{"id":1626,"date":"2023-02-14T09:05:37","date_gmt":"2023-02-14T01:05:37","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=1626"},"modified":"2023-02-14T10:03:55","modified_gmt":"2023-02-14T02:03:55","slug":"math-explain","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/gamma\/math-explain\/","title":{"rendered":"\u6570\u5b66\u89e3\u91ca"},"content":{"rendered":"\n<p>\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u7684\u5b9a\u4e49\u53ef\u4ee5\u7528\u6982\u7387\u6765\u8fdb\u884c\u89e3\u91ca\u3002<br>\u5bf9\u4e8e\u5b57\u7b26\u4e32\\(s\\)\u5728\u8bed\u6599\u7684\u7edf\u8ba1\u6982\u7387\\(P\\)\u00a0\uff0c\u53ef\u4ee5\u8868\u8fbe\u4e3a\uff1a<\/p>\n\n\n\n<p>\\[P=\\frac {f}{T}\\]<\/p>\n\n\n\n<p>\u7531\u4e8e\\(T\\)\u00a0\u4e3a\u4e00\u4e2a\u5168\u5c40\u5e38\u6570\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bf4\\(P\\)\u6b63\u6bd4\u4e8e\\(f\\)\uff08\u5373\u00a0\\(P\u221df\\)\u00a0)\u3002<br>\u4e8e\u662f\u6709\uff1a\\(f\u221dP,f_1\u221dP_1,f_2\u221dP_2,&#8230;.,f_N\u221dP_N\\)\u00a0\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e24\u4e2a\u5b50\u5b57\u7b26\u4e32\\(\\{s_1,s_2\\}\\)\u62fc\u63a5\u800c\u6210\u7684\u5b57\u7b26\u4e32\\(s\\)\u4e3a\u4f8b\u3002<\/p>\n\n\n\n<p>\\[\\gamma_s=\\frac {f_s}{2}(\\frac {1}{f_1}+\\frac {1}{f_2})=\\frac {P_s}{2}(\\frac {1}{P_1}+\\frac {1}{P_2})\\]<\/p>\n\n\n\n<p>\u7531\u6761\u4ef6\u6982\u7387\u516c\u5f0f\\(P(AB)=P(A) \\cdot P(B|A)\\)\u53ef\u5f97\uff1a<\/p>\n\n\n\n<p>\\[P(s)=P(s_1s_2)=P(s_1)\\cdot P(s_2 | s_1)=P(s_2) \\cdot P(s_1 | s_2)\\]<\/p>\n\n\n\n<p>\u6240\u4ee5\uff1a<\/p>\n\n\n\n<p>\\[\\gamma_s=\\frac {f_s}{2}(\\frac {1}{f_1}+\\frac {1}{f_2})=\\frac {P_s}{2}(\\frac {1}{P_1}+\\frac {1}{P_2}) \\\\ = \\frac {P(s)}{2}[\\frac {1}{P(s_1)} + \\frac {1}{P(s_2)}] = \\frac {1}{2}[P(s_2|s_1) + P(s_1|s_2)]\\]<\/p>\n\n\n\n<p>\u63a8\u800c\u5e7f\u4e4b\uff0c\u5373\u53ef\u7406\u89e3\u76f8\u5173\u7cfb\u6570\u7684\u6570\u5b66\u542b\u4e49\u3002<\/p>\n\n\n\n<p>\\[\\gamma_s = \\frac {f}{N} \\sum \\limits_{i=1}^N \\frac {1}{f_i} = \\frac {P}{N} \\sum \\limits_{i=1}^N \\frac {1}{P_i} \\\\ = \\frac {P(s_1s_2&#8230;s_N)}{N} \\sum \\limits_{i=1}^N \\frac {1}{P(s_i)} = \\frac {1}{N} \\sum \\limits_{i=1}^N \\frac {P(s_1s_2&#8230;s_N)}{P(s_i)} \\\\ = \\frac {1}{N} \\sum \\limits_{i=1}^N P(k_i|s_i)\\]<\/p>\n\n\n\n<p>\u5176\u4e2d\\(k_i\\)\u4e3a\u4ece\u5b50\u5b57\u7b26\u4e32\\(\\{s_1,s_2,&#8230;..,s_N\\}\\)\u4e2d\u53bb\u9664\\(s_i\\)\u7684\u96c6\u5408\u3002<\/p>\n\n\n\n<p>\u7531\u4e8e\u5b57\u7b26\u4e32\\(s\\)\u662f\u7531\u5b50\u5b57\u7b26\u4e32\\(\\{s_1,s_2,&#8230;..,s_N\\}\\)\u987a\u5e8f\u62fc\u63a5\u800c\u6210\u3002\u56e0\u6b64\uff0c\u6bcf\u4e2a\u5b50\u5b57\u7b26\u4e32\u51fa\u73b0\u7684\u4f4d\u7f6e\u90fd\u662f\u56fa\u5b9a\u7684\uff0c\u4e0d\u5b58\u5728\u6392\u5217\u7684\u95ee\u9898\u3002\u6240\u4ee5\u53ef\u4ee5\u5c06\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u7684\u5b9a\u4e49\u63a8\u5e7f\uff0c\u5e76\u7528\u4e8e\u4e00\u822c\u6027\u6982\u7387\u4e8b\u4ef6\u7684\u76f8\u5173\u6027\u5224\u65ad\u3002<\/p>\n\n\n\n<p>\u6982\u7387\u4e2d\u7684\u94fe\u5f0f\u6cd5\u5219\uff0c\u5728\u8fd9\u91cc\u53ef\u4ee5\u6362\u4e00\u4e2a\u89d2\u5ea6\u8fdb\u884c\u8868\u8fbe\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}) \\\\ =\\frac {f_1}{T} \\cdot \\frac {f_{12}}{f_1} \\cdot \\frac {f_{123}}{f_{12}}&#8230;&#8230;\\cdot \\frac {f_{123&#8230;&#8230;N}}{f_{12&#8230;&#8230;N-1}} = \\frac {f}{T}\\]<\/p>\n\n\n\n<p>\u4ece\u4ee5\u4e0a\u5206\u6790\u53ef\u4ee5\u770b\u51fa\u76f8\u5173\u7cfb\u6570\\(\\gamma\\)\u662f\u63cf\u8ff0\u5404\u4e2a\u5b50\u5b57\u7b26\u4e32\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\uff1b\u800c\u6982\u7387\u53ea\u662f\u63cf\u8ff0\u5b57\u7b26\u4e32\u5728\u6574\u4e2a\u8bed\u6599\u4e2d\u51fa\u73b0\u7684\u6982\u7387\u3002\u4e24\u8005\u4e4b\u95f4\u5185\u5728\u6db5\u4e49\u6709\u5f88\u5927\u5dee\u522b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76f8\u5173\u7cfb\u6570\u7684\u5b9a\u4e49\u53ef\u4ee5\u7528\u6982\u7387\u6765\u8fdb\u884c\u89e3\u91ca\u3002\u5bf9\u4e8e\u5b57\u7b26\u4e32\u5728\u8bed\u6599\u7684\u7edf\u8ba1\u6982\u7387\u00a0\uff0c\u53ef\u4ee5\u8868\u8fbe\u4e3a\uff1a \\[P=\\frac {f}{T [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":144,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1626","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1626"}],"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=1626"}],"version-history":[{"count":17,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1626\/revisions"}],"predecessor-version":[{"id":1656,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1626\/revisions\/1656"}],"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=1626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}