\u3000\u3000\u5728\u901a\u4fe1\u9886\u57df\uff0c\u4fe1\u9053\u5bb9\u91cf\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u662f\u6307\u5728\u7279\u5b9a\u7684\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u6240\u80fd\u4f20\u8f93\u7684\u6700\u5927\u4fe1\u606f\u901f\u7387\u3002\u800c\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\u662f\u8ba1\u7b97\u4fe1\u9053\u5bb9\u91cf\u7684\u7ecf\u5178\u516c\u5f0f\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u901a\u4fe1\u7cfb\u7edf\u7684\u8bbe\u8ba1\u548c\u4f18\u5316\u4e2d\u3002\u672c\u6587\u5c06\u4ece\u4fe1\u606f\u4f20\u8f93\u7684\u89d2\u5ea6\u51fa\u53d1\uff0c\u8be6\u7ec6\u4ecb\u7ecd\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\u7684\u63a8\u5bfc\u8fc7\u7a0b\u3002<\/p>\n\n\n\n
\u3000\u3000\u5728\u4fe1\u606f\u4f20\u8f93\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u9700\u8981\u4f20\u8f93\u4e00\u4e2a\u6d88\u606f\u6216\u8005\u4fe1\u53f7\u3002\u5047\u8bbe\u4e00\u4e2a\u6d88\u606f\u6709 $M$ \u79cd\u53ef\u80fd\u7684\u53d6\u503c\uff0c\u6bcf\u4e2a\u53d6\u503c\u53d1\u751f\u7684\u6982\u7387\u5206\u522b\u4e3a $p_1. p_2. …, p_M$\uff0c\u5219\u8be5\u6d88\u606f\u7684\u4fe1\u606f\u91cf\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000I = – \\sum_{i=1}^{M} p_i \\log_2 p_i<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000\u5176\u4e2d $\\log_2$ \u8868\u793a\u4ee5 $2$ \u4e3a\u5e95\u7684\u5bf9\u6570\u3002\u4fe1\u606f\u91cf\u7684\u5355\u4f4d\u901a\u5e38\u662f\u6bd4\u7279(bit)\u6216\u8005\u9999\u519c(Shannon)\uff0c\u4e00\u4e2a\u6bd4\u7279\u8868\u793a\u4e00\u4e2a\u4e8c\u8fdb\u5236\u4fe1\u606f\u5355\u4f4d\uff0c\u4e00\u4e2a\u9999\u519c\u8868\u793a\u4e00\u4e2a\u4fe1\u606f\u5355\u4f4d\u3002<\/p>\n\n\n\n
\u3000\u3000\u5728\u901a\u4fe1\u4e2d\uff0c\u4fe1\u606f\u901a\u5e38\u9700\u8981\u7ecf\u8fc7\u4fe1\u9053\u8fdb\u884c\u4f20\u8f93\u3002\u4fe1\u9053\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u4e2a\u9ed1\u76d2\u5b50\uff0c\u8f93\u5165\u662f\u6d88\u606f\u6216\u8005\u4fe1\u53f7\uff0c\u8f93\u51fa\u662f\u63a5\u6536\u5230\u7684\u6d88\u606f\u6216\u8005\u4fe1\u53f7\u3002\u4fe1\u9053\u7684\u8f93\u51fa\u53ef\u80fd\u4f1a\u53d7\u5230\u566a\u58f0\u3001\u5e72\u6270\u7b49\u56e0\u7d20\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u5bfc\u81f4\u4f20\u8f93\u9519\u8bef\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u4fe1\u9053\u7684\u6027\u80fd\u8fdb\u884c\u91cf\u5316\uff0c\u4ee5\u4fbf\u4e8e\u8bbe\u8ba1\u548c\u4f18\u5316\u901a\u4fe1\u7cfb\u7edf\u3002<\/p>\n\n\n\n
\u3000\u3000\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4fe1\u9053\u4f20\u8f93\u7684\u5e73\u5747\u4fe1\u606f\u901f\u7387\u6765\u91cf\u5316\u4fe1\u9053\u7684\u6027\u80fd\uff0c\u5b83\u8868\u793a\u5355\u4f4d\u65f6\u95f4\u5185\u4f20\u8f93\u7684\u5e73\u5747\u4fe1\u606f\u91cf\u3002\u8bbe\u4fe1\u9053\u7684\u8f93\u5165\u4e3a $X$\uff0c\u8f93\u51fa\u4e3a $Y$\uff0c\u5219\u4fe1\u9053\u7684\u5e73\u5747\u4fe1\u606f\u901f\u7387\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000R = \\frac{H(Y)}{T}<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000\u5176\u4e2d $T$ \u8868\u793a\u5355\u4f4d\u65f6\u95f4\uff0c$H(Y)$ \u8868\u793a\u63a5\u6536\u7aef\u63a5\u6536\u5230\u7684\u4fe1\u53f7\u6240\u643a\u5e26\u7684\u4fe1\u606f\u91cf\u7684\u5e73\u5747\u503c\u3002\u663e\u7136\uff0c\u5f53 $T$ \u8d8a\u5927\u65f6\uff0c\u5e73\u5747\u4fe1\u606f\u901f\u7387\u8d8a\u5927\u3002<\/p>\n\n\n\n
\u3000\u3000\u4fe1\u9053\u5bb9\u91cf\u662f\u6307\u5728\u7279\u5b9a\u7684\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u6240\u80fd\u4f20\u8f93\u7684\u6700\u5927\u4fe1\u606f\u901f\u7387\u3002\u5b83\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u56e0\u4e3a\u5b83\u544a\u8bc9\u6211\u4eec\u5728\u7406\u60f3\u6761\u4ef6\u4e0b\uff0c\u901a\u4fe1\u7cfb\u7edf\u6240\u80fd\u8fbe\u5230\u7684\u6700\u5927\u4f20\u8f93\u901f\u7387\u3002\u5728\u5b9e\u9645\u901a\u4fe1\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u5e0c\u671b\u8bbe\u8ba1\u7684\u901a\u4fe1\u7cfb\u7edf\u7684\u4f20\u8f93\u901f\u7387\u5c3d\u53ef\u80fd\u63a5\u8fd1\u4fe1\u9053\u5bb9\u91cf\u3002<\/p>\n\n\n\n
\u3000\u3000\u5728\u901a\u4fe1\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7f16\u7801\u7684\u65b9\u5f0f\u6765\u63d0\u9ad8\u4fe1\u9053\u7684\u4f20\u8f93\u6548\u7387\u3002\u7f16\u7801\u662f\u6307\u5c06\u4e00\u79cd\u4fe1\u606f\u8f6c\u6362\u6210\u53e6\u4e00\u79cd\u4fe1\u606f\u7684\u8fc7\u7a0b\u3002\u5728\u901a\u4fe1\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u4fe1\u9053\u7f16\u7801\u6765\u63d0\u9ad8\u4fe1\u9053\u7684\u4f20\u8f93\u6548\u7387\u3002<\/p>\n\n\n\n
\u3000\u3000\u9999\u519c\u7684\u4fe1\u9053\u7f16\u7801\u5b9a\u7406\u63d0\u4f9b\u4e86\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u7ed3\u8bba\uff1a\u5728\u4efb\u610f\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u90fd\u5b58\u5728\u4e00\u79cd\u7f16\u7801\u65b9\u5f0f\uff0c\u4f7f\u5f97\u5728\u4fe1\u9053\u5bb9\u91cf\u5185\u7684\u4fe1\u606f\u901f\u7387\u4e0b\uff0c\u53ef\u4ee5\u4fdd\u8bc1\u65e0\u9650\u63a5\u8fd1\u4e8e\u96f6\u8bef\u7801\u7387\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528\u9999\u519c\u7f16\u7801\uff0c\u5c31\u53ef\u4ee5\u5728\u4efb\u610f\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u8fbe\u5230\u65e0\u9650\u63a5\u8fd1\u4e8e\u4fe1\u9053\u5bb9\u91cf\u7684\u4f20\u8f93\u901f\u7387\u3002<\/p>\n\n\n\n
\u3000\u3000\u6839\u636e\u9999\u519c\u7684\u4fe1\u9053\u7f16\u7801\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\uff1a<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000C = \\max_{p(x)} I(X;Y)<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000\u5176\u4e2d $C$ \u8868\u793a\u4fe1\u9053\u5bb9\u91cf\uff0c$I(X;Y)$ \u8868\u793a\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u3002\u4e92\u4fe1\u606f\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u8868\u793a\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u76f8\u5173\u7a0b\u5ea6\u3002\u4e92\u4fe1\u606f\u8d8a\u5927\uff0c\u8868\u793a\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u8d8a\u5f3a\u3002<\/p>\n\n\n\n
\u3000\u3000\u6839\u636e\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4e92\u4fe1\u606f\u7684\u8868\u8fbe\u5f0f\uff1a<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000I(X;Y) = H(Y) – H(Y|X)<\/p>\n\n\n\n
\u3000\u3000$$<\/p>\n\n\n\n
\u3000\u3000\u5176\u4e2d $H(Y)$ \u8868\u793a\u8f93\u51fa\u7684\u71b5\uff0c$H(Y|X)$ \u8868\u793a\u5728\u5df2\u77e5\u8f93\u5165\u7684\u6761\u4ef6\u4e0b\uff0c\u8f93\u51fa\u7684\u71b5\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5728\u6240\u6709\u53ef\u80fd\u7684\u8f93\u5165\u5206\u5e03 $p(x)$ \u4e2d\uff0c\u4e92\u4fe1\u606f\u7684\u6700\u5927\u503c\u5c31\u662f\u4fe1\u9053\u5bb9\u91cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6700\u5927\u5316\u4e92\u4fe1\u606f\u7684\u65b9\u5f0f\u6765\u8ba1\u7b97\u4fe1\u9053\u5bb9\u91cf\u3002<\/p>\n\n\n\n
\u3000\u3000\u672c\u6587\u4ece\u4fe1\u606f\u4f20\u8f93\u7684\u89d2\u5ea6\u51fa\u53d1\uff0c\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\u7684\u63a8\u5bfc\u8fc7\u7a0b\u3002\u4fe1\u9053\u5bb9\u91cf\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u544a\u8bc9\u6211\u4eec\u5728\u7406\u60f3\u6761\u4ef6\u4e0b\uff0c\u901a\u4fe1\u7cfb\u7edf\u6240\u80fd\u8fbe\u5230\u7684\u6700\u5927\u4f20\u8f93\u901f\u7387\u3002\u9999\u519c\u7684\u4fe1\u9053\u7f16\u7801\u5b9a\u7406\u63d0\u4f9b\u4e86\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u7ed3\u8bba\uff1a\u5728\u4efb\u610f\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u90fd\u5b58\u5728\u4e00\u79cd\u7f16\u7801\u65b9\u5f0f\uff0c\u4f7f\u5f97\u5728\u4fe1\u9053\u5bb9\u91cf\u5185\u7684\u4fe1\u606f\u901f\u7387\u4e0b\uff0c\u53ef\u4ee5\u4fdd\u8bc1\u65e0\u9650\u63a5\u8fd1\u4e8e\u96f6\u8bef\u7801\u7387\u3002\u540c\u65f6\uff0c\u6211\u4eec\u8fd8\u4ecb\u7ecd\u4e86\u4e92\u4fe1\u606f\u7684\u6982\u5ff5\u548c\u8ba1\u7b97\u65b9\u5f0f\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\u6765\u8bbe\u8ba1\u548c\u4f18\u5316\u901a\u4fe1\u7cfb\u7edf\uff0c\u4ee5\u8fbe\u5230\u6700\u5927\u7684\u4f20\u8f93\u6548\u7387\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5728\u901a\u4fe1\u9886\u57df\uff0c\u4fe1\u9053\u5bb9\u91cf\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u662f\u6307\u5728\u7279\u5b9a\u7684\u4fe1\u9053\u6761\u4ef6\u4e0b\uff0c\u6240\u80fd\u4f20\u8f93\u7684\u6700\u5927\u4fe1\u606f\u901f\u7387\u3002\u800c\u9999\u519c\u7684\u4fe1\u9053\u5bb9\u91cf\u516c\u5f0f\u662f\u8ba1\u7b97\u4fe1\u9053\u5bb9\u91cf\u7684\u7ecf\u5178\u516c\u5f0f\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u901a\u4fe1\u7cfb\u7edf\u7684\u8bbe\u8ba1\u548c\u4f18\u5316\u4e2d\u3002<\/p>\n","protected":false},"author":1,"featured_media":3671,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","footnotes":""},"categories":[36],"tags":[45],"class_list":["post-7354","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","tag-txxt"],"_links":{"self":[{"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/posts\/7354"}],"collection":[{"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/comments?post=7354"}],"version-history":[{"count":0,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/posts\/7354\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/media\/3671"}],"wp:attachment":[{"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/media?parent=7354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/categories?post=7354"},{"taxonomy":"post_tag","embeddable":true,"href":"\/\/www.viralrail.com\/wp-json\/wp\/v2\/tags?post=7354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}