{"id":44963,"date":"2023-12-11T15:04:28","date_gmt":"2023-12-11T07:04:28","guid":{"rendered":"https:\/\/wx.kaifamiao.info\/?p=44963"},"modified":"2023-12-11T15:04:28","modified_gmt":"2023-12-11T07:04:28","slug":"%e8%af%b7%e4%bd%a0%e8%af%b4%e4%b8%80%e8%af%b4%e4%ba%a4%e5%8f%89%e7%86%b5%ef%bc%8c%e4%b9%9f%e5%8f%af%e4%bb%a5%e5%86%8d%e8%af%b4%e4%b8%80%e4%b8%8b%e5%85%b6%e4%bb%96%e7%9a%84%e4%bd%a0%e4%ba%86%e8%a7%a3-2","status":"publish","type":"post","link":"http:\/\/wx.kaifamiao.info\/index.php\/2023\/12\/11\/%e8%af%b7%e4%bd%a0%e8%af%b4%e4%b8%80%e8%af%b4%e4%ba%a4%e5%8f%89%e7%86%b5%ef%bc%8c%e4%b9%9f%e5%8f%af%e4%bb%a5%e5%86%8d%e8%af%b4%e4%b8%80%e4%b8%8b%e5%85%b6%e4%bb%96%e7%9a%84%e4%bd%a0%e4%ba%86%e8%a7%a3-2\/","title":{"rendered":"\u8bf7\u4f60\u8bf4\u4e00\u8bf4\u4ea4\u53c9\u71b5\uff0c\u4e5f\u53ef\u4ee5\u518d\u8bf4\u4e00\u4e0b\u5176\u4ed6\u7684\u4f60\u4e86\u89e3\u7684\u71b5"},"content":{"rendered":"

“`” \u53c2\u8003\u56de\u7b54\uff1a<\/p>\n

\u4e3a\u4e86\u66f4\u597d\u7684\u7406\u89e3\uff0c\u9700\u8981\u4e86\u89e3\u7684\u6982\u7387\u5fc5\u5907\u77e5\u8bc6\u6709\uff1a<\/p>\n

\u5927\u5199\u5b57\u6bcdX\u8868\u793a\u968f\u673a\u53d8\u91cf\uff0c\u5c0f\u5199\u5b57\u6bcdx\u8868\u793a\u968f\u673a\u53d8\u91cfX\u7684\u67d0\u4e2a\u5177\u4f53\u7684\u53d6\u503c\uff1b<\/p>\n

P(X)\u8868\u793a\u968f\u673a\u53d8\u91cfX\u7684\u6982\u7387\u5206\u5e03\uff0cP(X,Y)\u8868\u793a\u968f\u673a\u53d8\u91cfX\u3001Y\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\uff0cP(Y|X)\u8868\u793a\u5df2\u77e5\u968f\u673a\u53d8\u91cfX\u7684\u60c5\u51b5\u4e0b\u968f\u673a\u53d8\u91cfY\u7684\u6761\u4ef6\u6982\u7387\u5206\u5e03\uff1b<\/p>\n

p(X=x)\u8868\u793a\u968f\u673a\u53d8\u91cfX\u53d6\u67d0\u4e2a\u5177\u4f53\u503c\u7684\u6982\u7387\uff0c\u7b80\u8bb0\u4e3ap(x)\uff1b<\/p>\n

p(X=x,Y=y) \u8868\u793a\u8054\u5408\u6982\u7387\uff0c\u7b80\u8bb0\u4e3ap(x,y)\uff0cp(Y=y|X=x)\u8868\u793a\u6761\u4ef6\u6982\u7387\uff0c\u7b80\u8bb0\u4e3ap(y|x)\uff0c\u4e14\u6709\uff1ap(x,y)=p(x)*p(y|x)\u3002<\/p>\n

\u71b5\uff1a\u5982\u679c\u4e00\u4e2a\u968f\u673a\u53d8\u91cfX\u7684\u53ef\u80fd\u53d6\u503c\u4e3aX={x1,x2,\u2026,xk}\uff0c\u5176\u6982\u7387\u5206\u5e03\u4e3aP(X=xi)=pi\uff08i= 1,2,…,n\uff09\uff0c\u5219\u968f\u673a\u53d8\u91cfX\u7684\u71b5\u5b9a\u4e49\u4e3a\uff1a<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552628844270_3B250DDFC84CF6C235AF2C7A40959E1F""><\/p>\n

\u628a\u6700\u524d\u9762\u7684\u8d1f\u53f7\u653e\u5230\u6700\u540e\uff0c\u4fbf\u6210\u4e86\uff1a<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552628831409_948251326D8B5A5E0F784CB3F18C2980""><\/p>\n

\u4e0a\u9762\u4e24\u4e2a\u71b5\u7684\u516c\u5f0f\uff0c\u65e0\u8bba\u7528\u54ea\u4e2a\u90fd\u884c\uff0c\u800c\u4e14\u4e24\u8005\u7b49\u4ef7\uff0c\u4e00\u4e2a\u610f\u601d\uff08\u8fd9\u4e24\u4e2a\u516c\u5f0f\u5728\u4e0b\u6587\u4e2d\u90fd\u4f1a\u7528\u5230\uff09\u3002<\/p>\n

\u8054\u5408\u71b5\uff1a\u4e24\u4e2a\u968f\u673a\u53d8\u91cfX\uff0cY\u7684\u8054\u5408\u5206\u5e03\uff0c\u53ef\u4ee5\u5f62\u6210\u8054\u5408\u71b5Joint Entropy\uff0c\u7528H(X,Y)\u8868\u793a\u3002<\/p>\n

\u6761\u4ef6\u71b5\uff1a\u5728\u968f\u673a\u53d8\u91cfX\u53d1\u751f\u7684\u524d\u63d0\u4e0b\uff0c\u968f\u673a\u53d8\u91cfY\u53d1\u751f\u6240\u65b0\u5e26\u6765\u7684\u71b5\u5b9a\u4e49\u4e3aY\u7684\u6761\u4ef6\u71b5\uff0c\u7528H(Y|X)\u8868\u793a\uff0c\u7528\u6765\u8861\u91cf\u5728\u5df2\u77e5\u968f\u673a\u53d8\u91cfX\u7684\u6761\u4ef6\u4e0b\u968f\u673a\u53d8\u91cfY\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/p>\n

\u4e14\u6709\u6b64\u5f0f\u5b50\u6210\u7acb\uff1aH(Y|X)=H(X,Y)-H(X)\uff0c\u6574\u4e2a\u5f0f\u5b50\u8868\u793a(X,Y)\u53d1\u751f\u6240\u5305\u542b\u7684\u71b5\u51cf\u53bbX\u5355\u72ec\u53d1\u751f\u5305\u542b\u7684\u71b5\u3002\u81f3\u4e8e\u600e\u4e48\u5f97\u6765\u7684\u8bf7\u770b\u63a8\u5bfc\uff1a<\/p>\n

<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552628862555_DBA6F761056A8FA361E96F7E44D51F7B""><\/p>\n

\u7b80\u5355\u89e3\u91ca\u4e0b\u4e0a\u9762\u7684\u63a8\u5bfc\u8fc7\u7a0b\u3002\u6574\u4e2a\u5f0f\u5b50\u51716\u884c\uff0c\u5176\u4e2d<\/p>\n

\u7b2c\u4e8c\u884c\u63a8\u5230\u7b2c\u4e09\u884c\u7684\u4f9d\u636e\u662f\u8fb9\u7f18\u5206\u5e03p(x)\u7b49\u4e8e\u8054\u5408\u5206\u5e03p(x,y)\u7684\u548c\uff1b<\/p>\n

\u7b2c\u4e09\u884c\u63a8\u5230\u7b2c\u56db\u884c\u7684\u4f9d\u636e\u662f\u628a\u516c\u56e0\u5b50logp(x)\u4e58\u8fdb\u53bb\uff0c\u7136\u540e\u628ax,y\u5199\u5728\u4e00\u8d77\uff1b<\/p>\n

\u7b2c\u56db\u884c\u63a8\u5230\u7b2c\u4e94\u884c\u7684\u4f9d\u636e\u662f\uff1a\u56e0\u4e3a\u4e24\u4e2asigma\u90fd\u6709p(x,y)\uff0c\u6545\u63d0\u53d6\u516c\u56e0\u5b50p(x,y)\u653e\u5230\u5916\u8fb9\uff0c\u7136\u540e\u628a\u91cc\u8fb9\u7684-logp(x,y)-logp(x)\uff09\u5199\u6210-log(p(x,y)\/p(x)) \uff1b<\/p>\n

\u7b2c\u4e94\u884c\u63a8\u5230\u7b2c\u516d\u884c\u7684\u4f9d\u636e\u662f\uff1ap(x,y)=p(x)*p(y|x)\uff0c\u6545p(x,y)\/p(x)=p(y|x)\u3002<\/p>\n

\u76f8\u5bf9\u71b5\uff1a\u53c8\u79f0\u4e92\u71b5\uff0c\u4ea4\u53c9\u71b5\uff0c\u9274\u522b\u4fe1\u606f\uff0cKullback\u71b5\uff0cKullback-Leible\u6563\u5ea6\u7b49\u3002\u8bbep(x)\u3001q(x)\u662fX\u4e2d\u53d6\u503c\u7684\u4e24\u4e2a\u6982\u7387\u5206\u5e03\uff0c\u5219p\u5bf9q\u7684\u76f8\u5bf9\u71b5\u662f\uff1a<\/p>\n

\u00a0<\/p>\n

<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552629023555_C02FB3427E1B13721C2959339A772391""><\/p>\n

\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\uff0c\u76f8\u5bf9\u71b5\u53ef\u4ee5\u5ea6\u91cf\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u7684\u201c\u8ddd\u79bb\u201d\uff0c\u4e14\u6709D(p||q) \u2260D(q||p)\u3002\u53e6\u5916\uff0c\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0cD(p||q)\u662f\u5fc5\u7136\u5927\u4e8e\u7b49\u4e8e0\u7684\u3002<\/p>\n

<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552629067145_2AFF64353274BF7FB937B02DB97A4C34""><\/p>\n

\u4e92\u4fe1\u606f\uff1a\u4e24\u4e2a\u968f\u673a\u53d8\u91cfX\uff0cY\u7684\u4e92\u4fe1\u606f\u5b9a\u4e49\u4e3aX\uff0cY\u7684\u8054\u5408\u5206\u5e03\u548c\u5404\u81ea\u72ec\u7acb\u5206\u5e03\u4e58\u79ef\u7684\u76f8\u5bf9\u71b5\uff0c\u7528I(X,Y)\u8868\u793a\uff1a<\/p>\n

\u4e14\u6709I(X,Y)=D(P(X,Y)||P(X)P(Y))\u3002\u4e0b\u9762\uff0c\u54b1\u4eec\u6765\u8ba1\u7b97\u4e0bH(Y)-I(X,Y)\u7684\u7ed3\u679c\uff0c\u5982\u4e0b\uff1a<img alt=""img"" referrerpolicy=""no-referrer"" src=""https:\/\/uploadfiles.nowcoder.com\/images\/20190315\/311436_1552629089441_E5901FDE59A91E2C17235E648AE8046F""><\/p>\n

\u901a\u8fc7\u4e0a\u9762\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6211\u4eec\u53d1\u73b0\u7adf\u7136\u6709H(Y)-I(X,Y)=H(Y|X)\u3002\u6545\u901a\u8fc7\u6761\u4ef6\u71b5\u7684\u5b9a\u4e49\uff0c\u6709\uff1aH(Y|X)=H(X,Y)-H(X)\uff0c\u800c\u6839\u636e\u4e92\u4fe1\u606f\u5b9a\u4e49\u5c55\u5f00\u5f97\u5230H(Y|X)=H(Y)-I(X,Y)\uff0c\u628a\u524d\u8005\u8ddf\u540e\u8005\u7ed3\u5408\u8d77\u6765\uff0c\u4fbf\u6709I(X,Y)= H(X)+H(Y)-H(X,Y)\uff0c\u6b64\u7ed3\u8bba\u88ab\u591a\u6570\u6587\u732e\u4f5c\u4e3a\u4e92\u4fe1\u606f\u7684\u5b9a\u4e49\u3002<\/p>\n

<pre><code> "“`
\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"

“`” \u53c2\u8003\u56de\u7b54\uff1a \u4e3a\u4e86\u66f4\u597d\u7684\u7406\u89e3\uff0c\u9700\u8981\u4e86\u89e3\u7684\u6982\u7387\u5fc5\u5907\u77e5\u8bc6\u6709\uff1a \u5927\u5199\u5b57\u6bcdX\u8868\u793a\u968f\u673a\u53d8\u91cf […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[101],"tags":[],"class_list":["post-44963","post","type-post","status-publish","format-standard","hentry","category-c"],"_links":{"self":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/44963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/comments?post=44963"}],"version-history":[{"count":1,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/44963\/revisions"}],"predecessor-version":[{"id":44964,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/44963\/revisions\/44964"}],"wp:attachment":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/media?parent=44963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/categories?post=44963"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/tags?post=44963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}