{"id":10172,"date":"2022-11-07T17:48:15","date_gmt":"2022-11-07T09:48:15","guid":{"rendered":"http:\/\/139.9.1.231\/?p=10172"},"modified":"2022-11-07T17:48:27","modified_gmt":"2022-11-07T09:48:27","slug":"k-l","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/11\/07\/k-l\/","title":{"rendered":"K-L\u6563\u5ea6\uff08\u76f8\u5bf9\u71b5\uff09"},"content":{"rendered":"\n<p>        <code>Kullback-Leibler Divergence<\/code>\uff0c\u5373<code>K-L\u6563\u5ea6<\/code>\uff0c\u662f\u4e00\u79cd<strong>\u91cf\u5316\u4e24\u79cd\u6982\u7387\u5206\u5e03P\u548cQ\u4e4b\u95f4\u5dee\u5f02<\/strong>\u7684\u65b9\u5f0f\uff0c\u53c8\u53eb<code>\u76f8\u5bf9\u71b5<\/code>\u3002\u5728\u6982\u7387\u5b66\u548c\u7edf\u8ba1\u5b66\u4e0a\uff0c\u6211\u4eec\u7ecf\u5e38\u4f1a\u4f7f\u7528\u4e00\u79cd<code>\u66f4\u7b80\u5355\u7684\u3001\u8fd1\u4f3c\u7684\u5206\u5e03<\/code>\u6765\u66ff\u4ee3<code>\u89c2\u5bdf\u6570\u636e<\/code>\u6216<code>\u592a\u590d\u6742\u7684\u5206\u5e03<\/code>\u3002K-L\u6563\u5ea6\u80fd\u5e2e\u52a9\u6211\u4eec\u5ea6\u91cf\u4f7f\u7528\u4e00\u4e2a\u5206\u5e03\u6765\u8fd1\u4f3c\u53e6\u4e00\u4e2a\u5206\u5e03\u65f6\u6240\u635f\u5931\u7684\u4fe1\u606f\u91cf\u3002<\/p>\n\n\n\n<h2>\u6570\u636e\u7684\u71b5<\/h2>\n\n\n\n<p>K-L\u6563\u5ea6\u6e90\u4e8e\u4fe1\u606f\u8bba\u3002\u4fe1\u606f\u8bba\u4e3b\u8981\u7814\u7a76\u5982\u4f55\u91cf\u5316\u6570\u636e\u4e2d\u7684\u4fe1\u606f\u3002\u6700\u91cd\u8981\u7684\u4fe1\u606f\u5ea6\u91cf\u5355\u4f4d\u662f<code>\u71b5<\/code>Entropy\uff0c\u4e00\u822c\u7528<code>H<\/code>\u8868\u793a\u3002\u5206\u5e03\u7684\u71b5\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-61.png\" alt=\"\" class=\"wp-image-10174\" width=\"274\" height=\"77\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-61.png 909w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-61-300x85.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-61-768x219.png 768w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/figure><\/div>\n\n\n\n<p>\u4e0a\u9762\u5bf9\u6570\u6ca1\u6709\u786e\u5b9a\u5e95\u6570\uff0c\u53ef\u4ee5\u662f<code>2<\/code>\u3001<code>e<\/code>\u6216<code>10<\/code>\uff0c\u7b49\u7b49\u3002\u5982\u679c\u6211\u4eec\u4f7f\u7528\u4ee5<code>2<\/code>\u4e3a\u5e95\u7684\u5bf9\u6570\u8ba1\u7b97H\u503c\u7684\u8bdd\uff0c\u53ef\u4ee5\u628a\u8fd9\u4e2a\u503c\u770b\u4f5c\u662f\u7f16\u7801\u4fe1\u606f\u6240\u9700\u8981\u7684\u6700\u5c11\u4e8c\u8fdb\u5236\u4f4d\u4e2a\u6570bits\u3002\u4e0a\u9762\u7a7a\u95f4\u8815\u866b\u7684\u4f8b\u5b50\u4e2d\uff0c\u4fe1\u606f\u6307\u7684\u662f\u6839\u636e\u89c2\u5bdf\u6240\u5f97\u7684\u7ecf\u9a8c\u5206\u5e03\u7ed9\u51fa\u7684\u8815\u866b\u7259\u9f7f\u6570\u91cf\u3002\u8ba1\u7b97\u53ef\u4ee5\u5f97\u5230\u539f\u59cb\u6570\u636e\u6982\u7387\u5206\u5e03\u7684\u71b5\u503c\u4e3a<code>3.12 bits<\/code>\u3002\u8fd9\u4e2a\u503c\u53ea\u662f\u544a\u8bc9\u6211\u4eec\u7f16\u7801\u8815\u866b\u7259\u9f7f\u6570\u91cf\u6982\u7387\u7684\u4fe1\u606f\u9700\u8981\u7684\u4e8c\u8fdb\u5236\u4f4d<code>bit<\/code>\u7684\u4f4d\u6570\u3002<\/p>\n\n\n\n<p>\u53ef\u662f\u71b5\u503c\u5e76\u6ca1\u6709\u7ed9\u51fa\u538b\u7f29\u6570\u636e\u5230\u6700\u5c0f\u71b5\u503c\u7684\u65b9\u6cd5\uff0c\u5373\u5982\u4f55\u7f16\u7801\u6570\u636e\u624d\u80fd\u8fbe\u5230\u6700\u4f18\uff08\u5b58\u50a8\u7a7a\u95f4\u6700\u4f18\uff09\u3002\u4f18\u5316\u4fe1\u606f\u7f16\u7801\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u610f\u601d\u7684\u4e3b\u9898\uff0c\u4f46\u5e76\u4e0d\u662f\u7406\u89e3K-L\u6563\u5ea6\u6240\u5fc5\u987b\u7684\u3002\u71b5\u7684\u4e3b\u8981\u4f5c\u7528\u662f\u544a\u8bc9\u6211\u4eec\u6700\u4f18\u7f16\u7801\u4fe1\u606f\u65b9\u6848\u7684\u7406\u8bba\u4e0b\u754c\uff08\u5b58\u50a8\u7a7a\u95f4\uff09\uff0c\u4ee5\u53ca\u5ea6\u91cf\u6570\u636e\u7684\u4fe1\u606f\u91cf\u7684\u4e00\u79cd\u65b9\u5f0f\u3002\u7406\u89e3\u4e86\u71b5\uff0c\u6211\u4eec\u5c31\u77e5\u9053\u6709\u591a\u5c11\u4fe1\u606f\u8574\u542b\u5728\u6570\u636e\u4e4b\u4e2d\uff0c\u73b0\u5728\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u5f53\u6211\u4eec\u7528\u4e00\u4e2a\u5e26\u53c2\u6570\u7684\u6982\u7387\u5206\u5e03\u6765\u8fd1\u4f3c\u66ff\u4ee3\u539f\u59cb\u6570\u636e\u5206\u5e03\u7684\u65f6\u5019\uff0c\u5230\u5e95\u635f\u5931\u4e86\u591a\u5c11\u4fe1\u606f\u3002<\/p>\n\n\n\n<h2>K-L\u6563\u5ea6\u5ea6\u91cf\u4fe1\u606f\u635f\u5931<\/h2>\n\n\n\n<p>\u53ea\u9700\u8981\u7a0d\u52a0\u4fee\u6539<code>\u71b5H<\/code>\u7684\u8ba1\u7b97\u516c\u5f0f\u5c31\u80fd\u5f97\u5230<code>K-L\u6563\u5ea6<\/code>\u7684\u8ba1\u7b97\u516c\u5f0f\u3002\u8bbe<code>p<\/code>\u4e3a\u89c2\u5bdf\u5f97\u5230\u7684\u6982\u7387\u5206\u5e03\uff0c<code>q<\/code>\u4e3a\u53e6\u4e00\u5206\u5e03\u6765\u8fd1\u4f3c<code>p<\/code>\uff0c\u5219<code>p<\/code>\u3001<code>q<\/code>\u7684<code>K-L\u6563\u5ea6<\/code>\u4e3a\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-62-1024x180.png\" alt=\"\" class=\"wp-image-10176\" width=\"504\" height=\"88\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-62-1024x180.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-62-300x53.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-62-768x135.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-62.png 1254w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><figcaption>entropy-p-q<\/figcaption><\/figure><\/div>\n\n\n\n<p>        \u663e\u7136\uff0c\u6839\u636e\u4e0a\u9762\u7684\u516c\u5f0f\uff0cK-L\u6563\u5ea6\u5176\u5b9e\u662f\u6570\u636e\u7684\u539f\u59cb\u5206\u5e03p\u548c\u8fd1\u4f3c\u5206\u5e03q\u4e4b\u95f4\u7684\u5bf9\u6570\u5dee\u503c\u7684\u671f\u671b\u3002\u5982\u679c\u7ee7\u7eed\u7528<code>2<\/code>\u4e3a\u5e95\u7684\u5bf9\u6570\u8ba1\u7b97\uff0c\u5219<strong>K-L\u6563\u5ea6\u503c\u8868\u793a\u4fe1\u606f\u635f\u5931\u7684\u4e8c\u8fdb\u5236\u4f4d\u6570<\/strong>\u3002\u4e0b\u9762\u516c\u5f0f\u4ee5\u671f\u671b\u8868\u8fbeK-L\u6563\u5ea6\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-63-1024x168.png\" alt=\"\" class=\"wp-image-10177\" width=\"431\" height=\"71\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-63-1024x168.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-63-300x49.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-63-768x126.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-63.png 1104w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/figure><\/div>\n\n\n\n<p>\u4e00\u822c\uff0cK-L\u6563\u5ea6\u4ee5\u4e0b\u9762\u7684\u4e66\u5199\u65b9\u5f0f\u66f4\u5e38\u89c1\uff1a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" src=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-64-1024x275.png\" alt=\"\" class=\"wp-image-10180\" width=\"316\" height=\"85\" srcset=\"http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-64-1024x275.png 1024w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-64-300x81.png 300w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-64-768x206.png 768w, http:\/\/139.9.1.231\/wp-content\/uploads\/2022\/11\/image-64.png 1046w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/figure><\/div>\n\n\n\n<p>\u6ce8\uff1a<code>log a - log b = log (a\/b)<\/code><\/p>\n\n\n\n<p>OK\uff0c\u73b0\u5728\u6211\u4eec\u77e5\u9053\u5f53\u7528\u4e00\u4e2a\u5206\u5e03\u6765\u8fd1\u4f3c\u53e6\u4e00\u4e2a\u5206\u5e03\u65f6\u5982\u4f55\u8ba1\u7b97\u4fe1\u606f\u635f\u5931\u91cf\u4e86<\/p>\n\n\n\n<h2>\u6563\u5ea6\u5e76\u975e\u8ddd\u79bb<\/h2>\n\n\n\n<p>\u5f88\u81ea\u7136\u5730\uff0c\u4e00\u4e9b\u540c\u5b66\u628aK-L\u6563\u5ea6\u770b\u4f5c\u662f\u4e0d\u540c\u5206\u5e03\u4e4b\u95f4\u8ddd\u79bb\u7684\u5ea6\u91cf\u3002\u8fd9\u662f\u4e0d\u5bf9\u7684\uff0c\u56e0\u4e3a\u4eceK-L\u6563\u5ea6\u7684\u8ba1\u7b97\u516c\u5f0f\u5c31\u53ef\u4ee5\u770b\u51fa\u5b83\u4e0d\u7b26\u5408\u5bf9\u79f0\u6027\uff08\u8ddd\u79bb\u5ea6\u91cf\u5e94\u8be5\u6ee1\u8db3\u5bf9\u79f0\u6027\uff09\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u7528<code>p<\/code>\u8fd1\u4f3c<code>q<\/code>\u548c\u7528<code>q<\/code>\u8fd1\u4f3c<code>p<\/code>\uff0c\u4e8c\u8005\u6240\u635f\u5931\u7684\u4fe1\u606f\u5e76\u4e0d\u662f\u4e00\u6837\u7684\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u4f60\u719f\u6089\u795e\u7ecf\u7f51\u7edc\uff0c\u4f60\u80af\u80fd\u5df2\u7ecf\u731c\u5230\u6211\u4eec\u63a5\u4e0b\u6765\u8981\u5b66\u4e60\u7684\u5185\u5bb9\u3002\u9664\u53bb\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u7684\u7ec6\u8282\u4fe1\u606f\u4e0d\u8c08\uff0c\u6574\u4e2a\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5176\u5b9e\u662f\u5728\u6784\u9020\u4e00\u4e2a\u53c2\u6570\u6570\u91cf\u5de8\u5927\u7684\u51fd\u6570\uff08\u767e\u4e07\u7ea7\uff0c\u751a\u81f3\u66f4\u591a\uff09\uff0c\u4e0d\u59a8\u8bb0\u4e3a<code>f(x)<\/code>\uff0c\u901a\u8fc7\u8bbe\u5b9a\u76ee\u6807\u51fd\u6570\uff0c\u53ef\u4ee5\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u903c\u8fd1\u975e\u5e38\u590d\u6742\u7684\u771f\u5b9e\u51fd\u6570<code>g(x)<\/code>\u3002\u8bad\u7ec3\u7684\u5173\u952e\u662f\u8981\u8bbe\u5b9a\u76ee\u6807\u51fd\u6570\uff0c\u53cd\u9988\u7ed9\u795e\u7ecf\u7f51\u7edc\u5f53\u524d\u7684\u8868\u73b0\u5982\u4f55\u3002\u8bad\u7ec3\u8fc7\u7a0b\u5c31\u662f\u4e0d\u65ad\u51cf\u5c0f\u76ee\u6807\u51fd\u6570\u503c\u7684\u8fc7\u7a0b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kullback-Leibler Divergence\uff0c\u5373K-L\u6563\u5ea6\uff0c\u662f\u4e00\u79cd\u91cf\u5316\u4e24\u79cd\u6982\u7387\u5206\u5e03P\u548cQ\u4e4b\u95f4\u5dee\u5f02\u7684\u65b9 &hellip; <a href=\"http:\/\/139.9.1.231\/index.php\/2022\/11\/07\/k-l\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">K-L\u6563\u5ea6\uff08\u76f8\u5bf9\u71b5\uff09<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[29],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10172"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=10172"}],"version-history":[{"count":6,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10172\/revisions"}],"predecessor-version":[{"id":10182,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10172\/revisions\/10182"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=10172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=10172"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=10172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}