{"id":1661,"date":"2023-02-14T10:02:55","date_gmt":"2023-02-14T02:02:55","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=1661"},"modified":"2023-02-15T09:15:31","modified_gmt":"2023-02-15T01:15:31","slug":"relate-question","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/gamma\/relate-question\/","title":{"rendered":"\u5176\u4ed6\u76f8\u5173\u95ee\u9898"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">\u968f\u5b57\u7b26\u4e32\\(s\\)\u7684\u957f\u5ea6\u589e\u52a0\uff0c\u5176\u5bf9\u5e94\u7684\u7edf\u8ba1\u9891\u6b21\\(f\\)\u5c06\u6700\u7ec8\u6536\u655b\u81f31\u3002<\/h3>\n\n\n\n<p>\\[ \\mathop {\\lim }\\limits_{N \\to \\infty } f = 1 \\]<\/p>\n\n\n\n<p>\u5b57\u7b26\u4e32\\(s\\)\u7531\u5b50\u5b57\u7b26\u4e32\\(\\{s_1,s_2,&#8230;..,s_N\\}\\)\u987a\u5e8f\u62fc\u63a5\u800c\u6210\u3002\u56e0\u6b64\uff0c\u5b57\u7b26\u4e32\\(s\\)\u7684\u6982\u7387\u94fe\u5f0f\u6cd5\u5219\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\\[P(s_1s_2&#8230;s_N)=P(s_1)P(s_2|s_1)P(s_3|s_1s_2)\u22c5\u22c5\u22c5P(s_N|s_1s_2&#8230;s_{N\u22121}) \\]<\/p>\n\n\n\n<p>\u5b9e\u9645\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e00\u4e2a\u6982\u7387\u56e0\u5b50\\(P_i&lt;1\\)\uff0c\u6240\u4ee5\\(P(s_1s_2&#8230;s_N)\\)\u968f\\(N\\)\u589e\u5927\u5c06\u8d8b\u8fd1\u4e8e0\uff0c\u4f46\u59cb\u7ec8\u5927\u4e8e0\u3002\u7531\u4e8e\\(P=\\frac {f}{T}\\)&nbsp;\uff0c\u6240\u4ee5\\(f\\)\u4e5f\u5e94\u5f53\u8d8b\u8fd1\u4e8e0\u3002\u8003\u8651\u5230\u201c\u4eba\u62e9\u539f\u7406\u201d\uff1a\u5b57\u7b26\u4e32\\(s\\)\u8981\u4e48\u5728\u8bed\u6599\u4e2d\u51fa\u73b0\u81f3\u5c111\u6b21\uff1b\u8981\u4e48\u5728\u8111\u6d77\u4e2d\u81f3\u5c11\u51fa\u73b01\u6b21\u3002\u6240\u4ee5\uff0c\u8fd9\u4e2a\u9891\u6b21\\(f\\)\u6700\u7ec8\u8d8b\u8fd1\u4e8e1\u3002<\/p>\n\n\n\n<p>\u82e5\u8981\\(P(s_1s_2&#8230;s_N)\\)\u4e0d\u6536\u655b\u81f30\uff0c\u5219\u53ea\u80fd\u6bcf\u4e00\u4e2a\u6982\u7387\u56e0\u5b50\\(P_i=1\\)\u3002\u90a3\u4e48\u5c31\u610f\u5473\u7740\u5b50\u5b57\u7b26\u4e32\\(\\{s_1,s_2,&#8230;..,s_N\\}\\)\u5c06\u5b8c\u5168\u76f8\u5173\uff08\u5373\u540c\u65f6\u51fa\u73b0\uff0c\u540c\u65f6\u6d88\u5931\uff09\u3002\u8fd9\u79cd\u60c5\u51b5\u5728\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a2\u65f6\uff0c\u8fd8\u6bd4\u8f83\u5e38\u89c1\u3002\u5f53\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a4\u65f6\uff0c\u53ef\u4ee5\u5f52\u7ed3\u5176\u4e3a\u201c\u6210\u8bed\u201d\u3002\u8d85\u8fc7\u957f\u5ea64\u4ee5\u540e\uff0c\u8fd9\u79cd\u540c\u65f6\u51fa\u73b0\u7684\u60c5\u51b5\u5c31\u975e\u5e38\u7f55\u89c1\u4e86\u3002\u53ea\u80fd\u662f\u67d0\u4e9b\u7279\u5b9a\u540d\u79f0\uff0c\u624d\u4f1a\u9047\u5230\u8fd9\u6837\u7684\u60c5\u51b5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b57\u7b26\u96c6\u4e2d\u6240\u6709\u5b57\u7b26\u4e32\u7684\u76f8\u5173\u7cfb\u6570\u4e0b\u9650\u662f\u591a\u5c11\uff1f<\/h3>\n\n\n\n<p>\u76f8\u5173\u7cfb\u6570\u7684\u7406\u8bba\u4e0b\u9650\u503c\u662f\u96f6\u3002\u6392\u9664\u8fd9\u4e2a\u96f6\u503c\u4e4b\u540e\uff0c\u8fd8\u6709\u4e00\u4e2a\u975e\u96f6\u4e0b\u9650\u503c\u3002<br>\u6839\u636e\u76f8\u5173\u7cfb\u6570\u7684\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>\\[\\gamma (s|s_1s_2&#8230;s_n) = \\frac {f}{N} \\sum \\limits_{i=1}^N \\frac {1}{f_i}\\]<\/p>\n\n\n\n<p>\u8bbe\u6240\u6709\u5b57\u7b26\u4e32\u7684\u6700\u5927\u9891\u6b21\u4e3a\\(f_{max}\\)&nbsp;\uff0c\u8fd9\u4e2a\u503c\u4e5f\u4e0d\u4f1a\u8d85\u8fc7\u7edf\u8ba1\u603b\u6b21\u6570\\(T\\)&nbsp;\u3002<br>\u6240\u4ee5\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n<p>\\[\\gamma_{min}= \\frac {f}{N} \\sum \\limits_{i=1}^N \\frac {1}{f_i} \\ge \\frac {f}{N} \\sum \\limits_{i=1}^N \\frac {1}{f_{max}} = \\frac {f}{f_{max}} \\ge \\frac {1}{f_{max}} \\gg \\frac {1}{T}\\]<\/p>\n\n\n\n<p>\u56e0\u6b64\u53ef\u4ee5\u5927\u81f4\u901a\u8fc7\u5b9e\u9645\u8ba1\u7b97\u51fa\u7684\u6700\u5c0f\u975e\u96f6\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\uff0c\u4f30\u8ba1\u51fa\\(T\\)\u3002\u6216\u8005\u6362\u4e2a\u89d2\u5ea6\u8bf4\uff0c\u8bed\u6599\u957f\u5ea6\u51b3\u5b9a\u4e86\u76f8\u5173\u7cfb\u6570\u7684\u975e\u96f6\u4e0b\u9650\u3002<\/p>\n\n\n\n<p>\u5b9e\u9645\u4e0a\u6700\u5c0f\u975e\u96f6\u76f8\u5173\u7cfb\u6570\uff1a\\(\\gamma_{min}\u223c\\frac {1}{f_{max}}=\\frac {1}{f_{\u7684}}=\\frac {1}{30888903}\u22433.2374\u00d710^{\u22128}&nbsp;\\)\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6700\u5927\u5339\u914d\u6cd5\u4e3a\u4ec0\u4e48\u7279\u522b\u9002\u5408\u505a\u5206\u8bcd\u7b97\u6cd5\uff1f<\/h3>\n\n\n\n<p>\u6700\u5927\u5339\u914d\u6cd5\u5305\u62ec\uff1a\u6b63\u5411\u6700\u5927\u5339\u914d\u6cd5\uff0c\u9006\u5411\u6700\u5927\u5339\u914d\u6cd5\uff0c\u53cc\u5411\u6700\u5927\u5339\u914d\u6cd5\u3002\u8fd9\u4e9b\u5206\u8bcd\u7b97\u6cd5\uff0c\u662f\u521d\u671f\u6700\u9002\u5408\u5206\u8bcd\u7684\u7b97\u6cd5\u3002\u8fd9\u5176\u4e2d\u8574\u6db5\u7684\u539f\u7406\u662f\u4ec0\u4e48\uff1f<\/p>\n\n\n\n<p>\u6211\u4eec\u77e5\u9053\u5b57\u7b26\u4e32\\(\\{s_1,s_2,&#8230;..,s_N\\}\\)\u7684\u76f8\u5173\u7cfb\u6570\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\\[\\gamma (s|s_1s_2&#8230;s_n) = \\frac {f}{N} \\sum \\limits_{i=1}^N \\frac {1}{f_i}\\]<\/p>\n\n\n\n<p>\u91c7\u7528\u6700\u5927\u5339\u914d\u6cd5\u505a\u5206\u8bcd\u7b97\u6cd5\u65f6\uff0c\u5bf9\u516c\u5f0f\u91cc\u9762\u7684\u4e24\u4e2a\u53c2\u6570\u6709\u5f71\u54cd\uff1a<\/p>\n\n\n\n<p>\uff081\uff09&nbsp;\\(N\\)\u503c\u964d\u4f4e\u3002<br>\u5b57\u7b26\u4e32\u8d8a\u957f\uff0c\u6240\u9700\u8981\u5206\u6210\u7684\u4efd\u6570\u5c31\u8d8a\u5c11\u3002\u56e0\u6b64\\(N\\)\u503c\u964d\u4f4e\u3002<\/p>\n\n\n\n<p>\uff082\uff09\\(f_i\\)\u503c\u964d\u4f4e<br>\u7531\u524d\u9762\u7684\u6027\u8d28\u53ef\u4ee5\u77e5\u9053\uff1a\u5b57\u7b26\u4e32\u8d8a\u957f\uff0c\u5176\u5bf9\u5e94\u7684\u9891\u6b21\u4f1a\u964d\u4f4e\u3002<\/p>\n\n\n\n<p>\u4e24\u4e2a\u56e0\u7d20\u53e0\u52a0\u8d77\u6765\uff0c\u4f1a\u4f7f\u5f97\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u7684\u6570\u503c\u63d0\u9ad8\u3002\u67d0\u79cd\u610f\u4e49\u4e0a\uff1a<strong>\u6700\u5927\u5206\u8bcd\u7b97\u6cd5\u662f\u4e00\u79cd\u76f8\u5173\u7cfb\u6570<\/strong>\\(\\gamma\\)<strong>\u901f\u5347\u7684\u65b9\u6cd5<\/strong>\u3002\u8fd9\u91cc\u7684\u8bc1\u660e\u662f\u4e0d\u5b8c\u5907\u7684\uff0c\u53ea\u80fd\u505a\u51fa\u7b80\u5355\u7684\u5b9a\u6027\u5206\u6790\u7ed3\u8bba\u3002<\/p>\n\n\n\n<p>\u4e0d\u8fc7\u6839\u636e\u201c\u4eba\u62e9\u539f\u7406\u201d\uff1a\\(N\\)\u503c\u548c\\(f_i\\)&nbsp;\u80fd\u964d\u4f4e\u5230\u4f55\u79cd\u7a0b\u5ea6\uff0c\u5b8c\u5168\u53d7\u5236\u4e8e\u8bed\u6599\u5e93\u3002\u5982\u679c\u8bed\u6599\u5e93\u4e2d\u4e0d\u5b58\u5728\u67d0\u4e2a\u5b57\u7b26\u62fc\u63a5\u7ec4\u5408\uff0c\u5c31\u9700\u8981\u56de\u5f52\u5230\u6309\u5355\u5b57\u8fdb\u884c\u5206\u6790\u548c\u8ba1\u7b97\u3002\u8fd9\u70b9\u4e0a\u4e5f\u4e0e\u6700\u5927\u5206\u8bcd\u7b97\u6cd5\u7684\u5177\u4f53\u6b65\u9aa4\u76f8\u543b\u5408\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\"><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u4e0e\u4fe1\u606f\u71b5\\(H\\)\u7684\u5173\u7cfb\u5982\u4f55\uff1f<\/h3>\n\n\n\n<p>\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u8861\u91cf\u7684\u662f\u5b50\u5b57\u7b26\u4e32\u4e4b\u95f4\u7684\u5173\u8054\u7a0b\u5ea6\uff1b\u4fe1\u606f\u71b5\\(H\\)\u8861\u91cf\u7684\u662f\u5b50\u5b57\u7b26\u4e32\u6240\u5305\u542b\u7684\u4fe1\u606f\u91cf\u3002\u4ece\u57fa\u672c\u5b9a\u4e49\u4e0a\uff0c\u5c31\u53ef\u4ee5\u77e5\u9053\u4e24\u8005\u4e4b\u95f4\u5e76\u65e0\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\u6839\u636e\u4fe1\u606f\u71b5\u7684\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>\\[H=-\\sum \\limits_{i=1}^N P_i{log}_2 P_i = &#8211; \\sum \\limits_{i=1}^N P(s_i) {log}_2 P(s_i) = &#8211; \\sum \\limits_{i=1}^N \\frac {f_i}{T} {log}_2 \\frac {f_i}{T}\\]<\/p>\n\n\n\n<p>\u4fe1\u606f\u71b5\u7684\u5177\u4f53\u8ba1\u7b97\u4e2d\u8fd8\u4e0e\u7edf\u8ba1\u6570\u91cf\\(T\\)\u76f8\u5173\uff0c\u800c\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u7684\u5177\u4f53\u8ba1\u7b97\u5219\u4e0e\u7edf\u8ba1\u6570\u91cf\\(T\\)\u65e0\u5173\u3002<\/p>\n\n\n\n<p>\u6839\u636e\u524d\u9762\u7684\u8ba8\u8bba\u7ed3\u679c\u53ef\u4ee5\u4e86\u89e3\u5230\uff1a\u4e00\u4e2a\u5b57\u7b26\u4e32\u96c6\u5408\u7684\u6700\u5c0f\u975e\u96f6\u76f8\u5173\u7cfb\u6570\\(\\gamma_{min}\\)\u4e0e\\(\\frac {1}{T}\\)\u5b58\u5728\u4e00\u4e2a\u56fa\u5b9a\u7684\u6b63\u6bd4\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u5229\u7528\u8fd9\u4e2a\\(\\gamma_{min}\\)\u66ff\u4ee3\\(\\frac {1}{T}\\)\u8fdb\u884c\u4fe1\u606f\u71b5\u7684\u6570\u503c\u4f30\u7b97\u3002<\/p>\n\n\n\n<p>\u4e5f\u53ef\u4ee5\u9009\u62e9\u4e00\u4e2a\u5408\u9002\u7684\u8bcd\u6c47\uff08\u4f8b\u5982\uff1a\u201c\u5783\u573e\u201d\uff09\uff0c\u5c06\u5176\u4fe1\u606f\u71b5\u89c4\u5b9a\u4e3a1\u3002\u901a\u8fc7\u89e3\u65b9\u7a0b\u83b7\u5f97\\(T\\)\u7684\u6570\u503c\u3002\u7136\u540e\u518d\u7528\u8fd9\u4e2a\\(T\\)\u503c\u53bb\u8ba1\u7b97\u5176\u4ed6\u5b57\u7b26\u4e32\u7684\u71b5\u3002\u4e0d\u8fc7\uff0c\u603b\u4f53\u6765\u8bf4\uff0c\u57fa\u672c\u4e0e\u8bcd\u6c47\u9891\u6b21\u6bd4\u6210\u53cd\u6bd4\u4f8b\u3002<\/p>\n\n\n\n<p>\u4e24\u8005\u5728\u5176\u4e2d\u4e00\u4e2a\u65b9\u9762\u5177\u6709\u4e00\u81f4\u6027\u7684\u53d6\u5411\uff1a\u53d1\u751f\u9891\u6b21\u4f4e\u7684\u5b57\u7b26\u4e32\u5bf9\u6570\u503c\u7684\u8d21\u732e\u6bd4\u8f83\u5927\u3002\u53d1\u751f\u9891\u6b21\u4f4e\u7684\u5b57\u7b26\u4e32\u5bf9\u4e8e\u4fe1\u606f\u71b5\\(H\\)\u800c\u8a00\uff0c\u662f\u56e0\u4e3a\u5176\u6240\u5305\u542b\u7684\u4fe1\u606f\u91cf\u5927\uff1b\u5bf9\u4e8e\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u800c\u8a00\uff0c\u5219\u662f\u5b57\u7b26\u4e32\u8f83\u957f\uff0c\u80fd\u663e\u8457\u63d0\u5347\u5b9e\u9645\u6570\u503c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u968f\u5b57\u7b26\u4e32\u7684\u957f\u5ea6\u589e\u52a0\uff0c\u5176\u5bf9\u5e94\u7684\u7edf\u8ba1\u9891\u6b21\u5c06\u6700\u7ec8\u6536\u655b\u81f31\u3002 \\[ \\mathop {\\lim }\\limits_{N [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":144,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1661","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1661"}],"collection":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/comments?post=1661"}],"version-history":[{"count":14,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1661\/revisions"}],"predecessor-version":[{"id":1779,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1661\/revisions\/1779"}],"up":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/144"}],"wp:attachment":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/media?parent=1661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}