className":118242},[23],[25,118244,118245],{"xmlns":27},[29,118246,118247,118265],{},[32,118248,118249,118255,118257,118259,118261,118263],{},[32,118250,118251,118253],{},[35,118252,10694],{"mathvariant":209},[35,118254,21893],{"mathvariant":209},[110,118256,113],{"stretchy":112},[35,118258,944],{},[35,118260,210],{"mathvariant":209},[35,118262,11],{},[110,118264,120],{"stretchy":112},[39,118266,118267],{"encoding":41},"\\mathrm{KL}(q\\|p)",[15,118269,118271],{"className":118270,"ariaHidden":46},[45],[15,118272,118274,118277,118283,118286,118289,118292,118295],{"className":118273},[50],[15,118275],{"className":118276,"style":139},[54],[15,118278,118280],{"className":118279},[59],[15,118281,32663],{"className":118282},[59,32662],[15,118284,113],{"className":118285},[146],[15,118287,944],{"className":118288,"style":981},[59,60],[15,118290,210],{"className":118291},[59],[15,118293,11],{"className":118294},[59,60],[15,118296,120],{"className":118297},[153]," 是 f-散度（",[15,118300,118302,118326],{"className":118301,"translate":19},[18],[15,118303,118305],{"className":118304},[23],[25,118306,118307],{"xmlns":27},[29,118308,118309,118323],{},[32,118310,118311,118313,118315,118317,118319,118321],{},[35,118312,37],{},[110,118314,123],{},[35,118316,769],{},[35,118318,4100],{},[110,118320,4103],{},[35,118322,769],{},[39,118324,118325],{"encoding":41},"f=t\\log t",[15,118327,118329,118347],{"className":118328,"ariaHidden":46},[45],[15,118330,118332,118335,118338,118341,118344],{"className":118331},[50],[15,118333],{"className":118334,"style":55},[54],[15,118336,37],{"className":118337,"style":61},[59,60],[15,118339],{"className":118340,"style":158},[157],[15,118342,123],{"className":118343},[162],[15,118345],{"className":118346,"style":158},[157],[15,118348,118350,118353,118356,118359,118364,118367],{"className":118349},[50],[15,118351],{"className":118352,"style":55},[54],[15,118354,769],{"className":118355},[59,60],[15,118357],{"className":118358,"style":406},[157],[15,118360,4154,118362],{"className":118361},[1484],[15,118363,4158],{"style":4157},[15,118365],{"className":118366,"style":406},[157],[15,118368,769],{"className":118369},[59,60],"）。反过来，任何以 ",[15,118372,118374,118406],{"className":118373,"translate":19},[18],[15,118375,118377],{"className":118376},[23],[25,118378,118379],{"xmlns":27},[29,118380,118381,118403],{},[32,118382,118383,118389,118391,118393,118395,118397,118399,118401],{},[195,118384,118385,118387],{},[35,118386,223],{"mathvariant":222},[35,118388,944],{},[110,118390,230],{"stretchy":112},[35,118392,4100],{},[110,118394,4103],{},[110,118396,113],{"stretchy":112},[110,118398,3299],{},[110,118400,120],{"stretchy":112},[110,118402,257],{"stretchy":112},[39,118404,118405],{"encoding":41},"\\mathbb E_q[\\log(\\cdot)]",[15,118407,118409],{"className":118408,"ariaHidden":46},[45],[15,118410,118412,118415,118455,118458,118463,118466,118469],{"className":118411},[50],[15,118413],{"className":118414,"style":270},[54],[15,118416,118418,118421],{"className":118417},[59],[15,118419,223],{"className":118420},[59,366],[15,118422,118424],{"className":118423},[281],[15,118425,118427,118447],{"className":118426},[285,286],[15,118428,118430,118444],{"className":118429},[290],[15,118431,118433],{"className":118432,"style":44929},[294],[15,118434,118435,118438],{"style":382},[15,118436],{"className":118437,"style":303},[302],[15,118439,118441],{"className":118440},[307,308,309,310],[15,118442,944],{"className":118443,"style":981},[59,60,310],[15,118445,318],{"className":118446},[317],[15,118448,118450],{"className":118449},[290],[15,118451,118453],{"className":118452,"style":325},[294],[15,118454],{},[15,118456,230],{"className":118457},[146],[15,118459,4154,118461],{"className":118460},[1484],[15,118462,4158],{"style":4157},[15,118464,113],{"className":118465},[146],[15,118467,3299],{"className":118468},[59],[15,118470,20390],{"className":118471},[153]," 为组成部分的目标都可以用 f-散度的语言重写；",[15,118474,118476,118489],{"className":118475,"translate":19},[18],[15,118477,118479],{"className":118478},[23],[25,118480,118481],{"xmlns":27},[29,118482,118483,118487],{},[32,118484,118485],{},[35,118486,44754],{},[39,118488,49090],{"encoding":41},[15,118490,118492],{"className":118491,"ariaHidden":46},[45],[15,118493,118495,118498],{"className":118494},[50],[15,118496],{"className":118497,"style":2345},[54],[15,118499,44754],{"className":118500,"style":44784},[59,60],"-VI、",[15,118503,118505,118522],{"className":118504,"translate":19},[18],[15,118506,118508],{"className":118507},[23],[25,118509,118510],{"xmlns":27},[29,118511,118512,118520],{},[32,118513,118514],{},[6814,118515,118516,118518],{},[35,118517,37449],{},[115,118519,2463],{},[39,118521,40394],{"encoding":41},[15,118523,118525],{"className":118524,"ariaHidden":46},[45],[15,118526,118528,118531],{"className":118527},[50],[15,118529],{"className":118530,"style":40404},[54],[15,118532,118534,118537],{"className":118533},[59],[15,118535,37449],{"className":118536},[59,60],[15,118538,118540],{"className":118539},[281],[15,118541,118543],{"className":118542},[285],[15,118544,118546],{"className":118545},[290],[15,118547,118549],{"className":118548,"style":20028},[294],[15,118550,118551,118554],{"style":6865},[15,118552],{"className":118553,"style":303},[302],[15,118555,118557],{"className":118556},[307,308,309,310],[15,118558,2463],{"className":118559},[59,310],"-VI 等就换用别的 ",[15,118562,118564,118577],{"className":118563,"translate":19},[18],[15,118565,118567],{"className":118566},[23],[25,118568,118569],{"xmlns":27},[29,118570,118571,118575],{},[32,118572,118573],{},[35,118574,37],{},[39,118576,37],{"encoding":41},[15,118578,118580],{"className":118579,"ariaHidden":46},[45],[15,118581,118583,118586],{"className":118582},[50],[15,118584],{"className":118585,"style":55},[54],[15,118587,37],{"className":118588,"style":61},[59,60],"，在 3.1 节所说的「零回避」（mass-covering）与「零强制」（mode-seeking）两种极端行为之间取舍。",[2311,118591,118593],{"id":118592},"_73-互信息估计","7.3 互信息估计",[11,118595,118596],{},"互信息可写成",[15,118598,118600],{"className":118599,"translate":19},[180],[15,118601,118603,118718],{"className":118602,"translate":19},[18],[15,118604,118606],{"className":118605},[23],[25,118607,118608],{"xmlns":27,"display":189},[29,118609,118610,118715],{},[32,118611,118612,118614,118616,118618,118620,118622,118624,118626,118632,118634,118644,118646,118648,118650,118656,118659,118665,118667,118669,118683,118685,118695,118697,118703,118705,118711,118713],{},[35,118613,33868],{},[110,118615,113],{"stretchy":112},[35,118617,598],{},[110,118619,33875],{"separator":46},[35,118621,5401],{},[110,118623,120],{"stretchy":112},[110,118625,123],{},[32,118627,118628,118630],{},[35,118629,10694],{"mathvariant":209},[35,118631,21893],{"mathvariant":209},[110,118633,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,118635,118636,118638],{},[35,118637,206],{},[32,118639,118640,118642],{},[35,118641,598],{},[35,118643,5401],{},[1297,118645,1299],{},[35,118647,210],{"mathvariant":209},[1297,118649,1299],{},[195,118651,118652,118654],{},[35,118653,206],{},[35,118655,598],{},[110,118657,118658],{},"⊗",[195,118660,118661,118663],{},[35,118662,206],{},[35,118664,5401],{},[110,118666,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,118668,123],{},[195,118670,118671,118673],{},[35,118672,199],{},[32,118674,118675,118677,118679,118681],{},[35,118676,769],{},[35,118678,4100],{},[110,118680,4103],{},[35,118682,769],{},[110,118684,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,118686,118687,118689],{},[35,118688,206],{},[32,118690,118691,118693],{},[35,118692,598],{},[35,118694,5401],{},[35,118696,210],{"mathvariant":209},[195,118698,118699,118701],{},[35,118700,206],{},[35,118702,598],{},[110,118704,118658],{},[195,118706,118707,118709],{},[35,118708,206],{},[35,118710,5401],{},[110,118712,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,118714,551],{"separator":46},[39,118716,118717],{"encoding":41},"I(X;Y)\n=\\mathrm{KL}\\big(P_{XY}\\,\\|\\,P_X\\otimes P_Y\\big)\n=D_{t\\log t}\\big(P_{XY}\\|P_X\\otimes P_Y\\big),",[15,118719,118721,118757,118879,118940,119114],{"className":118720,"ariaHidden":46},[45],[15,118722,118724,118727,118730,118733,118736,118739,118742,118745,118748,118751,118754],{"className":118723},[50],[15,118725],{"className":118726,"style":139},[54],[15,118728,33868],{"className":118729,"style":8887},[59,60],[15,118731,113],{"className":118732},[146],[15,118734,598],{"className":118735,"style":8887},[59,60],[15,118737,33875],{"className":118738},[573],[15,118740],{"className":118741,"style":406},[157],[15,118743,5401],{"className":118744,"style":2587},[59,60],[15,118746,120],{"className":118747},[153],[15,118749],{"className":118750,"style":158},[157],[15,118752,123],{"className":118753},[162],[15,118755],{"className":118756,"style":158},[157],[15,118758,118760,118763,118769,118775,118821,118824,118827,118830,118870,118873,118876],{"className":118759},[50],[15,118761],{"className":118762,"style":20563},[54],[15,118764,118766],{"className":118765},[59],[15,118767,32663],{"className":118768},[59,32662],[15,118770,118772],{"className":118771},[59],[15,118773,113],{"className":118774},[419,9674],[15,118776,118778,118781],{"className":118777},[59],[15,118779,206],{"className":118780,"style":334},[59,60],[15,118782,118784],{"className":118783},[281],[15,118785,118787,118813],{"className":118786},[285,286],[15,118788,118790,118810],{"className":118789},[290],[15,118791,118793],{"className":118792,"style":379},[294],[15,118794,118795,118798],{"style":11136},[15,118796],{"className":118797,"style":303},[302],[15,118799,118801],{"className":118800},[307,308,309,310],[15,118802,118804,118807],{"className":118803},[59,310],[15,118805,598],{"className":118806,"style":8887},[59,60,310],[15,118808,5401],{"className":118809,"style":2587},[59,60,310],[15,118811,318],{"className":118812},[317],[15,118814,118816],{"className":118815},[290],[15,118817,118819],{"className":118818,"style":7968},[294],[15,118820],{},[15,118822],{"className":118823,"style":406},[157],[15,118825,210],{"className":118826},[59],[15,118828],{"className":118829,"style":406},[157],[15,118831,118833,118836],{"className":118832},[59],[15,118834,206],{"className":118835,"style":334},[59,60],[15,118837,118839],{"className":118838},[281],[15,118840,118842,118862],{"className":118841},[285,286],[15,118843,118845,118859],{"className":118844},[290],[15,118846,118848],{"className":118847,"style":379},[294],[15,118849,118850,118853],{"style":11136},[15,118851],{"className":118852,"style":303},[302],[15,118854,118856],{"className":118855},[307,308,309,310],[15,118857,598],{"className":118858,"style":8887},[59,60,310],[15,118860,318],{"className":118861},[317],[15,118863,118865],{"className":118864},[290],[15,118866,118868],{"className":118867,"style":7968},[294],[15,118869],{},[15,118871],{"className":118872,"style":2587},[157],[15,118874,118658],{"className":118875},[2591],[15,118877],{"className":118878,"style":2587},[157],[15,118880,118882,118885,118925,118931,118934,118937],{"className":118881},[50],[15,118883],{"className":118884,"style":20563},[54],[15,118886,118888,118891],{"className":118887},[59],[15,118889,206],{"className":118890,"style":334},[59,60],[15,118892,118894],{"className":118893},[281],[15,118895,118897,118917],{"className":118896},[285,286],[15,118898,118900,118914],{"className":118899},[290],[15,118901,118903],{"className":118902,"style":379},[294],[15,118904,118905,118908],{"style":11136},[15,118906],{"className":118907,"style":303},[302],[15,118909,118911],{"className":118910},[307,308,309,310],[15,118912,5401],{"className":118913,"style":2587},[59,60,310],[15,118915,318],{"className":118916},[317],[15,118918,118920],{"className":118919},[290],[15,118921,118923],{"className":118922,"style":7968},[294],[15,118924],{},[15,118926,118928],{"className":118927},[59],[15,118929,120],{"className":118930},[419,9674],[15,118932],{"className":118933,"style":158},[157],[15,118935,123],{"className":118936},[162],[15,118938],{"className":118939,"style":158},[157],[15,118941,118943,118946,119010,119016,119062,119065,119105,119108,119111],{"className":118942},[50],[15,118944],{"className":118945,"style":20563},[54],[15,118947,118949,118952],{"className":118948},[59],[15,118950,199],{"className":118951,"style":277},[59,60],[15,118953,118955],{"className":118954},[281],[15,118956,118958,119002],{"className":118957},[285,286],[15,118959,118961,118999],{"className":118960},[290],[15,118962,118964],{"className":118963,"style":295},[294],[15,118965,118966,118969],{"style":298},[15,118967],{"className":118968,"style":303},[302],[15,118970,118972],{"className":118971},[307,308,309,310],[15,118973,118975,118978,118981,118993,118996],{"className":118974},[59,310],[15,118976,769],{"className":118977},[59,60,310],[15,118979],{"className":118980,"style":42366},[157,310],[15,118982,118984,118987,118990],{"className":118983},[1484,310],[15,118985,47658],{"className":118986},[310],[15,118988,47662],{"className":118989},[310],[15,118991,4158],{"className":118992,"style":4157},[310],[15,118994],{"className":118995,"style":42366},[157,310],[15,118997,769],{"className":118998},[59,60,310],[15,119000,318],{"className":119001},[317],[15,119003,119005],{"className":119004},[290],[15,119006,119008],{"className":119007,"style":325},[294],[15,119009],{},[15,119011,119013],{"className":119012},[59],[15,119014,113],{"className":119015},[419,9674],[15,119017,119019,119022],{"className":119018},[59],[15,119020,206],{"className":119021,"style":334},[59,60],[15,119023,119025],{"className":119024},[281],[15,119026,119028,119054],{"className":119027},[285,286],[15,119029,119031,119051],{"className":119030},[290],[15,119032,119034],{"className":119033,"style":379},[294],[15,119035,119036,119039],{"style":11136},[15,119037],{"className":119038,"style":303},[302],[15,119040,119042],{"className":119041},[307,308,309,310],[15,119043,119045,119048],{"className":119044},[59,310],[15,119046,598],{"className":119047,"style":8887},[59,60,310],[15,119049,5401],{"className":119050,"style":2587},[59,60,310],[15,119052,318],{"className":119053},[317],[15,119055,119057],{"className":119056},[290],[15,119058,119060],{"className":119059,"style":7968},[294],[15,119061],{},[15,119063,210],{"className":119064},[59],[15,119066,119068,119071],{"className":119067},[59],[15,119069,206],{"className":119070,"style":334},[59,60],[15,119072,119074],{"className":119073},[281],[15,119075,119077,119097],{"className":119076},[285,286],[15,119078,119080,119094],{"className":119079},[290],[15,119081,119083],{"className":119082,"style":379},[294],[15,119084,119085,119088],{"style":11136},[15,119086],{"className":119087,"style":303},[302],[15,119089,119091],{"className":119090},[307,308,309,310],[15,119092,598],{"className":119093,"style":8887},[59,60,310],[15,119095,318],{"className":119096},[317],[15,119098,119100],{"className":119099},[290],[15,119101,119103],{"className":119102,"style":7968},[294],[15,119104],{},[15,119106],{"className":119107,"style":2587},[157],[15,119109,118658],{"className":119110},[2591],[15,119112],{"className":119113,"style":2587},[157],[15,119115,119117,119120,119160,119166],{"className":119116},[50],[15,119118],{"className":119119,"style":20563},[54],[15,119121,119123,119126],{"className":119122},[59],[15,119124,206],{"className":119125,"style":334},[59,60],[15,119127,119129],{"className":119128},[281],[15,119130,119132,119152],{"className":119131},[285,286],[15,119133,119135,119149],{"className":119134},[290],[15,119136,119138],{"className":119137,"style":379},[294],[15,119139,119140,119143],{"style":11136},[15,119141],{"className":119142,"style":303},[302],[15,119144,119146],{"className":119145},[307,308,309,310],[15,119147,5401],{"className":119148,"style":2587},[59,60,310],[15,119150,318],{"className":119151},[317],[15,119153,119155],{"className":119154},[290],[15,119156,119158],{"className":119157,"style":7968},[294],[15,119159],{},[15,119161,119163],{"className":119162},[59],[15,119164,120],{"className":119165},[419,9674],[15,119167,551],{"className":119168},[573],[11,119170,119171,119172,119200,119201,119229,119230,119288],{},"因此它是 f-散度的特例。MINE 用 Donsker–Varadhan 对偶估计它，f-MINE 则对一般 ",[15,119173,119175,119188],{"className":119174,"translate":19},[18],[15,119176,119178],{"className":119177},[23],[25,119179,119180],{"xmlns":27},[29,119181,119182,119186],{},[32,119183,119184],{},[35,119185,37],{},[39,119187,37],{"encoding":41},[15,119189,119191],{"className":119190,"ariaHidden":46},[45],[15,119192,119194,119197],{"className":119193},[50],[15,119195],{"className":119196,"style":55},[54],[15,119198,37],{"className":119199,"style":61},[59,60]," 用 4.4 节的对偶；不同 ",[15,119202,119204,119217],{"className":119203,"translate":19},[18],[15,119205,119207],{"className":119206},[23],[25,119208,119209],{"xmlns":27},[29,119210,119211,119215],{},[32,119212,119213],{},[35,119214,37],{},[39,119216,37],{"encoding":41},[15,119218,119220],{"className":119219,"ariaHidden":46},[45],[15,119221,119223,119226],{"className":119222},[50],[15,119224],{"className":119225,"style":55},[54],[15,119227,37],{"className":119228,"style":61},[59,60],"（KL、JS、",[15,119231,119233,119250],{"className":119232,"translate":19},[18],[15,119234,119236],{"className":119235},[23],[25,119237,119238],{"xmlns":27},[29,119239,119240,119248],{},[32,119241,119242],{},[6814,119243,119244,119246],{},[35,119245,37449],{},[115,119247,2463],{},[39,119249,40394],{"encoding":41},[15,119251,119253],{"className":119252,"ariaHidden":46},[45],[15,119254,119256,119259],{"className":119255},[50],[15,119257],{"className":119258,"style":40404},[54],[15,119260,119262,119265],{"className":119261},[59],[15,119263,37449],{"className":119264},[59,60],[15,119266,119268],{"className":119267},[281],[15,119269,119271],{"className":119270},[285],[15,119272,119274],{"className":119273},[290],[15,119275,119277],{"className":119276,"style":20028},[294],[15,119278,119279,119282],{"style":6865},[15,119280],{"className":119281,"style":303},[302],[15,119283,119285],{"className":119284},[307,308,309,310],[15,119286,2463],{"className":119287},[59,310],"）给出不同的「MI 下界」和不同的方差—偏差折衷。对比式学习的 InfoNCE 也是 KL 下界的一种变体。",[2311,119290,119292],{"id":119291},"_74-表示学习","7.4 表示学习",[11,119294,119295,119296,119340],{},"任何表示 ",[15,119297,119299,119319],{"className":119298,"translate":19},[18],[15,119300,119302],{"className":119301},[23],[25,119303,119304],{"xmlns":27},[29,119305,119306,119316],{},[32,119307,119308,119310,119312,119314],{},[35,119309,5392],{},[110,119311,113],{"stretchy":112},[35,119313,598],{},[110,119315,120],{"stretchy":112},[39,119317,119318],{"encoding":41},"T(X)",[15,119320,119322],{"className":119321,"ariaHidden":46},[45],[15,119323,119325,119328,119331,119334,119337],{"className":119324},[50],[15,119326],{"className":119327,"style":139},[54],[15,119329,5392],{"className":119330,"style":334},[59,60],[15,119332,113],{"className":119333},[146],[15,119335,598],{"className":119336,"style":8887},[59,60],[15,119338,120],{"className":119339},[153]," 都满足（4.5 节）",[15,119342,119344],{"className":119343,"translate":19},[180],[15,119345,119347,119427],{"className":119346,"translate":19},[18],[15,119348,119350],{"className":119349},[23],[25,119351,119352],{"xmlns":27,"display":189},[29,119353,119354,119424],{},[32,119355,119356,119362,119364,119378,119380,119394,119396,119398,119404,119406,119412,119414,119420,119422],{},[195,119357,119358,119360],{},[35,119359,199],{},[35,119361,37],{},[110,119363,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[195,119365,119366,119368],{},[35,119367,206],{},[32,119369,119370,119372,119374,119376],{},[35,119371,5392],{},[110,119373,113],{"stretchy":112},[35,119375,598],{},[110,119377,120],{"stretchy":112},[35,119379,210],{"mathvariant":209},[195,119381,119382,119384],{},[35,119383,213],{},[32,119385,119386,119388,119390,119392],{},[35,119387,5392],{},[110,119389,113],{"stretchy":112},[35,119391,598],{},[110,119393,120],{"stretchy":112},[110,119395,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,119397,9952],{},[195,119399,119400,119402],{},[35,119401,199],{},[35,119403,37],{},[110,119405,113],{"stretchy":112},[195,119407,119408,119410],{},[35,119409,206],{},[35,119411,598],{},[35,119413,210],{"mathvariant":209},[195,119415,119416,119418],{},[35,119417,213],{},[35,119419,598],{},[110,119421,120],{"stretchy":112},[110,119423,551],{"separator":46},[39,119425,119426],{"encoding":41},"D_f\\big(P_{T(X)}\\|Q_{T(X)}\\big)\n\\le D_f(P_X\\|Q_X),",[15,119428,119430,119606],{"className":119429,"ariaHidden":46},[45],[15,119431,119433,119437,119477,119483,119536,119539,119591,119597,119600,119603],{"className":119432},[50],[15,119434],{"className":119435,"style":119436},[54],"height:1.2052em;vertical-align:-0.3552em;",[15,119438,119440,119443],{"className":119439},[59],[15,119441,199],{"className":119442,"style":277},[59,60],[15,119444,119446],{"className":119445},[281],[15,119447,119449,119469],{"className":119448},[285,286],[15,119450,119452,119466],{"className":119451},[290],[15,119453,119455],{"className":119454,"style":295},[294],[15,119456,119457,119460],{"style":298},[15,119458],{"className":119459,"style":303},[302],[15,119461,119463],{"className":119462},[307,308,309,310],[15,119464,37],{"className":119465,"style":61},[59,60,310],[15,119467,318],{"className":119468},[317],[15,119470,119472],{"className":119471},[290],[15,119473,119475],{"className":119474,"style":325},[294],[15,119476],{},[15,119478,119480],{"className":119479},[59],[15,119481,113],{"className":119482},[419,9674],[15,119484,119486,119489],{"className":119485},[59],[15,119487,206],{"className":119488,"style":334},[59,60],[15,119490,119492],{"className":119491},[281],[15,119493,119495,119528],{"className":119494},[285,286],[15,119496,119498,119525],{"className":119497},[290],[15,119499,119501],{"className":119500,"style":6098},[294],[15,119502,119504,119507],{"style":119503},"top:-2.5198em;margin-left:-0.1389em;margin-right:0.05em;",[15,119505],{"className":119506,"style":303},[302],[15,119508,119510],{"className":119509},[307,308,309,310],[15,119511,119513,119516,119519,119522],{"className":119512},[59,310],[15,119514,5392],{"className":119515,"style":334},[59,60,310],[15,119517,113],{"className":119518},[146,310],[15,119520,598],{"className":119521,"style":8887},[59,60,310],[15,119523,120],{"className":119524},[153,310],[15,119526,318],{"className":119527},[317],[15,119529,119531],{"className":119530},[290],[15,119532,119534],{"className":119533,"style":6144},[294],[15,119535],{},[15,119537,210],{"className":119538},[59],[15,119540,119542,119545],{"className":119541},[59],[15,119543,213],{"className":119544},[59,60],[15,119546,119548],{"className":119547},[281],[15,119549,119551,119583],{"className":119550},[285,286],[15,119552,119554,119580],{"className":119553},[290],[15,119555,119557],{"className":119556,"style":6098},[294],[15,119558,119559,119562],{"style":75573},[15,119560],{"className":119561,"style":303},[302],[15,119563,119565],{"className":119564},[307,308,309,310],[15,119566,119568,119571,119574,119577],{"className":119567},[59,310],[15,119569,5392],{"className":119570,"style":334},[59,60,310],[15,119572,113],{"className":119573},[146,310],[15,119575,598],{"className":119576,"style":8887},[59,60,310],[15,119578,120],{"className":119579},[153,310],[15,119581,318],{"className":119582},[317],[15,119584,119586],{"className":119585},[290],[15,119587,119589],{"className":119588,"style":6144},[294],[15,119590],{},[15,119592,119594],{"className":119593},[59],[15,119595,120],{"className":119596},[419,9674],[15,119598],{"className":119599,"style":158},[157],[15,119601,9952],{"className":119602},[162],[15,119604],{"className":119605,"style":158},[157],[15,119607,119609,119612,119652,119655,119695,119698,119738,119741],{"className":119608},[50],[15,119610],{"className":119611,"style":270},[54],[15,119613,119615,119618],{"className":119614},[59],[15,119616,199],{"className":119617,"style":277},[59,60],[15,119619,119621],{"className":119620},[281],[15,119622,119624,119644],{"className":119623},[285,286],[15,119625,119627,119641],{"className":119626},[290],[15,119628,119630],{"className":119629,"style":295},[294],[15,119631,119632,119635],{"style":298},[15,119633],{"className":119634,"style":303},[302],[15,119636,119638],{"className":119637},[307,308,309,310],[15,119639,37],{"className":119640,"style":61},[59,60,310],[15,119642,318],{"className":119643},[317],[15,119645,119647],{"className":119646},[290],[15,119648,119650],{"className":119649,"style":325},[294],[15,119651],{},[15,119653,113],{"className":119654},[146],[15,119656,119658,119661],{"className":119657},[59],[15,119659,206],{"className":119660,"style":334},[59,60],[15,119662,119664],{"className":119663},[281],[15,119665,119667,119687],{"className":119666},[285,286],[15,119668,119670,119684],{"className":119669},[290],[15,119671,119673],{"className":119672,"style":379},[294],[15,119674,119675,119678],{"style":11136},[15,119676],{"className":119677,"style":303},[302],[15,119679,119681],{"className":119680},[307,308,309,310],[15,119682,598],{"className":119683,"style":8887},[59,60,310],[15,119685,318],{"className":119686},[317],[15,119688,119690],{"className":119689},[290],[15,119691,119693],{"className":119692,"style":7968},[294],[15,119694],{},[15,119696,210],{"className":119697},[59],[15,119699,119701,119704],{"className":119700},[59],[15,119702,213],{"className":119703},[59,60],[15,119705,119707],{"className":119706},[281],[15,119708,119710,119730],{"className":119709},[285,286],[15,119711,119713,119727],{"className":119712},[290],[15,119714,119716],{"className":119715,"style":379},[294],[15,119717,119718,119721],{"style":382},[15,119719],{"className":119720,"style":303},[302],[15,119722,119724],{"className":119723},[307,308,309,310],[15,119725,598],{"className":119726,"style":8887},[59,60,310],[15,119728,318],{"className":119729},[317],[15,119731,119733],{"className":119732},[290],[15,119734,119736],{"className":119735,"style":7968},[294],[15,119737],{},[15,119739,120],{"className":119740},[153],[15,119742,551],{"className":119743},[573],[11,119745,119746],{},"即「编码不会创造信息」。这为对比学习、域对齐、特征选择提供了可证伪的约束：任何声称「表示后差异更大」的方法都必然在某个环节违反了 DPI，需要解释为什么。",[2311,119748,119750],{"id":119749},"_75-域适应","7.5 域适应",[11,119752,119753,119754,119784,119785,119815],{},"在源域 ",[15,119755,119757,119771],{"className":119756,"translate":19},[18],[15,119758,119760],{"className":119759},[23],[25,119761,119762],{"xmlns":27},[29,119763,119764,119768],{},[32,119765,119766],{},[35,119767,25737],{"mathvariant":597},[39,119769,119770],{"encoding":41},"\\mathcal S",[15,119772,119774],{"className":119773,"ariaHidden":46},[45],[15,119775,119777,119780],{"className":119776},[50],[15,119778],{"className":119779,"style":664},[54],[15,119781,25737],{"className":119782,"style":119783},[59,624],"margin-right:0.075em;"," 与目标域 ",[15,119786,119788,119802],{"className":119787,"translate":19},[18],[15,119789,119791],{"className":119790},[23],[25,119792,119793],{"xmlns":27},[29,119794,119795,119799],{},[32,119796,119797],{},[35,119798,5392],{"mathvariant":597},[39,119800,119801],{"encoding":41},"\\mathcal T",[15,119803,119805],{"className":119804,"ariaHidden":46},[45],[15,119806,119808,119811],{"className":119807},[50],[15,119809],{"className":119810,"style":664},[54],[15,119812,5392],{"className":119813,"style":119814},[59,624],"margin-right:0.2542em;"," 上，衡量分布漂移的现代方法（DANN、ADDA）本质上用 f-散度或 IPM 对齐边缘分布；其中用 JS 的（GAN 式）对齐与用 MMD\u002FWasserstein 的对齐，区别正是 6.2 节的几何与支撑问题。",[2311,119817,119819],{"id":119818},"_76-假设检验","7.6 假设检验",[11,119821,119822],{},"f-散度是假设检验的错误指数：",[10027,119824,119825,119892],{},[6665,119826,119827,119830,119831,19966],{},[1225,119828,119829],{},"Stein 引理","：在固定第一类错误下，第二类错误的最优指数为 ",[15,119832,119834,119862],{"className":119833,"translate":19},[18],[15,119835,119837],{"className":119836},[23],[25,119838,119839],{"xmlns":27},[29,119840,119841,119859],{},[32,119842,119843,119849,119851,119853,119855,119857],{},[32,119844,119845,119847],{},[35,119846,10694],{"mathvariant":209},[35,119848,21893],{"mathvariant":209},[110,119850,113],{"stretchy":112},[35,119852,206],{},[35,119854,210],{"mathvariant":209},[35,119856,213],{},[110,119858,120],{"stretchy":112},[39,119860,119861],{"encoding":41},"\\mathrm{KL}(P\\|Q)",[15,119863,119865],{"className":119864,"ariaHidden":46},[45],[15,119866,119868,119871,119877,119880,119883,119886,119889],{"className":119867},[50],[15,119869],{"className":119870,"style":139},[54],[15,119872,119874],{"className":119873},[59],[15,119875,32663],{"className":119876},[59,32662],[15,119878,113],{"className":119879},[146],[15,119881,206],{"className":119882,"style":334},[59,60],[15,119884,210],{"className":119885},[59],[15,119887,213],{"className":119888},[59,60],[15,119890,120],{"className":119891},[153],[6665,119893,119894,9400,119897,120176],{},[1225,119895,119896],{},"Chernoff 信息",[15,119898,119900,119974],{"className":119899,"translate":19},[18],[15,119901,119903],{"className":119902},[23],[25,119904,119905],{"xmlns":27},[29,119906,119907,119971],{},[32,119908,119909,119911,119913,119915,119917,119919,119921,119923,119943,119945,119947,119949,119951,119953,119961,119963,119965,119967,119969],{},[35,119910,39294],{},[110,119912,113],{"stretchy":112},[35,119914,206],{},[110,119916,551],{"separator":46},[35,119918,213],{},[110,119920,120],{"stretchy":112},[110,119922,123],{},[195,119924,119925,119931],{},[32,119926,119927,119929],{},[35,119928,35432],{},[110,119930,4103],{},[32,119932,119933,119935,119937,119939,119941],{},[115,119934,126],{},[110,119936,7251],{},[35,119938,11339],{},[110,119940,7251],{},[115,119942,117],{},[110,119944,113],{"stretchy":112},[115,119946,117],{},[110,119948,4813],{},[35,119950,11339],{},[110,119952,120],{"stretchy":112},[7553,119954,119955,119957,119959],{},[35,119956,199],{},[35,119958,11339],{},[35,119960,1032],{},[110,119962,113],{"stretchy":112},[35,119964,206],{},[35,119966,210],{"mathvariant":209},[35,119968,213],{},[110,119970,120],{"stretchy":112},[39,119972,119973],{"encoding":41},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)",[15,119975,119977,120013,120090],{"className":119976,"ariaHidden":46},[45],[15,119978,119980,119983,119986,119989,119992,119995,119998,120001,120004,120007,120010],{"className":119979},[50],[15,119981],{"className":119982,"style":139},[54],[15,119984,39294],{"className":119985,"style":10782},[59,60],[15,119987,113],{"className":119988},[146],[15,119990,206],{"className":119991,"style":334},[59,60],[15,119993,551],{"className":119994},[573],[15,119996],{"className":119997,"style":406},[157],[15,119999,213],{"className":120000},[59,60],[15,120002,120],{"className":120003},[153],[15,120005],{"className":120006,"style":158},[157],[15,120008,123],{"className":120009},[162],[15,120011],{"className":120012,"style":158},[157],[15,120014,120016,120019,120075,120078,120081,120084,120087],{"className":120015},[50],[15,120017],{"className":120018,"style":35556},[54],[15,120020,120022,120025],{"className":120021},[1484],[15,120023,35432],{"className":120024},[1484],[15,120026,120028],{"className":120027},[281],[15,120029,120031,120067],{"className":120030},[285,286],[15,120032,120034,120064],{"className":120033},[290],[15,120035,120038],{"className":120036,"style":120037},[294],"height:0.242em;",[15,120039,120040,120043],{"style":35578},[15,120041],{"className":120042,"style":303},[302],[15,120044,120046],{"className":120045},[307,308,309,310],[15,120047,120049,120052,120055,120058,120061],{"className":120048},[59,310],[15,120050,126],{"className":120051},[59,310],[15,120053,7251],{"className":120054},[162,310],[15,120056,11339],{"className":120057},[59,60,310],[15,120059,7251],{"className":120060},[162,310],[15,120062,117],{"className":120063},[59,310],[15,120065,318],{"className":120066},[317],[15,120068,120070],{"className":120069},[290],[15,120071,120073],{"className":120072,"style":35606},[294],[15,120074],{},[15,120076,113],{"className":120077},[146],[15,120079,117],{"className":120080},[59],[15,120082],{"className":120083,"style":2587},[157],[15,120085,4813],{"className":120086},[2591],[15,120088],{"className":120089,"style":2587},[157],[15,120091,120093,120097,120100,120103,120161,120164,120167,120170,120173],{"className":120092},[50],[15,120094],{"className":120095,"style":120096},[54],"height:1.1244em;vertical-align:-0.2831em;",[15,120098,11339],{"className":120099},[59,60],[15,120101,120],{"className":120102},[153],[15,120104,120106,120109],{"className":120105},[59],[15,120107,199],{"className":120108,"style":277},[59,60],[15,120110,120112],{"className":120111},[281],[15,120113,120115,120153],{"className":120114},[285,286],[15,120116,120118,120150],{"className":120117},[290],[15,120119,120121,120136],{"className":120120,"style":52085},[294],[15,120122,120124,120127],{"style":120123},"top:-2.4169em;margin-left:-0.0278em;margin-right:0.05em;",[15,120125],{"className":120126,"style":303},[302],[15,120128,120130],{"className":120129},[307,308,309,310],[15,120131,120133],{"className":120132},[59,310],[15,120134,11339],{"className":120135},[59,60,310],[15,120137,120138,120141],{"style":6865},[15,120139],{"className":120140,"style":303},[302],[15,120142,120144],{"className":120143},[307,308,309,310],[15,120145,120147],{"className":120146},[59,310],[15,120148,1032],{"className":120149,"style":49599},[59,60,310],[15,120151,318],{"className":120152},[317],[15,120154,120156],{"className":120155},[290],[15,120157,120159],{"className":120158,"style":8547},[294],[15,120160],{},[15,120162,113],{"className":120163},[146],[15,120165,206],{"className":120166,"style":334},[59,60],[15,120168,210],{"className":120169},[59],[15,120171,213],{"className":120172},[59,60],[15,120174,120],{"className":120175},[153],"，即 Rényi\u002Fα-族中的最优点；对称检验的指数由它决定。",[11,120178,120179],{},"因此 f-散度不只是「训练目标」，也是统计判决的极限性能。",[528,120181,120183],{"id":120182},"_8-差分隐私f-dp","8. 差分隐私（f-DP）",[11,120185,120186,120187,120190,120191,6494,120194,120222,120223,120264],{},"一个较新的应用是把 f-散度的语言搬到隐私保护。差分隐私（DP）要求相邻数据集的输出分布「难以区分」。Dong–Roth–Su 提出 ",[1225,120188,120189],{},"f-差分隐私（f-DP）","：用一个",[1225,120192,120193],{},"权衡函数（tradeoff function）",[15,120195,120197,120210],{"className":120196,"translate":19},[18],[15,120198,120200],{"className":120199},[23],[25,120201,120202],{"xmlns":27},[29,120203,120204,120208],{},[32,120205,120206],{},[35,120207,37],{},[39,120209,37],{"encoding":41},[15,120211,120213],{"className":120212,"ariaHidden":46},[45],[15,120214,120216,120219],{"className":120215},[50],[15,120217],{"className":120218,"style":55},[54],[15,120220,37],{"className":120221,"style":61},[59,60]," 刻画两个输出分布 ",[15,120224,120226,120243],{"className":120225,"translate":19},[18],[15,120227,120229],{"className":120228},[23],[25,120230,120231],{"xmlns":27},[29,120232,120233,120241],{},[32,120234,120235,120237,120239],{},[35,120236,206],{},[110,120238,551],{"separator":46},[35,120240,213],{},[39,120242,556],{"encoding":41},[15,120244,120246],{"className":120245,"ariaHidden":46},[45],[15,120247,120249,120252,120255,120258,120261],{"className":120248},[50],[15,120250],{"className":120251,"style":566},[54],[15,120253,206],{"className":120254,"style":334},[59,60],[15,120256,551],{"className":120257},[573],[15,120259],{"className":120260,"style":406},[157],[15,120262,213],{"className":120263},[59,60]," 上「漏报率—误报率」的权衡曲线：",[15,120266,120268],{"className":120267,"translate":19},[180],[15,120269,120271,120368],{"className":120270,"translate":19},[18],[15,120272,120274],{"className":120273},[23],[25,120275,120276],{"xmlns":27,"display":189},[29,120277,120278,120365],{},[32,120279,120280,120282,120284,120286,120288,120290,120292,120294,120296,120298,120300,120311,120313,120315,120317,120319,120321,120323,120325,120327,120329,120331,120333,120335,120337,120339,120341,120343,120345,120347,120349,120351,120353,120355,120357,120359,120361,120363],{},[35,120281,5392],{},[110,120283,113],{"stretchy":112},[35,120285,206],{},[110,120287,551],{"separator":46},[35,120289,213],{},[110,120291,120],{"stretchy":112},[110,120293,113],{"stretchy":112},[35,120295,44754],{},[110,120297,120],{"stretchy":112},[110,120299,123],{},[6016,120301,120302,120309],{},[32,120303,120304,120307],{},[35,120305,120306],{},"inf",[110,120308,4103],{},[35,120310,603],{},[110,120312,2898],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,120314,206],{},[110,120316,113],{"stretchy":112},[35,120318,603],{},[110,120320,120],{"stretchy":112},[1297,120322,4283],{},[110,120324,1015],{},[1297,120326,4283],{},[35,120328,213],{},[110,120330,113],{"stretchy":112},[35,120332,603],{},[110,120334,120],{"stretchy":112},[110,120336,6928],{},[115,120338,117],{},[110,120340,4813],{},[35,120342,44754],{},[110,120344,2908],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[110,120346,551],{"separator":46},[157,120348],{"width":3262},[35,120350,44754],{},[110,120352,5909],{},[110,120354,230],{"stretchy":112},[115,120356,126],{},[110,120358,551],{"separator":46},[115,120360,117],{},[110,120362,257],{"stretchy":112},[35,120364,4375],{"mathvariant":209},[39,120366,120367],{"encoding":41},"T(P,Q)(\\alpha)\n=\\inf_{A}\\big\\{P(A)\\ :\\ Q(A)\\ge1-\\alpha\\big\\},\n\\qquad \\alpha\\in[0,1] .",[15,120369,120371,120416,120511,120538,120556,120592],{"className":120370,"ariaHidden":46},[45],[15,120372,120374,120377,120380,120383,120386,120389,120392,120395,120398,120401,120404,120407,120410,120413],{"className":120373},[50],[15,120375],{"className":120376,"style":139},[54],[15,120378,5392],{"className":120379,"style":334},[59,60],[15,120381,113],{"className":120382},[146],[15,120384,206],{"className":120385,"style":334},[59,60],[15,120387,551],{"className":120388},[573],[15,120390],{"className":120391,"style":406},[157],[15,120393,213],{"className":120394},[59,60],[15,120396,120],{"className":120397},[153],[15,120399,113],{"className":120400},[146],[15,120402,44754],{"className":120403,"style":44784},[59,60],[15,120405,120],{"className":120406},[153],[15,120408],{"className":120409,"style":158},[157],[15,120411,123],{"className":120412},[162],[15,120414],{"className":120415,"style":158},[157],[15,120417,120419,120423,120475,120478,120484,120487,120490,120493,120496,120499,120502,120505,120508],{"className":120418},[50],[15,120420],{"className":120421,"style":120422},[54],"height:1.5943em;vertical-align:-0.7443em;",[15,120424,120426],{"className":120425},[1484,13716],[15,120427,120429,120466],{"className":120428},[285,286],[15,120430,120432,120463],{"className":120431},[290],[15,120433,120435,120450],{"className":120434,"style":12597},[294],[15,120436,120438,120441],{"style":120437},"top:-2.3557em;margin-left:0em;",[15,120439],{"className":120440,"style":461},[302],[15,120442,120444],{"className":120443},[307,308,309,310],[15,120445,120447],{"className":120446},[59,310],[15,120448,603],{"className":120449},[59,60,310],[15,120451,120452,120455],{"style":11863},[15,120453],{"className":120454,"style":461},[302],[15,120456,120457],{},[15,120458,120460,120461],{"className":120459},[1484],"in",[15,120462,37],{"style":94834},[15,120464,318],{"className":120465},[317],[15,120467,120469],{"className":120468},[290],[15,120470,120473],{"className":120471,"style":120472},[294],"height:0.7443em;",[15,120474],{},[15,120476],{"className":120477,"style":406},[157],[15,120479,120481],{"className":120480},[59],[15,120482,2898],{"className":120483},[419,9674],[15,120485,206],{"className":120486,"style":334},[59,60],[15,120488,113],{"className":120489},[146],[15,120491,603],{"className":120492},[59,60],[15,120494,120],{"className":120495},[153],[15,120497,4283],{"className":120498},[157],[15,120500],{"className":120501,"style":158},[157],[15,120503,1015],{"className":120504},[162],[15,120506,4283],{"className":120507},[157],[15,120509],{"className":120510,"style":158},[157],[15,120512,120514,120517,120520,120523,120526,120529,120532,120535],{"className":120513},[50],[15,120515],{"className":120516,"style":139},[54],[15,120518,213],{"className":120519},[59,60],[15,120521,113],{"className":120522},[146],[15,120524,603],{"className":120525},[59,60],[15,120527,120],{"className":120528},[153],[15,120530],{"className":120531,"style":158},[157],[15,120533,6928],{"className":120534},[162],[15,120536],{"className":120537,"style":158},[157],[15,120539,120541,120544,120547,120550,120553],{"className":120540},[50],[15,120542],{"className":120543,"style":12578},[54],[15,120545,117],{"className":120546},[59],[15,120548],{"className":120549,"style":2587},[157],[15,120551,4813],{"className":120552},[2591],[15,120554],{"className":120555,"style":2587},[157],[15,120557,120559,120562,120565,120571,120574,120577,120580,120583,120586,120589],{"className":120558},[50],[15,120560],{"className":120561,"style":20563},[54],[15,120563,44754],{"className":120564,"style":44784},[59,60],[15,120566,120568],{"className":120567},[59],[15,120569,2908],{"className":120570},[419,9674],[15,120572,551],{"className":120573},[573],[15,120575],{"className":120576,"style":3634},[157],[15,120578],{"className":120579,"style":406},[157],[15,120581,44754],{"className":120582,"style":44784},[59,60],[15,120584],{"className":120585,"style":158},[157],[15,120587,5909],{"className":120588},[162],[15,120590],{"className":120591,"style":158},[157],[15,120593,120595,120598,120601,120604,120607,120610,120613,120616],{"className":120594},[50],[15,120596],{"className":120597,"style":139},[54],[15,120599,230],{"className":120600},[146],[15,120602,126],{"className":120603},[59],[15,120605,551],{"className":120606},[573],[15,120608],{"className":120609,"style":406},[157],[15,120611,117],{"className":120612},[59],[15,120614,257],{"className":120615},[153],[15,120617,4375],{"className":120618},[59],[11,120620,120621,120622,78067,120650,120678,120679,120754,120755,120894],{},"机制 ",[15,120623,120625,120638],{"className":120624,"translate":19},[18],[15,120626,120628],{"className":120627},[23],[25,120629,120630],{"xmlns":27},[29,120631,120632,120636],{},[32,120633,120634],{},[35,120635,25567],{},[39,120637,25567],{"encoding":41},[15,120639,120641],{"className":120640,"ariaHidden":46},[45],[15,120642,120644,120647],{"className":120643},[50],[15,120645],{"className":120646,"style":664},[54],[15,120648,25567],{"className":120649,"style":25601},[59,60],[15,120651,120653,120666],{"className":120652,"translate":19},[18],[15,120654,120656],{"className":120655},[23],[25,120657,120658],{"xmlns":27},[29,120659,120660,120664],{},[32,120661,120662],{},[35,120663,37],{},[39,120665,37],{"encoding":41},[15,120667,120669],{"className":120668,"ariaHidden":46},[45],[15,120670,120672,120675],{"className":120671},[50],[15,120673],{"className":120674,"style":55},[54],[15,120676,37],{"className":120677,"style":61},[59,60],"-DP，若对所有相邻 ",[15,120680,120682,120704],{"className":120681,"translate":19},[18],[15,120683,120685],{"className":120684},[23],[25,120686,120687],{"xmlns":27},[29,120688,120689,120701],{},[32,120690,120691,120693,120695],{},[35,120692,199],{},[110,120694,551],{"separator":46},[6814,120696,120697,120699],{},[35,120698,199],{},[110,120700,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[39,120702,120703],{"encoding":41},"D,D'",[15,120705,120707],{"className":120706,"ariaHidden":46},[45],[15,120708,120710,120713,120716,120719,120722],{"className":120709},[50],[15,120711],{"className":120712,"style":64161},[54],[15,120714,199],{"className":120715,"style":277},[59,60],[15,120717,551],{"className":120718},[573],[15,120720],{"className":120721,"style":406},[157],[15,120723,120725,120728],{"className":120724},[59],[15,120726,199],{"className":120727,"style":277},[59,60],[15,120729,120731],{"className":120730},[281],[15,120732,120734],{"className":120733},[285],[15,120735,120737],{"className":120736},[290],[15,120738,120740],{"className":120739,"style":6862},[294],[15,120741,120742,120745],{"style":6865},[15,120743],{"className":120744,"style":303},[302],[15,120746,120748],{"className":120747},[307,308,309,310],[15,120749,120751],{"className":120750},[59,310],[15,120752,6820],{"className":120753},[59,310],"，恒有 ",[15,120756,120758,120802],{"className":120757,"translate":19},[18],[15,120759,120761],{"className":120760},[23],[25,120762,120763],{"xmlns":27},[29,120764,120765,120799],{},[32,120766,120767,120769,120771,120773,120775,120777,120779,120781,120783,120785,120791,120793,120795,120797],{},[35,120768,5392],{},[110,120770,113],{"stretchy":112},[35,120772,25567],{},[110,120774,113],{"stretchy":112},[35,120776,199],{},[110,120778,120],{"stretchy":112},[110,120780,551],{"separator":46},[35,120782,25567],{},[110,120784,113],{"stretchy":112},[6814,120786,120787,120789],{},[35,120788,199],{},[110,120790,6820],{"mathvariant":209,"lspace":1247,"rspace":1247},[110,120792,120],{"stretchy":112},[110,120794,120],{"stretchy":112},[110,120796,6928],{},[35,120798,37],{},[39,120800,120801],{"encoding":41},"T(M(D),M(D'))\\ge f",[15,120803,120805,120885],{"className":120804,"ariaHidden":46},[45],[15,120806,120808,120811,120814,120817,120820,120823,120826,120829,120832,120835,120838,120841,120873,120876,120879,120882],{"className":120807},[50],[15,120809],{"className":120810,"style":6843},[54],[15,120812,5392],{"className":120813,"style":334},[59,60],[15,120815,113],{"className":120816},[146],[15,120818,25567],{"className":120819,"style":25601},[59,60],[15,120821,113],{"className":120822},[146],[15,120824,199],{"className":120825,"style":277},[59,60],[15,120827,120],{"className":120828},[153],[15,120830,551],{"className":120831},[573],[15,120833],{"className":120834,"style":406},[157],[15,120836,25567],{"className":120837,"style":25601},[59,60],[15,120839,113],{"className":120840},[146],[15,120842,120844,120847],{"className":120843},[59],[15,120845,199],{"className":120846,"style":277},[59,60],[15,120848,120850],{"className":120849},[281],[15,120851,120853],{"className":120852},[285],[15,120854,120856],{"className":120855},[290],[15,120857,120859],{"className":120858,"style":6862},[294],[15,120860,120861,120864],{"style":6865},[15,120862],{"className":120863,"style":303},[302],[15,120865,120867],{"className":120866},[307,308,309,310],[15,120868,120870],{"className":120869},[59,310],[15,120871,6820],{"className":120872},[59,310],[15,120874,19047],{"className":120875},[153],[15,120877],{"className":120878,"style":158},[157],[15,120880,6928],{"className":120881},[162],[15,120883],{"className":120884,"style":158},[157],[15,120886,120888,120891],{"className":120887},[50],[15,120889],{"className":120890,"style":55},[54],[15,120892,37],{"className":120893,"style":61},[59,60],"。可以证明：",[10027,120896,120897],{},[6665,120898,120899,32089,120902,120974,120975,121023,121024,121052],{},[1225,120900,120901],{},"权衡曲线与 f-散度互相决定。",[15,120903,120905,120935],{"className":120904,"translate":19},[18],[15,120906,120908],{"className":120907},[23],[25,120909,120910],{"xmlns":27},[29,120911,120912,120932],{},[32,120913,120914,120916,120918,120920,120922,120924,120926,120928,120930],{},[35,120915,5392],{},[110,120917,113],{"stretchy":112},[35,120919,206],{},[110,120921,551],{"separator":46},[35,120923,213],{},[110,120925,120],{"stretchy":112},[110,120927,113],{"stretchy":112},[35,120929,44754],{},[110,120931,120],{"stretchy":112},[39,120933,120934],{"encoding":41},"T(P,Q)(\\alpha)",[15,120936,120938],{"className":120937,"ariaHidden":46},[45],[15,120939,120941,120944,120947,120950,120953,120956,120959,120962,120965,120968,120971],{"className":120940},[50],[15,120942],{"className":120943,"style":139},[54],[15,120945,5392],{"className":120946,"style":334},[59,60],[15,120948,113],{"className":120949},[146],[15,120951,206],{"className":120952,"style":334},[59,60],[15,120954,551],{"className":120955},[573],[15,120957],{"className":120958,"style":406},[157],[15,120960,213],{"className":120961},[59,60],[15,120963,120],{"className":120964},[153],[15,120966,113],{"className":120967},[146],[15,120969,44754],{"className":120970,"style":44784},[59,60],[15,120972,120],{"className":120973},[153]," 只依赖似然比 ",[15,120976,120978,120999],{"className":120977,"translate":19},[18],[15,120979,120981],{"className":120980},[23],[25,120982,120983],{"xmlns":27},[29,120984,120985,120997],{},[32,120986,120987,120989,120991,120993,120995],{},[35,120988,244],{},[35,120990,206],{},[35,120992,941],{"mathvariant":209},[35,120994,244],{},[35,120996,213],{},[39,120998,114641],{"encoding":41},[15,121000,121002],{"className":121001,"ariaHidden":46},[45],[15,121003,121005,121008,121011,121014,121017,121020],{"className":121004},[50],[15,121006],{"className":121007,"style":139},[54],[15,121009,244],{"className":121010},[59,60],[15,121012,206],{"className":121013,"style":334},[59,60],[15,121015,941],{"className":121016},[59],[15,121018,244],{"className":121019},[59,60],[15,121021,213],{"className":121022},[59,60]," 的分布，因此 ",[15,121025,121027,121040],{"className":121026,"translate":19},[18],[15,121028,121030],{"className":121029},[23],[25,121031,121032],{"xmlns":27},[29,121033,121034,121038],{},[32,121035,121036],{},[35,121037,5392],{},[39,121039,5392],{"encoding":41},[15,121041,121043],{"className":121042,"ariaHidden":46},[45],[15,121044,121046,121049],{"className":121045},[50],[15,121047],{"className":121048,"style":664},[54],[15,121050,5392],{"className":121051,"style":334},[59,60]," 与\"全体 f-散度\"携带同样的信息。对 hockey-stick 生成元族",[15,121054,121056],{"className":121055,"translate":19},[180],[15,121057,121059,121126],{"className":121058,"translate":19},[18],[15,121060,121062],{"className":121061},[23],[25,121063,121064],{"xmlns":27,"display":189},[29,121065,121066,121123],{},[32,121067,121068,121075,121077,121079,121081,121083,121085,121087,121089,121091,121093,121095,121097,121099,121101,121103,121105,121107,121109,121111,121113,121115,121117,121119,121121],{},[195,121069,121070,121072],{},[35,121071,4158],{},[35,121073,121074],{},"γ",[110,121076,113],{"stretchy":112},[35,121078,769],{},[110,121080,120],{"stretchy":112},[110,121082,123],{},[35,121084,52387],{},[110,121086,4103],{},[110,121088,2898],{"stretchy":112},[115,121090,126],{},[110,121092,551],{"separator":46},[1297,121094,1299],{},[35,121096,769],{},[110,121098,4813],{},[35,121100,121074],{},[110,121102,2908],{"stretchy":112},[110,121104,551],{"separator":46},[157,121106],{"width":3262},[35,121108,121074],{},[110,121110,5909],{},[110,121112,230],{"stretchy":112},[115,121114,126],{},[110,121116,551],{"separator":46},[115,121118,117],{},[110,121120,257],{"stretchy":112},[110,121122,551],{"separator":46},[39,121124,121125],{"encoding":41},"g_\\gamma(t)=\\max\\{0,\\,t-\\gamma\\},\n\\qquad \\gamma\\in[0,1],",[15,121127,121129,121194,121230,121263],{"className":121128,"ariaHidden":46},[45],[15,121130,121132,121135,121176,121179,121182,121185,121188,121191],{"className":121131},[50],[15,121133],{"className":121134,"style":270},[54],[15,121136,121138,121141],{"className":121137},[59],[15,121139,4158],{"className":121140,"style":981},[59,60],[15,121142,121144],{"className":121143},[281],[15,121145,121147,121168],{"className":121146},[285,286],[15,121148,121150,121165],{"className":121149},[290],[15,121151,121153],{"className":121152,"style":44929},[294],[15,121154,121155,121158],{"style":18843},[15,121156],{"className":121157,"style":303},[302],[15,121159,121161],{"className":121160},[307,308,309,310],[15,121162,121074],{"className":121163,"style":121164},[59,60,310],"margin-right:0.0556em;",[15,121166,318],{"className":121167},[317],[15,121169,121171],{"className":121170},[290],[15,121172,121174],{"className":121173,"style":325},[294],[15,121175],{},[15,121177,113],{"className":121178},[146],[15,121180,769],{"className":121181},[59,60],[15,121183,120],{"className":121184},[153],[15,121186],{"className":121187,"style":158},[157],[15,121189,123],{"className":121190},[162],[15,121192],{"className":121193,"style":158},[157],[15,121195,121197,121200,121203,121206,121209,121212,121215,121218,121221,121224,121227],{"className":121196},[50],[15,121198],{"className":121199,"style":139},[54],[15,121201,52387],{"className":121202},[1484],[15,121204,2898],{"className":121205},[146],[15,121207,126],{"className":121208},[59],[15,121210,551],{"className":121211},[573],[15,121213],{"className":121214,"style":406},[157],[15,121216],{"className":121217,"style":406},[157],[15,121219,769],{"className":121220},[59,60],[15,121222],{"className":121223,"style":2587},[157],[15,121225,4813],{"className":121226},[2591],[15,121228],{"className":121229,"style":2587},[157],[15,121231,121233,121236,121239,121242,121245,121248,121251,121254,121257,121260],{"className":121232},[50],[15,121234],{"className":121235,"style":139},[54],[15,121237,121074],{"className":121238,"style":121164},[59,60],[15,121240,2908],{"className":121241},[153],[15,121243,551],{"className":121244},[573],[15,121246],{"className":121247,"style":3634},[157],[15,121249],{"className":121250,"style":406},[157],[15,121252,121074],{"className":121253,"style":121164},[59,60],[15,121255],{"className":121256,"style":158},[157],[15,121258,5909],{"className":121259},[162],[15,121261],{"className":121262,"style":158},[157],[15,121264,121266,121269,121272,121275,121278,121281,121284,121287],{"className":121265},[50],[15,121267],{"className":121268,"style":139},[54],[15,121270,230],{"className":121271},[146],[15,121273,126],{"className":121274},[59],[15,121276,551],{"className":121277},[573],[15,121279],{"className":121280,"style":406},[157],[15,121282,117],{"className":121283},[59],[15,121285,257],{"className":121286},[153],[15,121288,551],{"className":121289},[573],[11,121291,121292,121293,121474,121475,8667,121504,121555],{},"（Dong–Roth–Su 的 ",[15,121294,121296,121344],{"className":121295,"translate":19},[18],[15,121297,121299],{"className":121298},[23],[25,121300,121301],{"xmlns":27},[29,121302,121303,121341],{},[32,121304,121305,121311,121313,121315,121317,121319,121321,121323,121325,121327,121329,121331,121333,121335,121337,121339],{},[195,121306,121307,121309],{},[35,121308,38665],{},[35,121310,121074],{},[110,121312,113],{"stretchy":112},[35,121314,769],{},[110,121316,120],{"stretchy":112},[110,121318,123],{},[35,121320,52387],{},[110,121322,4103],{},[110,121324,2898],{"stretchy":112},[115,121326,126],{},[110,121328,551],{"separator":46},[35,121330,769],{},[110,121332,4813],{},[115,121334,117],{},[110,121336,2470],{},[35,121338,121074],{},[110,121340,2908],{"stretchy":112},[39,121342,121343],{"encoding":41},"h_\\gamma(t)=\\max\\{0,t-1+\\gamma\\}",[15,121345,121347,121411,121444,121462],{"className":121346,"ariaHidden":46},[45],[15,121348,121350,121353,121393,121396,121399,121402,121405,121408],{"className":121349},[50],[15,121351],{"className":121352,"style":270},[54],[15,121354,121356,121359],{"className":121355},[59],[15,121357,38665],{"className":121358},[59,60],[15,121360,121362],{"className":121361},[281],[15,121363,121365,121385],{"className":121364},[285,286],[15,121366,121368,121382],{"className":121367},[290],[15,121369,121371],{"className":121370,"style":44929},[294],[15,121372,121373,121376],{"style":382},[15,121374],{"className":121375,"style":303},[302],[15,121377,121379],{"className":121378},[307,308,309,310],[15,121380,121074],{"className":121381,"style":121164},[59,60,310],[15,121383,318],{"className":121384},[317],[15,121386,121388],{"className":121387},[290],[15,121389,121391],{"className":121390,"style":325},[294],[15,121392],{},[15,121394,113],{"className":121395},[146],[15,121397,769],{"className":121398},[59,60],[15,121400,120],{"className":121401},[153],[15,121403],{"className":121404,"style":158},[157],[15,121406,123],{"className":121407},[162],[15,121409],{"className":121410,"style":158},[157],[15,121412,121414,121417,121420,121423,121426,121429,121432,121435,121438,121441],{"className":121413},[50],[15,121415],{"className":121416,"style":139},[54],[15,121418,52387],{"className":121419},[1484],[15,121421,2898],{"className":121422},[146],[15,121424,126],{"className":121425},[59],[15,121427,551],{"className":121428},[573],[15,121430],{"className":121431,"style":406},[157],[15,121433,769],{"className":121434},[59,60],[15,121436],{"className":121437,"style":2587},[157],[15,121439,4813],{"className":121440},[2591],[15,121442],{"className":121443,"style":2587},[157],[15,121445,121447,121450,121453,121456,121459],{"className":121446},[50],[15,121448],{"className":121449,"style":12578},[54],[15,121451,117],{"className":121452},[59],[15,121454],{"className":121455,"style":2587},[157],[15,121457,2470],{"className":121458},[2591],[15,121460],{"className":121461,"style":2587},[157],[15,121463,121465,121468,121471],{"className":121464},[50],[15,121466],{"className":121467,"style":139},[54],[15,121469,121074],{"className":121470,"style":121164},[59,60],[15,121472,2908],{"className":121473},[153]," 就是把 ",[15,121476,121478,121492],{"className":121477,"translate":19},[18],[15,121479,121481],{"className":121480},[23],[25,121482,121483],{"xmlns":27},[29,121484,121485,121489],{},[32,121486,121487],{},[35,121488,121074],{},[39,121490,121491],{"encoding":41},"\\gamma",[15,121493,121495],{"className":121494,"ariaHidden":46},[45],[15,121496,121498,121501],{"className":121497},[50],[15,121499],{"className":121500,"style":2276},[54],[15,121502,121074],{"className":121503,"style":121164},[59,60],[15,121505,121507,121525],{"className":121506,"translate":19},[18],[15,121508,121510],{"className":121509},[23],[25,121511,121512],{"xmlns":27},[29,121513,121514,121522],{},[32,121515,121516,121518,121520],{},[115,121517,117],{},[110,121519,4813],{},[35,121521,121074],{},[39,121523,121524],{"encoding":41},"1-\\gamma",[15,121526,121528,121546],{"className":121527,"ariaHidden":46},[45],[15,121529,121531,121534,121537,121540,121543],{"className":121530},[50],[15,121532],{"className":121533,"style":12578},[54],[15,121535,117],{"className":121536},[59],[15,121538],{"className":121539,"style":2587},[157],[15,121541,4813],{"className":121542},[2591],[15,121544],{"className":121545,"style":2587},[157],[15,121547,121549,121552],{"className":121548},[50],[15,121550],{"className":121551,"style":2276},[54],[15,121553,121074],{"className":121554,"style":121164},[59,60]," 的同一族），变分表示给出干净的检验集形式：",[15,121557,121559],{"className":121558,"translate":19},[180],[15,121560,121562,121640],{"className":121561,"translate":19},[18],[15,121563,121565],{"className":121564},[23],[25,121566,121567],{"xmlns":27,"display":189},[29,121568,121569,121637],{},[32,121570,121571,121581,121583,121585,121587,121589,121591,121593,121609,121611,121613,121615,121617,121619,121621,121623,121625,121627,121629,121631,121633,121635],{},[195,121572,121573,121575],{},[35,121574,199],{},[195,121576,121577,121579],{},[35,121578,4158],{},[35,121580,121074],{},[110,121582,113],{"stretchy":112},[35,121584,206],{},[35,121586,210],{"mathvariant":209},[35,121588,213],{},[110,121590,120],{"stretchy":112},[110,121592,123],{},[6016,121594,121595,121601],{},[32,121596,121597,121599],{},[35,121598,35432],{},[110,121600,4103],{},[32,121602,121603,121605,121607],{},[35,121604,603],{},[110,121606,5909],{},[35,121608,603],{"mathvariant":597},[110,121610,2898],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,121612,206],{},[110,121614,113],{"stretchy":112},[35,121616,603],{},[110,121618,120],{"stretchy":112},[110,121620,4813],{},[35,121622,121074],{},[1297,121624,1299],{},[35,121626,213],{},[110,121628,113],{"stretchy":112},[35,121630,603],{},[110,121632,120],{"stretchy":112},[110,121634,2908],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[35,121636,4375],{"mathvariant":209},[39,121638,121639],{"encoding":41},"D_{g_\\gamma}(P\\|Q)\n=\\sup_{A\\in\\mathcal A}\\big\\{P(A)\n-\\gamma\\,Q(A)\\big\\}.",[15,121641,121643,121757,121846],{"className":121642,"ariaHidden":46},[45],[15,121644,121646,121650,121733,121736,121739,121742,121745,121748,121751,121754],{"className":121645},[50],[15,121647],{"className":121648,"style":121649},[54],"height:1.0973em;vertical-align:-0.3473em;",[15,121651,121653,121656],{"className":121652},[59],[15,121654,199],{"className":121655,"style":277},[59,60],[15,121657,121659],{"className":121658},[281],[15,121660,121662,121724],{"className":121661},[285,286],[15,121663,121665,121721],{"className":121664},[290],[15,121666,121668],{"className":121667,"style":44929},[294],[15,121669,121670,121673],{"style":298},[15,121671],{"className":121672,"style":303},[302],[15,121674,121676],{"className":121675},[307,308,309,310],[15,121677,121679],{"className":121678},[59,310],[15,121680,121682,121685],{"className":121681},[59,310],[15,121683,4158],{"className":121684,"style":981},[59,60,310],[15,121686,121688],{"className":121687},[281],[15,121689,121691,121712],{"className":121690},[285,286],[15,121692,121694,121709],{"className":121693},[290],[15,121695,121697],{"className":121696,"style":74262},[294],[15,121698,121700,121703],{"style":121699},"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;",[15,121701],{"className":121702,"style":30206},[302],[15,121704,121706],{"className":121705},[307,30210,9674,310],[15,121707,121074],{"className":121708,"style":121164},[59,60,310],[15,121710,318],{"className":121711},[317],[15,121713,121715],{"className":121714},[290],[15,121716,121719],{"className":121717,"style":121718},[294],"height:0.2819em;",[15,121720],{},[15,121722,318],{"className":121723},[317],[15,121725,121727],{"className":121726},[290],[15,121728,121731],{"className":121729,"style":121730},[294],"height:0.3473em;",[15,121732],{},[15,121734,113],{"className":121735},[146],[15,121737,206],{"className":121738,"style":334},[59,60],[15,121740,210],{"className":121741},[59],[15,121743,213],{"className":121744},[59,60],[15,121746,120],{"className":121747},[153],[15,121749],{"className":121750,"style":158},[157],[15,121752,123],{"className":121753},[162],[15,121755],{"className":121756,"style":158},[157],[15,121758,121760,121763,121816,121819,121825,121828,121831,121834,121837,121840,121843],{"className":121759},[50],[15,121761],{"className":121762,"style":36353},[54],[15,121764,121766],{"className":121765},[1484,13716],[15,121767,121769,121808],{"className":121768},[285,286],[15,121770,121772,121805],{"className":121771},[290],[15,121773,121775,121795],{"className":121774,"style":2345},[294],[15,121776,121777,121780],{"style":36368},[15,121778],{"className":121779,"style":461},[302],[15,121781,121783],{"className":121782},[307,308,309,310],[15,121784,121786,121789,121792],{"className":121785},[59,310],[15,121787,603],{"className":121788},[59,60,310],[15,121790,5909],{"className":121791},[162,310],[15,121793,603],{"className":121794},[59,624,310],[15,121796,121797,121800],{"style":11863},[15,121798],{"className":121799,"style":461},[302],[15,121801,121802],{},[15,121803,35432],{"className":121804},[1484],[15,121806,318],{"className":121807},[317],[15,121809,121811],{"className":121810},[290],[15,121812,121814],{"className":121813,"style":36406},[294],[15,121815],{},[15,121817],{"className":121818,"style":406},[157],[15,121820,121822],{"className":121821},[59],[15,121823,2898],{"className":121824},[419,9674],[15,121826,206],{"className":121827,"style":334},[59,60],[15,121829,113],{"className":121830},[146],[15,121832,603],{"className":121833},[59,60],[15,121835,120],{"className":121836},[153],[15,121838],{"className":121839,"style":2587},[157],[15,121841,4813],{"className":121842},[2591],[15,121844],{"className":121845,"style":2587},[157],[15,121847,121849,121852,121855,121858,121861,121864,121867,121870,121876],{"className":121848},[50],[15,121850],{"className":121851,"style":20563},[54],[15,121853,121074],{"className":121854,"style":121164},[59,60],[15,121856],{"className":121857,"style":406},[157],[15,121859,213],{"className":121860},[59,60],[15,121862,113],{"className":121863},[146],[15,121865,603],{"className":121866},[59,60],[15,121868,120],{"className":121869},[153],[15,121871,121873],{"className":121872},[59],[15,121874,2908],{"className":121875},[419,9674],[15,121877,4375],{"className":121878},[59],[11,121880,121881,121883,121884,121958,121959,2280,122128,122156,122157,122250],{},[1225,121882,107277],{}," 一方面，任意 ",[15,121885,121887,121909],{"className":121886,"translate":19},[18],[15,121888,121890],{"className":121889},[23],[25,121891,121892],{"xmlns":27},[29,121893,121894,121906],{},[32,121895,121896,121898,121900,121902,121904],{},[115,121897,126],{},[110,121899,9952],{},[35,121901,4158],{},[110,121903,9952],{},[115,121905,117],{},[39,121907,121908],{"encoding":41},"0\\le g\\le1",[15,121910,121912,121931,121949],{"className":121911,"ariaHidden":46},[45],[15,121913,121915,121919,121922,121925,121928],{"className":121914},[50],[15,121916],{"className":121917,"style":121918},[54],"height:0.7804em;vertical-align:-0.136em;",[15,121920,126],{"className":121921},[59],[15,121923],{"className":121924,"style":158},[157],[15,121926,9952],{"className":121927},[162],[15,121929],{"className":121930,"style":158},[157],[15,121932,121934,121937,121940,121943,121946],{"className":121933},[50],[15,121935],{"className":121936,"style":15417},[54],[15,121938,4158],{"className":121939,"style":981},[59,60],[15,121941],{"className":121942,"style":158},[157],[15,121944,9952],{"className":121945},[162],[15,121947],{"className":121948,"style":158},[157],[15,121950,121952,121955],{"className":121951},[50],[15,121953],{"className":121954,"style":172},[54],[15,121956,117],{"className":121957},[59]," 可写为指示函数的线性组合（层叠公式），而 ",[15,121960,121962,122002],{"className":121961,"translate":19},[18],[15,121963,121965],{"className":121964},[23],[25,121966,121967],{"xmlns":27},[29,121968,121969,121999],{},[32,121970,121971,121977,121979,121981,121983,121985,121987,121993,121995,121997],{},[195,121972,121973,121975],{},[35,121974,223],{},[35,121976,206],{},[110,121978,230],{"stretchy":112},[35,121980,4158],{},[110,121982,257],{"stretchy":112},[110,121984,4813],{},[35,121986,121074],{},[195,121988,121989,121991],{},[35,121990,223],{},[35,121992,213],{},[110,121994,230],{"stretchy":112},[35,121996,4158],{},[110,121998,257],{"stretchy":112},[39,122000,122001],{"encoding":41},"E_P[g]-\\gamma E_Q[g]",[15,122003,122005,122070],{"className":122004,"ariaHidden":46},[45],[15,122006,122008,122011,122052,122055,122058,122061,122064,122067],{"className":122007},[50],[15,122009],{"className":122010,"style":139},[54],[15,122012,122014,122017],{"className":122013},[59],[15,122015,223],{"className":122016,"style":25861},[59,60],[15,122018,122020],{"className":122019},[281],[15,122021,122023,122044],{"className":122022},[285,286],[15,122024,122026,122041],{"className":122025},[290],[15,122027,122029],{"className":122028,"style":379},[294],[15,122030,122032,122035],{"style":122031},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[15,122033],{"className":122034,"style":303},[302],[15,122036,122038],{"className":122037},[307,308,309,310],[15,122039,206],{"className":122040,"style":334},[59,60,310],[15,122042,318],{"className":122043},[317],[15,122045,122047],{"className":122046},[290],[15,122048,122050],{"className":122049,"style":7968},[294],[15,122051],{},[15,122053,230],{"className":122054},[146],[15,122056,4158],{"className":122057,"style":981},[59,60],[15,122059,257],{"className":122060},[153],[15,122062],{"className":122063,"style":2587},[157],[15,122065,4813],{"className":122066},[2591],[15,122068],{"className":122069,"style":2587},[157],[15,122071,122073,122076,122079,122119,122122,122125],{"className":122072},[50],[15,122074],{"className":122075,"style":270},[54],[15,122077,121074],{"className":122078,"style":121164},[59,60],[15,122080,122082,122085],{"className":122081},[59],[15,122083,223],{"className":122084,"style":25861},[59,60],[15,122086,122088],{"className":122087},[281],[15,122089,122091,122111],{"className":122090},[285,286],[15,122092,122094,122108],{"className":122093},[290],[15,122095,122097],{"className":122096,"style":379},[294],[15,122098,122099,122102],{"style":122031},[15,122100],{"className":122101,"style":303},[302],[15,122103,122105],{"className":122104},[307,308,309,310],[15,122106,213],{"className":122107},[59,60,310],[15,122109,318],{"className":122110},[317],[15,122112,122114],{"className":122113},[290],[15,122115,122117],{"className":122116,"style":325},[294],[15,122118],{},[15,122120,230],{"className":122121},[146],[15,122123,4158],{"className":122124,"style":981},[59,60],[15,122126,257],{"className":122127},[153],[15,122129,122131,122144],{"className":122130,"translate":19},[18],[15,122132,122134],{"className":122133},[23],[25,122135,122136],{"xmlns":27},[29,122137,122138,122142],{},[32,122139,122140],{},[35,122141,4158],{},[39,122143,4158],{"encoding":41},[15,122145,122147],{"className":122146,"ariaHidden":46},[45],[15,122148,122150,122153],{"className":122149},[50],[15,122151],{"className":122152,"style":2276},[54],[15,122154,4158],{"className":122155,"style":981},[59,60]," 的线性泛函，故其上确界在指示函数 ",[15,122158,122160,122182],{"className":122159,"translate":19},[18],[15,122161,122163],{"className":122162},[23],[25,122164,122165],{"xmlns":27},[29,122166,122167,122179],{},[32,122168,122169,122171,122173],{},[35,122170,4158],{},[110,122172,123],{},[195,122174,122175,122177],{},[115,122176,117],{"mathvariant":75213},[35,122178,603],{},[39,122180,122181],{"encoding":41},"g=\\mathbf1_A",[15,122183,122185,122203],{"className":122184,"ariaHidden":46},[45],[15,122186,122188,122191,122194,122197,122200],{"className":122187},[50],[15,122189],{"className":122190,"style":2276},[54],[15,122192,4158],{"className":122193,"style":981},[59,60],[15,122195],{"className":122196,"style":158},[157],[15,122198,123],{"className":122199},[162],[15,122201],{"className":122202,"style":158},[157],[15,122204,122206,122210],{"className":122205},[50],[15,122207],{"className":122208,"style":122209},[54],"height:0.7944em;vertical-align:-0.15em;",[15,122211,122213,122216],{"className":122212},[59],[15,122214,117],{"className":122215},[59,75558],[15,122217,122219],{"className":122218},[281],[15,122220,122222,122242],{"className":122221},[285,286],[15,122223,122225,122239],{"className":122224},[290],[15,122226,122228],{"className":122227,"style":379},[294],[15,122229,122230,122233],{"style":382},[15,122231],{"className":122232,"style":303},[302],[15,122234,122236],{"className":122235},[307,308,309,310],[15,122237,603],{"className":122238},[59,60,310],[15,122240,318],{"className":122241},[317],[15,122243,122245],{"className":122244},[290],[15,122246,122248],{"className":122247,"style":7968},[294],[15,122249],{}," 上达到：",[15,122252,122254],{"className":122253,"translate":19},[180],[15,122255,122257,122359],{"className":122256,"translate":19},[18],[15,122258,122260],{"className":122259},[23],[25,122261,122262],{"xmlns":27,"display":189},[29,122263,122264,122356],{},[32,122265,122266,122286,122288,122294,122296,122298,122300,122302,122304,122310,122312,122314,122316,122318,122320,122330,122332,122334,122336,122338,122340,122342,122344,122346,122348,122350,122352,122354],{},[6016,122267,122268,122274],{},[32,122269,122270,122272],{},[35,122271,35432],{},[110,122273,4103],{},[32,122275,122276,122278,122280,122282,122284],{},[115,122277,126],{},[110,122279,9952],{},[35,122281,4158],{},[110,122283,9952],{},[115,122285,117],{},[110,122287,2898],{"stretchy":112},[195,122289,122290,122292],{},[35,122291,223],{},[35,122293,206],{},[110,122295,230],{"stretchy":112},[35,122297,4158],{},[110,122299,257],{"stretchy":112},[110,122301,4813],{},[35,122303,121074],{},[195,122305,122306,122308],{},[35,122307,223],{},[35,122309,213],{},[110,122311,230],{"stretchy":112},[35,122313,4158],{},[110,122315,257],{"stretchy":112},[110,122317,2908],{"stretchy":112},[110,122319,123],{},[6016,122321,122322,122328],{},[32,122323,122324,122326],{},[35,122325,35432],{},[110,122327,4103],{},[35,122329,603],{},[110,122331,2898],{"stretchy":112},[35,122333,206],{},[110,122335,113],{"stretchy":112},[35,122337,603],{},[110,122339,120],{"stretchy":112},[110,122341,4813],{},[35,122343,121074],{},[35,122345,213],{},[110,122347,113],{"stretchy":112},[35,122349,603],{},[110,122351,120],{"stretchy":112},[110,122353,2908],{"stretchy":112},[110,122355,551],{"separator":46},[39,122357,122358],{"encoding":41},"\\sup_{0\\le g\\le1}\\{E_P[g]-\\gamma E_Q[g]\\}\n=\\sup_{A}\\{P(A)-\\gamma Q(A)\\},",[15,122360,122362,122490,122558,122637],{"className":122361,"ariaHidden":46},[45],[15,122363,122365,122369,122429,122432,122472,122475,122478,122481,122484,122487],{"className":122364},[50],[15,122366],{"className":122367,"style":122368},[54],"height:1.7977em;vertical-align:-1.0477em;",[15,122370,122372],{"className":122371},[1484,13716],[15,122373,122375,122420],{"className":122374},[285,286],[15,122376,122378,122417],{"className":122377},[290],[15,122379,122381,122407],{"className":122380,"style":2345},[294],[15,122382,122383,122386],{"style":60922},[15,122384],{"className":122385,"style":461},[302],[15,122387,122389],{"className":122388},[307,308,309,310],[15,122390,122392,122395,122398,122401,122404],{"className":122391},[59,310],[15,122393,126],{"className":122394},[59,310],[15,122396,9952],{"className":122397},[162,310],[15,122399,4158],{"className":122400,"style":981},[59,60,310],[15,122402,9952],{"className":122403},[162,310],[15,122405,117],{"className":122406},[59,310],[15,122408,122409,122412],{"style":11863},[15,122410],{"className":122411,"style":461},[302],[15,122413,122414],{},[15,122415,35432],{"className":122416},[1484],[15,122418,318],{"className":122419},[317],[15,122421,122423],{"className":122422},[290],[15,122424,122427],{"className":122425,"style":122426},[294],"height:1.0477em;",[15,122428],{},[15,122430,2898],{"className":122431},[146],[15,122433,122435,122438],{"className":122434},[59],[15,122436,223],{"className":122437,"style":25861},[59,60],[15,122439,122441],{"className":122440},[281],[15,122442,122444,122464],{"className":122443},[285,286],[15,122445,122447,122461],{"className":122446},[290],[15,122448,122450],{"className":122449,"style":379},[294],[15,122451,122452,122455],{"style":122031},[15,122453],{"className":122454,"style":303},[302],[15,122456,122458],{"className":122457},[307,308,309,310],[15,122459,206],{"className":122460,"style":334},[59,60,310],[15,122462,318],{"className":122463},[317],[15,122465,122467],{"className":122466},[290],[15,122468,122470],{"className":122469,"style":7968},[294],[15,122471],{},[15,122473,230],{"className":122474},[146],[15,122476,4158],{"className":122477,"style":981},[59,60],[15,122479,257],{"className":122480},[153],[15,122482],{"className":122483,"style":2587},[157],[15,122485,4813],{"className":122486},[2591],[15,122488],{"className":122489,"style":2587},[157],[15,122491,122493,122496,122499,122539,122542,122545,122549,122552,122555],{"className":122492},[50],[15,122494],{"className":122495,"style":270},[54],[15,122497,121074],{"className":122498,"style":121164},[59,60],[15,122500,122502,122505],{"className":122501},[59],[15,122503,223],{"className":122504,"style":25861},[59,60],[15,122506,122508],{"className":122507},[281],[15,122509,122511,122531],{"className":122510},[285,286],[15,122512,122514,122528],{"className":122513},[290],[15,122515,122517],{"className":122516,"style":379},[294],[15,122518,122519,122522],{"style":122031},[15,122520],{"className":122521,"style":303},[302],[15,122523,122525],{"className":122524},[307,308,309,310],[15,122526,213],{"className":122527},[59,60,310],[15,122529,318],{"className":122530},[317],[15,122532,122534],{"className":122533},[290],[15,122535,122537],{"className":122536,"style":325},[294],[15,122538],{},[15,122540,230],{"className":122541},[146],[15,122543,4158],{"className":122544,"style":981},[59,60],[15,122546,122548],{"className":122547},[153],"]}",[15,122550],{"className":122551,"style":158},[157],[15,122553,123],{"className":122554},[162],[15,122556],{"className":122557,"style":158},[157],[15,122559,122561,122565,122613,122616,122619,122622,122625,122628,122631,122634],{"className":122560},[50],[15,122562],{"className":122563,"style":122564},[54],"height:1.6888em;vertical-align:-0.9388em;",[15,122566,122568],{"className":122567},[1484,13716],[15,122569,122571,122604],{"className":122570},[285,286],[15,122572,122574,122601],{"className":122573},[290],[15,122575,122577,122591],{"className":122576,"style":2345},[294],[15,122578,122579,122582],{"style":36368},[15,122580],{"className":122581,"style":461},[302],[15,122583,122585],{"className":122584},[307,308,309,310],[15,122586,122588],{"className":122587},[59,310],[15,122589,603],{"className":122590},[59,60,310],[15,122592,122593,122596],{"style":11863},[15,122594],{"className":122595,"style":461},[302],[15,122597,122598],{},[15,122599,35432],{"className":122600},[1484],[15,122602,318],{"className":122603},[317],[15,122605,122607],{"className":122606},[290],[15,122608,122611],{"className":122609,"style":122610},[294],"height:0.9388em;",[15,122612],{},[15,122614,2898],{"className":122615},[146],[15,122617,206],{"className":122618,"style":334},[59,60],[15,122620,113],{"className":122621},[146],[15,122623,603],{"className":122624},[59,60],[15,122626,120],{"className":122627},[153],[15,122629],{"className":122630,"style":2587},[157],[15,122632,4813],{"className":122633},[2591],[15,122635],{"className":122636,"style":2587},[157],[15,122638,122640,122643,122646,122649,122652,122655,122658],{"className":122639},[50],[15,122641],{"className":122642,"style":139},[54],[15,122644,121074],{"className":122645,"style":121164},[59,60],[15,122647,213],{"className":122648},[59,60],[15,122650,113],{"className":122651},[146],[15,122653,603],{"className":122654},[59,60],[15,122656,60999],{"className":122657},[153],[15,122659,551],{"className":122660},[573],[11,122662,122663,122664,122837,122838,18708,122984,123099,123100,123248,123249,123535],{},"且由 ",[15,122665,122667,122709],{"className":122666,"translate":19},[18],[15,122668,122670],{"className":122669},[23],[25,122671,122672],{"xmlns":27},[29,122673,122674,122706],{},[32,122675,122676,122682,122684,122686,122688,122690,122696,122698,122700,122702,122704],{},[195,122677,122678,122680],{},[35,122679,223],{},[35,122681,206],{},[110,122683,230],{"stretchy":112},[35,122685,4158],{},[110,122687,257],{"stretchy":112},[110,122689,123],{},[195,122691,122692,122694],{},[35,122693,223],{},[35,122695,213],{},[110,122697,230],{"stretchy":112},[35,122699,4158],{},[1297,122701,1299],{},[35,122703,769],{},[110,122705,257],{"stretchy":112},[39,122707,122708],{"encoding":41},"E_P[g]=E_Q[g\\,t]",[15,122710,122712,122776],{"className":122711,"ariaHidden":46},[45],[15,122713,122715,122718,122758,122761,122764,122767,122770,122773],{"className":122714},[50],[15,122716],{"className":122717,"style":139},[54],[15,122719,122721,122724],{"className":122720},[59],[15,122722,223],{"className":122723,"style":25861},[59,60],[15,122725,122727],{"className":122726},[281],[15,122728,122730,122750],{"className":122729},[285,286],[15,122731,122733,122747],{"className":122732},[290],[15,122734,122736],{"className":122735,"style":379},[294],[15,122737,122738,122741],{"style":122031},[15,122739],{"className":122740,"style":303},[302],[15,122742,122744],{"className":122743},[307,308,309,310],[15,122745,206],{"className":122746,"style":334},[59,60,310],[15,122748,318],{"className":122749},[317],[15,122751,122753],{"className":122752},[290],[15,122754,122756],{"className":122755,"style":7968},[294],[15,122757],{},[15,122759,230],{"className":122760},[146],[15,122762,4158],{"className":122763,"style":981},[59,60],[15,122765,257],{"className":122766},[153],[15,122768],{"className":122769,"style":158},[157],[15,122771,123],{"className":122772},[162],[15,122774],{"className":122775,"style":158},[157],[15,122777,122779,122782,122822,122825,122828,122831,122834],{"className":122778},[50],[15,122780],{"className":122781,"style":270},[54],[15,122783,122785,122788],{"className":122784},[59],[15,122786,223],{"className":122787,"style":25861},[59,60],[15,122789,122791],{"className":122790},[281],[15,122792,122794,122814],{"className":122793},[285,286],[15,122795,122797,122811],{"className":122796},[290],[15,122798,122800],{"className":122799,"style":379},[294],[15,122801,122802,122805],{"style":122031},[15,122803],{"className":122804,"style":303},[302],[15,122806,122808],{"className":122807},[307,308,309,310],[15,122809,213],{"className":122810},[59,60,310],[15,122812,318],{"className":122813},[317],[15,122815,122817],{"className":122816},[290],[15,122818,122820],{"className":122819,"style":325},[294],[15,122821],{},[15,122823,230],{"className":122824},[146],[15,122826,4158],{"className":122827,"style":981},[59,60],[15,122829],{"className":122830,"style":406},[157],[15,122832,769],{"className":122833},[59,60],[15,122835,257],{"className":122836},[153],"，左端点态上确界为 ",[15,122839,122841,122877],{"className":122840,"translate":19},[18],[15,122842,122844],{"className":122843},[23],[25,122845,122846],{"xmlns":27},[29,122847,122848,122874],{},[32,122849,122850,122856,122858,122860,122862,122864,122866,122872],{},[195,122851,122852,122854],{},[35,122853,223],{},[35,122855,213],{},[110,122857,230],{"stretchy":112},[110,122859,113],{"stretchy":112},[35,122861,769],{},[110,122863,4813],{},[35,122865,121074],{},[6814,122867,122868,122870],{},[110,122869,120],{"stretchy":112},[110,122871,2470],{},[110,122873,257],{"stretchy":112},[39,122875,122876],{"encoding":41},"E_Q[(t-\\gamma)^+]",[15,122878,122880,122942],{"className":122879,"ariaHidden":46},[45],[15,122881,122883,122886,122926,122930,122933,122936,122939],{"className":122882},[50],[15,122884],{"className":122885,"style":270},[54],[15,122887,122889,122892],{"className":122888},[59],[15,122890,223],{"className":122891,"style":25861},[59,60],[15,122893,122895],{"className":122894},[281],[15,122896,122898,122918],{"className":122897},[285,286],[15,122899,122901,122915],{"className":122900},[290],[15,122902,122904],{"className":122903,"style":379},[294],[15,122905,122906,122909],{"style":122031},[15,122907],{"className":122908,"style":303},[302],[15,122910,122912],{"className":122911},[307,308,309,310],[15,122913,213],{"className":122914},[59,60,310],[15,122916,318],{"className":122917},[317],[15,122919,122921],{"className":122920},[290],[15,122922,122924],{"className":122923,"style":325},[294],[15,122925],{},[15,122927,122929],{"className":122928},[146],"[(",[15,122931,769],{"className":122932},[59,60],[15,122934],{"className":122935,"style":2587},[157],[15,122937,4813],{"className":122938},[2591],[15,122940],{"className":122941,"style":2587},[157],[15,122943,122945,122949,122952,122981],{"className":122944},[50],[15,122946],{"className":122947,"style":122948},[54],"height:1.0213em;vertical-align:-0.25em;",[15,122950,121074],{"className":122951,"style":121164},[59,60],[15,122953,122955,122958],{"className":122954},[153],[15,122956,120],{"className":122957},[153],[15,122959,122961],{"className":122960},[281],[15,122962,122964],{"className":122963},[285],[15,122965,122967],{"className":122966},[290],[15,122968,122970],{"className":122969,"style":21009},[294],[15,122971,122972,122975],{"style":6865},[15,122973],{"className":122974,"style":303},[302],[15,122976,122978],{"className":122977},[307,308,309,310],[15,122979,2470],{"className":122980},[2591,310],[15,122982,257],{"className":122983},[153],[15,122985,122987,123009],{"className":122986,"translate":19},[18],[15,122988,122990],{"className":122989},[23],[25,122991,122992],{"xmlns":27},[29,122993,122994,123006],{},[32,122995,122996],{},[195,122997,122998,123000],{},[35,122999,199],{},[195,123001,123002,123004],{},[35,123003,4158],{},[35,123005,121074],{},[39,123007,123008],{"encoding":41},"D_{g_\\gamma}",[15,123010,123012],{"className":123011,"ariaHidden":46},[45],[15,123013,123015,123019],{"className":123014},[50],[15,123016],{"className":123017,"style":123018},[54],"height:1.0307em;vertical-align:-0.3473em;",[15,123020,123022,123025],{"className":123021},[59],[15,123023,199],{"className":123024,"style":277},[59,60],[15,123026,123028],{"className":123027},[281],[15,123029,123031,123091],{"className":123030},[285,286],[15,123032,123034,123088],{"className":123033},[290],[15,123035,123037],{"className":123036,"style":44929},[294],[15,123038,123039,123042],{"style":298},[15,123040],{"className":123041,"style":303},[302],[15,123043,123045],{"className":123044},[307,308,309,310],[15,123046,123048],{"className":123047},[59,310],[15,123049,123051,123054],{"className":123050},[59,310],[15,123052,4158],{"className":123053,"style":981},[59,60,310],[15,123055,123057],{"className":123056},[281],[15,123058,123060,123080],{"className":123059},[285,286],[15,123061,123063,123077],{"className":123062},[290],[15,123064,123066],{"className":123065,"style":74262},[294],[15,123067,123068,123071],{"style":121699},[15,123069],{"className":123070,"style":30206},[302],[15,123072,123074],{"className":123073},[307,30210,9674,310],[15,123075,121074],{"className":123076,"style":121164},[59,60,310],[15,123078,318],{"className":123079},[317],[15,123081,123083],{"className":123082},[290],[15,123084,123086],{"className":123085,"style":121718},[294],[15,123087],{},[15,123089,318],{"className":123090},[317],[15,123092,123094],{"className":123093},[290],[15,123095,123097],{"className":123096,"style":121730},[294],[15,123098],{},"。另一方面取 ",[15,123101,123103,123139],{"className":123102,"translate":19},[18],[15,123104,123106],{"className":123105},[23],[25,123107,123108],{"xmlns":27},[29,123109,123110,123136],{},[32,123111,123112,123118,123120],{},[6814,123113,123114,123116],{},[35,123115,4158],{},[110,123117,7573],{},[110,123119,123],{},[195,123121,123122,123124],{},[115,123123,117],{"mathvariant":75213},[32,123125,123126,123128,123130,123132,123134],{},[110,123127,2898],{"stretchy":112},[35,123129,769],{},[110,123131,2903],{},[35,123133,121074],{},[110,123135,2908],{"stretchy":112},[39,123137,123138],{"encoding":41},"g^*=\\mathbf 1_{\\{t>\\gamma\\}}",[15,123140,123142,123186],{"className":123141,"ariaHidden":46},[45],[15,123143,123145,123148,123177,123180,123183],{"className":123144},[50],[15,123146],{"className":123147,"style":64015},[54],[15,123149,123151,123154],{"className":123150},[59],[15,123152,4158],{"className":123153,"style":981},[59,60],[15,123155,123157],{"className":123156},[281],[15,123158,123160],{"className":123159},[285],[15,123161,123163],{"className":123162},[290],[15,123164,123166],{"className":123165,"style":8499},[294],[15,123167,123168,123171],{"style":6865},[15,123169],{"className":123170,"style":303},[302],[15,123172,123174],{"className":123173},[307,308,309,310],[15,123175,7573],{"className":123176},[2591,310],[15,123178],{"className":123179,"style":158},[157],[15,123181,123],{"className":123182},[162],[15,123184],{"className":123185,"style":158},[157],[15,123187,123189,123193],{"className":123188},[50],[15,123190],{"className":123191,"style":123192},[54],"height:0.9996em;vertical-align:-0.3552em;",[15,123194,123196,123199],{"className":123195},[59],[15,123197,117],{"className":123198},[59,75558],[15,123200,123202],{"className":123201},[281],[15,123203,123205,123240],{"className":123204},[285,286],[15,123206,123208,123237],{"className":123207},[290],[15,123209,123211],{"className":123210,"style":6098},[294],[15,123212,123213,123216],{"style":75573},[15,123214],{"className":123215,"style":303},[302],[15,123217,123219],{"className":123218},[307,308,309,310],[15,123220,123222,123225,123228,123231,123234],{"className":123221},[59,310],[15,123223,2898],{"className":123224},[146,310],[15,123226,769],{"className":123227},[59,60,310],[15,123229,2903],{"className":123230},[162,310],[15,123232,121074],{"className":123233,"style":121164},[59,60,310],[15,123235,2908],{"className":123236},[153,310],[15,123238,318],{"className":123239},[317],[15,123241,123243],{"className":123242},[290],[15,123244,123246],{"className":123245,"style":6144},[294],[15,123247],{}," 恰有 ",[15,123250,123252,123316],{"className":123251,"translate":19},[18],[15,123253,123255],{"className":123254},[23],[25,123256,123257],{"xmlns":27},[29,123258,123259,123313],{},[32,123260,123261,123267,123269,123275,123277,123279,123281,123283,123285,123287,123289,123295,123297,123299,123301,123303,123305,123311],{},[195,123262,123263,123265],{},[35,123264,223],{},[35,123266,213],{},[110,123268,230],{"stretchy":112},[6814,123270,123271,123273],{},[35,123272,4158],{},[110,123274,7573],{},[110,123276,113],{"stretchy":112},[35,123278,769],{},[110,123280,4813],{},[35,123282,121074],{},[110,123284,120],{"stretchy":112},[110,123286,257],{"stretchy":112},[110,123288,123],{},[195,123290,123291,123293],{},[35,123292,223],{},[35,123294,213],{},[110,123296,230],{"stretchy":112},[110,123298,113],{"stretchy":112},[35,123300,769],{},[110,123302,4813],{},[35,123304,121074],{},[6814,123306,123307,123309],{},[110,123308,120],{"stretchy":112},[110,123310,2470],{},[110,123312,257],{"stretchy":112},[39,123314,123315],{"encoding":41},"E_Q[g^*(t-\\gamma)]=E_Q[(t-\\gamma)^+]",[15,123317,123319,123412,123433,123494],{"className":123318,"ariaHidden":46},[45],[15,123320,123322,123325,123365,123368,123397,123400,123403,123406,123409],{"className":123321},[50],[15,123323],{"className":123324,"style":270},[54],[15,123326,123328,123331],{"className":123327},[59],[15,123329,223],{"className":123330,"style":25861},[59,60],[15,123332,123334],{"className":123333},[281],[15,123335,123337,123357],{"className":123336},[285,286],[15,123338,123340,123354],{"className":123339},[290],[15,123341,123343],{"className":123342,"style":379},[294],[15,123344,123345,123348],{"style":122031},[15,123346],{"className":123347,"style":303},[302],[15,123349,123351],{"className":123350},[307,308,309,310],[15,123352,213],{"className":123353},[59,60,310],[15,123355,318],{"className":123356},[317],[15,123358,123360],{"className":123359},[290],[15,123361,123363],{"className":123362,"style":325},[294],[15,123364],{},[15,123366,230],{"className":123367},[146],[15,123369,123371,123374],{"className":123370},[59],[15,123372,4158],{"className":123373,"style":981},[59,60],[15,123375,123377],{"className":123376},[281],[15,123378,123380],{"className":123379},[285],[15,123381,123383],{"className":123382},[290],[15,123384,123386],{"className":123385,"style":8499},[294],[15,123387,123388,123391],{"style":6865},[15,123389],{"className":123390,"style":303},[302],[15,123392,123394],{"className":123393},[307,308,309,310],[15,123395,7573],{"className":123396},[2591,310],[15,123398,113],{"className":123399},[146],[15,123401,769],{"className":123402},[59,60],[15,123404],{"className":123405,"style":2587},[157],[15,123407,4813],{"className":123408},[2591],[15,123410],{"className":123411,"style":2587},[157],[15,123413,123415,123418,123421,123424,123427,123430],{"className":123414},[50],[15,123416],{"className":123417,"style":139},[54],[15,123419,121074],{"className":123420,"style":121164},[59,60],[15,123422,20390],{"className":123423},[153],[15,123425],{"className":123426,"style":158},[157],[15,123428,123],{"className":123429},[162],[15,123431],{"className":123432,"style":158},[157],[15,123434,123436,123439,123479,123482,123485,123488,123491],{"className":123435},[50],[15,123437],{"className":123438,"style":270},[54],[15,123440,123442,123445],{"className":123441},[59],[15,123443,223],{"className":123444,"style":25861},[59,60],[15,123446,123448],{"className":123447},[281],[15,123449,123451,123471],{"className":123450},[285,286],[15,123452,123454,123468],{"className":123453},[290],[15,123455,123457],{"className":123456,"style":379},[294],[15,123458,123459,123462],{"style":122031},[15,123460],{"className":123461,"style":303},[302],[15,123463,123465],{"className":123464},[307,308,309,310],[15,123466,213],{"className":123467},[59,60,310],[15,123469,318],{"className":123470},[317],[15,123472,123474],{"className":123473},[290],[15,123475,123477],{"className":123476,"style":325},[294],[15,123478],{},[15,123480,122929],{"className":123481},[146],[15,123483,769],{"className":123484},[59,60],[15,123486],{"className":123487,"style":2587},[157],[15,123489,4813],{"className":123490},[2591],[15,123492],{"className":123493,"style":2587},[157],[15,123495,123497,123500,123503,123532],{"className":123496},[50],[15,123498],{"className":123499,"style":122948},[54],[15,123501,121074],{"className":123502,"style":121164},[59,60],[15,123504,123506,123509],{"className":123505},[153],[15,123507,120],{"className":123508},[153],[15,123510,123512],{"className":123511},[281],[15,123513,123515],{"className":123514},[285],[15,123516,123518],{"className":123517},[290],[15,123519,123521],{"className":123520,"style":21009},[294],[15,123522,123523,123526],{"style":6865},[15,123524],{"className":123525,"style":303},[302],[15,123527,123529],{"className":123528},[307,308,309,310],[15,123530,2470],{"className":123531},[2591,310],[15,123533,257],{"className":123534},[153],"，故等号可取。",[11,123537,123538,123539,123567,123568,123619,123620,123656,123657,15795,123760,123811,123812,123979,123980,124038,124039,124067],{},"几何解释：",[15,123540,123542,123555],{"className":123541,"translate":19},[18],[15,123543,123545],{"className":123544},[23],[25,123546,123547],{"xmlns":27},[29,123548,123549,123553],{},[32,123550,123551],{},[35,123552,121074],{},[39,123554,121491],{"encoding":41},[15,123556,123558],{"className":123557,"ariaHidden":46},[45],[15,123559,123561,123564],{"className":123560},[50],[15,123562],{"className":123563,"style":2276},[54],[15,123565,121074],{"className":123566,"style":121164},[59,60]," 扫过 ",[15,123569,123571,123592],{"className":123570,"translate":19},[18],[15,123572,123574],{"className":123573},[23],[25,123575,123576],{"xmlns":27},[29,123577,123578,123590],{},[32,123579,123580,123582,123584,123586,123588],{},[110,123581,230],{"stretchy":112},[115,123583,126],{},[110,123585,551],{"separator":46},[115,123587,117],{},[110,123589,257],{"stretchy":112},[39,123591,36814],{"encoding":41},[15,123593,123595],{"className":123594,"ariaHidden":46},[45],[15,123596,123598,123601,123604,123607,123610,123613,123616],{"className":123597},[50],[15,123599],{"className":123600,"style":139},[54],[15,123602,230],{"className":123603},[146],[15,123605,126],{"className":123606},[59],[15,123608,551],{"className":123609},[573],[15,123611],{"className":123612,"style":406},[157],[15,123614,117],{"className":123615},[59],[15,123617,257],{"className":123618},[153]," 时，右端就是权衡曲线（ROC 下边界）各条斜率为 ",[15,123621,123623,123641],{"className":123622,"translate":19},[18],[15,123624,123626],{"className":123625},[23],[25,123627,123628],{"xmlns":27},[29,123629,123630,123638],{},[32,123631,123632,123634,123636],{},[115,123633,117],{},[35,123635,941],{"mathvariant":209},[35,123637,121074],{},[39,123639,123640],{"encoding":41},"1\u002F\\gamma",[15,123642,123644],{"className":123643,"ariaHidden":46},[45],[15,123645,123647,123650,123653],{"className":123646},[50],[15,123648],{"className":123649,"style":139},[54],[15,123651,8589],{"className":123652},[59],[15,123654,121074],{"className":123655,"style":121164},[59,60]," 的支撑线的截距——",[1225,123658,123659,123660,123688,123689,123759],{},"知道整条曲线 ",[15,123661,123663,123676],{"className":123662,"translate":19},[18],[15,123664,123666],{"className":123665},[23],[25,123667,123668],{"xmlns":27},[29,123669,123670,123674],{},[32,123671,123672],{},[35,123673,5392],{},[39,123675,5392],{"encoding":41},[15,123677,123679],{"className":123678,"ariaHidden":46},[45],[15,123680,123682,123685],{"className":123681},[50],[15,123683],{"className":123684,"style":664},[54],[15,123686,5392],{"className":123687,"style":334},[59,60]," 就知道全部 ",[15,123690,123692,123710],{"className":123691,"translate":19},[18],[15,123693,123695],{"className":123694},[23],[25,123696,123697],{"xmlns":27},[29,123698,123699,123707],{},[32,123700,123701],{},[195,123702,123703,123705],{},[35,123704,4158],{},[35,123706,121074],{},[39,123708,123709],{"encoding":41},"g_\\gamma",[15,123711,123713],{"className":123712,"ariaHidden":46},[45],[15,123714,123716,123719],{"className":123715},[50],[15,123717],{"className":123718,"style":92958},[54],[15,123720,123722,123725],{"className":123721},[59],[15,123723,4158],{"className":123724,"style":981},[59,60],[15,123726,123728],{"className":123727},[281],[15,123729,123731,123751],{"className":123730},[285,286],[15,123732,123734,123748],{"className":123733},[290],[15,123735,123737],{"className":123736,"style":44929},[294],[15,123738,123739,123742],{"style":18843},[15,123740],{"className":123741,"style":303},[302],[15,123743,123745],{"className":123744},[307,308,309,310],[15,123746,121074],{"className":123747,"style":121164},[59,60,310],[15,123749,318],{"className":123750},[317],[15,123752,123754],{"className":123753},[290],[15,123755,123757],{"className":123756,"style":325},[294],[15,123758],{},"-散度",[15,123761,123763,123781],{"className":123762,"translate":19},[18],[15,123764,123766],{"className":123765},[23],[25,123767,123768],{"xmlns":27},[29,123769,123770,123778],{},[32,123771,123772,123774,123776],{},[35,123773,121074],{},[110,123775,123],{},[115,123777,117],{},[39,123779,123780],{"encoding":41},"\\gamma=1",[15,123782,123784,123802],{"className":123783,"ariaHidden":46},[45],[15,123785,123787,123790,123793,123796,123799],{"className":123786},[50],[15,123788],{"className":123789,"style":2276},[54],[15,123791,121074],{"className":123792,"style":121164},[59,60],[15,123794],{"className":123795,"style":158},[157],[15,123797,123],{"className":123798},[162],[15,123800],{"className":123801,"style":158},[157],[15,123803,123805,123808],{"className":123804},[50],[15,123806],{"className":123807,"style":172},[54],[15,123809,117],{"className":123810},[59]," 时立刻给出 ",[15,123813,123815,123867],{"className":123814,"translate":19},[18],[15,123816,123818],{"className":123817},[23],[25,123819,123820],{"xmlns":27},[29,123821,123822,123864],{},[32,123823,123824,123830,123832,123842,123844,123846,123848,123850,123852,123854,123856,123858,123860,123862],{},[32,123825,123826,123828],{},[35,123827,5392],{"mathvariant":209},[35,123829,34850],{"mathvariant":209},[110,123831,123],{},[195,123833,123834,123840],{},[32,123835,123836,123838],{},[35,123837,35432],{},[110,123839,4103],{},[35,123841,603],{},[110,123843,2898],{"stretchy":112},[35,123845,206],{},[110,123847,113],{"stretchy":112},[35,123849,603],{},[110,123851,120],{"stretchy":112},[110,123853,4813],{},[35,123855,213],{},[110,123857,113],{"stretchy":112},[35,123859,603],{},[110,123861,120],{"stretchy":112},[110,123863,2908],{"stretchy":112},[39,123865,123866],{"encoding":41},"\\mathrm{TV}=\\sup_A\\{P(A)-Q(A)\\}",[15,123868,123870,123891,123961],{"className":123869,"ariaHidden":46},[45],[15,123871,123873,123876,123882,123885,123888],{"className":123872},[50],[15,123874],{"className":123875,"style":664},[54],[15,123877,123879],{"className":123878},[59],[15,123880,86762],{"className":123881,"style":4157},[59,32662],[15,123883],{"className":123884,"style":158},[157],[15,123886,123],{"className":123887},[162],[15,123889],{"className":123890,"style":158},[157],[15,123892,123894,123897,123937,123940,123943,123946,123949,123952,123955,123958],{"className":123893},[50],[15,123895],{"className":123896,"style":139},[54],[15,123898,123900,123903],{"className":123899},[1484],[15,123901,35432],{"className":123902},[1484],[15,123904,123906],{"className":123905},[281],[15,123907,123909,123929],{"className":123908},[285,286],[15,123910,123912,123926],{"className":123911},[290],[15,123913,123915],{"className":123914,"style":35575},[294],[15,123916,123917,123920],{"style":35578},[15,123918],{"className":123919,"style":303},[302],[15,123921,123923],{"className":123922},[307,308,309,310],[15,123924,603],{"className":123925},[59,60,310],[15,123927,318],{"className":123928},[317],[15,123930,123932],{"className":123931},[290],[15,123933,123935],{"className":123934,"style":37020},[294],[15,123936],{},[15,123938,2898],{"className":123939},[146],[15,123941,206],{"className":123942,"style":334},[59,60],[15,123944,113],{"className":123945},[146],[15,123947,603],{"className":123948},[59,60],[15,123950,120],{"className":123951},[153],[15,123953],{"className":123954,"style":2587},[157],[15,123956,4813],{"className":123957},[2591],[15,123959],{"className":123960,"style":2587},[157],[15,123962,123964,123967,123970,123973,123976],{"className":123963},[50],[15,123965],{"className":123966,"style":139},[54],[15,123968,213],{"className":123969},[59,60],[15,123971,113],{"className":123972},[146],[15,123974,603],{"className":123975},[59,60],[15,123977,60999],{"className":123978},[153],"）。反过来，知道单个标量散度（如 KL 或 ",[15,123981,123983,124000],{"className":123982,"translate":19},[18],[15,123984,123986],{"className":123985},[23],[25,123987,123988],{"xmlns":27},[29,123989,123990,123998],{},[32,123991,123992],{},[6814,123993,123994,123996],{},[35,123995,37449],{},[115,123997,2463],{},[39,123999,40394],{"encoding":41},[15,124001,124003],{"className":124002,"ariaHidden":46},[45],[15,124004,124006,124009],{"className":124005},[50],[15,124007],{"className":124008,"style":40404},[54],[15,124010,124012,124015],{"className":124011},[59],[15,124013,37449],{"className":124014},[59,60],[15,124016,124018],{"className":124017},[281],[15,124019,124021],{"className":124020},[285],[15,124022,124024],{"className":124023},[290],[15,124025,124027],{"className":124026,"style":20028},[294],[15,124028,124029,124032],{"style":6865},[15,124030],{"className":124031,"style":303},[302],[15,124033,124035],{"className":124034},[307,308,309,310],[15,124036,2463],{"className":124037},[59,310],"）只对 ",[15,124040,124042,124055],{"className":124041,"translate":19},[18],[15,124043,124045],{"className":124044},[23],[25,124046,124047],{"xmlns":27},[29,124048,124049,124053],{},[32,124050,124051],{},[35,124052,5392],{},[39,124054,5392],{"encoding":41},[15,124056,124058],{"className":124057,"ariaHidden":46},[45],[15,124059,124061,124064],{"className":124060},[50],[15,124062],{"className":124063,"style":664},[54],[15,124065,5392],{"className":124066,"style":334},[59,60]," 施加一个切向约束（4.7 节的不等式网络），信息严格更少；",[10027,124069,124070,124302],{},[6665,124071,124072,124073,19966],{},"在「小隐私预算」下，所有 f-DP 都由**高斯差分隐私（GDP）**统一逼近，其权衡函数 ",[15,124074,124076,124134],{"className":124075,"translate":19},[18],[15,124077,124079],{"className":124078},[23],[25,124080,124081],{"xmlns":27},[29,124082,124083,124131],{},[32,124084,124085,124092,124094,124096,124098,124100,124103,124105,124115,124117,124119,124121,124123,124125,124127,124129],{},[195,124086,124087,124090],{},[35,124088,124089],{},"G",[35,124091,2364],{},[110,124093,113],{"stretchy":112},[35,124095,44754],{},[110,124097,120],{"stretchy":112},[110,124099,123],{},[35,124101,124102],{"mathvariant":209},"Φ",[110,124104,113],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[6814,124106,124107,124109],{},[35,124108,124102],{"mathvariant":209},[32,124110,124111,124113],{},[110,124112,4813],{},[115,124114,117],{},[110,124116,113],{"stretchy":112},[115,124118,117],{},[110,124120,4813],{},[35,124122,44754],{},[110,124124,120],{"stretchy":112},[110,124126,4813],{},[35,124128,2364],{},[110,124130,120],{"fence":112,"stretchy":46,"minsize":9450,"maxsize":9450},[39,124132,124133],{"encoding":41},"G_\\mu(\\alpha)=\\Phi\\big(\\Phi^{-1}(1-\\alpha)-\\mu\\big)",[15,124135,124137,124201,124266,124287],{"className":124136,"ariaHidden":46},[45],[15,124138,124140,124143,124183,124186,124189,124192,124195,124198],{"className":124139},[50],[15,124141],{"className":124142,"style":270},[54],[15,124144,124146,124149],{"className":124145},[59],[15,124147,124089],{"className":124148},[59,60],[15,124150,124152],{"className":124151},[281],[15,124153,124155,124175],{"className":124154},[285,286],[15,124156,124158,124172],{"className":124157},[290],[15,124159,124161],{"className":124160,"style":44929},[294],[15,124162,124163,124166],{"style":382},[15,124164],{"className":124165,"style":303},[302],[15,124167,124169],{"className":124168},[307,308,309,310],[15,124170,2364],{"className":124171},[59,60,310],[15,124173,318],{"className":124174},[317],[15,124176,124178],{"className":124177},[290],[15,124179,124181],{"className":124180,"style":325},[294],[15,124182],{},[15,124184,113],{"className":124185},[146],[15,124187,44754],{"className":124188,"style":44784},[59,60],[15,124190,120],{"className":124191},[153],[15,124193],{"className":124194,"style":158},[157],[15,124196,123],{"className":124197},[162],[15,124199],{"className":124200,"style":158},[157],[15,124202,124204,124207,124210,124216,124251,124254,124257,124260,124263],{"className":124203},[50],[15,124205],{"className":124206,"style":20563},[54],[15,124208,124102],{"className":124209},[59],[15,124211,124213],{"className":124212},[59],[15,124214,113],{"className":124215},[419,9674],[15,124217,124219,124222],{"className":124218},[59],[15,124220,124102],{"className":124221},[59],[15,124223,124225],{"className":124224},[281],[15,124226,124228],{"className":124227},[285],[15,124229,124231],{"className":124230},[290],[15,124232,124234],{"className":124233,"style":20028},[294],[15,124235,124236,124239],{"style":6865},[15,124237],{"className":124238,"style":303},[302],[15,124240,124242],{"className":124241},[307,308,309,310],[15,124243,124245,124248],{"className":124244},[59,310],[15,124246,4813],{"className":124247},[59,310],[15,124249,117],{"className":124250},[59,310],[15,124252,113],{"className":124253},[146],[15,124255,117],{"className":124256},[59],[15,124258],{"className":124259,"style":2587},[157],[15,124261,4813],{"className":124262},[2591],[15,124264],{"className":124265,"style":2587},[157],[15,124267,124269,124272,124275,124278,124281,124284],{"className":124268},[50],[15,124270],{"className":124271,"style":139},[54],[15,124273,44754],{"className":124274,"style":44784},[59,60],[15,124276,120],{"className":124277},[153],[15,124279],{"className":124280,"style":2587},[157],[15,124282,4813],{"className":124283},[2591],[15,124285],{"className":124286,"style":2587},[157],[15,124288,124290,124293,124296],{"className":124289},[50],[15,124291],{"className":124292,"style":20563},[54],[15,124294,2364],{"className":124295},[59,60],[15,124297,124299],{"className":124298},[59],[15,124300,120],{"className":124301},[419,9674],[6665,124303,124304,124305,124308,124309,124337],{},"权衡函数族在",[1225,124306,124307],{},"组合","（post-processing、串联）下封闭，并装备了一个与 f-散度\"散度序\"同构的偏序——这与 f-散度族的\"",[15,124310,124312,124325],{"className":124311,"translate":19},[18],[15,124313,124315],{"className":124314},[23],[25,124316,124317],{"xmlns":27},[29,124318,124319,124323],{},[32,124320,124321],{},[110,124322,6928],{},[39,124324,55489],{"encoding":41},[15,124326,124328],{"className":124327,"ariaHidden":46},[45],[15,124329,124331,124334],{"className":124330},[50],[15,124332],{"className":124333,"style":43188},[54],[15,124335,6928],{"className":124336},[162]," 比较\"在结构上完全平行。",[11,124339,124340],{},"这说明 f-散度不仅统一了信息论度量，也统一了现代隐私的定义框架：用一条凸曲线代替一个标量数字。",[528,124342,124344],{"id":124343},"_9-计算实例","9. 计算实例",[2311,124346,124348],{"id":124347},"_91-正态分布","9.1 正态分布",[11,124350,534,124351,5645,124526,10180],{},[15,124352,124354,124392],{"className":124353,"translate":19},[18],[15,124355,124357],{"className":124356},[23],[25,124358,124359],{"xmlns":27},[29,124360,124361,124389],{},[32,124362,124363,124365,124367,124369,124371,124377,124379,124387],{},[35,124364,206],{},[110,124366,123],{},[35,124368,38284],{},[110,124370,113],{"stretchy":112},[195,124372,124373,124375],{},[35,124374,2364],{},[115,124376,117],{},[110,124378,551],{"separator":46},[7553,124380,124381,124383,124385],{},[35,124382,2332],{},[115,124384,117],{},[115,124386,2463],{},[110,124388,120],{"stretchy":112},[39,124390,124391],{"encoding":41},"P=N(\\mu_1,\\sigma_1^2)",[15,124393,124395,124413],{"className":124394,"ariaHidden":46},[45],[15,124396,124398,124401,124404,124407,124410],{"className":124397},[50],[15,124399],{"className":124400,"style":664},[54],[15,124402,206],{"className":124403,"style":334},[59,60],[15,124405],{"className":124406,"style":158},[157],[15,124408,123],{"className":124409},[162],[15,124411],{"className":124412,"style":158},[157],[15,124414,124416,124419,124422,124425,124465,124468,124471,124523],{"className":124415},[50],[15,124417],{"className":124418,"style":20003},[54],[15,124420,38284],{"className":124421,"style":25601},[59,60],[15,124423,113],{"className":124424},[146],[15,124426,124428,124431],{"className":124427},[59],[15,124429,2364],{"className":124430},[59,60],[15,124432,124434],{"className":124433},[281],[15,124435,124437,124457],{"className":124436},[285,286],[15,124438,124440,124454],{"className":124439},[290],[15,124441,124443],{"className":124442,"style":11133},[294],[15,124444,124445,124448],{"style":382},[15,124446],{"className":124447,"style":303},[302],[15,124449,124451],{"className":124450},[307,308,309,310],[15,124452,117],{"className":124453},[59,310],[15,124455,318],{"className":124456},[317],[15,124458,124460],{"className":124459},[290],[15,124461,124463],{"className":124462,"style":7968},[294],[15,124464],{},[15,124466,551],{"className":124467},[573],[15,124469],{"className":124470,"style":406},[157],[15,124472,124474,124477],{"className":124473},[59],[15,124475,2332],{"className":124476,"style":981},[59,60],[15,124478,124480],{"className":124479},[281],[15,124481,124483,124515],{"className":124482},[285,286],[15,124484,124486,124512],{"className":124485},[290],[15,124487,124489,124501],{"className":124488,"style":20028},[294],[15,124490,124492,124495],{"style":124491},"top:-2.4519em;margin-left:-0.0359em;margin-right:0.05em;",[15,124493],{"className":124494,"style":303},[302],[15,124496,124498],{"className":124497},[307,308,309,310],[15,124499,117],{"className":124500},[59,310],[15,124502,124503,124506],{"style":6865},[15,124504],{"className":124505,"style":303},[302],[15,124507,124509],{"className":124508},[307,308,309,310],[15,124510,2463],{"className":124511},[59,310],[15,124513,318],{"className":124514},[317],[15,124516,124518],{"className":124517},[290],[15,124519,124521],{"className":124520,"style":52124},[294],[15,124522],{},[15,124524,120],{"className":124525},[153],[15,124527,124529,124567],{"className":124528,"translate":19},[18],[15,124530,124532],{"className":124531},[23],[25,124533,124534],{"xmlns":27},[29,124535,124536,124564],{},[32,124537,124538,124540,124542,124544,124546,124552,124554,124562],{},[35,124539,213],{},[110,124541,123],{},[35,124543,38284],{},[110,124545,113],{"stretchy":112},[195,124547,124548,124550],{},[35,124549,2364],{},[115,124551,2463],{},[110,124553,551],{"separator":46},[7553,124555,124556,124558,124560],{},[35,124557,2332],{},[115,124559,2463],{},[115,124561,2463],{},[110,124563,120],{"stretchy":112},[39,124565,124566],{"encoding":41},"Q=N(\\mu_2,\\sigma_2^2)",[15,124568,124570,124588],{"className":124569,"ariaHidden":46},[45],[15,124571,124573,124576,124579,124582,124585],{"className":124572},[50],[15,124574],{"className":124575,"style":566},[54],[15,124577,213],{"className":124578},[59,60],[15,124580],{"className":124581,"style":158},[157],[15,124583,123],{"className":124584},[162],[15,124586],{"className":124587,"style":158},[157],[15,124589,124591,124594,124597,124600,124640,124643,124646,124697],{"className":124590},[50],[15,124592],{"className":124593,"style":20003},[54],[15,124595,38284],{"className":124596,"style":25601},[59,60],[15,124598,113],{"className":124599},[146],[15,124601,124603,124606],{"className":124602},[59],[15,124604,2364],{"className":124605},[59,60],[15,124607,124609],{"className":124608},[281],[15,124610,124612,124632],{"className":124611},[285,286],[15,124613,124615,124629],{"className":124614},[290],[15,124616,124618],{"className":124617,"style":11133},[294],[15,124619,124620,124623],{"style":382},[15,124621],{"className":124622,"style":303},[302],[15,124624,124626],{"className":124625},[307,308,309,310],[15,124627,2463],{"className":124628},[59,310],[15,124630,318],{"className":124631},[317],[15,124633,124635],{"className":124634},[290],[15,124636,124638],{"className":124637,"style":7968},[294],[15,124639],{},[15,124641,551],{"className":124642},[573],[15,124644],{"className":124645,"style":406},[157],[15,124647,124649,124652],{"className":124648},[59],[15,124650,2332],{"className":124651,"style":981},[59,60],[15,124653,124655],{"className":124654},[281],[15,124656,124658,124689],{"className":124657},[285,286],[15,124659,124661,124686],{"className":124660},[290],[15,124662,124664,124675],{"className":124663,"style":20028},[294],[15,124665,124666,124669],{"style":124491},[15,124667],{"className":124668,"style":303},[302],[15,124670,124672],{"className":124671},[307,308,309,310],[15,124673,2463],{"className":124674},[59,310],[15,124676,124677,124680],{"style":6865},[15,124678],{"className":124679,"style":303},[302],[15,124681,124683],{"className":124682},[307,308,309,310],[15,124684,2463],{"className":124685},[59,310],[15,124687,318],{"className":124688},[317],[15,124690,124692],{"className":124691},[290],[15,124693,124695],{"className":124694,"style":52124},[294],[15,124696],{},[15,124698,120],{"className":124699},[153],[11,124701,124702],{},[1225,124703,124704],{},"KL（经典公式）。",[15,124706,124708],{"className":124707,"translate":19},[180],[15,124709,124711,124823],{"className":124710,"translate":19},[18],[15,124712,124714],{"className":124713},[23],[25,124715,124716],{"xmlns":27,"display":189},[29,124717,124718,124820],{},[32,124719,124720,124730,124732,124734,124736,124738,124740,124742,124744,124746,124760,124762,124810,124812,124818],{},[195,124721,124722,124724],{},[35,124723,199],{},[32,124725,124726,124728],{},[35,124727,10694],{},[35,124729,21893],{},[110,124731,113],{"stretchy":112},[35,124733,206],{},[35,124735,210],{"mathvariant":209},[35,124737,213],{},[110,124739,120],{"stretchy":112},[110,124741,123],{},[35,124743,4100],{},[110,124745,4103],{},[238,124747,124748,124754],{},[195,124749,124750,124752],{},[35,124751,2332],{},[115,124753,2463],{},[195,124755,124756,124758],{},[35,124757,2332],{},[115,124759,117],{},[110,124761,2470],{},[238,124763,124764,124798],{},[32,124765,124766,124774,124776,124778,124784,124786,124792],{},[7553,124767,124768,124770,124772],{},[35,124769,2332],{},[115,124771,117],{},[115,124773,2463],{},[110,124775,2470],{},[110,124777,113],{"stretchy":112},[195,124779,124780,124782],{},[35,124781,2364],{},[115,124783,117],{},[110,124785,4813],{},[195,124787,124788,124790],{},[35,124789,2364],{},[115,124791,2463],{},[6814,124793,124794,124796],{},[110,124795,120],{"stretchy":112},[115,124797,2463],{},[32,124799,124800,124802],{},[115,124801,2463],{},[7553,124803,124804,124806,124808],{},[35,124805,2332],{},[115,124807,2463],{},[115,124809,2463],{},[110,124811,4813],{},[238,124813,124814,124816],{},[115,124815,117],{},[115,124817,2463],{},[35,124819,4375],{"mathvariant":209},[39,124821,124822],{"encoding":41},"D_{KL}(P\\|Q)=\\log\\frac{\\sigma_2}{\\sigma_1}\n+\\frac{\\sigma_1^2+(\\mu_1-\\mu_2)^2}{2\\sigma_2^2}\n-\\frac12 .",[15,124824,124826,124902,125063,125373],{"className":124825,"ariaHidden":46},[45],[15,124827,124829,124832,124878,124881,124884,124887,124890,124893,124896,124899],{"className":124828},[50],[15,124830],{"className":124831,"style":139},[54],[15,124833,124835,124838],{"className":124834},[59],[15,124836,199],{"className":124837,"style":277},[59,60],[15,124839,124841],{"className":124840},[281],[15,124842,124844,124870],{"className":124843},[285,286],[15,124845,124847,124867],{"className":124846},[290],[15,124848,124850],{"className":124849,"style":379},[294],[15,124851,124852,124855],{"style":298},[15,124853],{"className":124854,"style":303},[302],[15,124856,124858],{"className":124857},[307,308,309,310],[15,124859,124861,124864],{"className":124860},[59,310],[15,124862,10694],{"className":124863,"style":10782},[59,60,310],[15,124865,21893],{"className":124866},[59,60,310],[15,124868,318],{"className":124869},[317],[15,124871,124873],{"className":124872},[290],[15,124874,124876],{"className":124875,"style":7968},[294],[15,124877],{},[15,124879,113],{"className":124880},[146],[15,124882,206],{"className":124883,"style":334},[59,60],[15,124885,210],{"className":124886},[59],[15,124888,213],{"className":124889},[59,60],[15,124891,120],{"className":124892},[153],[15,124894],{"className":124895,"style":158},[157],[15,124897,123],{"className":124898},[162],[15,124900],{"className":124901,"style":158},[157],[15,124903,124905,124909,124914,124917,125054,125057,125060],{"className":124904},[50],[15,124906],{"className":124907,"style":124908},[54],"height:1.9436em;vertical-align:-0.836em;",[15,124910,4154,124912],{"className":124911},[1484],[15,124913,4158],{"style":4157},[15,124915],{"className":124916,"style":406},[157],[15,124918,124920,124923,125051],{"className":124919},[59],[15,124921],{"className":124922},[146,441],[15,124924,124926],{"className":124925},[238],[15,124927,124929,125042],{"className":124928},[285,286],[15,124930,124932,125039],{"className":124931},[290],[15,124933,124935,124983,124991],{"className":124934,"style":3554},[294],[15,124936,124937,124940],{"style":457},[15,124938],{"className":124939,"style":461},[302],[15,124941,124943],{"className":124942},[59],[15,124944,124946,124949],{"className":124945},[59],[15,124947,2332],{"className":124948,"style":981},[59,60],[15,124950,124952],{"className":124951},[281],[15,124953,124955,124975],{"className":124954},[285,286],[15,124956,124958,124972],{"className":124957},[290],[15,124959,124961],{"className":124960,"style":11133},[294],[15,124962,124963,124966],{"style":18843},[15,124964],{"className":124965,"style":303},[302],[15,124967,124969],{"className":124968},[307,308,309,310],[15,124970,117],{"className":124971},[59,310],[15,124973,318],{"className":124974},[317],[15,124976,124978],{"className":124977},[290],[15,124979,124981],{"className":124980,"style":7968},[294],[15,124982],{},[15,124984,124985,124988],{"style":473},[15,124986],{"className":124987,"style":461},[302],[15,124989],{"className":124990,"style":481},[480],[15,124992,124993,124996],{"style":484},[15,124994],{"className":124995,"style":461},[302],[15,124997,124999],{"className":124998},[59],[15,125000,125002,125005],{"className":125001},[59],[15,125003,2332],{"className":125004,"style":981},[59,60],[15,125006,125008],{"className":125007},[281],[15,125009,125011,125031],{"className":125010},[285,286],[15,125012,125014,125028],{"className":125013},[290],[15,125015,125017],{"className":125016,"style":11133},[294],[15,125018,125019,125022],{"style":18843},[15,125020],{"className":125021,"style":303},[302],[15,125023,125025],{"className":125024},[307,308,309,310],[15,125026,2463],{"className":125027},[59,310],[15,125029,318],{"className":125030},[317],[15,125032,125034],{"className":125033},[290],[15,125035,125037],{"className":125036,"style":7968},[294],[15,125038],{},[15,125040,318],{"className":125041},[317],[15,125043,125045],{"className":125044},[290],[15,125046,125049],{"className":125047,"style":125048},[294],"height:0.836em;",[15,125050],{},[15,125052],{"className":125053},[153,441],[15,125055],{"className":125056,"style":2587},[157],[15,125058,2470],{"className":125059},[2591],[15,125061],{"className":125062,"style":2587},[157],[15,125064,125066,125070,125364,125367,125370],{"className":125065},[50],[15,125067],{"className":125068,"style":125069},[54],"height:2.4434em;vertical-align:-0.9523em;",[15,125071,125073,125076,125361],{"className":125072},[59],[15,125074],{"className":125075},[146,441],[15,125077,125079],{"className":125078},[238],[15,125080,125082,125352],{"className":125081},[285,286],[15,125083,125085,125349],{"className":125084},[290],[15,125086,125088,125152,125160],{"className":125087,"style":37723},[294],[15,125089,125090,125093],{"style":457},[15,125091],{"className":125092,"style":461},[302],[15,125094,125096,125099],{"className":125095},[59],[15,125097,2463],{"className":125098},[59],[15,125100,125102,125105],{"className":125101},[59],[15,125103,2332],{"className":125104,"style":981},[59,60],[15,125106,125108],{"className":125107},[281],[15,125109,125111,125143],{"className":125110},[285,286],[15,125112,125114,125140],{"className":125113},[290],[15,125115,125117,125129],{"className":125116,"style":97563},[294],[15,125118,125120,125123],{"style":125119},"top:-2.4337em;margin-left:-0.0359em;margin-right:0.05em;",[15,125121],{"className":125122,"style":303},[302],[15,125124,125126],{"className":125125},[307,308,309,310],[15,125127,2463],{"className":125128},[59,310],[15,125130,125131,125134],{"style":97584},[15,125132],{"className":125133,"style":303},[302],[15,125135,125137],{"className":125136},[307,308,309,310],[15,125138,2463],{"className":125139},[59,310],[15,125141,318],{"className":125142},[317],[15,125144,125146],{"className":125145},[290],[15,125147,125150],{"className":125148,"style":125149},[294],"height:0.2663em;",[15,125151],{},[15,125153,125154,125157],{"style":473},[15,125155],{"className":125156,"style":461},[302],[15,125158],{"className":125159,"style":481},[480],[15,125161,125162,125165],{"style":484},[15,125163],{"className":125164,"style":461},[302],[15,125166,125168,125219,125222,125225,125228,125231,125271,125274,125277,125280,125320],{"className":125167},[59],[15,125169,125171,125174],{"className":125170},[59],[15,125172,2332],{"className":125173,"style":981},[59,60],[15,125175,125177],{"className":125176},[281],[15,125178,125180,125211],{"className":125179},[285,286],[15,125181,125183,125208],{"className":125182},[290],[15,125184,125186,125197],{"className":125185,"style":20028},[294],[15,125187,125188,125191],{"style":124491},[15,125189],{"className":125190,"style":303},[302],[15,125192,125194],{"className":125193},[307,308,309,310],[15,125195,117],{"className":125196},[59,310],[15,125198,125199,125202],{"style":6865},[15,125200],{"className":125201,"style":303},[302],[15,125203,125205],{"className":125204},[307,308,309,310],[15,125206,2463],{"className":125207},[59,310],[15,125209,318],{"className":125210},[317],[15,125212,125214],{"className":125213},[290],[15,125215,125217],{"className":125216,"style":52124},[294],[15,125218],{},[15,125220],{"className":125221,"style":2587},[157],[15,125223,2470],{"className":125224},[2591],[15,125226],{"className":125227,"style":2587},[157],[15,125229,113],{"className":125230},[146],[15,125232,125234,125237],{"className":125233},[59],[15,125235,2364],{"className":125236},[59,60],[15,125238,125240],{"className":125239},[281],[15,125241,125243,125263],{"className":125242},[285,286],[15,125244,125246,125260],{"className":125245},[290],[15,125247,125249],{"className":125248,"style":11133},[294],[15,125250,125251,125254],{"style":382},[15,125252],{"className":125253,"style":303},[302],[15,125255,125257],{"className":125256},[307,308,309,310],[15,125258,117],{"className":125259},[59,310],[15,125261,318],{"className":125262},[317],[15,125264,125266],{"className":125265},[290],[15,125267,125269],{"className":125268,"style":7968},[294],[15,125270],{},[15,125272],{"className":125273,"style":2587},[157],[15,125275,4813],{"className":125276},[2591],[15,125278],{"className":125279,"style":2587},[157],[15,125281,125283,125286],{"className":125282},[59],[15,125284,2364],{"className":125285},[59,60],[15,125287,125289],{"className":125288},[281],[15,125290,125292,125312],{"className":125291},[285,286],[15,125293,125295,125309],{"className":125294},[290],[15,125296,125298],{"className":125297,"style":11133},[294],[15,125299,125300,125303],{"style":382},[15,125301],{"className":125302,"style":303},[302],[15,125304,125306],{"className":125305},[307,308,309,310],[15,125307,2463],{"className":125308},[59,310],[15,125310,318],{"className":125311},[317],[15,125313,125315],{"className":125314},[290],[15,125316,125318],{"className":125317,"style":7968},[294],[15,125319],{},[15,125321,125323,125326],{"className":125322},[153],[15,125324,120],{"className":125325},[153],[15,125327,125329],{"className":125328},[281],[15,125330,125332],{"className":125331},[285],[15,125333,125335],{"className":125334},[290],[15,125336,125338],{"className":125337,"style":20028},[294],[15,125339,125340,125343],{"style":6865},[15,125341],{"className":125342,"style":303},[302],[15,125344,125346],{"className":125345},[307,308,309,310],[15,125347,2463],{"className":125348},[59,310],[15,125350,318],{"className":125351},[317],[15,125353,125355],{"className":125354},[290],[15,125356,125359],{"className":125357,"style":125358},[294],"height:0.9523em;",[15,125360],{},[15,125362],{"className":125363},[153,441],[15,125365],{"className":125366,"style":2587},[157],[15,125368,4813],{"className":125369},[2591],[15,125371],{"className":125372,"style":2587},[157],[15,125374,125376,125379,125441],{"className":125375},[50],[15,125377],{"className":125378,"style":25903},[54],[15,125380,125382,125385,125438],{"className":125381},[59],[15,125383],{"className":125384},[146,441],[15,125386,125388],{"className":125387},[238],[15,125389,125391,125430],{"className":125390},[285,286],[15,125392,125394,125427],{"className":125393},[290],[15,125395,125397,125408,125416],{"className":125396,"style":22889},[294],[15,125398,125399,125402],{"style":457},[15,125400],{"className":125401,"style":461},[302],[15,125403,125405],{"className":125404},[59],[15,125406,2463],{"className":125407},[59],[15,125409,125410,125413],{"style":473},[15,125411],{"className":125412,"style":461},[302],[15,125414],{"className":125415,"style":481},[480],[15,125417,125418,125421],{"style":484},[15,125419],{"className":125420,"style":461},[302],[15,125422,125424],{"className":125423},[59],[15,125425,117],{"className":125426},[59],[15,125428,318],{"className":125429},[317],[15,125431,125433],{"className":125432},[290],[15,125434,125436],{"className":125435,"style":3778},[294],[15,125437],{},[15,125439],{"className":125440},[153,441],[15,125442,4375],{"className":125443},[59],[11,125445,125446,125818,125819,125896],{},[1225,125447,53741,125448,125506,125507,2745,125662,991],{},[15,125449,125451,125468],{"className":125450,"translate":19},[18],[15,125452,125454],{"className":125453},[23],[25,125455,125456],{"xmlns":27},[29,125457,125458,125466],{},[32,125459,125460],{},[6814,125461,125462,125464],{},[35,125463,37449],{},[115,125465,2463],{},[39,125467,40394],{"encoding":41},[15,125469,125471],{"className":125470,"ariaHidden":46},[45],[15,125472,125474,125477],{"className":125473},[50],[15,125475],{"className":125476,"style":40404},[54],[15,125478,125480,125483],{"className":125479},[59],[15,125481,37449],{"className":125482},[59,60],[15,125484,125486],{"className":125485},[281],[15,125487,125489],{"className":125488},[285],[15,125490,125492],{"className":125491},[290],[15,125493,125495],{"className":125494,"style":20028},[294],[15,125496,125497,125500],{"style":6865},[15,125498],{"className":125499,"style":303},[302],[15,125501,125503],{"className":125502},[307,308,309,310],[15,125504,2463],{"className":125505},[59,310],"（等方差 ",[15,125508,125510,125540],{"className":125509,"translate":19},[18],[15,125511,125513],{"className":125512},[23],[25,125514,125515],{"xmlns":27},[29,125516,125517,125537],{},[32,125518,125519,125525,125527,125533,125535],{},[195,125520,125521,125523],{},[35,125522,2332],{},[115,125524,117],{},[110,125526,123],{},[195,125528,125529,125531],{},[35,125530,2332],{},[115,125532,2463],{},[110,125534,123],{},[35,125536,2332],{},[39,125538,125539],{"encoding":41},"\\sigma_1=\\sigma_2=\\sigma",[15,125541,125543,125598,125653],{"className":125542,"ariaHidden":46},[45],[15,125544,125546,125549,125589,125592,125595],{"className":125545},[50],[15,125547],{"className":125548,"style":13374},[54],[15,125550,125552,125555],{"className":125551},[59],[15,125553,2332],{"className":125554,"style":981},[59,60],[15,125556,125558],{"className":125557},[281],[15,125559,125561,125581],{"className":125560},[285,286],[15,125562,125564,125578],{"className":125563},[290],[15,125565,125567],{"className":125566,"style":11133},[294],[15,125568,125569,125572],{"style":18843},[15,125570],{"className":125571,"style":303},[302],[15,125573,125575],{"className":125574},[307,308,309,310],[15,125576,117],{"className":125577},[59,310],[15,125579,318],{"className":125580},[317],[15,125582,125584],{"className":125583},[290],[15,125585,125587],{"className":125586,"style":7968},[294],[15,125588],{},[15,125590],{"className":125591,"style":158},[157],[15,125593,123],{"className":125594},[162],[15,125596],{"className":125597,"style":158},[157],[15,125599,125601,125604,125644,125647,125650],{"className":125600},[50],[15,125602],{"className":125603,"style":13374},[54],[15,125605,125607,125610],{"className":125606},[59],[15,125608,2332],{"className":125609,"style":981},[59,60],[15,125611,125613],{"className":125612},[281],[15,125614,125616,125636],{"className":125615},[285,286],[15,125617,125619,125633],{"className":125618},[290],[15,125620,125622],{"className":125621,"style":11133},[294],[15,125623,125624,125627],{"style":18843},[15,125625],{"className":125626,"style":303},[302],[15,125628,125630],{"className":125629},[307,308,309,310],[15,125631,2463],{"className":125632},[59,310],[15,125634,318],{"className":125635},[317],[15,125637,125639],{"className":125638},[290],[15,125640,125642],{"className":125641,"style":7968},[294],[15,125643],{},[15,125645],{"className":125646,"style":158},[157],[15,125648,123],{"className":125649},[162],[15,125651],{"className":125652,"style":158},[157],[15,125654,125656,125659],{"className":125655},[50],[15,125657],{"className":125658,"style":2345},[54],[15,125660,2332],{"className":125661,"style":981},[59,60],[15,125663,125665,125696],{"className":125664,"translate":19},[18],[15,125666,125668],{"className":125667},[23],[25,125669,125670],{"xmlns":27},[29,125671,125672,125693],{},[32,125673,125674,125677,125679,125685,125687],{},[35,125675,125676],{"mathvariant":209},"Δ",[110,125678,123],{},[195,125680,125681,125683],{},[35,125682,2364],{},[115,125684,117],{},[110,125686,4813],{},[195,125688,125689,125691],{},[35,125690,2364],{},[115,125692,2463],{},[39,125694,125695],{"encoding":41},"\\Delta=\\mu_1-\\mu_2",[15,125697,125699,125717,125772],{"className":125698,"ariaHidden":46},[45],[15,125700,125702,125705,125708,125711,125714],{"className":125701},[50],[15,125703],{"className":125704,"style":664},[54],[15,125706,125676],{"className":125707},[59],[15,125709],{"className":125710,"style":158},[157],[15,125712,123],{"className":125713},[162],[15,125715],{"className":125716,"style":158},[157],[15,125718,125720,125723,125763,125766,125769],{"className":125719},[50],[15,125721],{"className":125722,"style":40321},[54],[15,125724,125726,125729],{"className":125725},[59],[15,125727,2364],{"className":125728},[59,60],[15,125730,125732],{"className":125731},[281],[15,125733,125735,125755],{"className":125734},[285,286],[15,125736,125738,125752],{"className":125737},[290],[15,125739,125741],{"className":125740,"style":11133},[294],[15,125742,125743,125746],{"style":382},[15,125744],{"className":125745,"style":303},[302],[15,125747,125749],{"className":125748},[307,308,309,310],[15,125750,117],{"className":125751},[59,310],[15,125753,318],{"className":125754},[317],[15,125756,125758],{"className":125757},[290],[15,125759,125761],{"className":125760,"style":7968},[294],[15,125762],{},[15,125764],{"className":125765,"style":2587},[157],[15,125767,4813],{"className":125768},[2591],[15,125770],{"className":125771,"style":2587},[157],[15,125773,125775,125778],{"className":125774},[50],[15,125776],{"className":125777,"style":2276},[54],[15,125779,125781,125784],{"className":125780},[59],[15,125782,2364],{"className":125783},[59,60],[15,125785,125787],{"className":125786},[281],[15,125788,125790,125810],{"className":125789},[285,286],[15,125791,125793,125807],{"className":125792},[290],[15,125794,125796],{"className":125795,"style":11133},[294],[15,125797,125798,125801],{"style":382},[15,125799],{"className":125800,"style":303},[302],[15,125802,125804],{"className":125803},[307,308,309,310],[15,125805,2463],{"className":125806},[59,310],[15,125808,318],{"className":125809},[317],[15,125811,125813],{"className":125812},[290],[15,125814,125816],{"className":125815,"style":7968},[294],[15,125817],{}," 计算 ",[15,125820,125822,125846],{"className":125821,"translate":19},[18],[15,125823,125825],{"className":125824},[23],[25,125826,125827],{"xmlns":27},[29,125828,125829,125843],{},[32,125830,125831,125833,125839,125841],{},[110,125832,1287],{},[6814,125834,125835,125837],{},[35,125836,11],{},[115,125838,2463],{},[35,125840,941],{"mathvariant":209},[35,125842,944],{},[39,125844,125845],{"encoding":41},"\\int p^2\u002Fq",[15,125847,125849],{"className":125848,"ariaHidden":46},[45],[15,125850,125852,125855,125858,125861,125890,125893],{"className":125851},[50],[15,125853],{"className":125854,"style":50328},[54],[15,125856,1287],{"className":125857,"style":5617},[1484,1485,5616],[15,125859],{"className":125860,"style":406},[157],[15,125862,125864,125867],{"className":125863},[59],[15,125865,11],{"className":125866},[59,60],[15,125868,125870],{"className":125869},[281],[15,125871,125873],{"className":125872},[285],[15,125874,125876],{"className":125875},[290],[15,125877,125879],{"className":125878,"style":20028},[294],[15,125880,125881,125884],{"style":6865},[15,125882],{"className":125883,"style":303},[302],[15,125885,125887],{"className":125886},[307,308,309,310],[15,125888,2463],{"className":125889},[59,310],[15,125891,941],{"className":125892},[59],[15,125894,944],{"className":125895,"style":981},[59,60],"：由配方可得",[15,125898,125900],{"className":125899,"translate":19},[180],[15,125901,125903,125964],{"className":125902,"translate":19},[18],[15,125904,125906],{"className":125905},[23],[25,125907,125908],{"xmlns":27,"display":189},[29,125909,125910,125961],{},[32,125911,125912,125914,125924,125926,125928,125930,125932,125935,125937,125939,125959],{},[110,125913,1287],{},[238,125915,125916,125922],{},[6814,125917,125918,125920],{},[35,125919,11],{},[115,125921,2463],{},[35,125923,944],{},[1297,125925,1299],{},[35,125927,244],{},[35,125929,774],{},[110,125931,123],{},[35,125933,125934],{},"exp",[110,125936,4103],{},[1297,125938,1304],{},[32,125940,125941,125943,125957],{},[110,125942,113],{"fence":46},[238,125944,125945,125951],{},[6814,125946,125947,125949],{},[35,125948,125676],{"mathvariant":209},[115,125950,2463],{},[6814,125952,125953,125955],{},[35,125954,2332],{},[115,125956,2463],{},[110,125958,120],{"fence":46},[110,125960,551],{"separator":46},[39,125962,125963],{"encoding":41},"\\int \\frac{p^2}{q}\\,dx\n=\\exp\\!\\left(\\frac{\\Delta^2}{\\sigma^2}\\right),",[15,125965,125967,126085],{"className":125966,"ariaHidden":46},[45],[15,125968,125970,125973,125976,125979,126067,126070,126073,126076,126079,126082],{"className":125969},[50],[15,125971],{"className":125972,"style":37698},[54],[15,125974,1287],{"className":125975,"style":1487},[1484,1485,1486],[15,125977],{"className":125978,"style":406},[157],[15,125980,125982,125985,126064],{"className":125981},[59],[15,125983],{"className":125984},[146,441],[15,125986,125988],{"className":125987},[238],[15,125989,125991,126056],{"className":125990},[285,286],[15,125992,125994,126053],{"className":125993},[290],[15,125995,125997,126008,126016],{"className":125996,"style":37723},[294],[15,125998,125999,126002],{"style":457},[15,126000],{"className":126001,"style":461},[302],[15,126003,126005],{"className":126004},[59],[15,126006,944],{"className":126007,"style":981},[59,60],[15,126009,126010,126013],{"style":473},[15,126011],{"className":126012,"style":461},[302],[15,126014],{"className":126015,"style":481},[480],[15,126017,126018,126021],{"style":484},[15,126019],{"className":126020,"style":461},[302],[15,126022,126024],{"className":126023},[59],[15,126025,126027,126030],{"className":126026},[59],[15,126028,11],{"className":126029},[59,60],[15,126031,126033],{"className":126032},[281],[15,126034,126036],{"className":126035},[285],[15,126037,126039],{"className":126038},[290],[15,126040,126042],{"className":126041,"style":20028},[294],[15,126043,126044,126047],{"style":6865},[15,126045],{"className":126046,"style":303},[302],[15,126048,126050],{"className":126049},[307,308,309,310],[15,126051,2463],{"className":126052},[59,310],[15,126054,318],{"className":126055},[317],[15,126057,126059],{"className":126058},[290],[15,126060,126062],{"className":126061,"style":506},[294],[15,126063],{},[15,126065],{"className":126066},[153,441],[15,126068],{"className":126069,"style":406},[157],[15,126071,244],{"className":126072},[59,60],[15,126074,774],{"className":126075},[59,60],[15,126077],{"className":126078,"style":158},[157],[15,126080,123],{"className":126081},[162],[15,126083],{"className":126084,"style":158},[157],[15,126086,126088,126091,126094,126097,126100,126229,126232],{"className":126087},[50],[15,126089],{"className":126090,"style":87258},[54],[15,126092,125934],{"className":126093},[1484],[15,126095],{"className":126096,"style":1512},[157],[15,126098],{"className":126099,"style":406},[157],[15,126101,126103,126109,126223],{"className":126102},[410],[15,126104,126106],{"className":126105,"style":415},[146,414],[15,126107,113],{"className":126108},[419,309],[15,126110,126112,126115,126220],{"className":126111},[59],[15,126113],{"className":126114},[146,441],[15,126116,126118],{"className":126117},[238],[15,126119,126121,126212],{"className":126120},[285,286],[15,126122,126124,126209],{"className":126123},[290],[15,126125,126127,126164,126172],{"className":126126,"style":37723},[294],[15,126128,126129,126132],{"style":457},[15,126130],{"className":126131,"style":461},[302],[15,126133,126135],{"className":126134},[59],[15,126136,126138,126141],{"className":126137},[59],[15,126139,2332],{"className":126140,"style":981},[59,60],[15,126142,126144],{"className":126143},[281],[15,126145,126147],{"className":126146},[285],[15,126148,126150],{"className":126149},[290],[15,126151,126153],{"className":126152,"style":45032},[294],[15,126154,126155,126158],{"style":45035},[15,126156],{"className":126157,"style":303},[302],[15,126159,126161],{"className":126160},[307,308,309,310],[15,126162,2463],{"className":126163},[59,310],[15,126165,126166,126169],{"style":473},[15,126167],{"className":126168,"style":461},[302],[15,126170],{"className":126171,"style":481},[480],[15,126173,126174,126177],{"style":484},[15,126175],{"className":126176,"style":461},[302],[15,126178,126180],{"className":126179},[59],[15,126181,126183,126186],{"className":126182},[59],[15,126184,125676],{"className":126185},[59],[15,126187,126189],{"className":126188},[281],[15,126190,126192],{"className":126191},[285],[15,126193,126195],{"className":126194},[290],[15,126196,126198],{"className":126197,"style":20028},[294],[15,126199,126200,126203],{"style":6865},[15,126201],{"className":126202,"style":303},[302],[15,126204,126206],{"className":126205},[307,308,309,310],[15,126207,2463],{"className":126208},[59,310],[15,126210,318],{"className":126211},[317],[15,126213,126215],{"className":126214},[290],[15,126216,126218],{"className":126217,"style":3778},[294],[15,126219],{},[15,126221],{"className":126222},[153,441],[15,126224,126226],{"className":126225,"style":415},[153,414],[15,126227,120],{"className":126228},[419,309],[15,126230],{"className":126231,"style":406},[157],[15,126233,551],{"className":126234},[573],[11,126236,48159],{},[15,126238,126240],{"className":126239,"translate":19},[180],[15,126241,126243,126351],{"className":126242,"translate":19},[18],[15,126244,126246],{"className":126245},[23],[25,126247,126248],{"xmlns":27,"display":189},[29,126249,126250,126348],{},[32,126251,126252,126258,126260,126262,126264,126266,126268,126270,126272,126292,126294,126296,126298,126300,126302,126312,126314,126316,126318,126320,126322,126324,126344,126346],{},[6814,126253,126254,126256],{},[35,126255,37449],{},[115,126257,2463],{},[110,126259,113],{"stretchy":112},[35,126261,206],{},[35,126263,210],{"mathvariant":209},[35,126265,213],{},[110,126267,120],{"stretchy":112},[110,126269,123],{},[110,126271,1287],{},[238,126273,126274,126290],{},[32,126275,126276,126278,126280,126282,126284],{},[110,126277,113],{"stretchy":112},[35,126279,11],{},[110,126281,4813],{},[35,126283,944],{},[6814,126285,126286,126288],{},[110,126287,120],{"stretchy":112},[115,126289,2463],{},[35,126291,944],{},[1297,126293,1299],{},[35,126295,244],{},[35,126297,774],{},[110,126299,123],{},[110,126301,1287],{},[238,126303,126304,126310],{},[6814,126305,126306,126308],{},[35,126307,11],{},[115,126309,2463],{},[35,126311,944],{},[110,126313,4813],{},[115,126315,117],{},[110,126317,123],{},[35,126319,125934],{},[110,126321,4103],{},[1297,126323,1304],{},[32,126325,126326,126328,126342],{},[110,126327,113],{"fence":46},[238,126329,126330,126336],{},[6814,126331,126332,126334],{},[35,126333,125676],{"mathvariant":209},[115,126335,2463],{},[6814,126337,126338,126340],{},[35,126339,2332],{},[115,126341,2463],{},[110,126343,120],{"fence":46},[110,126345,4813],{},[115,126347,49510],{},[39,126349,126350],{"encoding":41},"\\chi^2(P\\|Q)=\\int\\frac{(p-q)^2}{q}\\,dx\n=\\int\\frac{p^2}{q}-1\n=\\exp\\!\\left(\\frac{\\Delta^2}{\\sigma^2}\\right)\n-1 .",[15,126352,126354,126413,126549,126658,126676,126829],{"className":126353,"ariaHidden":46},[45],[15,126355,126357,126360,126389,126392,126395,126398,126401,126404,126407,126410],{"className":126356},[50],[15,126358],{"className":126359,"style":37251},[54],[15,126361,126363,126366],{"className":126362},[59],[15,126364,37449],{"className":126365},[59,60],[15,126367,126369],{"className":126368},[281],[15,126370,126372],{"className":126371},[285],[15,126373,126375],{"className":126374},[290],[15,126376,126378],{"className":126377,"style":19735},[294],[15,126379,126380,126383],{"style":8277},[15,126381],{"className":126382,"style":303},[302],[15,126384,126386],{"className":126385},[307,308,309,310],[15,126387,2463],{"className":126388},[59,310],[15,126390,113],{"className":126391},[146],[15,126393,206],{"className":126394,"style":334},[59,60],[15,126396,210],{"className":126397},[59],[15,126399,213],{"className":126400},[59,60],[15,126402,120],{"className":126403},[153],[15,126405],{"className":126406,"style":158},[157],[15,126408,123],{"className":126409},[162],[15,126411],{"className":126412,"style":158},[157],[15,126414,126416,126419,126422,126425,126531,126534,126537,126540,126543,126546],{"className":126415},[50],[15,126417],{"className":126418,"style":37698},[54],[15,126420,1287],{"className":126421,"style":1487},[1484,1485,1486],[15,126423],{"className":126424,"style":406},[157],[15,126426,126428,126431,126528],{"className":126427},[59],[15,126429],{"className":126430},[146,441],[15,126432,126434],{"className":126433},[238],[15,126435,126437,126520],{"className":126436},[285,286],[15,126438,126440,126517],{"className":126439},[290],[15,126441,126443,126454,126462],{"className":126442,"style":37723},[294],[15,126444,126445,126448],{"style":457},[15,126446],{"className":126447,"style":461},[302],[15,126449,126451],{"className":126450},[59],[15,126452,944],{"className":126453,"style":981},[59,60],[15,126455,126456,126459],{"style":473},[15,126457],{"className":126458,"style":461},[302],[15,126460],{"className":126461,"style":481},[480],[15,126463,126464,126467],{"style":484},[15,126465],{"className":126466,"style":461},[302],[15,126468,126470,126473,126476,126479,126482,126485,126488],{"className":126469},[59],[15,126471,113],{"className":126472},[146],[15,126474,11],{"className":126475},[59,60],[15,126477],{"className":126478,"style":2587},[157],[15,126480,4813],{"className":126481},[2591],[15,126483],{"className":126484,"style":2587},[157],[15,126486,944],{"className":126487,"style":981},[59,60],[15,126489,126491,126494],{"className":126490},[153],[15,126492,120],{"className":126493},[153],[15,126495,126497],{"className":126496},[281],[15,126498,126500],{"className":126499},[285],[15,126501,126503],{"className":126502},[290],[15,126504,126506],{"className":126505,"style":20028},[294],[15,126507,126508,126511],{"style":6865},[15,126509],{"className":126510,"style":303},[302],[15,126512,126514],{"className":126513},[307,308,309,310],[15,126515,2463],{"className":126516},[59,310],[15,126518,318],{"className":126519},[317],[15,126521,126523],{"className":126522},[290],[15,126524,126526],{"className":126525,"style":506},[294],[15,126527],{},[15,126529],{"className":126530},[153,441],[15,126532],{"className":126533,"style":406},[157],[15,126535,244],{"className":126536},[59,60],[15,126538,774],{"className":126539},[59,60],[15,126541],{"className":126542,"style":158},[157],[15,126544,123],{"className":126545},[162],[15,126547],{"className":126548,"style":158},[157],[15,126550,126552,126555,126558,126561,126649,126652,126655],{"className":126551},[50],[15,126553],{"className":126554,"style":37698},[54],[15,126556,1287],{"className":126557,"style":1487},[1484,1485,1486],[15,126559],{"className":126560,"style":406},[157],[15,126562,126564,126567,126646],{"className":126563},[59],[15,126565],{"className":126566},[146,441],[15,126568,126570],{"className":126569},[238],[15,126571,126573,126638],{"className":126572},[285,286],[15,126574,126576,126635],{"className":126575},[290],[15,126577,126579,126590,126598],{"className":126578,"style":37723},[294],[15,126580,126581,126584],{"style":457},[15,126582],{"className":126583,"style":461},[302],[15,126585,126587],{"className":126586},[59],[15,126588,944],{"className":126589,"style":981},[59,60],[15,126591,126592,126595],{"style":473},[15,126593],{"className":126594,"style":461},[302],[15,126596],{"className":126597,"style":481},[480],[15,126599,126600,126603],{"style":484},[15,126601],{"className":126602,"style":461},[302],[15,126604,126606],{"className":126605},[59],[15,126607,126609,126612],{"className":126608},[59],[15,126610,11],{"className":126611},[59,60],[15,126613,126615],{"className":126614},[281],[15,126616,126618],{"className":126617},[285],[15,126619,126621],{"className":126620},[290],[15,126622,126624],{"className":126623,"style":20028},[294],[15,126625,126626,126629],{"style":6865},[15,126627],{"className":126628,"style":303},[302],[15,126630,126632],{"className":126631},[307,308,309,310],[15,126633,2463],{"className":126634},[59,310],[15,126636,318],{"className":126637},[317],[15,126639,126641],{"className":126640},[290],[15,126642,126644],{"className":126643,"style":506},[294],[15,126645],{},[15,126647],{"className":126648},[153,441],[15,126650],{"className":126651,"style":2587},[157],[15,126653,4813],{"className":126654},[2591],[15,126656],{"className":126657,"style":2587},[157],[15,126659,126661,126664,126667,126670,126673],{"className":126660},[50],[15,126662],{"className":126663,"style":172},[54],[15,126665,117],{"className":126666},[59],[15,126668],{"className":126669,"style":158},[157],[15,126671,123],{"className":126672},[162],[15,126674],{"className":126675,"style":158},[157],[15,126677,126679,126682,126685,126688,126691,126820,126823,126826],{"className":126678},[50],[15,126680],{"className":126681,"style":87258},[54],[15,126683,125934],{"className":126684},[1484],[15,126686],{"className":126687,"style":1512},[157],[15,126689],{"className":126690,"style":406},[157],[15,126692,126694,126700,126814],{"className":126693},[410],[15,126695,126697],{"className":126696,"style":415},[146,414],[15,126698,113],{"className":126699},[419,309],[15,126701,126703,126706,126811],{"className":126702},[59],[15,126704],{"className":126705},[146,441],[15,126707,126709],{"className":126708},[238],[15,126710,126712,126803],{"className":126711},[285,286],[15,126713,126715,126800],{"className":126714},[290],[15,126716,126718,126755,126763],{"className":126717,"style":37723},[294],[15,126719,126720,126723],{"style":457},[15,126721],{"className":126722,"style":461},[302],[15,126724,126726],{"className":126725},[59],[15,126727,126729,126732],{"className":126728},[59],[15,126730,2332],{"className":126731,"style":981},[59,60],[15,126733,126735],{"className":126734},[281],[15,126736,126738],{"className":126737},[285],[15,126739,126741],{"className":126740},[290],[15,126742,126744],{"className":126743,"style":45032},[294],[15,126745,126746,126749],{"style":45035},[15,126747],{"className":126748,"style":303},[302],[15,126750,126752],{"className":126751},[307,308,309,310],[15,126753,2463],{"className":126754},[59,310],[15,126756,126757,126760],{"style":473},[15,126758],{"className":126759,"style":461},[302],[15,126761],{"className":126762,"style":481},[480],[15,126764,126765,126768],{"style":484},[15,126766],{"className":126767,"style":461},[302],[15,126769,126771],{"className":126770},[59],[15,126772,126774,126777],{"className":126773},[59],[15,126775,125676],{"className":126776},[59],[15,126778,126780],{"className":126779},[281],[15,126781,126783],{"className":126782},[285],[15,126784,126786],{"className":126785},[290],[15,126787,126789],{"className":126788,"style":20028},[294],[15,126790,126791,126794],{"style":6865},[15,126792],{"className":126793,"style":303},[302],[15,126795,126797],{"className":126796},[307,308,309,310],[15,126798,2463],{"className":126799},[59,310],[15,126801,318],{"className":126802},[317],[15,126804,126806],{"className":126805},[290],[15,126807,126809],{"className":126808,"style":3778},[294],[15,126810],{},[15,126812],{"className":126813},[153,441],[15,126815,126817],{"className":126816,"style":415},[153,414],[15,126818,120],{"className":126819},[419,309],[15,126821],{"className":126822,"style":2587},[157],[15,126824,4813],{"className":126825},[2591],[15,126827],{"className":126828,"style":2587},[157],[15,126830,126832,126835],{"className":126831},[50],[15,126833],{"className":126834,"style":172},[54],[15,126836,49510],{"className":126837},[59],[11,126839,126840,126841,126899,126900,126999],{},"这印证了「无界」：两个虽很接近但支撑重叠的正态，",[15,126842,126844,126861],{"className":126843,"translate":19},[18],[15,126845,126847],{"className":126846},[23],[25,126848,126849],{"xmlns":27},[29,126850,126851,126859],{},[32,126852,126853],{},[6814,126854,126855,126857],{},[35,126856,37449],{},[115,126858,2463],{},[39,126860,40394],{"encoding":41},[15,126862,126864],{"className":126863,"ariaHidden":46},[45],[15,126865,126867,126870],{"className":126866},[50],[15,126868],{"className":126869,"style":40404},[54],[15,126871,126873,126876],{"className":126872},[59],[15,126874,37449],{"className":126875},[59,60],[15,126877,126879],{"className":126878},[281],[15,126880,126882],{"className":126881},[285],[15,126883,126885],{"className":126884},[290],[15,126886,126888],{"className":126887,"style":20028},[294],[15,126889,126890,126893],{"style":6865},[15,126891],{"className":126892,"style":303},[302],[15,126894,126896],{"className":126895},[307,308,309,310],[15,126897,2463],{"className":126898},[59,310]," 也会随 ",[15,126901,126903,126929],{"className":126902,"translate":19},[18],[15,126904,126906],{"className":126905},[23],[25,126907,126908],{"xmlns":27},[29,126909,126910,126926],{},[32,126911,126912,126918,126920],{},[6814,126913,126914,126916],{},[35,126915,125676],{"mathvariant":209},[115,126917,2463],{},[35,126919,941],{"mathvariant":209},[6814,126921,126922,126924],{},[35,126923,2332],{},[115,126925,2463],{},[39,126927,126928],{"encoding":41},"\\Delta^2\u002F\\sigma^2",[15,126930,126932],{"className":126931,"ariaHidden":46},[45],[15,126933,126935,126938,126967,126970],{"className":126934},[50],[15,126936],{"className":126937,"style":20003},[54],[15,126939,126941,126944],{"className":126940},[59],[15,126942,125676],{"className":126943},[59],[15,126945,126947],{"className":126946},[281],[15,126948,126950],{"className":126949},[285],[15,126951,126953],{"className":126952},[290],[15,126954,126956],{"className":126955,"style":20028},[294],[15,126957,126958,126961],{"style":6865},[15,126959],{"className":126960,"style":303},[302],[15,126962,126964],{"className":126963},[307,308,309,310],[15,126965,2463],{"className":126966},[59,310],[15,126968,941],{"className":126969},[59],[15,126971,126973,126976],{"className":126972},[59],[15,126974,2332],{"className":126975,"style":981},[59,60],[15,126977,126979],{"className":126978},[281],[15,126980,126982],{"className":126981},[285],[15,126983,126985],{"className":126984},[290],[15,126986,126988],{"className":126987,"style":20028},[294],[15,126989,126990,126993],{"style":6865},[15,126991],{"className":126992,"style":303},[302],[15,126994,126996],{"className":126995},[307,308,309,310],[15,126997,2463],{"className":126998},[59,310]," 指数爆炸。",[11,127001,127002,127005],{},[1225,127003,127004],{},"Hellinger²（等方差）。"," Bhattacharyya 系数",[15,127007,127009],{"className":127008,"translate":19},[180],[15,127010,127012,127086],{"className":127011,"translate":19},[18],[15,127013,127015],{"className":127014},[23],[25,127016,127017],{"xmlns":27,"display":189},[29,127018,127019,127083],{},[32,127020,127021,127023,127025,127027,127029,127031,127033,127035,127037,127039,127047,127049,127051,127053,127055,127081],{},[35,127022,39291],{},[35,127024,39294],{},[110,127026,113],{"stretchy":112},[35,127028,206],{},[110,127030,551],{"separator":46},[35,127032,213],{},[110,127034,120],{"stretchy":112},[110,127036,123],{},[110,127038,1287],{},[34339,127040,127041],{},[32,127042,127043,127045],{},[35,127044,11],{},[35,127046,944],{},[110,127048,123],{},[35,127050,125934],{},[110,127052,4103],{},[1297,127054,1304],{},[32,127056,127057,127059,127061,127079],{},[110,127058,113],{"fence":46},[110,127060,4813],{},[238,127062,127063,127069],{},[6814,127064,127065,127067],{},[35,127066,125676],{"mathvariant":209},[115,127068,2463],{},[32,127070,127071,127073],{},[115,127072,39303],{},[6814,127074,127075,127077],{},[35,127076,2332],{},[115,127078,2463],{},[110,127080,120],{"fence":46},[110,127082,551],{"separator":46},[39,127084,127085],{"encoding":41},"BC(P,Q)=\\int\\sqrt{pq}\n=\\exp\\!\\left(-\\frac{\\Delta^2}{8\\sigma^2}\\right),",[15,127087,127089,127128,127196],{"className":127088,"ariaHidden":46},[45],[15,127090,127092,127095,127098,127101,127104,127107,127110,127113,127116,127119,127122,127125],{"className":127091},[50],[15,127093],{"className":127094,"style":139},[54],[15,127096,39291],{"className":127097,"style":39387},[59,60],[15,127099,39294],{"className":127100,"style":10782},[59,60],[15,127102,113],{"className":127103},[146],[15,127105,206],{"className":127106,"style":334},[59,60],[15,127108,551],{"className":127109},[573],[15,127111],{"className":127112,"style":406},[157],[15,127114,213],{"className":127115},[59,60],[15,127117,120],{"className":127118},[153],[15,127120],{"className":127121,"style":158},[157],[15,127123,123],{"className":127124},[162],[15,127126],{"className":127127,"style":158},[157],[15,127129,127131,127134,127137,127140,127187,127190,127193],{"className":127130},[50],[15,127132],{"className":127133,"style":5777},[54],[15,127135,1287],{"className":127136,"style":1487},[1484,1485,1486],[15,127138],{"className":127139,"style":406},[157],[15,127141,127143],{"className":127142},[59,34367],[15,127144,127146,127179],{"className":127145},[285,286],[15,127147,127149,127176],{"className":127148},[290],[15,127150,127152,127164],{"className":127151,"style":6862},[294],[15,127153,127155,127158],{"className":127154,"style":11863},[6307],[15,127156],{"className":127157,"style":461},[302],[15,127159,127161],{"className":127160,"style":34387},[59],[15,127162,41605],{"className":127163,"style":981},[59,60],[15,127165,127166,127169],{"style":41350},[15,127167],{"className":127168,"style":461},[302],[15,127170,127172],{"className":127171,"style":34444},[34443],[6323,127173,127174],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,127175],{"d":34451},[15,127177,318],{"className":127178},[317],[15,127180,127182],{"className":127181},[290],[15,127183,127185],{"className":127184,"style":41370},[294],[15,127186],{},[15,127188],{"className":127189,"style":158},[157],[15,127191,123],{"className":127192},[162],[15,127194],{"className":127195,"style":158},[157],[15,127197,127199,127202,127205,127208,127211,127346,127349],{"className":127198},[50],[15,127200],{"className":127201,"style":87258},[54],[15,127203,125934],{"className":127204},[1484],[15,127206],{"className":127207,"style":1512},[157],[15,127209],{"className":127210,"style":406},[157],[15,127212,127214,127220,127223,127340],{"className":127213},[410],[15,127215,127217],{"className":127216,"style":415},[146,414],[15,127218,113],{"className":127219},[419,309],[15,127221,4813],{"className":127222},[59],[15,127224,127226,127229,127337],{"className":127225},[59],[15,127227],{"className":127228},[146,441],[15,127230,127232],{"className":127231},[238],[15,127233,127235,127329],{"className":127234},[285,286],[15,127236,127238,127326],{"className":127237},[290],[15,127239,127241,127281,127289],{"className":127240,"style":37723},[294],[15,127242,127243,127246],{"style":457},[15,127244],{"className":127245,"style":461},[302],[15,127247,127249,127252],{"className":127248},[59],[15,127250,39303],{"className":127251},[59],[15,127253,127255,127258],{"className":127254},[59],[15,127256,2332],{"className":127257,"style":981},[59,60],[15,127259,127261],{"className":127260},[281],[15,127262,127264],{"className":127263},[285],[15,127265,127267],{"className":127266},[290],[15,127268,127270],{"className":127269,"style":45032},[294],[15,127271,127272,127275],{"style":45035},[15,127273],{"className":127274,"style":303},[302],[15,127276,127278],{"className":127277},[307,308,309,310],[15,127279,2463],{"className":127280},[59,310],[15,127282,127283,127286],{"style":473},[15,127284],{"className":127285,"style":461},[302],[15,127287],{"className":127288,"style":481},[480],[15,127290,127291,127294],{"style":484},[15,127292],{"className":127293,"style":461},[302],[15,127295,127297],{"className":127296},[59],[15,127298,127300,127303],{"className":127299},[59],[15,127301,125676],{"className":127302},[59],[15,127304,127306],{"className":127305},[281],[15,127307,127309],{"className":127308},[285],[15,127310,127312],{"className":127311},[290],[15,127313,127315],{"className":127314,"style":20028},[294],[15,127316,127317,127320],{"style":6865},[15,127318],{"className":127319,"style":303},[302],[15,127321,127323],{"className":127322},[307,308,309,310],[15,127324,2463],{"className":127325},[59,310],[15,127327,318],{"className":127328},[317],[15,127330,127332],{"className":127331},[290],[15,127333,127335],{"className":127334,"style":3778},[294],[15,127336],{},[15,127338],{"className":127339},[153,441],[15,127341,127343],{"className":127342,"style":415},[153,414],[15,127344,120],{"className":127345},[419,309],[15,127347],{"className":127348,"style":406},[157],[15,127350,551],{"className":127351},[573],[11,127353,91793,127354,2745,127612,127867],{},[15,127355,127357,127411],{"className":127356,"translate":19},[18],[15,127358,127360],{"className":127359},[23],[25,127361,127362],{"xmlns":27},[29,127363,127364,127408],{},[32,127365,127366,127374,127376,127378,127380],{},[7553,127367,127368,127370,127372],{},[35,127369,33884],{},[1297,127371,42137],{},[115,127373,2463],{},[110,127375,123],{},[115,127377,117],{},[110,127379,4813],{},[6814,127381,127382,127384],{},[35,127383,7567],{},[32,127385,127386,127388,127394,127396,127398,127400,127406],{},[110,127387,4813],{},[6814,127389,127390,127392],{},[35,127391,125676],{"mathvariant":209},[115,127393,2463],{},[35,127395,941],{"mathvariant":209},[110,127397,113],{"stretchy":112},[115,127399,39303],{},[6814,127401,127402,127404],{},[35,127403,2332],{},[115,127405,2463],{},[110,127407,120],{"stretchy":112},[39,127409,127410],{"encoding":41},"H^2_{\\text{Bhattacharyya}}=1-e^{-\\Delta^2\u002F(8\\sigma^2)}",[15,127412,127414,127486,127504],{"className":127413,"ariaHidden":46},[45],[15,127415,127417,127420,127477,127480,127483],{"className":127416},[50],[15,127418],{"className":127419,"style":42885},[54],[15,127421,127423,127426],{"className":127422},[59],[15,127424,33884],{"className":127425,"style":34038},[59,60],[15,127427,127429],{"className":127428},[281],[15,127430,127432,127469],{"className":127431},[285,286],[15,127433,127435,127466],{"className":127434},[290],[15,127436,127438,127455],{"className":127437,"style":20028},[294],[15,127439,127440,127443],{"style":42909},[15,127441],{"className":127442,"style":303},[302],[15,127444,127446],{"className":127445},[307,308,309,310],[15,127447,127449],{"className":127448},[59,310],[15,127450,127452],{"className":127451},[59,4598,310],[15,127453,42137],{"className":127454},[59,310],[15,127456,127457,127460],{"style":6865},[15,127458],{"className":127459,"style":303},[302],[15,127461,127463],{"className":127462},[307,308,309,310],[15,127464,2463],{"className":127465},[59,310],[15,127467,318],{"className":127468},[317],[15,127470,127472],{"className":127471},[290],[15,127473,127475],{"className":127474,"style":42945},[294],[15,127476],{},[15,127478],{"className":127479,"style":158},[157],[15,127481,123],{"className":127482},[162],[15,127484],{"className":127485,"style":158},[157],[15,127487,127489,127492,127495,127498,127501],{"className":127488},[50],[15,127490],{"className":127491,"style":12578},[54],[15,127493,117],{"className":127494},[59],[15,127496],{"className":127497,"style":2587},[157],[15,127499,4813],{"className":127500},[2591],[15,127502],{"className":127503,"style":2587},[157],[15,127505,127507,127510],{"className":127506},[50],[15,127508],{"className":127509,"style":117281},[54],[15,127511,127513,127516],{"className":127512},[59],[15,127514,7567],{"className":127515},[59,60],[15,127517,127519],{"className":127518},[281],[15,127520,127522],{"className":127521},[285],[15,127523,127525],{"className":127524},[290],[15,127526,127528],{"className":127527,"style":117281},[294],[15,127529,127530,127533],{"style":6865},[15,127531],{"className":127532,"style":303},[302],[15,127534,127536],{"className":127535},[307,308,309,310],[15,127537,127539,127542,127571,127574,127577,127580,127609],{"className":127538},[59,310],[15,127540,4813],{"className":127541},[59,310],[15,127543,127545,127548],{"className":127544},[59,310],[15,127546,125676],{"className":127547},[59,310],[15,127549,127551],{"className":127550},[281],[15,127552,127554],{"className":127553},[285],[15,127555,127557],{"className":127556},[290],[15,127558,127560],{"className":127559,"style":38512},[294],[15,127561,127562,127565],{"style":38515},[15,127563],{"className":127564,"style":30206},[302],[15,127566,127568],{"className":127567},[307,30210,9674,310],[15,127569,2463],{"className":127570},[59,310],[15,127572,941],{"className":127573},[59,310],[15,127575,113],{"className":127576},[146,310],[15,127578,39303],{"className":127579},[59,310],[15,127581,127583,127586],{"className":127582},[59,310],[15,127584,2332],{"className":127585,"style":981},[59,60,310],[15,127587,127589],{"className":127588},[281],[15,127590,127592],{"className":127591},[285],[15,127593,127595],{"className":127594},[290],[15,127596,127598],{"className":127597,"style":38512},[294],[15,127599,127600,127603],{"style":38515},[15,127601],{"className":127602,"style":30206},[302],[15,127604,127606],{"className":127605},[307,30210,9674,310],[15,127607,2463],{"className":127608},[59,310],[15,127610,120],{"className":127611},[153,310],[15,127613,127615,127673],{"className":127614,"translate":19},[18],[15,127616,127618],{"className":127617},[23],[25,127619,127620],{"xmlns":27},[29,127621,127622,127670],{},[32,127623,127624,127630,127632,127634,127636,127638,127640,127668],{},[195,127625,127626,127628],{},[35,127627,199],{},[35,127629,37],{},[110,127631,123],{},[115,127633,2463],{},[110,127635,113],{"stretchy":112},[115,127637,117],{},[110,127639,4813],{},[6814,127641,127642,127644],{},[35,127643,7567],{},[32,127645,127646,127648,127654,127656,127658,127660,127666],{},[110,127647,4813],{},[6814,127649,127650,127652],{},[35,127651,125676],{"mathvariant":209},[115,127653,2463],{},[35,127655,941],{"mathvariant":209},[110,127657,113],{"stretchy":112},[115,127659,39303],{},[6814,127661,127662,127664],{},[35,127663,2332],{},[115,127665,2463],{},[110,127667,120],{"stretchy":112},[110,127669,120],{"stretchy":112},[39,127671,127672],{"encoding":41},"D_f=2(1-e^{-\\Delta^2\u002F(8\\sigma^2)})",[15,127674,127676,127731,127755],{"className":127675,"ariaHidden":46},[45],[15,127677,127679,127682,127722,127725,127728],{"className":127678},[50],[15,127680],{"className":127681,"style":4032},[54],[15,127683,127685,127688],{"className":127684},[59],[15,127686,199],{"className":127687,"style":277},[59,60],[15,127689,127691],{"className":127690},[281],[15,127692,127694,127714],{"className":127693},[285,286],[15,127695,127697,127711],{"className":127696},[290],[15,127698,127700],{"className":127699,"style":295},[294],[15,127701,127702,127705],{"style":298},[15,127703],{"className":127704,"style":303},[302],[15,127706,127708],{"className":127707},[307,308,309,310],[15,127709,37],{"className":127710,"style":61},[59,60,310],[15,127712,318],{"className":127713},[317],[15,127715,127717],{"className":127716},[290],[15,127718,127720],{"className":127719,"style":325},[294],[15,127721],{},[15,127723],{"className":127724,"style":158},[157],[15,127726,123],{"className":127727},[162],[15,127729],{"className":127730,"style":158},[157],[15,127732,127734,127737,127740,127743,127746,127749,127752],{"className":127733},[50],[15,127735],{"className":127736,"style":139},[54],[15,127738,2463],{"className":127739},[59],[15,127741,113],{"className":127742},[146],[15,127744,117],{"className":127745},[59],[15,127747],{"className":127748,"style":2587},[157],[15,127750,4813],{"className":127751},[2591],[15,127753],{"className":127754,"style":2587},[157],[15,127756,127758,127762,127864],{"className":127757},[50],[15,127759],{"className":127760,"style":127761},[54],"height:1.2369em;vertical-align:-0.25em;",[15,127763,127765,127768],{"className":127764},[59],[15,127766,7567],{"className":127767},[59,60],[15,127769,127771],{"className":127770},[281],[15,127772,127774],{"className":127773},[285],[15,127775,127777],{"className":127776},[290],[15,127778,127780],{"className":127779,"style":117281},[294],[15,127781,127782,127785],{"style":6865},[15,127783],{"className":127784,"style":303},[302],[15,127786,127788],{"className":127787},[307,308,309,310],[15,127789,127791,127794,127823,127826,127829,127832,127861],{"className":127790},[59,310],[15,127792,4813],{"className":127793},[59,310],[15,127795,127797,127800],{"className":127796},[59,310],[15,127798,125676],{"className":127799},[59,310],[15,127801,127803],{"className":127802},[281],[15,127804,127806],{"className":127805},[285],[15,127807,127809],{"className":127808},[290],[15,127810,127812],{"className":127811,"style":38512},[294],[15,127813,127814,127817],{"style":38515},[15,127815],{"className":127816,"style":30206},[302],[15,127818,127820],{"className":127819},[307,30210,9674,310],[15,127821,2463],{"className":127822},[59,310],[15,127824,941],{"className":127825},[59,310],[15,127827,113],{"className":127828},[146,310],[15,127830,39303],{"className":127831},[59,310],[15,127833,127835,127838],{"className":127834},[59,310],[15,127836,2332],{"className":127837,"style":981},[59,60,310],[15,127839,127841],{"className":127840},[281],[15,127842,127844],{"className":127843},[285],[15,127845,127847],{"className":127846},[290],[15,127848,127850],{"className":127849,"style":38512},[294],[15,127851,127852,127855],{"style":38515},[15,127853],{"className":127854,"style":30206},[302],[15,127856,127858],{"className":127857},[307,30210,9674,310],[15,127859,2463],{"className":127860},[59,310],[15,127862,120],{"className":127863},[153,310],[15,127865,120],{"className":127866},[153],"（本文约定）。",[11,127869,127870,127873],{},[1225,127871,127872],{},"α-散度（等方差）。"," 由 3.6 节",[15,127875,127877],{"className":127876,"translate":19},[180],[15,127878,127880,127988],{"className":127879,"translate":19},[18],[15,127881,127883],{"className":127882},[23],[25,127884,127885],{"xmlns":27,"display":189},[29,127886,127887,127985],{},[32,127888,127889,127895,127897,127915,127917,127919,127921,127961,127963,127965,127967,127969,127971,127983],{},[195,127890,127891,127893],{},[35,127892,199],{},[35,127894,44754],{},[110,127896,123],{},[238,127898,127899,127901],{},[115,127900,117],{},[32,127902,127903,127905,127907,127909,127911,127913],{},[35,127904,45180],{},[110,127906,113],{"stretchy":112},[115,127908,117],{},[110,127910,4813],{},[35,127912,45180],{},[110,127914,120],{"stretchy":112},[110,127916,113],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[115,127918,117],{},[110,127920,4813],{},[6814,127922,127923,127925],{},[35,127924,7567],{},[32,127926,127927,127929],{},[110,127928,4813],{},[238,127930,127931,127951],{},[32,127932,127933,127935,127937,127939,127941,127943,127945],{},[35,127934,45180],{},[110,127936,113],{"stretchy":112},[115,127938,117],{},[110,127940,4813],{},[35,127942,45180],{},[110,127944,120],{"stretchy":112},[6814,127946,127947,127949],{},[35,127948,125676],{"mathvariant":209},[115,127950,2463],{},[32,127952,127953,127955],{},[115,127954,2463],{},[6814,127956,127957,127959],{},[35,127958,2332],{},[115,127960,2463],{},[110,127962,120],{"fence":112,"stretchy":46,"minsize":17439,"maxsize":17439},[110,127964,551],{"separator":46},[157,127966],{"width":3262},[35,127968,45180],{},[110,127970,123],{},[238,127972,127973,127981],{},[32,127974,127975,127977,127979],{},[115,127976,117],{},[110,127978,2470],{},[35,127980,44754],{},[115,127982,2463],{},[110,127984,551],{"separator":46},[39,127986,127987],{"encoding":41},"D_\\alpha=\\frac{1}{a(1-a)}\n\\Big(1-\ne^{-\\frac{a(1-a)\\Delta^2}{2\\sigma^2}}\\Big),\n\\qquad a=\\frac{1+\\alpha}{2},",[15,127989,127991,128046,128153,128365],{"className":127990,"ariaHidden":46},[45],[15,127992,127994,127997,128037,128040,128043],{"className":127993},[50],[15,127995],{"className":127996,"style":15961},[54],[15,127998,128000,128003],{"className":127999},[59],[15,128001,199],{"className":128002,"style":277},[59,60],[15,128004,128006],{"className":128005},[281],[15,128007,128009,128029],{"className":128008},[285,286],[15,128010,128012,128026],{"className":128011},[290],[15,128013,128015],{"className":128014,"style":44929},[294],[15,128016,128017,128020],{"style":298},[15,128018],{"className":128019,"style":303},[302],[15,128021,128023],{"className":128022},[307,308,309,310],[15,128024,44754],{"className":128025,"style":44784},[59,60,310],[15,128027,318],{"className":128028},[317],[15,128030,128032],{"className":128031},[290],[15,128033,128035],{"className":128034,"style":7968},[294],[15,128036],{},[15,128038],{"className":128039,"style":158},[157],[15,128041,123],{"className":128042},[162],[15,128044],{"className":128045,"style":158},[157],[15,128047,128049,128052,128135,128141,128144,128147,128150],{"className":128048},[50],[15,128050],{"className":128051,"style":68569},[54],[15,128053,128055,128058,128132],{"className":128054},[59],[15,128056],{"className":128057},[146,441],[15,128059,128061],{"className":128060},[238],[15,128062,128064,128124],{"className":128063},[285,286],[15,128065,128067,128121],{"className":128066},[290],[15,128068,128070,128102,128110],{"className":128069,"style":22889},[294],[15,128071,128072,128075],{"style":457},[15,128073],{"className":128074,"style":461},[302],[15,128076,128078,128081,128084,128087,128090,128093,128096,128099],{"className":128077},[59],[15,128079,45180],{"className":128080},[59,60],[15,128082,113],{"className":128083},[146],[15,128085,117],{"className":128086},[59],[15,128088],{"className":128089,"style":2587},[157],[15,128091,4813],{"className":128092},[2591],[15,128094],{"className":128095,"style":2587},[157],[15,128097,45180],{"className":128098},[59,60],[15,128100,120],{"className":128101},[153],[15,128103,128104,128107],{"style":473},[15,128105],{"className":128106,"style":461},[302],[15,128108],{"className":128109,"style":481},[480],[15,128111,128112,128115],{"style":484},[15,128113],{"className":128114,"style":461},[302],[15,128116,128118],{"className":128117},[59],[15,128119,117],{"className":128120},[59],[15,128122,318],{"className":128123},[317],[15,128125,128127],{"className":128126},[290],[15,128128,128130],{"className":128129,"style":1601},[294],[15,128131],{},[15,128133],{"className":128134},[153,441],[15,128136,128138],{"className":128137},[59],[15,128139,113],{"className":128140},[419,3720],[15,128142,117],{"className":128143},[59],[15,128145],{"className":128146,"style":2587},[157],[15,128148,4813],{"className":128149},[2591],[15,128151],{"className":128152,"style":2587},[157],[15,128154,128156,128160,128338,128344,128347,128350,128353,128356,128359,128362],{"className":128155},[50],[15,128157],{"className":128158,"style":128159},[54],"height:1.9791em;vertical-align:-0.65em;",[15,128161,128163,128166],{"className":128162},[59],[15,128164,7567],{"className":128165},[59,60],[15,128167,128169],{"className":128168},[281],[15,128170,128172],{"className":128171},[285],[15,128173,128175],{"className":128174},[290],[15,128176,128179],{"className":128177,"style":128178},[294],"height:1.3291em;",[15,128180,128182,128185],{"style":128181},"top:-3.4534em;margin-right:0.05em;",[15,128183],{"className":128184,"style":461},[302],[15,128186,128188],{"className":128187},[307,308,309,310],[15,128189,128191,128194],{"className":128190},[59,310],[15,128192,4813],{"className":128193},[59,310],[15,128195,128197,128200,128335],{"className":128196},[59,310],[15,128198],{"className":128199},[146,441,307,30210,111323],[15,128201,128203],{"className":128202},[238],[15,128204,128206,128326],{"className":128205},[285,286],[15,128207,128209,128323],{"className":128208},[290],[15,128210,128213,128257,128265],{"className":128211,"style":128212},[294],"height:1.251em;",[15,128214,128216,128219],{"style":128215},"top:-2.5062em;",[15,128217],{"className":128218,"style":461},[302],[15,128220,128222],{"className":128221},[307,30210,9674,310],[15,128223,128225,128228],{"className":128224},[59,310],[15,128226,2463],{"className":128227},[59,310],[15,128229,128231,128234],{"className":128230},[59,310],[15,128232,2332],{"className":128233,"style":981},[59,60,310],[15,128235,128237],{"className":128236},[281],[15,128238,128240],{"className":128239},[285],[15,128241,128243],{"className":128242},[290],[15,128244,128247],{"className":128245,"style":128246},[294],"height:0.9384em;",[15,128248,128250,128254],{"style":128249},"top:-2.9384em;margin-right:0.1em;",[15,128251],{"className":128252,"style":128253},[302],"height:2.6444em;",[15,128255,2463],{"className":128256},[59,310],[15,128258,128259,128262],{"style":111360},[15,128260],{"className":128261,"style":461},[302],[15,128263],{"className":128264,"style":111367},[480,310],[15,128266,128268,128271],{"style":128267},"top:-3.5021em;",[15,128269],{"className":128270,"style":461},[302],[15,128272,128274],{"className":128273},[307,30210,9674,310],[15,128275,128277,128280,128283,128286,128289,128292,128295],{"className":128276},[59,310],[15,128278,45180],{"className":128279},[59,60,310],[15,128281,113],{"className":128282},[146,310],[15,128284,117],{"className":128285},[59,310],[15,128287,4813],{"className":128288},[2591,310],[15,128290,45180],{"className":128291},[59,60,310],[15,128293,120],{"className":128294},[153,310],[15,128296,128298,128301],{"className":128297},[59,310],[15,128299,125676],{"className":128300},[59,310],[15,128302,128304],{"className":128303},[281],[15,128305,128307],{"className":128306},[285],[15,128308,128310],{"className":128309},[290],[15,128311,128314],{"className":128312,"style":128313},[294],"height:1.0484em;",[15,128315,128317,128320],{"style":128316},"top:-3.0484em;margin-right:0.1em;",[15,128318],{"className":128319,"style":128253},[302],[15,128321,2463],{"className":128322},[59,310],[15,128324,318],{"className":128325},[317],[15,128327,128329],{"className":128328},[290],[15,128330,128333],{"className":128331,"style":128332},[294],"height:0.4938em;",[15,128334],{},[15,128336],{"className":128337},[153,441,307,30210,111323],[15,128339,128341],{"className":128340},[59],[15,128342,120],{"className":128343},[419,3720],[15,128345,551],{"className":128346},[573],[15,128348],{"className":128349,"style":3634},[157],[15,128351],{"className":128352,"style":406},[157],[15,128354,45180],{"className":128355},[59,60],[15,128357],{"className":128358,"style":158},[157],[15,128360,123],{"className":128361},[162],[15,128363],{"className":128364,"style":158},[157],[15,128366,128368,128371,128445],{"className":128367},[50],[15,128369],{"className":128370,"style":25903},[54],[15,128372,128374,128377,128442],{"className":128373},[59],[15,128375],{"className":128376},[146,441],[15,128378,128380],{"className":128379},[238],[15,128381,128383,128434],{"className":128382},[285,286],[15,128384,128386,128431],{"className":128385},[290],[15,128387,128389,128400,128408],{"className":128388,"style":22889},[294],[15,128390,128391,128394],{"style":457},[15,128392],{"className":128393,"style":461},[302],[15,128395,128397],{"className":128396},[59],[15,128398,2463],{"className":128399},[59],[15,128401,128402,128405],{"style":473},[15,128403],{"className":128404,"style":461},[302],[15,128406],{"className":128407,"style":481},[480],[15,128409,128410,128413],{"style":484},[15,128411],{"className":128412,"style":461},[302],[15,128414,128416,128419,128422,128425,128428],{"className":128415},[59],[15,128417,117],{"className":128418},[59],[15,128420],{"className":128421,"style":2587},[157],[15,128423,2470],{"className":128424},[2591],[15,128426],{"className":128427,"style":2587},[157],[15,128429,44754],{"className":128430,"style":44784},[59,60],[15,128432,318],{"className":128433},[317],[15,128435,128437],{"className":128436},[290],[15,128438,128440],{"className":128439,"style":3778},[294],[15,128441],{},[15,128443],{"className":128444},[153,441],[15,128446,551],{"className":128447},[573],[11,128449,128450,128451,32224,128480,128660,128661,128689],{},"在小 ",[15,128452,128454,128468],{"className":128453,"translate":19},[18],[15,128455,128457],{"className":128456},[23],[25,128458,128459],{"xmlns":27},[29,128460,128461,128465],{},[32,128462,128463],{},[35,128464,125676],{"mathvariant":209},[39,128466,128467],{"encoding":41},"\\Delta",[15,128469,128471],{"className":128470,"ariaHidden":46},[45],[15,128472,128474,128477],{"className":128473},[50],[15,128475],{"className":128476,"style":664},[54],[15,128478,125676],{"className":128479},[59],[15,128481,128483,128515],{"className":128482,"translate":19},[18],[15,128484,128486],{"className":128485},[23],[25,128487,128488],{"xmlns":27},[29,128489,128490,128512],{},[32,128491,128492,128494],{},[110,128493,32959],{},[238,128495,128496,128502],{},[6814,128497,128498,128500],{},[35,128499,125676],{"mathvariant":209},[115,128501,2463],{},[32,128503,128504,128506],{},[115,128505,2463],{},[6814,128507,128508,128510],{},[35,128509,2332],{},[115,128511,2463],{},[39,128513,128514],{"encoding":41},"\\approx\\frac{\\Delta^2}{2\\sigma^2}",[15,128516,128518,128530],{"className":128517,"ariaHidden":46},[45],[15,128519,128521,128524,128527],{"className":128520},[50],[15,128522],{"className":128523,"style":117161},[54],[15,128525,32959],{"className":128526},[162],[15,128528],{"className":128529,"style":158},[157],[15,128531,128533,128537],{"className":128532},[50],[15,128534],{"className":128535,"style":128536},[54],"height:1.3629em;vertical-align:-0.345em;",[15,128538,128540,128543,128657],{"className":128539},[59],[15,128541],{"className":128542},[146,441],[15,128544,128546],{"className":128545},[238],[15,128547,128549,128649],{"className":128548},[285,286],[15,128550,128552,128646],{"className":128551},[290],[15,128553,128555,128598,128606],{"className":128554,"style":113772},[294],[15,128556,128557,128560],{"style":2527},[15,128558],{"className":128559,"style":461},[302],[15,128561,128563],{"className":128562},[307,308,309,310],[15,128564,128566,128569],{"className":128565},[59,310],[15,128567,2463],{"className":128568},[59,310],[15,128570,128572,128575],{"className":128571},[59,310],[15,128573,2332],{"className":128574,"style":981},[59,60,310],[15,128576,128578],{"className":128577},[281],[15,128579,128581],{"className":128580},[285],[15,128582,128584],{"className":128583},[290],[15,128585,128587],{"className":128586,"style":45459},[294],[15,128588,128589,128592],{"style":45462},[15,128590],{"className":128591,"style":30206},[302],[15,128593,128595],{"className":128594},[307,30210,9674,310],[15,128596,2463],{"className":128597},[59,310],[15,128599,128600,128603],{"style":473},[15,128601],{"className":128602,"style":461},[302],[15,128604],{"className":128605,"style":481},[480],[15,128607,128608,128611],{"style":2550},[15,128609],{"className":128610,"style":461},[302],[15,128612,128614],{"className":128613},[307,308,309,310],[15,128615,128617],{"className":128616},[59,310],[15,128618,128620,128623],{"className":128619},[59,310],[15,128621,125676],{"className":128622},[59,310],[15,128624,128626],{"className":128625},[281],[15,128627,128629],{"className":128628},[285],[15,128630,128632],{"className":128631},[290],[15,128633,128635],{"className":128634,"style":38512},[294],[15,128636,128637,128640],{"style":38515},[15,128638],{"className":128639,"style":30206},[302],[15,128641,128643],{"className":128642},[307,30210,9674,310],[15,128644,2463],{"className":128645},[59,310],[15,128647,318],{"className":128648},[317],[15,128650,128652],{"className":128651},[290],[15,128653,128655],{"className":128654,"style":2572},[294],[15,128656],{},[15,128658],{"className":128659},[153,441],"，与 4.6 节的局部展开一致（且此时与 ",[15,128662,128664,128677],{"className":128663,"translate":19},[18],[15,128665,128667],{"className":128666},[23],[25,128668,128669],{"xmlns":27},[29,128670,128671,128675],{},[32,128672,128673],{},[35,128674,44754],{},[39,128676,49090],{"encoding":41},[15,128678,128680],{"className":128679,"ariaHidden":46},[45],[15,128681,128683,128686],{"className":128682},[50],[15,128684],{"className":128685,"style":2345},[54],[15,128687,44754],{"className":128688,"style":44784},[59,60]," 无关）。",[2311,128691,128693],{"id":128692},"_92-伯努利分布","9.2 伯努利分布",[11,128695,534,128696,5645,128773,15795,128850,128937,128938,129040,129041,129069,129070,129040,129236,991],{},[15,128697,128699,128731],{"className":128698,"translate":19},[18],[15,128700,128702],{"className":128701},[23],[25,128703,128704],{"xmlns":27},[29,128705,128706,128728],{},[32,128707,128708,128710,128712,128722,128724,128726],{},[35,128709,206],{},[110,128711,123],{},[32,128713,128714,128716,128718,128720],{},[35,128715,39291],{"mathvariant":209},[35,128717,7567],{"mathvariant":209},[35,128719,16450],{"mathvariant":209},[35,128721,82296],{"mathvariant":209},[110,128723,113],{"stretchy":112},[35,128725,11],{},[110,128727,120],{"stretchy":112},[39,128729,128730],{"encoding":41},"P=\\mathrm{Bern}(p)",[15,128732,128734,128752],{"className":128733,"ariaHidden":46},[45],[15,128735,128737,128740,128743,128746,128749],{"className":128736},[50],[15,128738],{"className":128739,"style":664},[54],[15,128741,206],{"className":128742,"style":334},[59,60],[15,128744],{"className":128745,"style":158},[157],[15,128747,123],{"className":128748},[162],[15,128750],{"className":128751,"style":158},[157],[15,128753,128755,128758,128764,128767,128770],{"className":128754},[50],[15,128756],{"className":128757,"style":139},[54],[15,128759,128761],{"className":128760},[59],[15,128762,84308],{"className":128763},[59,32662],[15,128765,113],{"className":128766},[146],[15,128768,11],{"className":128769},[59,60],[15,128771,120],{"className":128772},[153],[15,128774,128776,128808],{"className":128775,"translate":19},[18],[15,128777,128779],{"className":128778},[23],[25,128780,128781],{"xmlns":27},[29,128782,128783,128805],{},[32,128784,128785,128787,128789,128799,128801,128803],{},[35,128786,213],{},[110,128788,123],{},[32,128790,128791,128793,128795,128797],{},[35,128792,39291],{"mathvariant":209},[35,128794,7567],{"mathvariant":209},[35,128796,16450],{"mathvariant":209},[35,128798,82296],{"mathvariant":209},[110,128800,113],{"stretchy":112},[35,128802,944],{},[110,128804,120],{"stretchy":112},[39,128806,128807],{"encoding":41},"Q=\\mathrm{Bern}(q)",[15,128809,128811,128829],{"className":128810,"ariaHidden":46},[45],[15,128812,128814,128817,128820,128823,128826],{"className":128813},[50],[15,128815],{"className":128816,"style":566},[54],[15,128818,213],{"className":128819},[59,60],[15,128821],{"className":128822,"style":158},[157],[15,128824,123],{"className":128825},[162],[15,128827],{"className":128828,"style":158},[157],[15,128830,128832,128835,128841,128844,128847],{"className":128831},[50],[15,128833],{"className":128834,"style":139},[54],[15,128836,128838],{"className":128837},[59],[15,128839,84308],{"className":128840},[59,32662],[15,128842,113],{"className":128843},[146],[15,128845,944],{"className":128846,"style":981},[59,60],[15,128848,120],{"className":128849},[153],[15,128851,128853,128883],{"className":128852,"translate":19},[18],[15,128854,128856],{"className":128855},[23],[25,128857,128858],{"xmlns":27},[29,128859,128860,128880],{},[32,128861,128862,128864,128866,128868,128870,128872,128874,128876,128878],{},[35,128863,11],{},[110,128865,551],{"separator":46},[35,128867,944],{},[110,128869,5909],{},[110,128871,113],{"stretchy":112},[115,128873,126],{},[110,128875,551],{"separator":46},[115,128877,117],{},[110,128879,120],{"stretchy":112},[39,128881,128882],{"encoding":41},"p,q\\in(0,1)",[15,128884,128886,128913],{"className":128885,"ariaHidden":46},[45],[15,128887,128889,128892,128895,128898,128901,128904,128907,128910],{"className":128888},[50],[15,128890],{"className":128891,"style":31692},[54],[15,128893,11],{"className":128894},[59,60],[15,128896,551],{"className":128897},[573],[15,128899],{"className":128900,"style":406},[157],[15,128902,944],{"className":128903,"style":981},[59,60],[15,128905],{"className":128906,"style":158},[157],[15,128908,5909],{"className":128909},[162],[15,128911],{"className":128912,"style":158},[157],[15,128914,128916,128919,128922,128925,128928,128931,128934],{"className":128915},[50],[15,128917],{"className":128918,"style":139},[54],[15,128920,113],{"className":128921},[146],[15,128923,126],{"className":128924},[59],[15,128926,551],{"className":128927},[573],[15,128929],{"className":128930,"style":406},[157],[15,128932,117],{"className":128933},[59],[15,128935,120],{"className":128936},[153],"），似然比取值 ",[15,128939,128941,128967],{"className":128940,"translate":19},[18],[15,128942,128944],{"className":128943},[23],[25,128945,128946],{"xmlns":27},[29,128947,128948,128964],{},[32,128949,128950,128956,128958,128960,128962],{},[195,128951,128952,128954],{},[35,128953,769],{},[115,128955,117],{},[110,128957,123],{},[35,128959,11],{},[35,128961,941],{"mathvariant":209},[35,128963,944],{},[39,128965,128966],{"encoding":41},"t_1=p\u002Fq",[15,128968,128970,129025],{"className":128969,"ariaHidden":46},[45],[15,128971,128973,128976,129016,129019,129022],{"className":128972},[50],[15,128974],{"className":128975,"style":95925},[54],[15,128977,128979,128982],{"className":128978},[59],[15,128980,769],{"className":128981},[59,60],[15,128983,128985],{"className":128984},[281],[15,128986,128988,129008],{"className":128987},[285,286],[15,128989,128991,129005],{"className":128990},[290],[15,128992,128994],{"className":128993,"style":11133},[294],[15,128995,128996,128999],{"style":382},[15,128997],{"className":128998,"style":303},[302],[15,129000,129002],{"className":129001},[307,308,309,310],[15,129003,117],{"className":129004},[59,310],[15,129006,318],{"className":129007},[317],[15,129009,129011],{"className":129010},[290],[15,129012,129014],{"className":129013,"style":7968},[294],[15,129015],{},[15,129017],{"className":129018,"style":158},[157],[15,129020,123],{"className":129021},[162],[15,129023],{"className":129024,"style":158},[157],[15,129026,129028,129031,129034,129037],{"className":129027},[50],[15,129029],{"className":129030,"style":139},[54],[15,129032,11],{"className":129033},[59,60],[15,129035,941],{"className":129036},[59],[15,129038,944],{"className":129039,"style":981},[59,60],"（概率 ",[15,129042,129044,129057],{"className":129043,"translate":19},[18],[15,129045,129047],{"className":129046},[23],[25,129048,129049],{"xmlns":27},[29,129050,129051,129055],{},[32,129052,129053],{},[35,129054,944],{},[39,129056,944],{"encoding":41},[15,129058,129060],{"className":129059,"ariaHidden":46},[45],[15,129061,129063,129066],{"className":129062},[50],[15,129064],{"className":129065,"style":2276},[54],[15,129067,944],{"className":129068,"style":981},[59,60],"）与 ",[15,129071,129073,129115],{"className":129072,"translate":19},[18],[15,129074,129076],{"className":129075},[23],[25,129077,129078],{"xmlns":27},[29,129079,129080,129112],{},[32,129081,129082,129088,129090,129092,129094,129096,129098,129100,129102,129104,129106,129108,129110],{},[195,129083,129084,129086],{},[35,129085,769],{},[115,129087,126],{},[110,129089,123],{},[110,129091,113],{"stretchy":112},[115,129093,117],{},[110,129095,4813],{},[35,129097,11],{},[110,129099,120],{"stretchy":112},[35,129101,941],{"mathvariant":209},[110,129103,113],{"stretchy":112},[115,129105,117],{},[110,129107,4813],{},[35,129109,944],{},[110,129111,120],{"stretchy":112},[39,129113,129114],{"encoding":41},"t_0=(1-p)\u002F(1-q)",[15,129116,129118,129173,129194,129224],{"className":129117,"ariaHidden":46},[45],[15,129119,129121,129124,129164,129167,129170],{"className":129120},[50],[15,129122],{"className":129123,"style":95925},[54],[15,129125,129127,129130],{"className":129126},[59],[15,129128,769],{"className":129129},[59,60],[15,129131,129133],{"className":129132},[281],[15,129134,129136,129156],{"className":129135},[285,286],[15,129137,129139,129153],{"className":129138},[290],[15,129140,129142],{"className":129141,"style":11133},[294],[15,129143,129144,129147],{"style":382},[15,129145],{"className":129146,"style":303},[302],[15,129148,129150],{"className":129149},[307,308,309,310],[15,129151,126],{"className":129152},[59,310],[15,129154,318],{"className":129155},[317],[15,129157,129159],{"className":129158},[290],[15,129160,129162],{"className":129161,"style":7968},[294],[15,129163],{},[15,129165],{"className":129166,"style":158},[157],[15,129168,123],{"className":129169},[162],[15,129171],{"className":129172,"style":158},[157],[15,129174,129176,129179,129182,129185,129188,129191],{"className":129175},[50],[15,129177],{"className":129178,"style":139},[54],[15,129180,113],{"className":129181},[146],[15,129183,117],{"className":129184},[59],[15,129186],{"className":129187,"style":2587},[157],[15,129189,4813],{"className":129190},[2591],[15,129192],{"className":129193,"style":2587},[157],[15,129195,129197,129200,129203,129206,129209,129212,129215,129218,129221],{"className":129196},[50],[15,129198],{"className":129199,"style":139},[54],[15,129201,11],{"className":129202},[59,60],[15,129204,120],{"className":129205},[153],[15,129207,941],{"className":129208},[59],[15,129210,113],{"className":129211},[146],[15,129213,117],{"className":129214},[59],[15,129216],{"className":129217,"style":2587},[157],[15,129219,4813],{"className":129220},[2591],[15,129222],{"className":129223,"style":2587},[157],[15,129225,129227,129230,129233],{"className":129226},[50],[15,129228],{"className":129229,"style":139},[54],[15,129231,944],{"className":129232,"style":981},[59,60],[15,129234,120],{"className":129235},[153],[15,129237,129239,129257],{"className":129238,"translate":19},[18],[15,129240,129242],{"className":129241},[23],[25,129243,129244],{"xmlns":27},[29,129245,129246,129254],{},[32,129247,129248,129250,129252],{},[115,129249,117],{},[110,129251,4813],{},[35,129253,944],{},[39,129255,129256],{"encoding":41},"1-q",[15,129258,129260,129278],{"className":129259,"ariaHidden":46},[45],[15,129261,129263,129266,129269,129272,129275],{"className":129262},[50],[15,129264],{"className":129265,"style":12578},[54],[15,129267,117],{"className":129268},[59],[15,129270],{"className":129271,"style":2587},[157],[15,129273,4813],{"className":129274},[2591],[15,129276],{"className":129277,"style":2587},[157],[15,129279,129281,129284],{"className":129280},[50],[15,129282],{"className":129283,"style":2276},[54],[15,129285,944],{"className":129286,"style":981},[59,60],[15,129288,129290],{"className":129289,"translate":19},[180],[15,129291,129293,129375],{"className":129292,"translate":19},[18],[15,129294,129296],{"className":129295},[23],[25,129297,129298],{"xmlns":27,"display":189},[29,129299,129300,129372],{},[32,129301,129302,129312,129314,129316,129318,129320,129322,129324,129326,129328,129330,129336,129338,129340,129342,129344,129346,129348,129350,129352,129370],{},[195,129303,129304,129306],{},[35,129305,199],{},[32,129307,129308,129310],{},[35,129309,10694],{},[35,129311,21893],{},[110,129313,113],{"stretchy":112},[35,129315,206],{},[35,129317,210],{"mathvariant":209},[35,129319,213],{},[110,129321,120],{"stretchy":112},[110,129323,123],{},[35,129325,11],{},[35,129327,4100],{},[110,129329,4103],{},[238,129331,129332,129334],{},[35,129333,11],{},[35,129335,944],{},[110,129337,2470],{},[110,129339,113],{"stretchy":112},[115,129341,117],{},[110,129343,4813],{},[35,129345,11],{},[110,129347,120],{"stretchy":112},[35,129349,4100],{},[110,129351,4103],{},[238,129353,129354,129362],{},[32,129355,129356,129358,129360],{},[115,129357,117],{},[110,129359,4813],{},[35,129361,11],{},[32,129363,129364,129366,129368],{},[115,129365,117],{},[110,129367,4813],{},[35,129369,944],{},[110,129371,551],{"separator":46},[39,129373,129374],{"encoding":41},"D_{KL}(P\\|Q)=p\\log\\frac pq\n+(1-p)\\log\\frac{1-p}{1-q},",[15,129376,129378,129454,129545,129566],{"className":129377,"ariaHidden":46},[45],[15,129379,129381,129384,129430,129433,129436,129439,129442,129445,129448,129451],{"className":129380},[50],[15,129382],{"className":129383,"style":139},[54],[15,129385,129387,129390],{"className":129386},[59],[15,129388,199],{"className":129389,"style":277},[59,60],[15,129391,129393],{"className":129392},[281],[15,129394,129396,129422],{"className":129395},[285,286],[15,129397,129399,129419],{"className":129398},[290],[15,129400,129402],{"className":129401,"style":379},[294],[15,129403,129404,129407],{"style":298},[15,129405],{"className":129406,"style":303},[302],[15,129408,129410],{"className":129409},[307,308,309,310],[15,129411,129413,129416],{"className":129412},[59,310],[15,129414,10694],{"className":129415,"style":10782},[59,60,310],[15,129417,21893],{"className":129418},[59,60,310],[15,129420,318],{"className":129421},[317],[15,129423,129425],{"className":129424},[290],[15,129426,129428],{"className":129427,"style":7968},[294],[15,129429],{},[15,129431,113],{"className":129432},[146],[15,129434,206],{"className":129435,"style":334},[59,60],[15,129437,210],{"className":129438},[59],[15,129440,213],{"className":129441},[59,60],[15,129443,120],{"className":129444},[153],[15,129446],{"className":129447,"style":158},[157],[15,129449,123],{"className":129450},[162],[15,129452],{"className":129453,"style":158},[157],[15,129455,129457,129460,129463,129466,129471,129474,129536,129539,129542],{"className":129456},[50],[15,129458],{"className":129459,"style":22010},[54],[15,129461,11],{"className":129462},[59,60],[15,129464],{"className":129465,"style":406},[157],[15,129467,4154,129469],{"className":129468},[1484],[15,129470,4158],{"style":4157},[15,129472],{"className":129473,"style":406},[157],[15,129475,129477,129480,129533],{"className":129476},[59],[15,129478],{"className":129479},[146,441],[15,129481,129483],{"className":129482},[238],[15,129484,129486,129525],{"className":129485},[285,286],[15,129487,129489,129522],{"className":129488},[290],[15,129490,129492,129503,129511],{"className":129491,"style":3554},[294],[15,129493,129494,129497],{"style":457},[15,129495],{"className":129496,"style":461},[302],[15,129498,129500],{"className":129499},[59],[15,129501,944],{"className":129502,"style":981},[59,60],[15,129504,129505,129508],{"style":473},[15,129506],{"className":129507,"style":461},[302],[15,129509],{"className":129510,"style":481},[480],[15,129512,129513,129516],{"style":484},[15,129514],{"className":129515,"style":461},[302],[15,129517,129519],{"className":129518},[59],[15,129520,11],{"className":129521},[59,60],[15,129523,318],{"className":129524},[317],[15,129526,129528],{"className":129527},[290],[15,129529,129531],{"className":129530,"style":506},[294],[15,129532],{},[15,129534],{"className":129535},[153,441],[15,129537],{"className":129538,"style":2587},[157],[15,129540,2470],{"className":129541},[2591],[15,129543],{"className":129544,"style":2587},[157],[15,129546,129548,129551,129554,129557,129560,129563],{"className":129547},[50],[15,129549],{"className":129550,"style":139},[54],[15,129552,113],{"className":129553},[146],[15,129555,117],{"className":129556},[59],[15,129558],{"className":129559,"style":2587},[157],[15,129561,4813],{"className":129562},[2591],[15,129564],{"className":129565,"style":2587},[157],[15,129567,129569,129572,129575,129578,129581,129586,129589,129675],{"className":129568},[50],[15,129570],{"className":129571,"style":31303},[54],[15,129573,11],{"className":129574},[59,60],[15,129576,120],{"className":129577},[153],[15,129579],{"className":129580,"style":406},[157],[15,129582,4154,129584],{"className":129583},[1484],[15,129585,4158],{"style":4157},[15,129587],{"className":129588,"style":406},[157],[15,129590,129592,129595,129672],{"className":129591},[59],[15,129593],{"className":129594},[146,441],[15,129596,129598],{"className":129597},[238],[15,129599,129601,129664],{"className":129600},[285,286],[15,129602,129604,129661],{"className":129603},[290],[15,129605,129607,129630,129638],{"className":129606,"style":22889},[294],[15,129608,129609,129612],{"style":457},[15,129610],{"className":129611,"style":461},[302],[15,129613,129615,129618,129621,129624,129627],{"className":129614},[59],[15,129616,117],{"className":129617},[59],[15,129619],{"className":129620,"style":2587},[157],[15,129622,4813],{"className":129623},[2591],[15,129625],{"className":129626,"style":2587},[157],[15,129628,944],{"className":129629,"style":981},[59,60],[15,129631,129632,129635],{"style":473},[15,129633],{"className":129634,"style":461},[302],[15,129636],{"className":129637,"style":481},[480],[15,129639,129640,129643],{"style":484},[15,129641],{"className":129642,"style":461},[302],[15,129644,129646,129649,129652,129655,129658],{"className":129645},[59],[15,129647,117],{"className":129648},[59],[15,129650],{"className":129651,"style":2587},[157],[15,129653,4813],{"className":129654},[2591],[15,129656],{"className":129657,"style":2587},[157],[15,129659,11],{"className":129660},[59,60],[15,129662,318],{"className":129663},[317],[15,129665,129667],{"className":129666},[290],[15,129668,129670],{"className":129669,"style":506},[294],[15,129671],{},[15,129673],{"className":129674},[153,441],[15,129676,551],{"className":129677},[573],[15,129679,129681],{"className":129680,"translate":19},[180],[15,129682,129684,129784],{"className":129683,"translate":19},[18],[15,129685,129687],{"className":129686},[23],[25,129688,129689],{"xmlns":27,"display":189},[29,129690,129691,129781],{},[32,129692,129693,129703,129705,129707,129709,129711,129713,129715,129717,129719,129721,129723,129725,129727,129729,129735,129737,129739,129741,129743,129745,129747,129779],{},[195,129694,129695,129697],{},[35,129696,199],{},[32,129698,129699,129701],{},[35,129700,5392],{},[35,129702,34850],{},[110,129704,113],{"stretchy":112},[35,129706,206],{},[110,129708,551],{"separator":46},[35,129710,213],{},[110,129712,120],{"stretchy":112},[110,129714,123],{},[35,129716,4808],{"mathvariant":209},[35,129718,11],{},[110,129720,4813],{},[35,129722,944],{},[35,129724,4808],{"mathvariant":209},[110,129726,551],{"separator":46},[157,129728],{"width":3262},[6814,129730,129731,129733],{},[35,129732,37449],{},[115,129734,2463],{},[110,129736,113],{"stretchy":112},[35,129738,206],{},[35,129740,210],{"mathvariant":209},[35,129742,213],{},[110,129744,120],{"stretchy":112},[110,129746,123],{},[238,129748,129749,129765],{},[32,129750,129751,129753,129755,129757,129759],{},[110,129752,113],{"stretchy":112},[35,129754,11],{},[110,129756,4813],{},[35,129758,944],{},[6814,129760,129761,129763],{},[110,129762,120],{"stretchy":112},[115,129764,2463],{},[32,129766,129767,129769,129771,129773,129775,129777],{},[35,129768,944],{},[110,129770,113],{"stretchy":112},[115,129772,117],{},[110,129774,4813],{},[35,129776,944],{},[110,129778,120],{"stretchy":112},[110,129780,551],{"separator":46},[39,129782,129783],{"encoding":41},"D_{TV}(P,Q)=|p-q|,\\qquad\n\\chi^2(P\\|Q)=\\frac{(p-q)^2}{q(1-q)},",[15,129785,129787,129866,129887,129961],{"className":129786,"ariaHidden":46},[45],[15,129788,129790,129793,129839,129842,129845,129848,129851,129854,129857,129860,129863],{"className":129789},[50],[15,129791],{"className":129792,"style":139},[54],[15,129794,129796,129799],{"className":129795},[59],[15,129797,199],{"className":129798,"style":277},[59,60],[15,129800,129802],{"className":129801},[281],[15,129803,129805,129831],{"className":129804},[285,286],[15,129806,129808,129828],{"className":129807},[290],[15,129809,129811],{"className":129810,"style":379},[294],[15,129812,129813,129816],{"style":298},[15,129814],{"className":129815,"style":303},[302],[15,129817,129819],{"className":129818},[307,308,309,310],[15,129820,129822,129825],{"className":129821},[59,310],[15,129823,5392],{"className":129824,"style":334},[59,60,310],[15,129826,34850],{"className":129827,"style":2587},[59,60,310],[15,129829,318],{"className":129830},[317],[15,129832,129834],{"className":129833},[290],[15,129835,129837],{"className":129836,"style":7968},[294],[15,129838],{},[15,129840,113],{"className":129841},[146],[15,129843,206],{"className":129844,"style":334},[59,60],[15,129846,551],{"className":129847},[573],[15,129849],{"className":129850,"style":406},[157],[15,129852,213],{"className":129853},[59,60],[15,129855,120],{"className":129856},[153],[15,129858],{"className":129859,"style":158},[157],[15,129861,123],{"className":129862},[162],[15,129864],{"className":129865,"style":158},[157],[15,129867,129869,129872,129875,129878,129881,129884],{"className":129868},[50],[15,129870],{"className":129871,"style":139},[54],[15,129873,4808],{"className":129874},[59],[15,129876,11],{"className":129877},[59,60],[15,129879],{"className":129880,"style":2587},[157],[15,129882,4813],{"className":129883},[2591],[15,129885],{"className":129886,"style":2587},[157],[15,129888,129890,129893,129896,129899,129902,129905,129908,129937,129940,129943,129946,129949,129952,129955,129958],{"className":129889},[50],[15,129891],{"className":129892,"style":37251},[54],[15,129894,944],{"className":129895,"style":981},[59,60],[15,129897,4808],{"className":129898},[59],[15,129900,551],{"className":129901},[573],[15,129903],{"className":129904,"style":3634},[157],[15,129906],{"className":129907,"style":406},[157],[15,129909,129911,129914],{"className":129910},[59],[15,129912,37449],{"className":129913},[59,60],[15,129915,129917],{"className":129916},[281],[15,129918,129920],{"className":129919},[285],[15,129921,129923],{"className":129922},[290],[15,129924,129926],{"className":129925,"style":19735},[294],[15,129927,129928,129931],{"style":8277},[15,129929],{"className":129930,"style":303},[302],[15,129932,129934],{"className":129933},[307,308,309,310],[15,129935,2463],{"className":129936},[59,310],[15,129938,113],{"className":129939},[146],[15,129941,206],{"className":129942,"style":334},[59,60],[15,129944,210],{"className":129945},[59],[15,129947,213],{"className":129948},[59,60],[15,129950,120],{"className":129951},[153],[15,129953],{"className":129954,"style":158},[157],[15,129956,123],{"className":129957},[162],[15,129959],{"className":129960,"style":158},[157],[15,129962,129964,129968,130095],{"className":129963},[50],[15,129965],{"className":129966,"style":129967},[54],"height:2.4271em;vertical-align:-0.936em;",[15,129969,129971,129974,130092],{"className":129970},[59],[15,129972],{"className":129973},[146,441],[15,129975,129977],{"className":129976},[238],[15,129978,129980,130084],{"className":129979},[285,286],[15,129981,129983,130081],{"className":129982},[290],[15,129984,129986,130018,130026],{"className":129985,"style":37723},[294],[15,129987,129988,129991],{"style":457},[15,129989],{"className":129990,"style":461},[302],[15,129992,129994,129997,130000,130003,130006,130009,130012,130015],{"className":129993},[59],[15,129995,944],{"className":129996,"style":981},[59,60],[15,129998,113],{"className":129999},[146],[15,130001,117],{"className":130002},[59],[15,130004],{"className":130005,"style":2587},[157],[15,130007,4813],{"className":130008},[2591],[15,130010],{"className":130011,"style":2587},[157],[15,130013,944],{"className":130014,"style":981},[59,60],[15,130016,120],{"className":130017},[153],[15,130019,130020,130023],{"style":473},[15,130021],{"className":130022,"style":461},[302],[15,130024],{"className":130025,"style":481},[480],[15,130027,130028,130031],{"style":484},[15,130029],{"className":130030,"style":461},[302],[15,130032,130034,130037,130040,130043,130046,130049,130052],{"className":130033},[59],[15,130035,113],{"className":130036},[146],[15,130038,11],{"className":130039},[59,60],[15,130041],{"className":130042,"style":2587},[157],[15,130044,4813],{"className":130045},[2591],[15,130047],{"className":130048,"style":2587},[157],[15,130050,944],{"className":130051,"style":981},[59,60],[15,130053,130055,130058],{"className":130054},[153],[15,130056,120],{"className":130057},[153],[15,130059,130061],{"className":130060},[281],[15,130062,130064],{"className":130063},[285],[15,130065,130067],{"className":130066},[290],[15,130068,130070],{"className":130069,"style":20028},[294],[15,130071,130072,130075],{"style":6865},[15,130073],{"className":130074,"style":303},[302],[15,130076,130078],{"className":130077},[307,308,309,310],[15,130079,2463],{"className":130080},[59,310],[15,130082,318],{"className":130083},[317],[15,130085,130087],{"className":130086},[290],[15,130088,130090],{"className":130089,"style":1601},[294],[15,130091],{},[15,130093],{"className":130094},[153,441],[15,130096,551],{"className":130097},[573],[15,130099,130101],{"className":130100,"translate":19},[180],[15,130102,130104,130176],{"className":130103,"translate":19},[18],[15,130105,130107],{"className":130106},[23],[25,130108,130109],{"xmlns":27,"display":189},[29,130110,130111,130173],{},[32,130112,130113,130121,130123,130125,130127,130129,130131,130133,130135,130137,130145,130147,130171],{},[7553,130114,130115,130117,130119],{},[35,130116,33884],{},[1297,130118,42137],{},[115,130120,2463],{},[110,130122,113],{"stretchy":112},[35,130124,206],{},[110,130126,551],{"separator":46},[35,130128,213],{},[110,130130,120],{"stretchy":112},[110,130132,123],{},[115,130134,117],{},[110,130136,4813],{},[34339,130138,130139],{},[32,130140,130141,130143],{},[35,130142,11],{},[35,130144,944],{},[110,130146,4813],{},[34339,130148,130149],{},[32,130150,130151,130153,130155,130157,130159,130161,130163,130165,130167,130169],{},[110,130152,113],{"stretchy":112},[115,130154,117],{},[110,130156,4813],{},[35,130158,11],{},[110,130160,120],{"stretchy":112},[110,130162,113],{"stretchy":112},[115,130164,117],{},[110,130166,4813],{},[35,130168,944],{},[110,130170,120],{"stretchy":112},[35,130172,4375],{"mathvariant":209},[39,130174,130175],{"encoding":41},"H^2_{\\text{Bhattacharyya}}(P,Q)\n=1-\\sqrt{pq}-\\sqrt{(1-p)(1-q)} .",[15,130177,130179,130269,130287,130350],{"className":130178,"ariaHidden":46},[45],[15,130180,130182,130185,130242,130245,130248,130251,130254,130257,130260,130263,130266],{"className":130181},[50],[15,130183],{"className":130184,"style":46402},[54],[15,130186,130188,130191],{"className":130187},[59],[15,130189,33884],{"className":130190,"style":34038},[59,60],[15,130192,130194],{"className":130193},[281],[15,130195,130197,130234],{"className":130196},[285,286],[15,130198,130200,130231],{"className":130199},[290],[15,130201,130203,130220],{"className":130202,"style":19735},[294],[15,130204,130205,130208],{"style":42280},[15,130206],{"className":130207,"style":303},[302],[15,130209,130211],{"className":130210},[307,308,309,310],[15,130212,130214],{"className":130213},[59,310],[15,130215,130217],{"className":130216},[59,4598,310],[15,130218,42137],{"className":130219},[59,310],[15,130221,130222,130225],{"style":8277},[15,130223],{"className":130224,"style":303},[302],[15,130226,130228],{"className":130227},[307,308,309,310],[15,130229,2463],{"className":130230},[59,310],[15,130232,318],{"className":130233},[317],[15,130235,130237],{"className":130236},[290],[15,130238,130240],{"className":130239,"style":42316},[294],[15,130241],{},[15,130243,113],{"className":130244},[146],[15,130246,206],{"className":130247,"style":334},[59,60],[15,130249,551],{"className":130250},[573],[15,130252],{"className":130253,"style":406},[157],[15,130255,213],{"className":130256},[59,60],[15,130258,120],{"className":130259},[153],[15,130261],{"className":130262,"style":158},[157],[15,130264,123],{"className":130265},[162],[15,130267],{"className":130268,"style":158},[157],[15,130270,130272,130275,130278,130281,130284],{"className":130271},[50],[15,130273],{"className":130274,"style":12578},[54],[15,130276,117],{"className":130277},[59],[15,130279],{"className":130280,"style":2587},[157],[15,130282,4813],{"className":130283},[2591],[15,130285],{"className":130286,"style":2587},[157],[15,130288,130290,130294,130341,130344,130347],{"className":130289},[50],[15,130291],{"className":130292,"style":130293},[54],"height:1.04em;vertical-align:-0.2881em;",[15,130295,130297],{"className":130296},[59,34367],[15,130298,130300,130333],{"className":130299},[285,286],[15,130301,130303,130330],{"className":130302},[290],[15,130304,130306,130318],{"className":130305,"style":6862},[294],[15,130307,130309,130312],{"className":130308,"style":11863},[6307],[15,130310],{"className":130311,"style":461},[302],[15,130313,130315],{"className":130314,"style":34387},[59],[15,130316,41605],{"className":130317,"style":981},[59,60],[15,130319,130320,130323],{"style":41350},[15,130321],{"className":130322,"style":461},[302],[15,130324,130326],{"className":130325,"style":34444},[34443],[6323,130327,130328],{"xmlns":6325,"width":6326,"height":34447,"viewBox":34448,"preserveAspectRatio":6329},[6331,130329],{"d":34451},[15,130331,318],{"className":130332},[317],[15,130334,130336],{"className":130335},[290],[15,130337,130339],{"className":130338,"style":41370},[294],[15,130340],{},[15,130342],{"className":130343,"style":2587},[157],[15,130345,4813],{"className":130346},[2591],[15,130348],{"className":130349,"style":2587},[157],[15,130351,130353,130357,130443],{"className":130352},[50],[15,130354],{"className":130355,"style":130356},[54],"height:1.24em;vertical-align:-0.2561em;",[15,130358,130360],{"className":130359},[59,34367],[15,130361,130363,130435],{"className":130362},[285,286],[15,130364,130366,130432],{"className":130365},[290],[15,130367,130369,130420],{"className":130368,"style":83532},[294],[15,130370,130372,130375],{"className":130371,"style":83536},[6307],[15,130373],{"className":130374,"style":14846},[302],[15,130376,130378,130381,130384,130387,130390,130393,130396,130399,130402,130405,130408,130411,130414,130417],{"className":130377,"style":41161},[59],[15,130379,113],{"className":130380},[146],[15,130382,117],{"className":130383},[59],[15,130385],{"className":130386,"style":2587},[157],[15,130388,4813],{"className":130389},[2591],[15,130391],{"className":130392,"style":2587},[157],[15,130394,11],{"className":130395},[59,60],[15,130397,120],{"className":130398},[153],[15,130400,113],{"className":130401},[146],[15,130403,117],{"className":130404},[59],[15,130406],{"className":130407,"style":2587},[157],[15,130409,4813],{"className":130410},[2591],[15,130412],{"className":130413,"style":2587},[157],[15,130415,944],{"className":130416,"style":981},[59,60],[15,130418,120],{"className":130419},[153],[15,130421,130422,130425],{"style":83621},[15,130423],{"className":130424,"style":14846},[302],[15,130426,130428],{"className":130427,"style":83628},[34443],[6323,130429,130430],{"xmlns":6325,"width":6326,"height":83631,"viewBox":83632,"preserveAspectRatio":6329},[6331,130431],{"d":83635},[15,130433,318],{"className":130434},[317],[15,130436,130438],{"className":130437},[290],[15,130439,130441],{"className":130440,"style":83645},[294],[15,130442],{},[15,130444,4375],{"className":130445},[59],[11,130447,130448,130449,130529,130530,3853,130558,130609,130610,130919],{},"这些是检验公式是否自洽的好练习：例如把 ",[15,130450,130452,130474],{"className":130451,"translate":19},[18],[15,130453,130455],{"className":130454},[23],[25,130456,130457],{"xmlns":27},[29,130458,130459,130471],{},[32,130460,130461],{},[195,130462,130463,130465],{},[35,130464,199],{},[32,130466,130467,130469],{},[35,130468,10694],{},[35,130470,21893],{},[39,130472,130473],{"encoding":41},"D_{KL}",[15,130475,130477],{"className":130476,"ariaHidden":46},[45],[15,130478,130480,130483],{"className":130479},[50],[15,130481],{"className":130482,"style":15961},[54],[15,130484,130486,130489],{"className":130485},[59],[15,130487,199],{"className":130488,"style":277},[59,60],[15,130490,130492],{"className":130491},[281],[15,130493,130495,130521],{"className":130494},[285,286],[15,130496,130498,130518],{"className":130497},[290],[15,130499,130501],{"className":130500,"style":379},[294],[15,130502,130503,130506],{"style":298},[15,130504],{"className":130505,"style":303},[302],[15,130507,130509],{"className":130508},[307,308,309,310],[15,130510,130512,130515],{"className":130511},[59,310],[15,130513,10694],{"className":130514,"style":10782},[59,60,310],[15,130516,21893],{"className":130517},[59,60,310],[15,130519,318],{"className":130520},[317],[15,130522,130524],{"className":130523},[290],[15,130525,130527],{"className":130526,"style":7968},[294],[15,130528],{}," 对 ",[15,130531,130533,130546],{"className":130532,"translate":19},[18],[15,130534,130536],{"className":130535},[23],[25,130537,130538],{"xmlns":27},[29,130539,130540,130544],{},[32,130541,130542],{},[35,130543,11],{},[39,130545,11],{"encoding":41},[15,130547,130549],{"className":130548,"ariaHidden":46},[45],[15,130550,130552,130555],{"className":130551},[50],[15,130553],{"className":130554,"style":2276},[54],[15,130556,11],{"className":130557},[59,60],[15,130559,130561,130579],{"className":130560,"translate":19},[18],[15,130562,130564],{"className":130563},[23],[25,130565,130566],{"xmlns":27},[29,130567,130568,130576],{},[32,130569,130570,130572,130574],{},[35,130571,11],{},[110,130573,123],{},[35,130575,944],{},[39,130577,130578],{"encoding":41},"p=q",[15,130580,130582,130600],{"className":130581,"ariaHidden":46},[45],[15,130583,130585,130588,130591,130594,130597],{"className":130584},[50],[15,130586],{"className":130587,"style":2276},[54],[15,130589,11],{"className":130590},[59,60],[15,130592],{"className":130593,"style":158},[157],[15,130595,123],{"className":130596},[162],[15,130598],{"className":130599,"style":158},[157],[15,130601,130603,130606],{"className":130602},[50],[15,130604],{"className":130605,"style":2276},[54],[15,130607,944],{"className":130608,"style":981},[59,60]," 处做二阶展开，应回到 ",[15,130611,130613,130673],{"className":130612,"translate":19},[18],[15,130614,130616],{"className":130615},[23],[25,130617,130618],{"xmlns":27},[29,130619,130620,130670],{},[32,130621,130622,130656,130658,130664],{},[238,130623,130624,130640],{},[32,130625,130626,130628,130630,130632,130634],{},[110,130627,113],{"stretchy":112},[35,130629,11],{},[110,130631,4813],{},[35,130633,944],{},[6814,130635,130636,130638],{},[110,130637,120],{"stretchy":112},[115,130639,2463],{},[32,130641,130642,130644,130646,130648,130650,130652,130654],{},[115,130643,2463],{},[35,130645,944],{},[110,130647,113],{"stretchy":112},[115,130649,117],{},[110,130651,4813],{},[35,130653,944],{},[110,130655,120],{"stretchy":112},[110,130657,123],{},[238,130659,130660,130662],{},[115,130661,117],{},[115,130663,2463],{},[6814,130665,130666,130668],{},[35,130667,37449],{},[115,130669,2463],{},[39,130671,130672],{"encoding":41},"\\frac{(p-q)^2}{2q(1-q)}=\\frac12\\chi^2",[15,130674,130676,130816],{"className":130675,"ariaHidden":46},[45],[15,130677,130679,130683,130807,130810,130813],{"className":130678},[50],[15,130680],{"className":130681,"style":130682},[54],"height:1.6289em;vertical-align:-0.52em;",[15,130684,130686,130689,130804],{"className":130685},[59],[15,130687],{"className":130688},[146,441],[15,130690,130692],{"className":130691},[238],[15,130693,130695,130796],{"className":130694},[285,286],[15,130696,130698,130793],{"className":130697},[290],[15,130699,130701,130733,130741],{"className":130700,"style":38448},[294],[15,130702,130703,130706],{"style":2527},[15,130704],{"className":130705,"style":461},[302],[15,130707,130709],{"className":130708},[307,308,309,310],[15,130710,130712,130715,130718,130721,130724,130727,130730],{"className":130711},[59,310],[15,130713,2463],{"className":130714},[59,310],[15,130716,944],{"className":130717,"style":981},[59,60,310],[15,130719,113],{"className":130720},[146,310],[15,130722,117],{"className":130723},[59,310],[15,130725,4813],{"className":130726},[2591,310],[15,130728,944],{"className":130729,"style":981},[59,60,310],[15,130731,120],{"className":130732},[153,310],[15,130734,130735,130738],{"style":473},[15,130736],{"className":130737,"style":461},[302],[15,130739],{"className":130740,"style":481},[480],[15,130742,130743,130746],{"style":26418},[15,130744],{"className":130745,"style":461},[302],[15,130747,130749],{"className":130748},[307,308,309,310],[15,130750,130752,130755,130758,130761,130764],{"className":130751},[59,310],[15,130753,113],{"className":130754},[146,310],[15,130756,11],{"className":130757},[59,60,310],[15,130759,4813],{"className":130760},[2591,310],[15,130762,944],{"className":130763,"style":981},[59,60,310],[15,130765,130767,130770],{"className":130766},[153,310],[15,130768,120],{"className":130769},[153,310],[15,130771,130773],{"className":130772},[281],[15,130774,130776],{"className":130775},[285],[15,130777,130779],{"className":130778},[290],[15,130780,130782],{"className":130781,"style":38512},[294],[15,130783,130784,130787],{"style":38515},[15,130785],{"className":130786,"style":30206},[302],[15,130788,130790],{"className":130789},[307,30210,9674,310],[15,130791,2463],{"className":130792},[59,310],[15,130794,318],{"className":130795},[317],[15,130797,130799],{"className":130798},[290],[15,130800,130802],{"className":130801,"style":45602},[294],[15,130803],{},[15,130805],{"className":130806},[153,441],[15,130808],{"className":130809,"style":158},[157],[15,130811,123],{"className":130812},[162],[15,130814],{"className":130815,"style":158},[157],[15,130817,130819,130822,130890],{"className":130818},[50],[15,130820],{"className":130821,"style":2505},[54],[15,130823,130825,130828,130887],{"className":130824},[59],[15,130826],{"className":130827},[146,441],[15,130829,130831],{"className":130830},[238],[15,130832,130834,130879],{"className":130833},[285,286],[15,130835,130837,130876],{"className":130836},[290],[15,130838,130840,130854,130862],{"className":130839,"style":2524},[294],[15,130841,130842,130845],{"style":2527},[15,130843],{"className":130844,"style":461},[302],[15,130846,130848],{"className":130847},[307,308,309,310],[15,130849,130851],{"className":130850},[59,310],[15,130852,2463],{"className":130853},[59,310],[15,130855,130856,130859],{"style":473},[15,130857],{"className":130858,"style":461},[302],[15,130860],{"className":130861,"style":481},[480],[15,130863,130864,130867],{"style":2550},[15,130865],{"className":130866,"style":461},[302],[15,130868,130870],{"className":130869},[307,308,309,310],[15,130871,130873],{"className":130872},[59,310],[15,130874,117],{"className":130875},[59,310],[15,130877,318],{"className":130878},[317],[15,130880,130882],{"className":130881},[290],[15,130883,130885],{"className":130884,"style":2572},[294],[15,130886],{},[15,130888],{"className":130889},[153,441],[15,130891,130893,130896],{"className":130892},[59],[15,130894,37449],{"className":130895},[59,60],[15,130897,130899],{"className":130898},[281],[15,130900,130902],{"className":130901},[285],[15,130903,130905],{"className":130904},[290],[15,130906,130908],{"className":130907,"style":20028},[294],[15,130909,130910,130913],{"style":6865},[15,130911],{"className":130912,"style":303},[302],[15,130914,130916],{"className":130915},[307,308,309,310],[15,130917,2463],{"className":130918},[59,310],"，与 4.6 节吻合。",[2311,130921,130923],{"id":130922},"_93-用对偶表示反推-kl","9.3 用对偶表示反推 KL",[11,130925,130926,130927,5645,131012,131153,131154,9400],{},"取 ",[15,130928,130930,130959],{"className":130929,"translate":19},[18],[15,130931,130933],{"className":130932},[23],[25,130934,130935],{"xmlns":27},[29,130936,130937,130957],{},[32,130938,130939,130941,130943,130945,130947,130949,130951,130953,130955],{},[35,130940,37],{},[110,130942,113],{"stretchy":112},[35,130944,769],{},[110,130946,120],{"stretchy":112},[110,130948,123],{},[35,130950,769],{},[35,130952,4100],{},[110,130954,4103],{},[35,130956,769],{},[39,130958,4108],{"encoding":41},[15,130960,130962,130989],{"className":130961,"ariaHidden":46},[45],[15,130963,130965,130968,130971,130974,130977,130980,130983,130986],{"className":130964},[50],[15,130966],{"className":130967,"style":139},[54],[15,130969,37],{"className":130970,"style":61},[59,60],[15,130972,113],{"className":130973},[146],[15,130975,769],{"className":130976},[59,60],[15,130978,120],{"className":130979},[153],[15,130981],{"className":130982,"style":158},[157],[15,130984,123],{"className":130985},[162],[15,130987],{"className":130988,"style":158},[157],[15,130990,130992,130995,130998,131001,131006,131009],{"className":130991},[50],[15,130993],{"className":130994,"style":55},[54],[15,130996,769],{"className":130997},[59,60],[15,130999],{"className":131000,"style":406},[157],[15,131002,4154,131004],{"className":131003},[1484],[15,131005,4158],{"style":4157},[15,131007],{"className":131008,"style":406},[157],[15,131010,769],{"className":131011},[59,60],[15,131013,131015,131053],{"className":131014,"translate":19},[18],[15,131016,131018],{"className":131017},[23],[25,131019,131020],{"xmlns":27},[29,131021,131022,131050],{},[32,131023,131024,131030,131032,131034,131036,131038],{},[6814,131025,131026,131028],{},[35,131027,37],{},[110,131029,7573],{},[110,131031,113],{"stretchy":112},[35,131033,40237],{},[110,131035,120],{"stretchy":112},[110,131037,123],{},[6814,131039,131040,131042],{},[35,131041,7567],{},[32,131043,131044,131046,131048],{},[35,131045,40237],{},[110,131047,4813],{},[115,131049,117],{},[39,131051,131052],{"encoding":41},"f^*(y)=e^{y-1}",[15,131054,131056,131109],{"className":131055,"ariaHidden":46},[45],[15,131057,131059,131062,131091,131094,131097,131100,131103,131106],{"className":131058},[50],[15,131060],{"className":131061,"style":139},[54],[15,131063,131065,131068],{"className":131064},[59],[15,131066,37],{"className":131067,"style":61},[59,60],[15,131069,131071],{"className":131070},[281],[15,131072,131074],{"className":131073},[285],[15,131075,131077],{"className":131076},[290],[15,131078,131080],{"className":131079,"style":8499},[294],[15,131081,131082,131085],{"style":6865},[15,131083],{"className":131084,"style":303},[302],[15,131086,131088],{"className":131087},[307,308,309,310],[15,131089,7573],{"className":131090},[2591,310],[15,131092,113],{"className":131093},[146],[15,131095,40237],{"className":131096,"style":981},[59,60],[15,131098,120],{"className":131099},[153],[15,131101],{"className":131102,"style":158},[157],[15,131104,123],{"className":131105},[162],[15,131107],{"className":131108,"style":158},[157],[15,131110,131112,131115],{"className":131111},[50],[15,131113],{"className":131114,"style":20028},[54],[15,131116,131118,131121],{"className":131117},[59],[15,131119,7567],{"className":131120},[59,60],[15,131122,131124],{"className":131123},[281],[15,131125,131127],{"className":131126},[285],[15,131128,131130],{"className":131129},[290],[15,131131,131133],{"className":131132,"style":20028},[294],[15,131134,131135,131138],{"style":6865},[15,131136],{"className":131137,"style":303},[302],[15,131139,131141],{"className":131140},[307,308,309,310],[15,131142,131144,131147,131150],{"className":131143},[59,310],[15,131145,40237],{"className":131146,"style":981},[59,60,310],[15,131148,4813],{"className":131149},[2591,310],[15,131151,117],{"className":131152},[59,310],"，则对任意 ",[15,131155,131157,131170],{"className":131156,"translate":19},[18],[15,131158,131160],{"className":131159},[23],[25,131161,131162],{"xmlns":27},[29,131163,131164,131168],{},[32,131165,131166],{},[35,131167,4158],{},[39,131169,4158],{"encoding":41},[15,131171,131173],{"className":131172,"ariaHidden":46},[45],[15,131174,131176,131179],{"className":131175},[50],[15,131177],{"className":131178,"style":2276},[54],[15,131180,4158],{"className":131181,"style":981},[59,60],[15,131183,131185],{"className":131184,"translate":19},[180],[15,131186,131188,131260],{"className":131187,"translate":19},[18],[15,131189,131191],{"className":131190},[23],[25,131192,131193],{"xmlns":27,"display":189},[29,131194,131195,131257],{},[32,131196,131197,131207,131209,131211,131213,131215,131217,131219,131225,131227,131229,131231,131233,131239,131241,131253,131255],{},[195,131198,131199,131201],{},[35,131200,199],{},[32,131202,131203,131205],{},[35,131204,10694],{},[35,131206,21893],{},[110,131208,113],{"stretchy":112},[35,131210,206],{},[35,131212,210],{"mathvariant":209},[35,131214,213],{},[110,131216,120],{"stretchy":112},[110,131218,6928],{},[195,131220,131221,131223],{},[35,131222,223],{"mathvariant":222},[35,131224,206],{},[110,131226,230],{"stretchy":112},[35,131228,4158],{},[110,131230,257],{"stretchy":112},[110,131232,4813],{},[195,131234,131235,131237],{},[35,131236,223],{"mathvariant":222},[35,131238,213],{},[110,131240,230],{"stretchy":112},[6814,131242,131243,131245],{},[35,131244,7567],{},[32,131246,131247,131249,131251],{},[35,131248,4158],{},[110,131250,4813],{},[115,131252,117],{},[110,131254,257],{"stretchy":112},[110,131256,551],{"separator":46},[39,131258,131259],{"encoding":41},"D_{KL}(P\\|Q)\\ge \\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}],",[15,131261,131263,131339,131403],{"className":131262,"ariaHidden":46},[45],[15,131264,131266,131269,131315,131318,131321,131324,131327,131330,131333,131336],{"className":131265},[50],[15,131267],{"className":131268,"style":139},[54],[15,131270,131272,131275],{"className":131271},[59],[15,131273,199],{"className":131274,"style":277},[59,60],[15,131276,131278],{"className":131277},[281],[15,131279,131281,131307],{"className":131280},[285,286],[15,131282,131284,131304],{"className":131283},[290],[15,131285,131287],{"className":131286,"style":379},[294],[15,131288,131289,131292],{"style":298},[15,131290],{"className":131291,"style":303},[302],[15,131293,131295],{"className":131294},[307,308,309,310],[15,131296,131298,131301],{"className":131297},[59,310],[15,131299,10694],{"className":131300,"style":10782},[59,60,310],[15,131302,21893],{"className":131303},[59,60,310],[15,131305,318],{"className":131306},[317],[15,131308,131310],{"className":131309},[290],[15,131311,131313],{"className":131312,"style":7968},[294],[15,131314],{},[15,131316,113],{"className":131317},[146],[15,131319,206],{"className":131320,"style":334},[59,60],[15,131322,210],{"className":131323},[59],[15,131325,213],{"className":131326},[59,60],[15,131328,120],{"className":131329},[153],[15,131331],{"className":131332,"style":158},[157],[15,131334,6928],{"className":131335},[162],[15,131337],{"className":131338,"style":158},[157],[15,131340,131342,131345,131385,131388,131391,131394,131397,131400],{"className":131341},[50],[15,131343],{"className":131344,"style":139},[54],[15,131346,131348,131351],{"className":131347},[59],[15,131349,223],{"className":131350},[59,366],[15,131352,131354],{"className":131353},[281],[15,131355,131357,131377],{"className":131356},[285,286],[15,131358,131360,131374],{"className":131359},[290],[15,131361,131363],{"className":131362,"style":379},[294],[15,131364,131365,131368],{"style":382},[15,131366],{"className":131367,"style":303},[302],[15,131369,131371],{"className":131370},[307,308,309,310],[15,131372,206],{"className":131373,"style":334},[59,60,310],[15,131375,318],{"className":131376},[317],[15,131378,131380],{"className":131379},[290],[15,131381,131383],{"className":131382,"style":7968},[294],[15,131384],{},[15,131386,230],{"className":131387},[146],[15,131389,4158],{"className":131390,"style":981},[59,60],[15,131392,257],{"className":131393},[153],[15,131395],{"className":131396,"style":2587},[157],[15,131398,4813],{"className":131399},[2591],[15,131401],{"className":131402,"style":2587},[157],[15,131404,131406,131410,131450,131453,131491,131494],{"className":131405},[50],[15,131407],{"className":131408,"style":131409},[54],"height:1.1502em;vertical-align:-0.2861em;",[15,131411,131413,131416],{"className":131412},[59],[15,131414,223],{"className":131415},[59,366],[15,131417,131419],{"className":131418},[281],[15,131420,131422,131442],{"className":131421},[285,286],[15,131423,131425,131439],{"className":131424},[290],[15,131426,131428],{"className":131427,"style":379},[294],[15,131429,131430,131433],{"style":382},[15,131431],{"className":131432,"style":303},[302],[15,131434,131436],{"className":131435},[307,308,309,310],[15,131437,213],{"className":131438},[59,60,310],[15,131440,318],{"className":131441},[317],[15,131443,131445],{"className":131444},[290],[15,131446,131448],{"className":131447,"style":325},[294],[15,131449],{},[15,131451,230],{"className":131452},[146],[15,131454,131456,131459],{"className":131455},[59],[15,131457,7567],{"className":131458},[59,60],[15,131460,131462],{"className":131461},[281],[15,131463,131465],{"className":131464},[285],[15,131466,131468],{"className":131467},[290],[15,131469,131471],{"className":131470,"style":19735},[294],[15,131472,131473,131476],{"style":8277},[15,131474],{"className":131475,"style":303},[302],[15,131477,131479],{"className":131478},[307,308,309,310],[15,131480,131482,131485,131488],{"className":131481},[59,310],[15,131483,4158],{"className":131484,"style":981},[59,60,310],[15,131486,4813],{"className":131487},[2591,310],[15,131489,117],{"className":131490},[59,310],[15,131492,257],{"className":131493},[153],[15,131495,551],{"className":131496},[573],[11,131498,131499,131500,131602],{},"等号在 ",[15,131501,131503,131537],{"className":131502,"translate":19},[18],[15,131504,131506],{"className":131505},[23],[25,131507,131508],{"xmlns":27},[29,131509,131510,131534],{},[32,131511,131512,131514,131516,131518,131520,131522,131524,131526,131528,131530,131532],{},[35,131513,4158],{},[110,131515,123],{},[35,131517,4100],{},[110,131519,4103],{},[110,131521,113],{"stretchy":112},[35,131523,11],{},[35,131525,941],{"mathvariant":209},[35,131527,944],{},[110,131529,120],{"stretchy":112},[110,131531,2470],{},[115,131533,117],{},[39,131535,131536],{"encoding":41},"g=\\log(p\u002Fq)+1",[15,131538,131540,131558,131593],{"className":131539,"ariaHidden":46},[45],[15,131541,131543,131546,131549,131552,131555],{"className":131542},[50],[15,131544],{"className":131545,"style":2276},[54],[15,131547,4158],{"className":131548,"style":981},[59,60],[15,131550],{"className":131551,"style":158},[157],[15,131553,123],{"className":131554},[162],[15,131556],{"className":131557,"style":158},[157],[15,131559,131561,131564,131569,131572,131575,131578,131581,131584,131587,131590],{"className":131560},[50],[15,131562],{"className":131563,"style":139},[54],[15,131565,4154,131567],{"className":131566},[1484],[15,131568,4158],{"style":4157},[15,131570,113],{"className":131571},[146],[15,131573,11],{"className":131574},[59,60],[15,131576,941],{"className":131577},[59],[15,131579,944],{"className":131580,"style":981},[59,60],[15,131582,120],{"className":131583},[153],[15,131585],{"className":131586,"style":2587},[157],[15,131588,2470],{"className":131589},[2591],[15,131591],{"className":131592,"style":2587},[157],[15,131594,131596,131599],{"className":131595},[50],[15,131597],{"className":131598,"style":172},[54],[15,131600,117],{"className":131601},[59]," 处取到。代回：",[15,131604,131606],{"className":131605,"translate":19},[180],[15,131607,131609,131735],{"className":131608,"translate":19},[18],[15,131610,131612],{"className":131611},[23],[25,131613,131614],{"xmlns":27,"display":189},[29,131615,131616,131732],{},[32,131617,131618,131624,131626,131628,131630,131632,131634,131636,131638,131640,131642,131644,131646,131648,131654,131656,131676,131678,131680,131690,131692,131694,131696,131698,131700,131702,131704,131706,131708,131710,131720,131722,131724,131726,131728,131730],{},[195,131619,131620,131622],{},[35,131621,223],{"mathvariant":222},[35,131623,206],{},[110,131625,230],{"stretchy":112},[35,131627,4100],{},[110,131629,4103],{},[110,131631,113],{"stretchy":112},[35,131633,11],{},[35,131635,941],{"mathvariant":209},[35,131637,944],{},[110,131639,120],{"stretchy":112},[110,131641,2470],{},[115,131643,117],{},[110,131645,257],{"stretchy":112},[110,131647,4813],{},[195,131649,131650,131652],{},[35,131651,223],{"mathvariant":222},[35,131653,213],{},[110,131655,230],{"stretchy":112},[6814,131657,131658,131660],{},[35,131659,7567],{},[32,131661,131662,131664,131666,131668,131670,131672,131674],{},[35,131663,4100],{},[110,131665,4103],{},[110,131667,113],{"stretchy":112},[35,131669,11],{},[35,131671,941],{"mathvariant":209},[35,131673,944],{},[110,131675,120],{"stretchy":112},[110,131677,257],{"stretchy":112},[110,131679,123],{},[195,131681,131682,131684],{},[35,131683,199],{},[32,131685,131686,131688],{},[35,131687,10694],{},[35,131689,21893],{},[110,131691,113],{"stretchy":112},[35,131693,206],{},[35,131695,210],{"mathvariant":209},[35,131697,213],{},[110,131699,120],{"stretchy":112},[110,131701,2470],{},[115,131703,117],{},[110,131705,4813],{},[115,131707,117],{},[110,131709,123],{},[195,131711,131712,131714],{},[35,131713,199],{},[32,131715,131716,131718],{},[35,131717,10694],{},[35,131719,21893],{},[110,131721,113],{"stretchy":112},[35,131723,206],{},[35,131725,210],{"mathvariant":209},[35,131727,213],{},[110,131729,120],{"stretchy":112},[110,131731,551],{"separator":46},[39,131733,131734],{"encoding":41},"\\mathbb E_P[\\log(p\u002Fq)+1]\n-\\mathbb E_Q[e^{\\log(p\u002Fq)}]\n=D_{KL}(P\\|Q)+1-1=D_{KL}(P\\|Q),",[15,131736,131738,131816,131837,131955,132031,132049,132067],{"className":131737,"ariaHidden":46},[45],[15,131739,131741,131744,131784,131787,131792,131795,131798,131801,131804,131807,131810,131813],{"className":131740},[50],[15,131742],{"className":131743,"style":139},[54],[15,131745,131747,131750],{"className":131746},[59],[15,131748,223],{"className":131749},[59,366],[15,131751,131753],{"className":131752},[281],[15,131754,131756,131776],{"className":131755},[285,286],[15,131757,131759,131773],{"className":131758},[290],[15,131760,131762],{"className":131761,"style":379},[294],[15,131763,131764,131767],{"style":382},[15,131765],{"className":131766,"style":303},[302],[15,131768,131770],{"className":131769},[307,308,309,310],[15,131771,206],{"className":131772,"style":334},[59,60,310],[15,131774,318],{"className":131775},[317],[15,131777,131779],{"className":131778},[290],[15,131780,131782],{"className":131781,"style":7968},[294],[15,131783],{},[15,131785,230],{"className":131786},[146],[15,131788,4154,131790],{"className":131789},[1484],[15,131791,4158],{"style":4157},[15,131793,113],{"className":131794},[146],[15,131796,11],{"className":131797},[59,60],[15,131799,941],{"className":131800},[59],[15,131802,944],{"className":131803,"style":981},[59,60],[15,131805,120],{"className":131806},[153],[15,131808],{"className":131809,"style":2587},[157],[15,131811,2470],{"className":131812},[2591],[15,131814],{"className":131815,"style":2587},[157],[15,131817,131819,131822,131825,131828,131831,131834],{"className":131818},[50],[15,131820],{"className":131821,"style":139},[54],[15,131823,117],{"className":131824},[59],[15,131826,257],{"className":131827},[153],[15,131829],{"className":131830,"style":2587},[157],[15,131832,4813],{"className":131833},[2591],[15,131835],{"className":131836,"style":2587},[157],[15,131838,131840,131844,131884,131887,131943,131946,131949,131952],{"className":131839},[50],[15,131841],{"className":131842,"style":131843},[54],"height:1.2241em;vertical-align:-0.2861em;",[15,131845,131847,131850],{"className":131846},[59],[15,131848,223],{"className":131849},[59,366],[15,131851,131853],{"className":131852},[281],[15,131854,131856,131876],{"className":131855},[285,286],[15,131857,131859,131873],{"className":131858},[290],[15,131860,131862],{"className":131861,"style":379},[294],[15,131863,131864,131867],{"style":382},[15,131865],{"className":131866,"style":303},[302],[15,131868,131870],{"className":131869},[307,308,309,310],[15,131871,213],{"className":131872},[59,60,310],[15,131874,318],{"className":131875},[317],[15,131877,131879],{"className":131878},[290],[15,131880,131882],{"className":131881,"style":325},[294],[15,131883],{},[15,131885,230],{"className":131886},[146],[15,131888,131890,131893],{"className":131889},[59],[15,131891,7567],{"className":131892},[59,60],[15,131894,131896],{"className":131895},[281],[15,131897,131899],{"className":131898},[285],[15,131900,131902],{"className":131901},[290],[15,131903,131905],{"className":131904,"style":45120},[294],[15,131906,131907,131910],{"style":8277},[15,131908],{"className":131909,"style":303},[302],[15,131911,131913],{"className":131912},[307,308,309,310],[15,131914,131916,131928,131931,131934,131937,131940],{"className":131915},[59,310],[15,131917,131919,131922,131925],{"className":131918},[1484,310],[15,131920,47658],{"className":131921},[310],[15,131923,47662],{"className":131924},[310],[15,131926,4158],{"className":131927,"style":4157},[310],[15,131929,113],{"className":131930},[146,310],[15,131932,11],{"className":131933},[59,60,310],[15,131935,941],{"className":131936},[59,310],[15,131938,944],{"className":131939,"style":981},[59,60,310],[15,131941,120],{"className":131942},[153,310],[15,131944,257],{"className":131945},[153],[15,131947],{"className":131948,"style":158},[157],[15,131950,123],{"className":131951},[162],[15,131953],{"className":131954,"style":158},[157],[15,131956,131958,131961,132007,132010,132013,132016,132019,132022,132025,132028],{"className":131957},[50],[15,131959],{"className":131960,"style":139},[54],[15,131962,131964,131967],{"className":131963},[59],[15,131965,199],{"className":131966,"style":277},[59,60],[15,131968,131970],{"className":131969},[281],[15,131971,131973,131999],{"className":131972},[285,286],[15,131974,131976,131996],{"className":131975},[290],[15,131977,131979],{"className":131978,"style":379},[294],[15,131980,131981,131984],{"style":298},[15,131982],{"className":131983,"style":303},[302],[15,131985,131987],{"className":131986},[307,308,309,310],[15,131988,131990,131993],{"className":131989},[59,310],[15,131991,10694],{"className":131992,"style":10782},[59,60,310],[15,131994,21893],{"className":131995},[59,60,310],[15,131997,318],{"className":131998},[317],[15,132000,132002],{"className":132001},[290],[15,132003,132005],{"className":132004,"style":7968},[294],[15,132006],{},[15,132008,113],{"className":132009},[146],[15,132011,206],{"className":132012,"style":334},[59,60],[15,132014,210],{"className":132015},[59],[15,132017,213],{"className":132018},[59,60],[15,132020,120],{"className":132021},[153],[15,132023],{"className":132024,"style":2587},[157],[15,132026,2470],{"className":132027},[2591],[15,132029],{"className":132030,"style":2587},[157],[15,132032,132034,132037,132040,132043,132046],{"className":132033},[50],[15,132035],{"className":132036,"style":12578},[54],[15,132038,117],{"className":132039},[59],[15,132041],{"className":132042,"style":2587},[157],[15,132044,4813],{"className":132045},[2591],[15,132047],{"className":132048,"style":2587},[157],[15,132050,132052,132055,132058,132061,132064],{"className":132051},[50],[15,132053],{"className":132054,"style":172},[54],[15,132056,117],{"className":132057},[59],[15,132059],{"className":132060,"style":158},[157],[15,132062,123],{"className":132063},[162],[15,132065],{"className":132066,"style":158},[157],[15,132068,132070,132073,132119,132122,132125,132128,132131,132134],{"className":132069},[50],[15,132071],{"className":132072,"style":139},[54],[15,132074,132076,132079],{"className":132075},[59],[15,132077,199],{"className":132078,"style":277},[59,60],[15,132080,132082],{"className":132081},[281],[15,132083,132085,132111],{"className":132084},[285,286],[15,132086,132088,132108],{"className":132087},[290],[15,132089,132091],{"className":132090,"style":379},[294],[15,132092,132093,132096],{"style":298},[15,132094],{"className":132095,"style":303},[302],[15,132097,132099],{"className":132098},[307,308,309,310],[15,132100,132102,132105],{"className":132101},[59,310],[15,132103,10694],{"className":132104,"style":10782},[59,60,310],[15,132106,21893],{"className":132107},[59,60,310],[15,132109,318],{"className":132110},[317],[15,132112,132114],{"className":132113},[290],[15,132115,132117],{"className":132116,"style":7968},[294],[15,132118],{},[15,132120,113],{"className":132121},[146],[15,132123,206],{"className":132124,"style":334},[59,60],[15,132126,210],{"className":132127},[59],[15,132129,213],{"className":132130},[59,60],[15,132132,120],{"className":132133},[153],[15,132135,551],{"className":132136},[573],[11,132138,132139],{},"完全自洽。这给出了一个「可验证」的对偶表示练习。",[528,132141,132143],{"id":132142},"_10-结论","10. 结论",[11,132145,132146],{},"f-散度族的故事可以浓缩成三句话：",[6662,132148,132149,132452,132618],{},[6665,132150,132151,9400,132154,2745,132359,92469,132387,10180],{},[1225,132152,132153],{},"一个模板",[15,132155,132157,132213],{"className":132156,"translate":19},[18],[15,132158,132160],{"className":132159},[23],[25,132161,132162],{"xmlns":27},[29,132163,132164,132210],{},[32,132165,132166,132172,132174,132176,132178,132180,132182,132184,132190,132192,132194,132196,132198,132200,132202,132204,132206,132208],{},[195,132167,132168,132170],{},[35,132169,199],{},[35,132171,37],{},[110,132173,113],{"stretchy":112},[35,132175,206],{},[35,132177,210],{"mathvariant":209},[35,132179,213],{},[110,132181,120],{"stretchy":112},[110,132183,123],{},[195,132185,132186,132188],{},[35,132187,223],{"mathvariant":222},[35,132189,213],{},[110,132191,230],{"stretchy":112},[35,132193,37],{},[110,132195,113],{"stretchy":112},[35,132197,244],{},[35,132199,206],{},[35,132201,941],{"mathvariant":209},[35,132203,244],{},[35,132205,213],{},[110,132207,120],{"stretchy":112},[110,132209,257],{"stretchy":112},[39,132211,132212],{"encoding":41},"D_f(P\\|Q)=\\mathbb E_Q[f(dP\u002FdQ)]",[15,132214,132216,132286],{"className":132215,"ariaHidden":46},[45],[15,132217,132219,132222,132262,132265,132268,132271,132274,132277,132280,132283],{"className":132218},[50],[15,132220],{"className":132221,"style":270},[54],[15,132223,132225,132228],{"className":132224},[59],[15,132226,199],{"className":132227,"style":277},[59,60],[15,132229,132231],{"className":132230},[281],[15,132232,132234,132254],{"className":132233},[285,286],[15,132235,132237,132251],{"className":132236},[290],[15,132238,132240],{"className":132239,"style":295},[294],[15,132241,132242,132245],{"style":298},[15,132243],{"className":132244,"style":303},[302],[15,132246,132248],{"className":132247},[307,308,309,310],[15,132249,37],{"className":132250,"style":61},[59,60,310],[15,132252,318],{"className":132253},[317],[15,132255,132257],{"className":132256},[290],[15,132258,132260],{"className":132259,"style":325},[294],[15,132261],{},[15,132263,113],{"className":132264},[146],[15,132266,206],{"className":132267,"style":334},[59,60],[15,132269,210],{"className":132270},[59],[15,132272,213],{"className":132273},[59,60],[15,132275,120],{"className":132276},[153],[15,132278],{"className":132279,"style":158},[157],[15,132281,123],{"className":132282},[162],[15,132284],{"className":132285,"style":158},[157],[15,132287,132289,132292,132332,132335,132338,132341,132344,132347,132350,132353,132356],{"className":132288},[50],[15,132290],{"className":132291,"style":270},[54],[15,132293,132295,132298],{"className":132294},[59],[15,132296,223],{"className":132297},[59,366],[15,132299,132301],{"className":132300},[281],[15,132302,132304,132324],{"className":132303},[285,286],[15,132305,132307,132321],{"className":132306},[290],[15,132308,132310],{"className":132309,"style":379},[294],[15,132311,132312,132315],{"style":382},[15,132313],{"className":132314,"style":303},[302],[15,132316,132318],{"className":132317},[307,308,309,310],[15,132319,213],{"className":132320},[59,60,310],[15,132322,318],{"className":132323},[317],[15,132325,132327],{"className":132326},[290],[15,132328,132330],{"className":132329,"style":325},[294],[15,132331],{},[15,132333,230],{"className":132334},[146],[15,132336,37],{"className":132337,"style":61},[59,60],[15,132339,113],{"className":132340},[146],[15,132342,244],{"className":132343},[59,60],[15,132345,206],{"className":132346,"style":334},[59,60],[15,132348,941],{"className":132349},[59],[15,132351,244],{"className":132352},[59,60],[15,132354,213],{"className":132355},[59,60],[15,132357,20390],{"className":132358},[153],[15,132360,132362,132375],{"className":132361,"translate":19},[18],[15,132363,132365],{"className":132364},[23],[25,132366,132367],{"xmlns":27},[29,132368,132369,132373],{},[32,132370,132371],{},[35,132372,37],{},[39,132374,37],{"encoding":41},[15,132376,132378],{"className":132377,"ariaHidden":46},[45],[15,132379,132381,132384],{"className":132380},[50],[15,132382],{"className":132383,"style":55},[54],[15,132385,37],{"className":132386,"style":61},[59,60],[15,132388,132390,132413],{"className":132389,"translate":19},[18],[15,132391,132393],{"className":132392},[23],[25,132394,132395],{"xmlns":27},[29,132396,132397,132411],{},[32,132398,132399,132401,132403,132405,132407,132409],{},[35,132400,37],{},[110,132402,113],{"stretchy":112},[115,132404,117],{},[110,132406,120],{"stretchy":112},[110,132408,123],{},[115,132410,126],{},[39,132412,129],{"encoding":41},[15,132414,132416,132443],{"className":132415,"ariaHidden":46},[45],[15,132417,132419,132422,132425,132428,132431,132434,132437,132440],{"className":132418},[50],[15,132420],{"className":132421,"style":139},[54],[15,132423,37],{"className":132424,"style":61},[59,60],[15,132426,113],{"className":132427},[146],[15,132429,117],{"className":132430},[59],[15,132432,120],{"className":132433},[153],[15,132435],{"className":132436,"style":158},[157],[15,132438,123],{"className":132439},[162],[15,132441],{"className":132442,"style":158},[157],[15,132444,132446,132449],{"className":132445},[50],[15,132447],{"className":132448,"style":172},[54],[15,132450,126],{"className":132451},[59],[6665,132453,132454,9400,132457,132538,132539,132617],{},[1225,132455,132456],{},"两组对偶",[15,132458,132460,132482],{"className":132459,"translate":19},[18],[15,132461,132463],{"className":132462},[23],[25,132464,132465],{"xmlns":27},[29,132466,132467,132479],{},[32,132468,132469,132471,132473],{},[35,132470,37],{},[110,132472,21359],{},[6814,132474,132475,132477],{},[35,132476,37],{},[110,132478,7573],{},[39,132480,132481],{"encoding":41},"f\\leftrightarrow f^*",[15,132483,132485,132503],{"className":132484,"ariaHidden":46},[45],[15,132486,132488,132491,132494,132497,132500],{"className":132487},[50],[15,132489],{"className":132490,"style":55},[54],[15,132492,37],{"className":132493,"style":61},[59,60],[15,132495],{"className":132496,"style":158},[157],[15,132498,21359],{"className":132499},[162],[15,132501],{"className":132502,"style":158},[157],[15,132504,132506,132509],{"className":132505},[50],[15,132507],{"className":132508,"style":55},[54],[15,132510,132512,132515],{"className":132511},[59],[15,132513,37],{"className":132514,"style":61},[59,60],[15,132516,132518],{"className":132517},[281],[15,132519,132521],{"className":132520},[285],[15,132522,132524],{"className":132523},[290],[15,132525,132527],{"className":132526,"style":8499},[294],[15,132528,132529,132532],{"style":6865},[15,132530],{"className":132531,"style":303},[302],[15,132533,132535],{"className":132534},[307,308,309,310],[15,132536,7573],{"className":132537},[2591,310]," 给出变分表示（可用于估计与对抗训练）；",[15,132540,132542,132572],{"className":132541,"translate":19},[18],[15,132543,132545],{"className":132544},[23],[25,132546,132547],{"xmlns":27},[29,132548,132549,132569],{},[32,132550,132551,132553,132555,132557,132559,132561,132563,132565,132567],{},[35,132552,37],{},[110,132554,21359],{},[35,132556,769],{},[35,132558,37],{},[110,132560,113],{"stretchy":112},[115,132562,117],{},[35,132564,941],{"mathvariant":209},[35,132566,769],{},[110,132568,120],{"stretchy":112},[39,132570,132571],{"encoding":41},"f\\leftrightarrow t f(1\u002Ft)",[15,132573,132575,132593],{"className":132574,"ariaHidden":46},[45],[15,132576,132578,132581,132584,132587,132590],{"className":132577},[50],[15,132579],{"className":132580,"style":55},[54],[15,132582,37],{"className":132583,"style":61},[59,60],[15,132585],{"className":132586,"style":158},[157],[15,132588,21359],{"className":132589},[162],[15,132591],{"className":132592,"style":158},[157],[15,132594,132596,132599,132602,132605,132608,132611,132614],{"className":132595},[50],[15,132597],{"className":132598,"style":139},[54],[15,132600,769],{"className":132601},[59,60],[15,132603,37],{"className":132604,"style":61},[59,60],[15,132606,113],{"className":132607},[146],[15,132609,8589],{"className":132610},[59],[15,132612,769],{"className":132613},[59,60],[15,132615,120],{"className":132616},[153]," 给出方向对称性（可用于构造对称散度）。",[6665,132619,132620,132623],{},[1225,132621,132622],{},"一个不变量","：数据处理不等式，说明它是「信息量」而非「几何量」。正因如此，它与 Wasserstein\u002FMMD 在支撑分离时行为迥异。",[11,132625,132626],{},"经典文献可参考：Csiszár (1967)、Ali–Silvey (1966) 的原始定义；Liese–Vajda 的专著对 f-散度的对偶、拓扑与充分性做了系统处理；Amari 的信息几何给出 α-族与 Fisher 度量；Nowozin 等 (2016) 的 f-GAN、Belghazi 等 (2018) 的 MINE 把对偶表示变成可训练算法；Dong–Roth–Su (2022) 说明 f-散度的语言如何统一差分隐私。把这几条线索接起来，读者就能在「定义—性质—估计—应用」四个层面上自由穿梭。",{"title":132628,"searchDepth":132629,"depth":132629,"links":132630},"",2,[132631,132638,132643,132653,132663,132670,132675,132683,132684,132689],{"id":530,"depth":132629,"text":531,"children":132632},[132633,132635,132636,132637],{"id":2313,"depth":132634,"text":2314},3,{"id":5204,"depth":132634,"text":5205},{"id":5573,"depth":132634,"text":5574},{"id":7361,"depth":132634,"text":7362},{"id":8751,"depth":132629,"text":132639,"children":132640},"2. 为何 fff 凸且 f(1)=0f(1)=0f(1)=0",[132641,132642],{"id":8849,"depth":132634,"text":8850},{"id":10560,"depth":132634,"text":10561},{"id":21407,"depth":132629,"text":21408,"children":132644},[132645,132646,132647,132648,132649,132650,132651,132652],{"id":21469,"depth":132634,"text":21470},{"id":25548,"depth":132634,"text":25549},{"id":34509,"depth":132634,"text":34510},{"id":37148,"depth":132634,"text":37149},{"id":40437,"depth":132634,"text":40438},{"id":44736,"depth":132634,"text":44737},{"id":49375,"depth":132634,"text":49376},{"id":52489,"depth":132634,"text":52490},{"id":54912,"depth":132629,"text":54913,"children":132654},[132655,132656,132657,132658,132659,132660,132661,132662],{"id":55211,"depth":132634,"text":55212},{"id":56136,"depth":132634,"text":56137},{"id":58290,"depth":132634,"text":58291},{"id":60681,"depth":132634,"text":60682},{"id":74450,"depth":132634,"text":74451},{"id":78032,"depth":132634,"text":78033},{"id":82058,"depth":132634,"text":82059},{"id":96949,"depth":132634,"text":96950},{"id":99297,"depth":132629,"text":99298,"children":132664},[132665,132666,132667,132668,132669],{"id":99301,"depth":132634,"text":99302},{"id":101345,"depth":132634,"text":101346},{"id":103187,"depth":132634,"text":103188},{"id":105349,"depth":132634,"text":105350},{"id":108241,"depth":132634,"text":108242},{"id":108582,"depth":132629,"text":108583,"children":132671},[132672,132673,132674],{"id":108586,"depth":132634,"text":108587},{"id":114612,"depth":132634,"text":114613},{"id":116394,"depth":132634,"text":116395},{"id":117438,"depth":132629,"text":117439,"children":132676},[132677,132678,132679,132680,132681,132682],{"id":117507,"depth":132634,"text":117508},{"id":117701,"depth":132634,"text":117702},{"id":118592,"depth":132634,"text":118593},{"id":119291,"depth":132634,"text":119292},{"id":119749,"depth":132634,"text":119750},{"id":119818,"depth":132634,"text":119819},{"id":120182,"depth":132629,"text":120183},{"id":124343,"depth":132629,"text":124344,"children":132685},[132686,132687,132688],{"id":124347,"depth":132634,"text":124348},{"id":128692,"depth":132634,"text":128693},{"id":130922,"depth":132634,"text":130923},{"id":132142,"depth":132629,"text":132143},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 fff 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",false,true,"md",null,{},"\u002Fblog\u002F2026\u002F0011-about-the-f-divergence",{"title":6,"description":132690},"blog\u002F2026\u002F0011-about-the-f-divergence","f-散度族（f-divergence）用一个凸函数 f 统一刻画两个概率分布之间的差异，KL、JS、全变差、卡方、Hellinger、α-散度都是它的特例。",[132701,132702],"statistics","mathematics","2026-10-17T04:47:08+08:00","iwqHXZqjOaalRKrTl4b8l9DoWDfn8fPQY2GEv_zt_Xw",{"id":132706,"title":132707,"body":132708,"description":132884,"draft":132691,"enableCodeHighlight":132691,"enableCodeHightlight":132691,"enableComment":132692,"enableD2":132691,"enableKatex":132691,"extension":132693,"image":132628,"important":132691,"location":132694,"meta":132885,"navigation":132692,"ogImage":132694,"path":132886,"seo":132887,"stem":132888,"summary":132889,"tags":132890,"time":132892,"__hash__":132893},"blog\u002Fblog\u002F2026\u002F0012-shu-xue-yu-hua-jia.md","数学与画家",{"type":8,"value":132709,"toc":132882},[132710,132721,132751,132754,132757,132760,132763,132766,132769,132772,132775,132778,132781,132784,132787,132790,132793,132796,132799,132802,132805,132808,132811,132814,132817,132820,132823,132826,132829,132832,132835,132838,132841,132844,132847,132850,132853,132856,132859,132862,132865,132868,132871,132874,132877],[11,132711,132712,132713,132720],{},"前段时间，OpenAI 声称，他们用内部尚未正式发布的模型产出了七百多篇论文，「AI 接替数学家」的叙事于是再一次被推到台前。市场是狂热还是炒作，我已经疲于争论。那七百篇论文是否名副其实，也先放在一边。真正让我想写点东西的，",[45180,132714,132719],{"href":132715,"rel":132716,"target":132718},"https:\u002F\u002Fx.com\u002FNoe1017_Monad\u002Fstatus\u002F2112008540592410951",[132717],"nofollow","_blank","是 Twitter 上一条获得不少认同的帖子","。它把数学结构说成人类为了迁就自己那点脑容量而被迫发明的拐杖，把 AI 说成不需要几何直观、可以直接站在高维展开式里往下看的怪物。最后一句尤其漂亮：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",[132722,132723,132724],"blockquote",{},[11,132725,132726,132727,132729,132730,132732,132733,132735,132736,132738,132739,132741,132742,132744,132745,132747,132748,132750],{},"所谓优雅的数学结构，本质上是人类为了迁就自己那点可怜的脑容量，被迫发明出来的拐杖。  ",[97635,132728],{},"\n一个顶尖人类数学家的工作内存，撑死也就同时追踪五六个变量的交互。  ",[97635,132731],{},"\n当你在算一个偏微分方程或者组合不等式时，一旦展开到三阶以上，几十个交叉项涌出来，人脑就直接宕机了。  ",[97635,132734],{},"\n所以人类数学家极其厌恶展开高阶项，一旦看到高阶项发散，人类的本能反应是此路不通，赶紧退回来找对称性、找不变量、搞同调代数或者几何直观，试图不展开式子就把问题绕过去。  ",[97635,132737],{},"\n但 AI 没有这个生理缺陷。  ",[97635,132740],{},"\n对于上万个并发的 Agent 来说，同时追踪一万个五阶交叉项的系数变化，跟我们算 1+1 一样轻松。  ",[97635,132743],{},"\n在它的视野里，根本不需要什么几何直观，它直接站在高维的代数展开式里往下看，人类觉得像乱麻一样的百项高阶余项，在它眼里就是一张明明白白的线性方程组。  ",[97635,132746],{},"\n既然把式子硬展开到第七阶，再凑几个待定系数就能让所有讨厌的发散项精准归零，它为什么要费劲去帮你发明一个人类能看懂的新概念？  ",[97635,132749],{},"\n这 700 个结果背后最无奈的黑色幽默：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",[11,132752,132753],{},"这套论证值得认真对待，恰恰因为它错得很有代表性：它把人类的工作记忆、数学的审美偏好、AI 的暴力计算串成了一条看似严密的因果链。但这条链中间有一个关键的偷换——它把「人类因为认知限制而偏爱结构」偷换成了「结构只是认知限制的产物」。前者是发生学上的事实，后者是一个关于数学本体的判断。两者之间隔着一整个哲学鸿沟。",[11,132755,132756],{},"画家这个比喻，也许比「拐杖」更接近真相。画家画不出世界上的每一个光子，所以他发明了透视、明暗和构图。但这些都长在真实的结构上：透视是射影几何，明暗是光的传播，构图是视觉心理。一个能逐像素渲染世界的渲染器，仍然跑在同一套射影几何上。暴力计算并没有绕开结构。它把结构执行到了人眼跟不上的规模。数学里的「硬展开」也一样。",[11,132758,132759],{},"它对人类工作记忆的描述大体成立，对数学的判断则基本错了。结构就是数学本身，拐杖之说站不住。AI 同样依赖结构，只不过那种结构人读不懂。问题在于「能不能翻译」，美丑反而次要。而翻译，恰恰是当前 AI 数学产出链条上最缺失的一环。",[11,132761,132762],{},"先承认其中合理的部分。人类的工作记忆确实窄得可怜。Miller 在 1956 年给出著名的 7±2，后来 Cowan 又把它修正到 4±1 左右。数字有争议，但「窄」这个结论没有被推翻。数学家偏爱对称性、不变量、同调，厌恶把式子硬展开，很大程度上确实是认知经济学的产物：找不变量，本质上是把高维信息压缩成一两个人类握得住的符号。AI 在大规模符号展开和并行系数追踪上的优势也是真实的。AlphaTensor 找矩阵乘法算法、各种组合搜索里那些看似暴力、实则依赖结构化搜索空间的路线，确实绕开了人类偏好的那条美学路径。",[11,132764,132765],{},"问题出在下一步。从「人类因为认知限制而偏爱结构」推到「结构只是认知限制的产物」，这是一个发生学谬误。一个东西因为什么被发明出来，并不等于它是什么。望远镜是因为人眼太弱才被造出来的，但这不意味着望远镜里的木星卫星是人类的幻觉。十进制是因为人有十根手指才流行的，但这也不意味着素数分布依赖于手指的数量。数学结构也一样：它可能是因为人脑太窄才被优先发现的，但一旦被发现，它说的就是对象本身的事，与人类脑容量无关。",[11,132767,132768],{},"把 Galois 群说成「人类算不动五次方程，所以编个借口说它不可解」，是一种误解。它本身是一个定理：一个方程能用根式解，当且仅当它的 Galois 群可解。五次一般方程对应的对称群 S5 不是可解群，所以没有根式解。这个结论与人类的工作记忆无关。就算人类有无限的工作记忆，S5 依然不是可解群，这个定理依然成立。同样，Noether 定理把连续对称性和守恒律绑在一起。把它说成「人类看不懂，所以画个对称性的图安慰自己」，也是一种误解。它说的是物理世界的一条结构事实：如果世界没有这种对称性，相应的守恒律就不存在。同调群也常被误解成「空间太复杂，人类算不动，所以发明一个符号糊弄过去」。它探测的是空间的洞，而它作为不变量能被计算，本身依赖链复形这一整套结构。",[11,132770,132771],{},"此外，它的说服力有很大一部分来自修辞。「可怜的脑容量」「拐杖」「硬按」——这些词先把你放在一个需要被怜悯的位置，再让你接受结论。把修辞剥掉，论证的核心其实只有一句：人脑窄，AI 不窄，所以结构是拐杖。而这句话恰恰是跳步的。",[11,132773,132774],{},"退一步说，就算 AI 真的把式子硬展开到第七阶，把所有发散项精准归零，它拿到的只是一张针对这个特例的系数表，换一个情形就未必管用。它能告诉你「这里可以归零」，但不能告诉你「为什么这里必然可以归零」。前者是答案，后者才是数学。打个比方：给你七百个点，你总可以找到一个不超过 699 次的多项式，让它精确穿过每一个点。但这只是插值，够不上理解。它在七百个点之外没有任何预测力。硬展开加待定系数，本质上就是高维版本的插值——你用一个足够大的展开式，把眼前的项全部按住，然后宣布问题解决了。可数学要的是「为什么会这样，以及换一个情形会怎样」。「按住」远远不够。",[11,132776,132777],{},"照这个逻辑，AI 不需要几何直观，可以直接站在高维的代数展开式里往下看。这个画面假设存在一个「没有直观」的视角。但任何计算都发生在某种表示里，而表示本身就是一种结构。Transformer 的注意力是内容相关的路由，等变网络把对称性硬编码进架构，神经算子学的是函数空间之间的映射——这些做法都把结构写进了模型，只是藏得比较深。没有免费午餐定理早就说过，不存在对所有问题都最优的通用学习器。每一个能学的模型，都带着自己的归纳偏置。所谓「不需要直观的 AI」，只是把直观藏进了架构里，让人看不见而已。",[11,132779,132780],{},"AlphaTensor 常被拿来当例子，但它恰恰站在这个论证的反面。DeepMind 并没有枚举所有可能的算法。它在张量分解的结构化空间里做强化学习搜索。它能找到 Strassen 式的算法，正是因为搜索空间被结构约束过。把 AlphaTensor 说成「暴力硬算」的证据，是对它的误读。",[11,132782,132783],{},"更有意思的是，AI 自己的前沿正在往结构走，纯暴力那条路反而越走越窄。等变网络、神经算子、状态空间模型、注意力机制，都是在把某种先验写进模型。为什么？因为纯暴力在高维会指数爆炸。这个领域最聪明的一批人，正在用工程手段重新发明数学家一百年前就熟悉的那些东西：对称性、局部性、可分解性。AI 的研究者自己正在沿着那条路径追赶，「绕开审美」的预言并没有发生。",[11,132785,132786],{},"技术细节上也站不住。「高阶项发散」常被当作「项太多、人脑装不下」的同义词。但在很多场合，发散属于表示问题，跟项数多少关系不大：这个展开本身是一个渐近级数，并不收敛。渐近级数在前几项可以给出极好的近似，但继续展开不会逼近真值。你需要的是重求和、解析延拓，或者换一个表示。数学家看到发散就后退，是因为他们知道「继续展开」不会自动收敛。这时候该做的是换一种表示，把项数堆得更高没有用。AI 就算把发散项凑没了，也可能只找到一种形式上的消去，并未得到收敛的表示。",[11,132788,132789],{},"即便并行 Agent 真的能同时追踪一万个五阶交叉项，代价也不是零。算力、内存、通信都会随着项数组合爆炸。「并行」被当成了免费的午餐。更关键的是，这个天花板背后还有复杂性理论：在普遍接受的复杂性假设下，有些问题是内在难解的——问题本身的复杂度摆在那里，跟聪明与否关系不大。「人脑太小」和「问题太难」被混为一谈了。就算给一个无限工作记忆的理想智能体，它也会撞上指数爆炸。人类偏爱结构，既因为脑子小，也因为问题本身硬。",[11,132791,132792],{},"所以，AI 可以使用一种人读不懂的结构。硬展开同样有结构，只不过这种结构被执行到了人跟不上的规模。一个逐像素渲染的渲染器，算得比任何画家都细，却始终跑在射影几何上，把透视算到了人眼看不见的精度。AI 的硬展开也一样：它把代数结构展开到了人脑装不下的长度，却始终在代数结构之内。",[11,132794,132795],{},"「上帝拿计算器硬按」假设答案先于结构存在。它背后是一个很朴素的柏拉图式画面：答案早就躺在那里，结构只是人类够不着时用的梯子。但数学的实践不是这样。很多答案是在结构被发明出来之后才成为「答案」的。",[11,132797,132798],{},"一个猜想在 n=5 成立、在 n=6 崩掉，硬算给你两个数。结构告诉你边界在哪里，以及为什么边界在那里。两个数可以和无穷多个故事相容，结构帮你挑出正确的那个。更一般地，硬算只能处理有限多个情形。即使你在计算机上验证费马大定理到 n 等于十亿，也不构成对所有的 n 的证明。Wiles 的证明之所以成立，靠的是模形式这座桥，把问题接到了另一个世界。计算量的大小并非关键。",[11,132800,132801],{},"知道一个命题为真，和知道它为什么为真，不是一回事。前者是证明，后者是理解。硬算可以给你前者，未必给你后者。而且，硬算能证明的通常只是有限多个特例。一旦命题是全称的，你就需要结构、归纳或者某种不变量，才能跨过「有限」到「所有」的鸿沟。七百个结果里可能有一些本身就是关于有限对象的定理，本身就有价值。但如果它们大多是硬展开出来的特例，那么它们更像是一批精确的数值事实，未必是可迁移的定理。另外，「七百篇论文」和「七百个结果」不是一回事。前者可能包含大量增量工作，后者才是数学意义上的成果。这个区分本身就值得追问，但先放在一边。",[11,132803,132804],{},"数学史上早有「先有黑箱，后有理解」的先例。四色定理 1976 年由机器辅助证明，当时吵得很厉害。后来人类花了很多年去简化、去压缩，形式化验证也完成了，但「机器证明算不算理解」这个问题并没有完全消失。Kepler 猜想被 Hales 用大规模计算机辅助证明，后来又有 Flyspeck 项目做形式化验证。模式很清楚：先拿到一个可验证但不可读的答案，再花一代人把它翻译成人类握得住的结构。翻译可能失败，也可能要几代人，但「现在翻译不出来」从来不足以让人停下来。",[11,132806,132807],{},"而且，人类数学自己也早就遇到过不可读的问题。有限单群分类定理的证明上万页，散落在几百篇文章里，据说至今没有人从头到尾读完。这是人类自己造出来的黑箱。区别只在于规模：人类数学在二十世纪就已经开始生产超出个体阅读能力的结果，AI 只是把这个趋势推得更远。",[11,132809,132810],{},"黑箱当然有价值。它可以被引用、被使用、被当作下一步的踏脚石。但它的价值有一个天花板：验证成本无法摊销。一个你理解了的定理，可以在一段话里教给别人，可以在新问题里直接调用。一个你不理解的黑箱，每用一次都要重新跑一遍、重新信一遍。理解之所以重要，是因为它把验证成本压缩成了可复用的结构。没有理解，知识就不能以低成本累积。",[11,132812,132813],{},"把这种思路推到极端：也许黑箱就是数学的新常态。也许未来的数学单位会从定理变成证书。数学家追求的东西，也会从「看懂」转向「可验证、可组合、可规模化」。这是一个严肃的可能性，我不打算轻易否定它。但它比「AI 算得更快」是一个大得多的主张：它改变的是数学知识的定义，速度倒在其次。而且，就算走到那一步，信任基础设施本身仍然是结构：证书格式、证明助理、可复现性标准、社区共识。黑箱的未来并未取消结构，只不过把结构挪到了另一个地方。",[11,132815,132816],{},"至于审美，AI 正在用一个丑但有效的答案挑战「美是数学的先验判据」这个前提。这个前提站不住。",[11,132818,132819],{},"数学史上「丑的真理」屡见不鲜。三次方程的求根公式在 16 世纪就撞上了 casus irreducibilis：三个实根，却必须经过复数才能算出来。当时的数学家觉得这近乎荒谬。非欧几何刚出来的时候，高斯不敢公开发表。Cantor 的无穷集合遭到 Kronecker 的激烈反对。Weierstrass 造出处处连续、处处不可导的函数，被当时的许多人视为病态。Banach-Tarski 分球悖论更是像在说「数学不该长这样」。后来的处理方式，是扩写美的定义，把这些东西留下来。复数变成了复平面上的几何，非欧几何变成了曲率，病态函数催生了测度论，也逼着拓扑学重新审视连续与收敛。分球悖论则逼着人们去追问选择公理到底意味着什么。丑的东西待得够久，人类就会给它找一套它配得上的语言。语言找到了，它就不丑了。",[11,132821,132822],{},"所以，美更像事后的评价。数学家说一个证明美，通常是在说：它把原本分散的东西统一了，没有多余的假设，并且揭示了机制。这些都是理解完成之后的判词，很难充当发现之前的门槛。历史上真正被审美直觉挡在门外的结果——比如 Galois 生前没能发表的手稿——事后看，那是审美的失败，数学本身并没有失败。",[11,132824,132825],{},"但也不要走到另一个极端，把审美说成纯粹的非理性。审美其实是一个关于「可压缩性」的启发式：一个漂亮的证明，往往更容易推广、更容易迁移、更容易在别的问题里复用。它当然会犯错，但命中率并不低。数学家对丑的警惕，除了对陌生的恐惧，还包含一种合理怀疑：这东西也许无法一般化。把审美当成纯粹的偏见，这太便宜了。",[11,132827,132828],{},"所以，「能不能翻译」比「美不美」更值得问。丑是可以忍受的，只要它能在可接受的成本内被压缩成一套可迁移的结构。丑而无法批量翻译，才是真正的问题。对 AI 那七百个结果，关键在翻译成本：把它们变成人类可读的结构要花多大代价，这个代价能不能被规模化地摊薄。如果每个结果都需要一位数学家花十年去反推，那七百个结果的边际价值就取决于翻译的规模化程度——而这恰恰是 AI 可能帮上忙的地方：让 AI 去搜「能压缩这七百个结果的统一框架」。丑不可怕，可怕的是丑得无法批量处理。",[11,132830,132831],{},"「地球灭亡之前，人类没法理解的事情肯定存在。」这句话我同意。Gödel 的不完备定理保证了真而不可证的东西存在，复杂性理论则告诉我们，一大批问题在可接受的资源内算不动。但这句话不能推出「所以现在别理解了」。",[11,132833,132834],{},"从「存在无法理解的东西」推不出「眼前这七百个就是无法理解的」。这是一个很基本的逻辑错误：存在量词不能这样实例化。而且，可理解域的边界是未知的，历史上每一次都被推得比预期远得多。Hilbert 纲领失败了，但失败本身催生了证明论和可计算性理论，也深刻改变了模型论的问题意识。数学的边界更像一片雾。你往前走，雾就退一点。",[11,132836,132837],{},"理解有许多层次。我们理解热力学，不需要追踪每一个分子。同样，我们理解一个函数，不需要它的封闭形式。七百个结果可能在细粒度上不可读，但在粗粒度上仍然可以被理解：它们可能共享某种对称性、某种生成机制、某种还没被命名的结构。放弃理解需要「已经证明这里推不动」。「现在看着像一团乱麻」还不够。前者是数学，后者是情绪。",[11,132839,132840],{},"另外，AI 的方法太有针对性，这是数学界最实在的批评之一。以前一个理论出来，不仅解决目标问题，还会带来一整套工具箱，影响其他领域。现在的 AI 方法往往只解决目标问题，然后就结束了。",[11,132842,132843],{},"这条批评有它的道理。人类数学的溢出效应是结构性的。Galois 理论本来是为了解五次方程，产出的群论和域扩张后来成了整个代数的主干。Riemann 为了理解素数分布把复分析引进数论，他的几何工作又养活了微分几何和拓扑。同调代数从拓扑里长出来，最后变成了交换代数、代数几何、表示论的通用语法。目标问题是钩子，工具箱才是本体。数学界评价一个工作，隐含的标准是「它留下了什么可复用的东西」。「它证明了什么」只是起点。",[11,132845,132846],{},"AI 目前的产出恰好踩在这个标准的反面。AlphaTensor 找矩阵乘法算法、组合搜索、符号回归凑公式，共同特征是：针对特定实例、依赖大规模搜索、结果的可迁移性有限。它优化的是「这个问题有没有解、解是什么」。「这类问题的结构长什么样」则被放在一边。一个只针对单点的工具，边际价值确实低，尤其当它消耗的算力还能拿去做别的事。",[11,132848,132849],{},"但针对性太强，是 AI 的局限，还是当前阶段的局限？历史上「针对性太强」的批评也落在过人类自己头上。数值分析早期被纯数学家看不起，觉得是工程凑数，后来它长出了稳定性、收敛阶、条件数这一整套理论。概率论被当成赌博工具几百年，Kolmogorov 公理化之后才翻身。针对性强的工具，如果被反复使用，往往会倒逼出一般理论。差别在于：人类工具的一般化是被使用者的需求驱动的，慢但稳。AI 工具的一般化目前没有人系统性地做，因为发论文的激励在「又刷了一个纪录」，不在「把这套方法抽象成可复用的框架」。",[11,132851,132852],{},"所以，真正缺的，是有人负责把针对性的方法一般化。「AI 方法针对性太强」只是表象。人类数学家有同行评议和长期声誉在逼他们想「这东西能不能推广」。AI 数学的产出链条里，这个环节目前是断的。如果哪天真有团队认真做「把七百个硬展开结果反推成一个统一框架」，而且做成了，那这条批评就自动消解了。但这件事的难度不比发现那七百个结果低，甚至更高：归纳一个框架，靠的是猜对抽象层级，算力反而次要。而这恰恰是目前最说不清楚 AI 能不能做好的部分。",[11,132854,132855],{},"翻译是一项制度功能，很难靠某位数学家的英雄行为完成。人类数学之所以能把计算变成结构，靠的是一整套同行评议、教科书、研讨会和长期声誉的机器，在逼着每一代人去问「这东西能不能推广」。个别天才只是其中一环。AI 数学现在缺的，正是这台机器，算力和聪明的模型都还在其次。真正的瓶颈在分工，认知带宽不是主要问题。",[11,132857,132858],{},"这套论证的力量来自三个漂亮的偷换，把动机当成定义，把事后的判词当成先验的门槛，把答案当成理解。",[11,132860,132861],{},"但挑战是真的，只是位置放错了：我们把计算翻译成结构的制度，没有跟上计算的速度。「AI 比人算得快」只是表面。",[11,132863,132864],{},"画家画不出世界上的每一个光子，所以他发明透视。但透视是射影几何，跟「眼睛不行」没有关系。",[11,132866,132867],{},"今天最强的渲染器可以逐像素地硬算，但它仍然跑在透视的数学上。硬算并没有取消结构。它把结构算到了人眼跟不上的地方。",[11,132869,132870],{},"上帝或许真的在用计算器。但账本不是给计算器看的。人类接下来要做的，是翻译账本，让计算器的结果变得可读。",[11,132872,132873],{},"所以说，AI 在未来会彻底取代数学研究的劳动吗？",[11,132875,132876],{},"我认为不会，而且在未来很长一段时间里，都不会，至少在 AGI 诞生之前永远不会。",[132722,132878,132879],{},[11,132880,132881],{},"砸掉计算器解决不了问题。数学的下一份工作，也许要从「发现」转向「翻译」。",{"title":132628,"searchDepth":132629,"depth":132629,"links":132883},[],"前段时间，OpenAI 声称，他们用内部尚未正式发布的模型产出了七百多篇论文，「AI 接替数学家」的叙事于是再一次被推到台前。市场是狂热还是炒作，我已经疲于争论。那七百篇论文是否名副其实，也先放在一边。真正让我想写点东西的，是 Twitter 上一条获得不少认同的帖子。它把数学结构说成人类为了迁就自己那点脑容量而被迫发明的拐杖，把 AI 说成不需要几何直观、可以直接站在高维展开式里往下看的怪物。最后一句尤其漂亮：我们终于拿到了上帝账本里的答案，却发现上帝算账根本不用微积分，他老人家是直接拿计算器硬按出来的。",{},"\u002Fblog\u002F2026\u002F0012-shu-xue-yu-hua-jia",{"title":132707,"description":132884},"blog\u002F2026\u002F0012-shu-xue-yu-hua-jia","结构本身就是定理，AI 也有结构，只是那种结构人读不懂。关键在于可翻译性，以及把计算翻译成结构的制度是否跟得上。硬算常给出有限情形的答案而非「为什么」，而把针对性的结果一般化、翻译成可复用结构的制度，在 AI 数学的产出链条里是断的。",[132891],"thoughts","2026-10-25T16:52:45+08:00","MTXFn_wz9eNH537cFyhWDAYMtvfSTEdfulMeMndlEyU",{"id":132895,"title":132896,"body":132897,"description":132901,"draft":132691,"enableCodeHighlight":132691,"enableCodeHightlight":132691,"enableComment":132692,"enableD2":132691,"enableKatex":132691,"extension":132693,"image":132628,"important":132691,"location":132694,"meta":133225,"navigation":132692,"ogImage":132694,"path":133226,"seo":133227,"stem":133228,"summary":133229,"tags":133230,"time":133231,"__hash__":133232},"blog\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon.md","克劳德·香农小传",{"type":8,"value":132898,"toc":133215},[132899,132902,132905,132908,132911,132914,132917,132920,132923,132926,132929,132932,132935,132938,132941,132944,132947,132950,132953,132956,132963,132966,132969,132972,132975,132978,132981,132984,132987,132990,132993,132996,132999,133002,133005,133008,133011,133014,133017,133020,133023,133026,133029,133034,133037,133040,133043,133046,133049,133052,133055,133058,133061,133065,133068,133071,133074,133077,133080,133083,133086,133089,133092,133095,133098,133101,133104,133107,133112,133115,133118,133122,133128,133131,133134,133137,133140,133143,133146,133149,133152,133155,133158,133161,133165,133171,133174,133177,133180,133183,133186,133189,133192,133195,133198,133201,133204,133207,133210],[11,132900,132901],{},"美国 20 世纪 50 年代的某个深夜，贝尔实验室的走廊里很安静。一个瘦高的中年人骑着独轮车，从长长的走廊那头慢悠悠地滑过来，手里还抛着几个球。偶尔有加班的同事推开门，看一眼，笑一笑，又把头缩回去继续算他们的方程——大家早就习惯了。",[11,132903,132904],{},"克劳德·艾尔伍德·香农（Claude Elwood Shannon）最有分量的成就，是用一篇论文给「信息」下了数学定义，由此奠定了整个数字时代的理论根基。可是如果你问他的同事、家人和朋友他是个什么样的人，他们说的多半不是公式，而是独轮车、玩具、小机器和一个永远带着笑意的安静身影。",[528,132906,132907],{"id":132907},"密歇根小镇的修理少年",[11,132909,132910],{},"1916 年 4 月 30 日，香农出生在美国密歇根州的佩托斯基，不久后全家搬到北边一个叫盖洛德的小镇，他在那里长大。父亲老克劳德做过商人，也当过遗嘱认证法官；母亲梅布尔是语言教师，后来做了盖洛德中学的校长。姐姐凯瑟琳比他大几岁，日后成了数学教授。家里的气氛是安稳、务实的：父亲有生意头脑，母亲爱读书，孩子们被允许把时间花在自己感兴趣的东西上。",[11,132912,132913],{},"香农从小就是个「动手的孩子」。他爱做航模，也做过无线电遥控的小船。最著名的一桩少年轶事，是他和一个住在大约半英里外的朋友之间架设的电报线：两个孩子没有现成的电线，就利用沿途的铁丝围栏，把它们接起来当作通信线路，晚上各自守在家里，用莫尔斯电码互相「发报」。对一个中西部小镇的男孩来说，这既是游戏，也是他第一次亲手搭起「通信系统」。",[11,132915,132916],{},"他还干过一份差事：给西联电报公司送电报。镇上的人看见他骑着车来来往往，也许想不到，这个孩子日后会为「通信」写下一套完整的数学理论。他修收音机的本事在镇上小有名气，据说当地一家百货商店的收音机坏了，也会请他去看看。",[11,132918,132919],{},"这里得补一点背景：香农的少年时代，正好赶上 1920 年代美国的无线电热。广播电台一座座冒出来，杂志上登着教人自己绕线圈、装矿石收音机的图纸，成千上万个男孩在自家阁楼上折腾「无线电」。香农赶上了这个浪潮的浪尖，而且他不是照着图纸装，是喜欢把东西拆开，弄清里面到底怎么回事。回头看，他一生的路数大概就是这个：感兴趣的不是「怎么用」，而是「它是怎么被装起来的」。",[11,132921,132922],{},"他的偶像是爱迪生。后来他发现自己和爱迪生居然是远亲，高兴了好一阵子。少年时代他还读到爱伦·坡的小说《金甲虫》，书里主人公靠破译密码找到宝藏，这个故事在他心里种下了对密码的迷恋，多年以后，战时的密码工作和他的信息论，都与这份兴趣有着隐秘的联系。另外，坡还写过一篇《被窃的信》，讲的是「猜对方下一手会怎么出」的心理游戏——二十多年后，香农在一份机器设计的备忘录里，又把这篇小说翻出来引用了一次。",[11,132924,132925],{},"这个阶段的香农，已经显出日后的底色：不爱张扬，不太合群，但遇到「有意思的东西」就会安静地一头扎进去，一玩就是几个小时。",[528,132927,132928],{"id":132928},"一门选修课和一篇论文",[11,132930,132931],{},"1932 年，香农进入密歇根大学。他最后同时拿到了电气工程和数学两个学士学位，这个组合在当时并不常见，却像是为他日后的工作预先搭好的脚手架。",[11,132933,132934],{},"大学里有一件看起来很小的事，影响却极大：他在一门课上接触到了乔治·布尔的逻辑代数——一套只用「真」和「假」、「是」和「非」来做运算的符号系统。大多数同学把它当成一个哲学趣闻，香农却盯着它看了很久，因为他同时懂得电路：开关只有「开」和「关」两种状态，这不正好对应「真」和「假」吗？",[11,132936,132937],{},"毕业后，他去了麻省理工学院，做万尼瓦尔·布什的助手，管理一台著名的庞然大物——微分分析机。这是一台由轴、齿轮和大量继电器组成的机械模拟计算机，占满一间屋子。香农在它旁边一待就是很长时间，对着一堆纠缠的继电器电路琢磨：能不能找到一套规则，让人不靠反复试错就能设计出正确的开关电路？",[11,132939,132940],{},"1937 年，他交出了答案——硕士论文《继电器与开关电路的符号分析》。他证明了布尔代数可以用来描述和简化开关电路，也就是说，逻辑可以被「造」出来。",[11,132942,132943],{},"这篇论文在评价史上的位置，后来被反复提起。历史学家赫尔曼·戈德斯坦 1972 年写下了可能是最实在的一句：它「把数字电路设计从一门手艺变成了一门科学」。数学家所罗门·戈隆布则在 2001 年的悼文里说，这是「有史以来最伟大的硕士论文之一」。流传最广的一版出自哈佛大学的认知心理学家霍华德·加德纳，1985 年他写道，这或许「是这个世纪最重要、也最著名的硕士论文」。这句话后来被到处引用，有时还被人升格成「科学史家的定评」——其实加德纳是心理学家，不是科学史家，这一点值得记一笔。",[11,132945,132946],{},"还有一个评价来自他的老师本人。布什后来谈到这篇论文时说：「我当时就认为它是一篇经典之作——这个评价我很少给出。」",[11,132948,132949],{},"比论文本身更能说明问题的，是布什给人写推荐信时的措辞。1938 年，他在一封信里这样描述这个年轻人：「一个相当不合常规的年轻人……他非常害羞内向，极为谦逊，很容易被带偏。」在另一封推荐信里，布什又补了一句：「他腼腆、讨人喜欢，是需要被小心对待的那种人。」一位导师要一边极力推荐、一边提醒别人别把他吓跑，这件事本身就说明了香农是个什么样的人。",[11,132951,132952],{},"当时的他才二十出头，说起那篇论文却相当轻描淡写，更像是把两样好玩的东西拼到了一起。",[11,132954,132955],{},"其间他还在贝尔实验室度过了一个夏天，那是他与这家公司缘分的开始。布什后来建议他换个领域，于是他的博士论文竟是关于理论遗传学的，题目叫《理论遗传学的代数学》。为此他去了冷泉港，和遗传学家一起工作。他用数学处理孟德尔遗传，这篇论文并没有像硕士论文那样引起轰动，却再次显示了他的习惯：哪里有「结构」，就想用代数去看一看。",[11,132957,132958],{},[132959,132960],"img",{"alt":132961,"src":132962},"Claude Shannon in 1932","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162230267.png",[11,132964,132965],{},"1940 年，他拿到了博士学位。同一年，他与诺玛·莱沃结婚，但这段婚姻很短，两人很快就分开了。香农在感情上一向内敛，很少对外人谈起这些。",[528,132967,132968],{"id":132968},"普林斯顿的拜访与贝尔实验室的夜晚",[11,132970,132971],{},"博士毕业后，香农去了普林斯顿高等研究院，在那里的几个月里，他见到了爱因斯坦、哥德尔和冯·诺依曼等人。普林斯顿的气氛很学院，学者们常在林荫道上散步、低声争论。香农既敬佩他们，又觉得自己并不真正属于这里：他更愿意在一间堆满零件的屋子里琢磨东西。",[11,132973,132974],{},"倒是有两位年长的数学家早早看出了他的分量。诺伯特·维纳在 1940 年前后这样评价这个年轻人：「一个才华与智力都极为出众的人……他已经做出了极具原创性的工作，毫无疑问是正在升起的一颗星。」而冯·诺依曼后来跟他的一次闲谈，给这门学科留下了一个沿用至今的词——这件事我们放到 1948 年再说。",[11,132976,132977],{},"1941 年，他加入了贝尔实验室，那个年代的贝尔实验室是一座奇特的「自由王国」，管理层相信让聪明人自己找事做，终会有收获。香农正好适合这样的环境。战争期间，他参与了防空火力控制系统的研究，也接触了保密通信和密码学方面的工作，其中包括著名的 SIGSALY 加密话音系统的相关研究。",[11,132979,132980],{},"他在贝尔实验室交到了几个真正投契的朋友，其中两个往后会反复出现。",[11,132982,132983],{},"一位是约翰·皮尔斯，日后被称作「通信卫星之父」的工程师。皮尔斯差不多是香农在实验室里最好的思想对手，两个人互相扔点子、合写论文、交换成堆的书。皮尔斯留下的说法里有一条后来被引用得最多：香农谈起自己的想法时，常常是从听别人抱怨某个系统开始的——「他漫不经心地听着，然后发明出一个新系统。」皮尔斯三番五次跟他说「这个想法你应该写出来」，香农的回答通常是：「‘应该’是什么意思？」",[11,132985,132986],{},"另一位是巴尼·奥利弗，后来去了惠普，也是「搜寻地外文明」计划最早的推动者之一。奥利弗与香农、皮尔斯三人合写过那篇《脉码调制的哲学》，还一起申请了专利。奥利弗晚年这样回忆自己在这个圈子里的位置：「我们成了朋友，所以很多理论可以说是我替他接生的。他把想法扔给我……我比谁都更早知道信息论。」",[11,132988,132989],{},"他的生活节奏在同事眼里有些古怪：不太爱开会，常常关上办公室的门独自思考，下班时间也不固定。他当时住在纽约格林威治村，每天要往返于曼哈顿与实验室之间。据说他爱在深夜工作，走廊里的独轮车也是从这个时期开始出名的。他一边骑，一边思考难题，对他而言，玩耍和思考本是同一件事的两面。",[11,132991,132992],{},"1943 年初，英国数学家艾伦·图灵访问贝尔实验室。两人在食堂里一起喝茶聊天，由于图灵的密码工作属于机密，他们没法谈具体项目，聊的主要是更宽泛的话题：机器能不能思考？能不能教机器学东西？",[11,132994,132995],{},"图灵后来在饭桌上向人复述过他印象深刻的一点：「香农不只想往大脑里喂数据，他还想喂文化层面的东西！他想给它放音乐。」（这句话是旁人的转述，见于安德鲁·霍奇斯的图灵传记，不是两人当时的通信。）图灵自己则傲慢得很可爱，他说他并不想造一个「强大的大脑」：「我想要的只是一个平庸的大脑，差不多像美国电话电报公司总裁那样的。」",[11,132997,132998],{},"有意思的是，两个人对这次交谈的记忆并不一样。近四十年后，香农接受口述史访问时回忆说，他们那次「完全没谈密码」，「谈得更多的是人脑和计算机器」这类问题；至于他自己关于信息的那套想法，图灵当时「并不认为方向是对的」，他「得到的差不多是负面的反馈」。一次被后人追认为「两个天才难得交会」的谈话，在当事人那里，其实还带着一点被质疑的味道。",[11,133000,133001],{},"这是两个隐居于各自世界里的天才难得的一次交会：一个刚从布莱切利园的机密里走出来，一个正准备写下通信的数学理论，而他们在饭桌上真正关心的，是造一个会想东西的机器。",[11,133003,133004],{},"在这些年里，香农一边为战争做事，一边在心里慢慢酝酿一个更大的问题：通信的本质到底是什么？在 1945 年的一份内部保密备忘录里，他已经用概率论的语言分析密码系统，战后这份工作以《保密系统的通信理论》为题公开发表。密码学与通信理论，在他脑中是同一枚硬币的两面。",[528,133006,133007],{"id":133007},"一篇论文与一个安静的家",[11,133009,133010],{},"1948 年，《贝尔系统技术杂志》分两期连载了香农的论文《通信的数学理论》。这篇论文提出了一整套全新的概念：用「比特」衡量信息量；把信息源的不确定性定义为「熵」；证明了在噪声信道中，只要传输速率低于某个「信道容量」，就存在办法让错误率任意小。",[11,133012,133013],{},"「比特」这个词是同事约翰·图基提出来的，意思是「二进制数字」。图基是普林斯顿的统计学家，战争期间常驻贝尔实验室，据一份 1947 年 1 月的实验室备忘录，这个说法最迟在那时已经定下来了。香农在论文里最早把「bit」用作信息的单位，并且明确注明「此词由 J. W. 图基建议」。据说命名是在实验室的午餐桌上敲定的，有人提议叫「binit」，有人提议叫「bigit」，最后「bit」胜出。一个今天人人都在用的单位，诞生过程就是这么随便。",[11,133015,133016],{},"关于「熵」这个名字，有一个流传很广的故事：据说冯·诺依曼建议他用这个词，理由是反正没有人真正懂熵，辩论的时候他总能占上风。这个故事细节不一，可信度看起来也难以考证。",[11,133018,133019],{},"但值得补充的是，这个故事最早的出处其实是香农自己。1971 年，他在《科学美国人》上的一篇文章里回忆道：「我最头疼的是该叫它什么。我想过叫‘信息’，但这个词被用得太滥，于是决定叫‘不确定性’。后来我跟约翰·冯·诺依曼讨论，他有更好的主意。他对我说：‘你就叫它熵吧，有两个理由。第一，你的不确定性函数在统计力学里已经用这个名字了，它本来就有名字。第二，而且更重要：没有人真正知道熵到底是什么，所以辩论的时候你总是占上风。’」——所以这不是后人编的段子，而是他本人的追述；只是「1940 年前后的一次谈话、1971 年才写下来」这条时间线，本身也提醒我们：细节不必太当真。",[11,133021,133022],{},"论文发表之后的反响，皮尔斯有过一个很好的说法：这篇文章「像一颗炸弹，而且是一颗延时炸弹」。他后来在另一篇回顾里说，这件事「像一道凭空劈下来的闪电」，而且「我不知道还有哪套理论是这样一整套、几乎没什么前身和历史地冒出来的」。皮尔斯也留下了两句让同行记了一辈子的实话：1950 年以前发表的信息论文章，「大多数跟香农的工作没什么关系」；以及「我从没遇到过一个真正弄懂了信息论的物理学家」。",[11,133024,133025],{},"当时也不是没有冷脸。统计学家约瑟夫·杜布给 1949 年那本书写的书评就不客气，说它更像「有启发性」而非数学性的著作，「而且作者在数学上的意图并不总是体面的」。",[11,133027,133028],{},"真正把这篇论文推向公众的，是另一个人：洛克菲勒基金会的沃伦·韦弗。韦弗在战时管过科学动员，眼光极好。1949 年，他把自己的通俗介绍与香农的论文合在一起，出了《通信的数学理论》这本书。在给基金会主席的信里，韦弗把香农做的事比作「吉布斯为物理化学做过的事」。而在他自己那篇导言里，他写道：",[132722,133030,133031],{},[11,133032,133033],{},"「communication（通信）这个词在这里将取一个非常宽泛的含义，包括一个头脑影响另一个头脑的全部过程。这当然不限于书面和口头的言语，还包括音乐、绘画、戏剧、芭蕾，事实上包括人的一切行为。」",[11,133035,133036],{},"韦弗还给出了那个著名的三层划分——技术的层次（符号传得多准）、语义的层次（符号多准确地传达了意思）、效果的层次（收到的意思多有效地改变了人的行动）。他最后甚至写下这样一句近乎诗的话：在这套理论里，「熵不只说算术的语言，它还说语言的语言」。",[11,133038,133039],{},"这就是「信息论热」的起点：一篇极其克制的数学论文，配上一篇极其热情的导言。往后几十年里，各种拿「信息」「熵」「冗余」去解释生物、心理、语言、经济、管理的文章层出不穷——而这桩公案，我们后面还会看到香农本人的反应。",[11,133041,133042],{},"对同行来讲，这篇论文的分量是不需要解释的。多年后，大卫·斯莱皮安在自己编的《信息论关键论文选》前言里写道：「本世纪大概没有哪一件工作，比香农 1948 年那篇文章更深刻地改变了人对通信的理解。」1998 年，在论文发表五十周年的综述里，塞尔希奥·贝尔杜第一次用了那个后来被反复引用的比喻：它是「信息时代的《大宪章》」。顺便说一句，《科学美国人》1990 年那篇专访里其实写的是「数字时代的《大宪章》」——两个版本后来常被混在一起，都算在《科学美国人》头上。",[11,133044,133045],{},"有意思的是，这样一篇改变世界的论文，作者本人几乎没有因此改变生活。他在发表之后依旧是那个爱摆弄东西、不爱应酬的人。",[11,133047,133048],{},"1949 年 3 月，他与贝尔实验室里的数值分析员贝蒂（玛丽·伊丽莎白·摩尔）结婚。据说牵线的人是皮尔斯——皮尔斯当时是贝蒂的上司。贝蒂是罗格斯大学的数学毕业生，聪明、幽默、有主见，既是他生活上的伙伴，也是工作上的搭档：他的一些论文手稿甚至是她的字迹抄写的，这让后来的研究者困惑了很久。她会吹钢琴，他会单簧管，两人下班后会找一些二声部的谱子合着弹。两人后来有了三个孩子。",[11,133050,133051],{},"还有一件圈里人都知道的小事。香农这篇论文出来的时候，诺伯特·维纳其实也在同一片水域里作业——他 1948 年出的《控制论》同样掀起了巨浪。两人的关系始终客气，维纳却在 1946 到 1947 年间私下抱怨过：「我的一个竞争者，贝尔电话公司的香农，要抢在我前面发表文章了。」香农这边对维纳一直很尊敬，说他是「我年轻时候的偶像」；至于两个人气质上的差别，麻省理工的托马斯·凯拉思后来总结得很直白：「维纳喜欢出风头，香农则完全不在乎这些。」",[11,133053,133054],{},"1949 年到 1950 年，他还发表了关于计算机下棋的论文，提出了让机器评估棋局、搜索走法的基本思路，这些想法后来成了计算机博弈的源头。",[11,133056,133057],{},"这件事值得多说两句。1950 年 3 月，他在《哲学杂志》上发表了《为计算机下棋编制程序》——这是这个题目上的第一篇技术论文；同年 2 月，《科学美国人》上还有一篇面向大众的《一台会下棋的机器》。文章中他把下棋程序分成两类，一类是硬算到底的「A 型」，一类是只搜有意思的分支的「B 型」，他自己更看好后者；他还估算出棋局的变化量大约是 10 的 120 次方，这个数字后来被叫作「香农数」。更早一点，1949 年他就在家里做出了一台用继电器控制的下棋机器，并且把它演示给国际象棋大师爱德华·拉斯克看过。有意思的是图灵当时也在做类似的事：他和戴维·钱珀瑙恩在 1948 年前后设计过一个下棋程序，因为没机器可用，只能自己拿纸笔一步一步地「手动运行」。图灵 1950 年那篇《计算机器与智能》里，还引用了香农的棋类文章。从香农的 A 型\u002FB 型分类往下，洛斯阿拉莫斯 1956 年的 MANIAC、伯恩斯坦 1958 年在 IBM 704 上的程序、麦卡锡他们在麻省理工写的程序，一直到 1967 年格林布拉特的棋程序，用的都是这套架子。",[11,133059,133060],{},"香农夫妇很爱玩杂耍、下棋，家里也总有一些稀奇古怪的小发明。对孩子们来说，这位爸爸并不严厉，更像一个爱和他们一起折腾的大朋友。",[528,133062,133064],{"id":133063},"玩具机器与赌场","玩具、机器与赌场",[11,133066,133067],{},"如果说香农的理论成就是他的「正业」，那么他造的那些机器，就是他生活里最鲜活的部分。",[11,133069,133070],{},"1950 年，他做了一只名叫「忒修斯」的电动机械鼠，能够在迷宫里摸索前进，一旦走过一遍，它就能记住路线，第二次直接走到出口。名字来自那个用线团走出迷宫的希腊英雄。这只木老鼠本身只是个装着磁铁和几根铜丝触须的壳子，真正的「脑子」藏在地板下面：一整排从电话交换机上拆下来的继电器，驱动着一台带电磁铁的滑车，把老鼠拖着往四个方向走。触须碰到墙，对应的继电器就记下这一格有墙，老鼠拐九十度继续试，直到撞上一块铜做的「奶酪」，蜂鸣器响起来。二十五格的迷宫，大约两个比特记一格，全部记忆加起来也就几十个比特——而它第二次就能一路直着跑到出口。迷宫改了，它还能把学到的忘掉重学。这是最早的「学习机器」之一。香农自己后来开玩笑说：严格讲，「那只老鼠并没有在解迷宫，是迷宫在解那只老鼠。」",[11,133072,133073],{},"1951 年 3 月，他在梅西基金会的控制论会议上做了题为《一台迷宫求解机的展示》的报告（会议记录到 1952 年才出版，贝尔实验室同年还拍了一部短片，报纸杂志跟着报道了一轮，所以很多书上把年份写成 1952）。据说现场有位神经生理学家拉尔夫·杰拉德，看见老鼠在一个圈里绕来绕去，喊了一声「这是神经症！」，香农于是又给它加了一个「抗神经症回路」。",[11,133075,133076],{},"他造过一台「读心机器」，能根据人以前猜硬币正反的习惯来预测下一次选择。这件事有个具体的对手。贝尔实验室的同事戴夫·哈格尔巴格先做了一台专门猜硬币的机器，叫 SEER——「序列外推机器人」，机器里面记着八种局面（上一轮自己赢还是输、对手换没换招），每种局面配一个可以上下加减的计数器，靠这点统计去押下一次；据他那篇 1956 年的论文，这台机器跟人对打了九千多局，赢了大约五成三。香农 1953 年 3 月写了一份备忘录，标题就叫《一台读心的（？）机器》，开门见山地说，这是「对哈格尔巴格的机器的一个简化模型」。两人的机器后来被接在一起互相对打，因为没人按按钮，还得再串一台「裁判」机器来产生随机数。谁赢的说法不一：多数说法是香农那台简单些的机器小胜，也有说它「赢得相当轻松」的——但具体比分，恐怕已经没人说得清了。香农在备忘录里还写了一句有趣的话：这类游戏，冯·诺依曼和摩根施特恩用博弈论处理过，爱伦·坡在《被窃的信》里用心理学处理过，而他这台机器「更接近坡的玩法，而不是冯·诺依曼的」。",[11,133078,133079],{},"他还造过一台只有一个功能的「终极机器」：盒子上有一个开关，你把它拨到「开」，盒盖就会打开，伸出一只机械手，把开关拨回「关」，然后缩回去，盖上盖子。这个点子最初来自他的朋友马文·明斯基——1952 年夏天明斯基在贝尔实验室跟他共事，后来回忆说：「我提议做这个机器，香农喜欢它，就让公司做了一批，送给几位高管。」香农在自己的桌上留了一台。它是被作家阿瑟·克拉克写下来的，克拉克在贝尔实验室看见过它，1958 年这样描述：「它不过是一只小木匣，雪茄盒大小，一面装着开关。你一扳开关，里面就响起一阵愤怒而一本正经的嗡嗡声。盒盖慢慢抬起，一只手从下面伸出来，把开关拨回去，然后缩回盒里。盒盖啪地合上，像棺材合盖一样决绝……一台什么也不做、只把自己关掉的机器，让人有一种说不出的不祥感。」——半个多世纪后，这个点子在网上重新火了一遍，人们叫它「最没用的机器」，做的人多半并不知道它出自明斯基的玩笑和香农的手。",[11,133081,133082],{},"他还设计了一台只用罗马数字运算的计算机，起名 THROBAC，说的是「节俭的罗马数字回溯式计算机」，名字本身就像个玩笑。这台机器 1953 年 4 月留下了两份技术备忘录，实物今天是麻省理工博物馆的藏品。",[11,133084,133085],{},"他的「玩具房」是家里最神奇的地方。那里有各式各样的独轮车，其中包括一些特别古怪的设计：有一辆没有座垫，有一辆没有脚蹬，有一辆是双人的，还有一辆的轮毂是偏心的，踩起来人会一上一下地起伏——他说这是头一辆这么做的车，帮他调试的助手查理·曼宁一边担心他的安全，一边为它第一次骑成鼓掌。车库里的独轮车和「大小轮」堆得落了一层灰。有会杂耍的机器人，其中一个被装扮成喜剧演员 W.C. 菲尔兹的形象：那是用儿童建筑玩具搭出来的，用三个钢球，球在一个绷紧的鼓面上弹跳，靠两片摇摆的桨「接一下、抛一下」，出手的误差则用短短的沟槽去纠正——全机没有一个传感器。他还做过三个小丑的「永不掉球」杂耍装置，起因是贝蒂从蛋糕装饰店带回一个四英寸的小丑，「才一块九毛八」。他的得意是：「有史以来最厉害的杂耍家也没法把纪录保持几分钟，可我的小丑整夜都在抛，一次也不掉！」",[11,133087,133088],{},"据说他还造过会喷火的小号——一吹，喇叭口就喷出火苗；还有火箭动力的飞盘、烧汽油的弹跳杆、一双巨大的泡沫「水上行走鞋」、一根从厨房用缆线连到地下实验室的机械手指（一拉，手指就勾一勾，等于叫人）、一台能设定翻转次数的机械硬币、从门廊下滑到湖边的简易缆车。爱德华·索普第一次走进他家地下室时的感想，被传记作者记了下来：「一个搞小玩意的人的天堂……我这是遇到了终极小玩意爱好者。」",[11,133090,133091],{},"他对杂耍尤其着迷，甚至总结出了一个「杂耍定理」。它把五个量用一行等式联系起来：设每只手接球到把球抛出的时间为 D，球在空中滞留的时间为 F，一只手空着的比例为 V，那么 (F + D) × 手数 = (V + D) × 球数。这个式子直到今天还在杂耍圈里被引用。他也写过一篇《杂耍的科学》，投给了《科学美国人》，但那份稿子改了又改，最后没发表——他 1987 年接受采访时还说：「我是给《科学美国人》写了一篇，至今没发出来。」文章要等到他去世后，被收进 1993 年的《香农论文集》里才和读者见面。对别人来说，这些都是不务正业；对他来说，这是理解世界的另一种方式。",[11,133093,133094],{},"他的兴趣还延伸到了钱的世界。1961 年，他与数学家爱德华·索普合作，做了一台可穿戴的轮盘赌预测装置：一个香烟盒大小的模拟计算机，开关藏在鞋里用大脚趾操作，一只脚负责给轮盘计时，另一只负责给球计时，结果则用几个音调通过塞进一只耳朵的小喇叭报出来；连导线都用胶水粘上颜色，尽量跟皮肤和头发混在一起。它预测的不是具体哪一个格子，而是一段扇区。那年 8 月，他们带着它真的去了拉斯维加斯：香农在轮盘旁边计时，索普在赌台另一头下注，两位太太负责望风。机器是灵的，小堆的筹码慢慢变大堆；但麻烦在于那根比头发还细的耳机线老是断，一断就得停半天。有一次同桌一位女士「惊恐地看过来」，索普赶紧走开，才发现「那个小喇叭像一只外星虫子一样从我的耳道里探出头来」。香农自己事后总结得很平：「我们碰到一堆实际问题，实际上从来没赚到钱。」这件事他们守口如瓶到 1966 年才披露；今天它被追认为「第一台可穿戴计算机」，不过这个称呼是后人的追认，不是当时的说法。",[11,133096,133097],{},"同一件事还有个前传，主角是索普的黑杰克工作。索普那篇论文本来想叫《二十一点的制胜策略》，是香农劝他把标题改得平淡些，最后成了《二十一点的一种有利策略》，1961 年发表在《美国科学院院刊》上——投这篇稿子需要一位院士背书，香农正是那位数学部的院士，据索普回忆，香农在签字前把他「盘问」了一遍才放过他。后来那本《击败庄家》把算牌术传遍了全世界。至于去拉斯维加斯那次，是轮盘赌，不是黑杰克，很多人会把这两件事混在一起。",[11,133099,133100],{},"他对股票的态度同样如此。香农并不迷恋盯盘，他会买入自己看好的少数几家技术公司并长期持有，比如惠普、摩托罗拉，还有他的老朋友亨利·辛格尔顿掌舵的泰利达因——辛格尔顿从大学时代起就跟他相识，后来还把他请进了董事会。他 1987 年跟采访者算过这笔账：「泰利达因我们拿了二十五年，每年复合增长百分之二十七。」这个数字在当时的圈子里是件稀罕事。至于那个更著名的「年化百分之二十八、跑赢一千多家基金」的说法，出处是庞德斯通 2005 年的书，依据的是一份未曾发表的访谈笔记，听个大概即可，别当成审计过的账目。他自己对这套本事的总结倒是简单：「我们是基本面派，不是技术派。」他对那些画图形的人毫不客气，把「头肩顶」「深 V」之类称作「重要数据的一种非常粗糙的复制品」；至于经济学家说的有效市场，他直说「我根本不信」。他还留下一句在麻省理工流传很广的俏皮话：有人问他为什么不用自己那套选股方法，他说：「算了吧，手续费会把你吃光。」——另有一次他对人说：「我是靠股市挣钱的，不是靠证定理挣钱的。」家里的账目，其实主要是贝蒂在管。女儿佩吉后来说：「这从来都是他们两个人的项目……他们两个都是赌徒。」他们甚至用一台早期的苹果 II 型电脑，每晚算一遍持仓的增长速度。",[11,133102,133103],{},"同一时期，他还是 1956 年达特茅斯人工智能夏季研讨会的发起者之一，与麦卡锡、明斯基、罗切斯特一起，把「人工智能」这个话题带到了学界的桌面上。有个细节值得记下：他自己并不喜欢「人工智能」这个词，更愿意用老派的「自动机研究」——那年他和麦卡锡合编的那本论文集，名字就叫《自动机研究》。至于那场为期一个多月的讨论会，他本人到底待了多久，史料上并不清楚：会议没有留下正式的出席名单，有回忆说他到场聊过一两天就走了，也有同时代人的笔记把他记成在场者。能确定的是，他不是那个从头住到尾的人。",[11,133105,133106],{},"然而他又是个清醒的人。1956 年，他在《IRE 信息论汇刊》上写了一篇很短、不到六百词的社论，题目叫《跟风》。这篇文章今天读起来依然刺人：",[132722,133108,133109],{},[11,133110,133111],{},"「信息论在最近几年变成了一股科学上的跟风热潮。它本来只是通信工程师的一件技术工具，却在通俗媒体和学术媒体上都得到了异乎寻常的关注……它大概已经被吹到了超出它实际成就的高度。」「大自然的秘密很少会一次让出好几条。」「人们会很容易发现，用上几个带劲的词，比如信息、熵、冗余，并不能解决我们所有的问题。」「这个行当无疑是被卖出去的，如果不是被卖过头的话……我们该做的是研究，而不是宣传。几篇第一流的论文，胜过一大批构思拙劣或者半途而废的文章。」",[11,133113,133114],{},"一个创立了一门学科的人，反而最先劝大家别神化这门学科——这种低调，几乎成了他性格的标签。",[11,133116,133117],{},"这篇社论不是没人回应，恰恰相反。维纳在三个月后同一份刊物上写了一篇《什么是信息论？》，客气地反驳说，不应该把信息论缩得那么窄；彼得·埃利亚斯则在 1958 年写了一篇讽刺社论，题目叫《两篇著名的论文》，虚构了一篇题为《信息论、光合作用与宗教》的文章来嘲笑滥用，末尾写：「我建议我们别再写这种东西了，把大量人力释放出来，去做那些真正需要研究的、激动人心的重要问题。」它常被后人称作学界最早的一次「索卡尔式恶作剧」的前身。罗伯特·法诺对此的感受很直接：「我不喜欢‘信息论’这个名字。克劳德也不喜欢。因为它听起来像是一门关于‘信息’的理论——可它不是，它是关于信息传输的，不是关于信息的。太多人没弄明白这一点。」贝蒂说得更家常：「那些人把他的话拉来拉去，他有点被惹烦了。他们不明白他想做的是什么。」",[528,133119,133121],{"id":133120},"麻省理工的怪教授","麻省理工的「怪教授」",[11,133123,133124],{},[132959,133125],{"alt":133126,"src":133127},"Shannon SM ’40, PhD ’40, who taught at MIT from 1956 until his retirement in 1978, was known to many as the father of information theory and of modern digital communications.","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162232493.png",[11,133129,133130],{},"1956 年 1 月，香农向贝尔实验室请了长假，回到麻省理工做客座教授，头衔是「电气通信访问教授」；1957 年他正式留下，同时挂两个教授头衔——电气工程系的通信科学教授，以及数学系教授。1958 年 10 月，学校宣布他出任新设立的「唐纳科学讲席教授」，这笔讲席由费城的唐纳基金会捐资五十万美元设立，是当时麻省理工收到过的最大一笔讲席捐赠。他和家人搬到了马萨诸塞州的温彻斯特，住进一栋靠近上神秘湖的大房子。房子 1858 年为一位名叫艾伦·德怀特的女士所建，她是托马斯·杰斐逊的曾外孙女，房子的设计据说参考了蒙蒂塞洛。他们后来给它起了个名字：「熵之屋」。",[11,133132,133133],{},"在学生眼里，香农是个特别的老师。他不爱讲课，更不爱写文章，上课风格随意，有时偏离主题，把话题带到他自己最近在摆弄的玩意上。",[11,133135,133136],{},"莱昂纳德·克莱因罗克形容他的课「像一顿好饭：你去了，他给你的东西是干净的、直观的」。罗伯特·加拉格记得他讲课时的那种神情：「他不会说‘这一章的要点是什么什么’。他会说：‘昨天晚上我在琢磨这个，想出来一个挺有意思的看法。’说的时候嘴角还带着一点坏笑。」大卫·福尼则是被他的研究讨论班拉进这行的，福尼说，他的教学方法就是讲自己正在做的问题、半成品的结果、猜想；有些问题他有漂亮的结果，有些问题他除了把问题本身说清楚以外毫无进展——「而这对一个正在找论文题目的研究生来说，简直太好了。」赫尔曼·豪斯也记得一件小事：他去旁听香农的讨论班，香农「把我当作和他平等的人对待」，并且对他这个晚辈提了一个关键问题，后来长成了豪斯那本书的第四章。香农的课还有个技术性细节常被提起：他一边回答问题，一边用一只手把一截粉笔抛上抛下，从来没有失手过。有位学生的总结很干脆：「我们都像敬神一样敬香农。」",[11,133138,133139],{},"做导师这件事，他却躲得很彻底。他一生带出的博士生极少——按后来的统计，只有三个；同一时期，麦卡锡、明斯基那些人各自都带出了一整代人。加拉格的解释很实在：「他的博士生非常少……你要是待在麻省理工，身边站着香农这么个庞然大物，你得有相当大的自我，才敢开口请他带你。」有人劝他多带几个学生，他的回答是：「我当不了导师。我没办法给任何人建议。我不觉得自己有资格去建议别人。」",[11,133141,133142],{},"他的办公室很乱，邮件和文稿堆得老高，据说他很多信件长期无人回复。这件事有个物证：他给自己存信件的文件夹起了个名字，叫「我拖得太久还没回的信」。记者乔恩·格特纳有一句形容极为传神：「信号可以抵达克劳德·香农。然后就再也传不下去了。」有位 1969 年去麻省理工访问的苏联学者回忆，他在走廊里看见了「香农教授」的门牌，然后过了一年多才意识到，这扇门几乎没开过——香农已经很少来学校了。倒是有位同事借用他那间空掉的办公室时，在里面翻出一张一年前开出、还没兑现的支票。人们还常提到，他在教工俱乐部的午饭桌上算他的股票想法，餐巾纸写满就换一张。",[11,133144,133145],{},"他对学术的虚名、头衔、荣誉兴趣平平，常常对别人的称赞报以腼腆一笑。他的名头则越来越大：1966 年 12 月，美国国家科学奖章的消息公布，次年 2 月由约翰逊总统在白宫东厅颁发，同一年他还拿到了 IEEE 荣誉奖章。颁奖那天，七岁的女儿佩吉为了穿哪条裙子跟母亲争执了一路，最后是副总统汉弗莱的大笑把她吓到躲在母亲腿后面。贝蒂说：「他是个非常谦逊的人。他得过很多奖，但奖从没让他头脑发热，他也从不谈这些。」他那些荣誉博士的兜帽太多，于是自己做了一个可以旋转的架子挂起来，跟挂领带的架子差不多。",[11,133147,133148],{},"领奖和演讲则一直是他的软肋。1973 年，第一届「香农讲座」在以色列的阿什凯隆举行，埃尔温·伯利坎普后来回忆：「我从没见过那么严重的怯场。我根本想不到，一个人在朋友面前可以怕成这样。」他需要有人在后台替他做很久的心理建设，还得由一位朋友陪着才肯上台。他后来推掉类似的邀约时，理由是一句玩笑：「退休以后，贝蒂不擦窗户，我不做演讲。」",[11,133150,133151],{},"这些年里，他的另一桩爱好是音乐：他会吹单簧管，喜欢迪克西兰爵士乐，也常参加小型即兴演奏。楼下客厅里，他吹单簧管、贝蒂弹钢琴的二重奏，是这个家的日常。爵士乐里的即兴与结构，与他的科学趣味可谓同源。",[11,133153,133154],{},"他爱下棋，但并不在乎输赢；他自己做的下棋机器能赢一般水平的对手，他却更乐意站在旁边看机器怎么「思考」。他骑着独轮车穿过麻省理工的走廊，边走边杂耍，让路过的学生又惊又喜。",[11,133156,133157],{},"家里那三个孩子，是在一堆零件中间长大的。儿子罗伯特生于 1952 年，后来做计算机，1998 年先于父亲去世；安德鲁生于 1954 年，成了钢琴家和作曲家；女儿佩吉生于 1959 年，后来当了老师。家里那间被报纸叫作「玩具房」的两层附楼，孩子们只叫它「爸爸的房间」。佩吉回忆说，父亲在家工作的时间很多，去学校只是为了上课和见学生，「所以我从小到大觉得他老在身边，跟很多上班的人家不一样」。晚饭后谁洗碗，家里甚至有台会走的发条机器老鼠来决定：把它放在餐桌中间，看它往哪边掉下去，掉到谁那边就谁洗。有一次佩吉把一盒牙签撒在了门廊上，父亲没有生气，而是说：「你知道吗，用这个可以算出圆周率。」——他说的是投针问题。家里饭桌上的话题常常是股票，孩子们很早就被教着读《华尔街日报》。至于辅导作业，他会因为「新数学」的教材顺序不对而发一顿牢骚，然后一路讲到虚数上去，讲到孩子已经完全不指望他把题讲完。",[11,133159,133160],{},"1978 年，他从教授岗位上退休，此后更多地待在家中，把时间交给他的工坊、他的玩具和他的书。",[528,133162,133164],{"id":133163},"熵之屋里的晚年","「熵之屋」里的晚年",[11,133166,133167],{},[132959,133168],{"alt":133169,"src":133170},"Claude Shannon's electromechanical mouse, which he called Theseus, was one of the earliest attempts to \"teach\" a machine to \"learn\" and one of the first experiments in artificial intelligence.","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162229686.png",[11,133172,133173],{},"退休后的香农依然享受生活：造机器，玩杂耍，和贝蒂一起旅行、散步，在家里招待来访的朋友。他不太谈自己的成就，也不爱做回顾。很多年后，来访者发现他的家里很少有显眼的荣誉陈列，反倒到处是工作台、零件和各式玩具。",[11,133175,133176],{},"他的动手能力没有退化，反而更放得开了。他做了一台解魔方的机器——这是真的，不是传说，那台机器今天也在麻省理工博物馆里；他还为魔方写过一首七十来行、带脚注的打油诗，标明要用《Ta-Ra-Ra Boom-De-Ay》的调子唱。1985 年，他获得了第一届京都奖，去京都领奖时做了一场题为《通信与计算的发展，以及我的爱好》的演讲，那是他晚年最长、也最完整的一次公开表述。他在演讲里说，历史上真正重要的不是帝王将相，而是「达尔文、牛顿、贝多芬这样的思想者和创造者」。",[11,133178,133179],{},"进入 80 年代，他的记忆开始衰退。1983 年，他去看医生，结论是「很可能处在阿尔茨海默病非常非常早期的阶段」（这是贝蒂的原话）。起初是忘电话号码、忘名字、忘面孔，出门去趟杂货店会忘了怎么回来，字迹也开始发抖。",[11,133181,133182],{},"1985 年，在英国布莱顿举办的国际信息论研讨会上，出现了一件令人难忘的事。他和贝蒂没有事先打招呼就出现在会场，在几个报告厅里进出，直到有人认出他来，消息才传开。晚宴上主办方把他请上台，他只简短地讲了几句，就被自己的掌声淹没了，最后说了一句：「这——太荒唐了。」然后就没什么可说的了，于是从口袋里掏出三个球，当场抛了起来。事后有人问主持人该怎么形容这件事，得到的回答是：「就像牛顿突然出现在一场物理学会议上。」参会者排起长队请他签名，很多年轻研究者是平生第一次见到这位读了一辈子其论文的人。当时的信息论学会会长也回忆说，那天在场的人里，大部分其实并不认得他，「但有一种嗡嗡声：香农来了，在哪儿，在哪儿？」——那是他最后几次公开露面之一。第二年，学会正式邀请他出席了在密歇根安娜堡举行的研讨会，那时病情已经相当明显：他做了一场十几分钟的晚宴讲话，里面还塞满了趣闻和玩笑，可贝蒂替他挡掉了大部分寒暄。",[11,133184,133185],{},"此后，病情逐渐加重。女儿佩吉说：「他会到处乱走。我们住在一条繁忙的街边……看着自己的亲人得这种病，是件很可怕的事。」有一阵子，家里参加了当地医院的阿尔茨海默病研究，贝蒂充当对照组。佩吉说：「有些日子他认得人，有些日子不认……有时候还是原来那个爸爸，有时候完全不知道自己在哪儿。」1992 年，佩吉还跟他有过一次关于研究生院的正常交谈；到 1993 年，罗伯特·法诺问他一件从前的事，香农只是回答：「我不记得了。」",[11,133187,133188],{},"1993 年他摔了一跤，髋骨骨折，康复得很慢。贝蒂本想让他在家里，还在「熵之屋」里布置了一间放得下病床的房间，最后在佩吉的劝说下，把他送进了梅德福的一家护理机构。贝蒂几乎每天去两次，佩吉说她「非常尽心」。贝蒂自己回忆：「中午我过去，护士们会排队坐在一张长凳上等我，因为我一进门，他脸上就会亮起来，咧嘴笑。」他在那里还会把助行架拆开来，琢磨更好的设计；听到音乐就用手指打拍子；护理人员会给他出些简单的算术题；他也会朝着楼梯和门外走。90 年代，他渐渐认不出身边的人。2001 年 2 月 24 日，克劳德·香农在这家护理机构去世，享年 84 岁。他的大脑捐给了阿尔茨海默病研究。",[11,133190,133191],{},"贝蒂比他多活了十六年，2017 年 5 月去世。他们结婚六十八年，从他还在贝尔实验室算信道容量，一直到「熵之屋」里的人渐渐走完。",[11,133193,133194],{},"他早年还给自己画过一场想象中葬礼的速写，那张图一点也不悲伤：一支爵士乐队在前面开道，六位独轮车手抬着棺材（图上写着「6 个骑独轮车的人 \u002F 1 位亲人」），后面跟着哭泣的寡妇、八人杂耍队和一台八条腿的杂耍机器，一辆「棋局彩车」上，棋手戴维·利维正在跟电脑对局，再往后是四只按斯金纳的方法训练过的猫、各种小机器、慢跑的人和一支四百一十七人的乐队。一个人能这样安排自己的葬礼，说明他对「正经」和「不正经」的分界，从一开始就没怎么放在心上。",[528,133196,133197],{"id":133197},"一个把工作当成游戏的人",[11,133199,133200],{},"香农的一生没有戏剧性的冲突，没有激烈的论战，也没有惊人的野心，很多时候他就是在一间堆满零件的屋子里，对着一个有趣的问题发呆。他提出的理论，为今天的手机通信、互联网、数据压缩、纠错码和密码学等整个数字世界打下了地基；而他自己的日子，却过得像一个永远不肯长大的孩子。",[11,133202,133203],{},"同行对他的评价，几乎都带着一点无从下手的敬意。大卫·斯莱皮安说：「他真的是个天才。我认识的人里，只有他配得上这个词。」又说：「他数学并不算懂得深，但他能现造出他需要的数学。」罗伯特·加拉格的版本是：「他的眼光清澈得惊人。爱因斯坦也是这样。」至于他到底做了什么，加拉格还有一句更朴素的话：「是香农看出，二进制位是一切通信的基本元素。那是他真正的发现，整个通信革命都是从这里长出来的。」托马斯·科弗说：「香农把三个领域炸了出来。」詹姆斯·马西在密码学上补了一句：「毫不夸张地说，香农的文章标志着密码学从一门手艺变成了一门科学。」而马文·明斯基记住的却是另一面：「不管出现什么题目，他都带着兴致扑上去，用某种出人意料的办法去攻它。对他而言，问题看上去越难，找到新东西的机会就越大。」",[11,133205,133206],{},"他自己对这一切的解释，比任何评论都更实在。1987 年，他对采访者说：「我不认为我做事是为了得奖——虽然另一间屋子里放着两打奖章。我更主要是被好奇心驱动，从来不是为了钱。我只是想知道，东西到底是怎么被装起来的。」「答案找到之后，把它们写下来、发表出来，总是让我很痛苦……我做过很多事，从来没写出来过。太懒了吧。我楼上有一个文件夹，装的全是没写完的论文。」三年后，他又说了一句后来被引用得最多的话：「我一直在追逐自己感兴趣的东西，不太在意它有多少金钱价值，或者对世界有多少价值。我在完全没用的东西上花了很多时间。」",[11,133208,133209],{},"回望那些日常的小事：少年时在围栏上架起的电报线，独自在走廊里骑独轮车的深夜，家里摆满的各种怪机器，晚年杂耍时那一点羞涩的笑容，你会发现，这些并不是他「正业之外」的点缀，而恰恰是他创造力的来源。他相信好奇心，相信玩耍，也相信，好玩的东西往往藏着深刻的真理。",[132722,133211,133212],{},[11,133213,133214],{},"卡德班克和斯隆在《自然》上的讣文里写过一句很准的话：香农大概能排进二十世纪科学主要人物名单的前列，「尽管他的名字对公众来说相对陌生」。这大概正是他本人会满意的位置。",{"title":132628,"searchDepth":132629,"depth":132629,"links":133216},[133217,133218,133219,133220,133221,133222,133223,133224],{"id":132907,"depth":132629,"text":132907},{"id":132928,"depth":132629,"text":132928},{"id":132968,"depth":132629,"text":132968},{"id":133007,"depth":132629,"text":133007},{"id":133063,"depth":132629,"text":133064},{"id":133120,"depth":132629,"text":133121},{"id":133163,"depth":132629,"text":133164},{"id":133197,"depth":132629,"text":133197},{},"\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon",{"title":132896,"description":132901},"blog\u002F2026\u002F0010-biography-of-claude-shannon","从密歇根小镇那根架在铁丝围栏上的电报线，到贝尔实验室走廊里的独轮车，再到麻省理工那间堆满零件的办公室。他给「信息」下了数学定义，自己却一辈子只对有意思的东西负责。",[132891],"2026-10-16T22:03:15+08:00","FVIfEic5VrK7HmvsYttp69z46Fc79opnUYBtJpxN80w",1794483696963]