{"id":981,"date":"2021-12-30T20:23:47","date_gmt":"2021-12-30T12:23:47","guid":{"rendered":"http:\/\/139.9.1.231\/?p=981"},"modified":"2021-12-30T20:23:48","modified_gmt":"2021-12-30T12:23:48","slug":"kl","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2021\/12\/30\/kl\/","title":{"rendered":"KL\u6563\u5ea6\uff08\u76f8\u5bf9\u71b5\uff09"},"content":{"rendered":"\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img src=\"https:\/\/w.wallhaven.cc\/full\/pk\/wallhaven-pky7k9.jpg\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>\u5b9a\u4e49\uff1a<\/p>\n\n\n\n<p>\u82e5P\u548cQ\u662f\u5b9a\u4e49\u5728\u540c\u4e00\u6982\u7387\u7a7a\u95f4\u7684\u4e24\u4e2a\u6982\u7387\u6d4b\u5ea6\uff0c\u5b9a\u4e49P\u548cQ\u7684\u76f8\u5bf9\u71b5\u4e3a\uff1a<\/p>\n\n\n\n<p>$$D\\left( P\\| Q\\right) =\\sum _{x}P\\left( x\\right) \\log \\dfrac{p\\left( x\\right) }{Q\\left( x\\right) }$$<\/p>\n\n\n\n<p>\u6027\u8d28\uff1a\\( D\\left( P\\| Q\\right) \\) >=0 <\/p>\n\n\n\n<p>\u00a0       \u5728\u6982\u7387\u8bba\u6216\u4fe1\u606f\u8bba\u4e2d\uff0cKL\u6563\u5ea6( Kullback\u2013Leibler divergence)\uff0c\u53c8\u79f0\u76f8\u5bf9\u71b5\uff08relative entropy)\uff0c\u662f\u63cf\u8ff0\u4e24\u4e2a\u6982\u7387\u5206\u5e03P\u548cQ\u5dee\u5f02\u7684\u4e00\u79cd\u65b9\u6cd5\u3002\u5b83\u662f\u975e\u5bf9\u79f0\u7684\uff0c\u8fd9\u610f\u5473\u7740D(P||Q) \u2260 D(Q||P)\u3002\u7279\u522b\u7684\uff0c\u5728\u4fe1\u606f\u8bba\u4e2d\uff0cD(P||Q)\u8868\u793a\u5f53\u7528\u6982\u7387\u5206\u5e03Q\u6765\u62df\u5408\u771f\u5b9e\u5206\u5e03P\u65f6\uff0c\u4ea7\u751f\u7684\u4fe1\u606f\u635f\u8017\uff0c\u5176\u4e2dP\u8868\u793a\u771f\u5b9e\u5206\u5e03\uff0cQ\u8868\u793aP\u7684\u62df\u5408\u5206\u5e03\u3002\u6709\u4eba\u5c06KL\u6563\u5ea6\u79f0\u4e3aKL\u8ddd\u79bb\uff0c\u4f46\u4e8b\u5b9e\u4e0a\uff0cKL\u6563\u5ea6\u5e76\u4e0d\u6ee1\u8db3\u8ddd\u79bb\u7684\u6982\u5ff5\uff0c\u5e94\u4e3a:1\uff09KL\u6563\u5ea6\u4e0d\u662f\u5bf9\u79f0\u7684\uff1b2\uff09KL\u6563\u5ea6\u4e0d\u6ee1\u8db3\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3002<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#fc0509\">          KL\u6563\u5ea6\u5728\u4fe1\u606f\u8bba\u4e2d\u6709\u81ea\u5df1\u660e\u786e\u7684\u7269\u7406\u610f\u4e49\uff0c\u5b83\u662f\u7528\u6765\u5ea6\u91cf\u4f7f\u7528\u57fa\u4e8eQ\u5206\u5e03\u7684\u7f16\u7801\u6765\u7f16\u7801\u6765\u81eaP\u5206\u5e03\u7684\u6837\u672c\u5e73\u5747\u6240\u9700\u7684\u989d\u5916\u7684Bit\u4e2a\u6570\u3002\u800c\u5176\u5728<strong>\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u7269\u7406\u610f\u4e49\u5219\u662f\u7528\u6765\u5ea6\u91cf\u4e24\u4e2a\u51fd\u6570\u7684\u76f8\u4f3c\u7a0b\u5ea6\u6216\u8005\u76f8\u8fd1\u7a0b\u5ea6<\/strong>.<\/p>\n\n\n\n<p>\u57fa\u4e8eP\u7684\u7f16\u7801\u53bb\u7f16\u7801\u6765\u81eaP\u7684\u6837\u672c\uff0c\u5176\u6700\u4f18\u7f16\u7801\u5e73\u5747\u6240\u9700\u8981\u7684\u6bd4\u7279\u4e2a\u6570\uff08\u5373\u8fd9\u4e2a\u5b57\u7b26\u96c6\u7684\u71b5\uff09\u4e3a\uff1a<\/p>\n\n\n\n<p>$$H\\left( x\\right) =\\sum _{x}P\\left( x\\right) \\log \\left( \\dfrac{1}{p\\left( x\\right) }\\right)$$<\/p>\n\n\n\n<p>\u7528\u57fa\u4e8eP\u7684\u7f16\u7801\u53bb\u7f16\u7801\u6765\u81eaQ\u7684\u6837\u672c\uff0c\u5219\u6240\u9700\u8981\u7684\u6bd4\u7279\u4e2a\u6570\u53d8\u4e3a\uff1a<\/p>\n\n\n\n<p> $$H&#8217;\\left( x\\right) =\\sum _{x}P\\left( x\\right) \\log \\left( \\dfrac{1}{Q\\left( x\\right) }\\right)$$ <\/p>\n\n\n\n<p>\u4e8e\u662f\uff0c\u6211\u4eec\u5373\u53ef\u5f97\u51faP\u4e0eQ\u7684KL\u6563\u5ea6:<\/p>\n\n\n\n<p>$$D\\left( P\\| Q\\right) = H\\left( x\\right) -H&#8217;\\left( x\\right)$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49\uff1a \u82e5P\u548cQ\u662f\u5b9a\u4e49\u5728\u540c\u4e00\u6982\u7387\u7a7a\u95f4\u7684\u4e24\u4e2a\u6982\u7387\u6d4b\u5ea6\uff0c\u5b9a\u4e49P\u548cQ\u7684\u76f8\u5bf9\u71b5\u4e3a\uff1a $$D\\left( P\\| Q\\r &hellip; <a href=\"http:\/\/139.9.1.231\/index.php\/2021\/12\/30\/kl\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">KL\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":[4,12],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/981"}],"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=981"}],"version-history":[{"count":6,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/981\/revisions"}],"predecessor-version":[{"id":996,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/981\/revisions\/996"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=981"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}