{"id":8529,"date":"2024-06-05T09:01:01","date_gmt":"2024-06-05T01:01:01","guid":{"rendered":""},"modified":"2024-06-05T09:01:01","modified_gmt":"2024-06-05T01:01:01","slug":"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21","status":"publish","type":"post","link":"https:\/\/mushiming.com\/8529.html","title":{"rendered":"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<div class=\"toc\">\n<h4>\u4eceMIXMAX\u6982\u7387\u6a21\u578b\u7406\u89e3Bayesian\u5efa\u6a21\u65b9\u6cd5<\/h4>\n<ul>\n<li>\u50a8\u5907\u77e5\u8bc6<\/li>\n<li>\n<ul>\n<li>HMM-\u9690\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff08Hidden Markov Model\uff09<\/li>\n<li>GMM-\u6df7\u5408\u9ad8\u65af\u6a21\u578b<\/li>\n<li>\u591a\u5143\u9ad8\u65af\u5206\u5e03\uff08The Multivariate normal distribution\uff09<\/li>\n<li>\u591a\u5143\u9ad8\u65af\u8fd8\u662f\u6df7\u5408\u9ad8\u65af<\/li>\n<li>\u6761\u4ef6\u5206\u5e03\u3001\u8fb9\u7f18\u5206\u5e03\u3001\u8054\u5408\u5206\u5e03<\/li>\n<li>EM Expectation Maximum\u7b97\u6cd5<\/li>\n<li>MIX\u6240\u6307\u7684\u5c31\u662f\u9ad8\u65af\u6df7\u5408\u6a21\u578b<\/li>\n<li>MAX\u5c31\u662f\u8c01\u5927\u5c31\u7528\u8c01<\/li>\n<\/ul>\n<\/li>\n<li>Bayesian\u6982\u7387\u6a21\u578b<\/li>\n<li>\u7ed3\u8bed<\/li>\n<li>\u53c2\u8003\u6587\u6863<\/li>\n<\/ul>\n<\/div>\n<h2>\u50a8\u5907\u77e5\u8bc6<\/h2>\n<h3>HMM-\u9690\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff08Hidden Markov Model\uff09<\/h3>\n<p>HMM\u5efa\u6a21\u65f6\u9700\u8981\u76ee\u6807\u6709\u8fd9\u4e24\u4e2a\u7279\u5f81\uff1a<\/p>\n<ol>\n<li>\u57fa\u4e8e\u5e8f\u5217\u7684\uff0c\u6bd4\u5982\u65f6\u95f4\u5e8f\u5217\uff0c\u6216\u8005\u72b6\u6001\u5e8f\u5217\u3002<\/li>\n<li>\u6709\u4e24\u7c7b\u6570\u636e\uff0c\u4e00\u7c7b\u5e8f\u5217\u6570\u636e\u662f\u53ef\u4ee5\u89c2\u6d4b\u5230\u7684\uff0c\u5373\u89c2\u6d4b\u5e8f\u5217\uff1b\u800c\u53e6\u4e00\u7c7b\u6570\u636e\u662f\u4e0d\u80fd\u89c2\u5bdf\u5230\u7684\uff0c\u5373\u9690\u85cf\u72b6\u6001\u5e8f\u5217\uff0c\u7b80\u79f0\u72b6\u6001\u5e8f\u5217<\/li>\n<\/ol>\n<p>\u8bed\u97f3\u4fe1\u53f7\u662f\u5178\u578b\u7684\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\uff0c\u964d\u566a\u548c\u8bc6\u522b\u90fd\u53ef\u4ee5\u8ba4\u4e3a\u662fHMM\u8fc7\u7a0b\uff0c\u5e26\u566a\u8f93\u5165\u662f\u89c2\u6d4b\u5e8f\u5217\uff0c\u964d\u566a\u8fc7\u7a0b\u4f30\u8ba1\u5e72\u51c0\u8bed\u97f3\u5e8f\u5217\u5c31\u662f\u9690\u85cf\u72b6\u6001\u5e8f\u5217\uff0c\u8bc6\u522b\u4efb\u52a1\u4e2d\u4f30\u8ba1\u8bed\u97f3\u7684\u97f3\u7d20\uff08\u5b57\uff09\u5c31\u662f\u9690\u85cf\u72b6\u6001\u5e8f\u5217<\/p>\n<h3>GMM-\u6df7\u5408\u9ad8\u65af\u6a21\u578b<\/h3>\n<p>\u5bf9\u6df7\u5408\u9ad8\u65af\u6a21\u578b\u6709\u5f88\u591a\u5b9a\u4e49\uff0c\u4e0b\u56fe\u662f\u5bf9\u4e00\u4e2a\u6837\u70b9\u8fdb\u884c\u7684\u76f4\u65b9\u56fe\u7edf\u8ba1\uff0c\u53ef\u4ee5\u770b\u51fa\u4e24\u4e2a\u5c16\u5cf0\u7684\u5f62\u72b6\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u4e9b\u6837\u70b9\u5177\u5907\u4e24\u4e2a\u9ad8\u65af\u6df7\u5408\u7684\u7279\u70b9\u3002\u66f4\u7b80\u5355\u7684\u7406\u89e3\u5c31\u662f\u52a0\u578b\u6a21\u578b<br \/> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/2a4780d6cc9747a0b2e1dc7a8d62c034.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h3>\u591a\u5143\u9ad8\u65af\u5206\u5e03\uff08The Multivariate normal distribution\uff09<\/h3>\n<p>\u591a\u5143\u9ad8\u65af\u53ef\u4ee5\u7406\u89e3\u4e3a\u9ad8\u65af\u7684\u4e58\u6027\u8d28\u6a21\u578b\u3002<\/p>\n<h3>\u591a\u5143\u9ad8\u65af\u8fd8\u662f\u6df7\u5408\u9ad8\u65af<\/h3>\n<p>\u8fd9\u4e2a\u95ee\u9898\u5176\u5b9e\u633a\u4ee4\u4eba\u56f0\u60d1\u7684\uff0c\u5927\u81f4\u4e0a\u5206\u7c7b\u8981\u91c7\u7528\u6df7\u5408\u9ad8\u65af\uff0c\u6bcf\u4e00\u7c7b\u7684\u591a\u7ef4\u6982\u7387\u5206\u5e03\u5efa\u6a21\u7528\u591a\u5143\u9ad8\u65af\uff0c\u9ad8\u65af\u6df7\u5408\u6a21\u578b\uff08GMM\uff09\u53ca\u5176EM\u7b97\u6cd5\u7684\u7406\u89e3\u8fd9\u7bc7\u535a\u6587\u5bf9\u6b64\u5206\u6790\u7684\u5f88\u900f\u5f7b\uff0c\u8fd8\u987a\u4fbf\u5c06EM\u63a8\u5bfc\u4e86\u4e00\u904d\uff0c\u591a\u8bfb\u6b64\u6587\u80af\u5b9a\u53d7\u76ca\u3002<\/p>\n<h3>\u6761\u4ef6\u5206\u5e03\u3001\u8fb9\u7f18\u5206\u5e03\u3001\u8054\u5408\u5206\u5e03<\/h3>\n<p>\u9996\u5148\u8981\u56de\u987e\u6761\u4ef6\u6982\u7387\uff1a<\/p>\n<ol>\n<li>\u5047\u5b9a\u4e8b\u4ef6E\u548c\u4e8b\u4ef6F\u662f\u4e24\u4e2a\u7edf\u8ba1\u72ec\u7acb\u7684\u4e8b\u4ef6\uff0c\u90a3\u4e48\u4e8b\u4ef6EF\u6837\u672c\u7a7a\u95f4\u5c31\u662f\u6240\u6709\u65f6\u95f4E\u53d1\u751f\u7684\u53ef\u80fd\u6837\u672c\u548c\u4e8b\u4ef6F\u53d1\u751f\u7684\u53ef\u80fd\u6837\u672c\u7684\u6392\u5217\u7ec4\u5408\uff0c\u6211\u4eec\u5b9a\u4e49\u4e3a\u4e8b\u4ef6EF\u53d1\u751f\u7684\u6982\u7387\u4e3aP(EF)\uff0cE\u53d1\u751f\u7684\u6982\u7387\u4e3aP(E)\uff0cF\u53d1\u751f\u7684\u6982\u7387\u4e3aP(F)\u3002\u5047\u8bbe\u63b7\u9ab0\u5b50\uff0c\u7b2c\u4e00\u6b21\u6295\u63b7\u51fa\u6765\u4efb\u610f\u4e00\u4e2a\u6570\u5b57\u7684\u6982\u7387\u662f1\/6\uff0c\u7b2c\u4e8c\u6b21\u4e5f\u662f1\/6\uff0c\u90a3\u4e48\u4e24\u6b21\u7ec4\u5408\u7684\u6570\u5b57\u6982\u7387\u5c31\u662f1\/6 * 1\/6= 1\/36\u3002<\/li>\n<li>\u82e5F\u5df2\u7ecf\u53d1\u751f\uff0cF\u662f\u786e\u5b9a\u6027\u4e8b\u4ef6\uff0c\u90a3\u4e48\u8fd9\u4e2a\u786e\u5b9a\u6027\u4e8b\u4ef6\u51fa\u73b0\u4e86\u6982\u7387\u5373\u53ef\u8868\u793a\u4e3aP(F)\u3002\u5982\u679c\u5728F\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\uff0cE\u53d1\u751f\u7684\u6982\u7387\u662f\u4ec0\u4e48\u5462\uff1f\u5176\u5b9e\u5c31\u662fP(E)\u3002\u8fd9\u662f\u5f88\u663e\u7136\u7684\u4e8b\u60c5<\/li>\n<li>\u8bf4\u5230\u8fd9\u8981\u60f3\u4e00\u60f3\uff1a\u6761\u4ef6\u6982\u7387\u662f\u5565\uff1f\u6761\u4ef6\u6982\u7387\u662f\u8fd9\u4e00\u7cfb\u5217\u4e8b\u4ef6\u7684\u8054\u7cfb\uff0c\u4e0d\u7136\u95ee\u9898\u5c31\u592a\u7b80\u5355\u4e86\uff0c\u4e5f\u5c31\u65e0\u6cd5\u89e3\u51b3\u590d\u6742\u95ee\u9898\u4e86\u3002\u56e0\u4e3aF\u53d1\u751f\u4e86\uff0c\u6240\u4ee5\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5c31\u8981\u5c06F\uff08\u7b2c\u4e00\u6b21\uff1f\uff09\u7684\u6982\u7387\u9664\u53bb\uff0c\u53ea\u7559\u4e0bE\u7684\u6982\u7387\u3002<\/li>\n<li>\u5b9a\u4e49F\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\uff0cE\u4e8b\u4ef6\u7684\u6761\u4ef6\u6982\u7387\u4e3aP(E|F)\u3002\u6839\u636e\u4ee5\u4e0a\u63a8\u7406\u53ef\u4ee5\u7684\u51fa\u5982\u4e0b\u7ed3\u8bba\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E \u2223 F ) = P ( E F ) P ( F ) P(E|F)=\\frac{P(EF)}{P(F)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em; vertical-align: -0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5982\u6b64\u6298\u817e\u7684\u4e00\u4e2a\u521d\u8877\u662f\u6761\u4ef6\u6982\u7387\u7684\u53d8\u6362\u5f62\u5f0f\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E F ) = P ( E \u2223 F ) P ( F ) P(EF)=P(E|F)P(F) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u600e\u4e48\u89e3\u91ca\u5462\uff1f\u8fd9\u4e2a\u516c\u5f0f\u53ef\u4ee5\u5229\u7528F\u53d1\u751f\u7684\u6982\u7387\u548cF\u7ed9\u5b9a\u6761\u4ef6\u4e0bE\u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387\uff0c\u6765\u6c42\u89e3EF\u4ea4\u96c6\u6982\u7387\u3002<\/li>\n<li>\u4f1f\u5927\uff08\u590d\u6742\uff09\u7684\u6761\u4ef6\u6982\u7387\u4e58\u6cd5\u516c\u5f0f\u7531\u4e0a\u5f0f\u63a8\u5bfc\u51fa\u6765\uff1a\u5047\u8bbeEFG\u4e09\u4e2a\u72ec\u7acb\u4e8b\u4ef6\uff0c\u5219<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E F G ) = P ( E F ) \u2217 P ( G \u2223 E F ) = P ( E ) P ( F \u2223 E ) P ( G \u2223 E F ) P(EFG)=P(EF)*P(G|EF)=P(E)P(F|E)P(G|EF) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u4ee5\u6b64\u7c7b\u63a8\u5047\u8bbe\u4e00\u7cfb\u5217\u968f\u673a\u4e8b\u4ef6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> E 1 , E 2 . . . E n E_1,E_2...E_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6982\u7387\u53ef\u4ee5\u8868\u793a\u4e3a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E 1 E 2 . . . E n ) = P ( E 1 ) P ( E 2 \u2223 E 1 ) P ( E 3 \u2223 E 1 E 2 ) . . . P ( E n \u2223 E 1 E 2 . . . E n \u2212 1 ) = P ( E 1 ) P ( E 2 E 1 ) P ( E 1 ) P ( E 3 E 2 E 1 ) P ( E 1 E 2 ) . . . P ( E 1 E 2 . . . E n ) P ( E 1 E 2 . . . E n \u2212 1 ) P(E_1E_2...E_n)=P(E_1)P(E_2|E_1)P(E_3|E_1E_2)...P(E_n|E_1E_2...E_{n-1})\\\\ =P(E_1)\\frac{P(E_2E_1)}{P(E_1)}\\frac{P(E_3E_2E_1)}{P(E_1E_2)}...\\frac{P(E_1E_2...E_n)}{P(E_1E_2...E_{n-1})} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em; vertical-align: -0.936em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5230\u6b64\uff0c\u6700\u4f1f\u5927\u7684\u8d1d\u53f6\u65af\u6761\u4ef6\u6982\u7387\u516c\u5f0f\u53ef\u4ee5\u547c\u4e4b\u6b32\u51fa\u4e86\uff0c\u8fd8\u662f\u5047\u5b9a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> E E <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> F F <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><\/span><\/span><\/span><\/span>\u4e24\u4e2a\u4e8b\u4ef6\uff0c\u4e4b\u524d\u7684\u516c\u5f0f\u90fd\u662f\u6c42\u6761\u4ef6\u6982\u7387\uff0c\u6216\u8005\u662f\u51e0\u4e2a\u4e8b\u4ef6\u5171\u540c\u53d1\u751f\u7684\u6982\u7387\uff0c\u8ba4\u4e3a\u5355\u7eaf\u7684E\u548cF\u6982\u7387\u662f\u5df2\u77e5\u6761\u4ef6\uff0c\u8d1d\u53f6\u65af\u6982\u7387\u516c\u5f0f\u5219\u662f\u4e0a\u8ff0\u6761\u4ef6\u6982\u7387\u63a8\u6f14\u7684\u9006\u5411\u5f62\u5f0f\u3002\u8fd9\u91cc\u5b9a\u4e49<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> F c F^c <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> F F <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><\/span><\/span><\/span><\/span>\u7684\u4e92\u65a5\u4e8b\u4ef6\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u96c6\u5408\u91cc\u7684\u8865\u96c6\uff0c\u90a3\u4e48<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( F c ) = 1 \u2212 P ( F ) P(F^c)=1-P(F) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u90a3\u4e48<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> E E <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><\/span><\/span><\/span><\/span>\u53ef\u4ee5\u8868\u793a\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> E = E F \u222a E F c E=EF\\cup EF^c <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u222a<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5219<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E ) = P ( E F ) + P ( E F c ) = P ( E \u2223 F ) P ( F ) + P ( E \u2223 F c ) P ( F C ) = P ( E \u2223 F ) P ( F ) + P ( E \u2223 F c ) ( 1 \u2212 P ( F ) ) P(E)=P(EF)+P(EF^c)\\\\=P(E|F)P(F)+P(E|F^c)P(F^C)\\\\=P(E|F)P(F)+P(E|F^c)(1-P(F)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.714392em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.14133em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.714392em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault mtight\">C<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.714392em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u662f\u4e2a\u66f2\u7ebf\u6551\u56fd\u6c42\u6982\u7387\u7684\u597d\u65b9\u6cd5\uff0c\u4f8b\u5b50\u592a\u590d\u6742\u5c31\u4e0d\u6572\u952e\u76d8\u4e86\u3002<\/li>\n<li>\u5982\u679c\u4e0a\u9762\u8fd9\u4e2a\u770b\u660e\u767d\u4e86\uff0c\u90a3\u4e0b\u9762\u8fd9\u4e2a\u4e5f\u5c31\u4e0d\u96be\u7406\u89e3\u4e86\uff0c\u5728item 7\u7684\u57fa\u7840\u4e0a\uff0c\u5c06\u8d30\u5143\u4e8b\u4ef6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> F c F^c <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> F F <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><\/span><\/span><\/span><\/span>\u6269\u5c55\u5230\u4e00\u4e2a\u8054\u5408\u4e8b\u4ef6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> B i i \u2208 0 , N B_i\\quad i\\in 0,N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault\">N<\/span><\/span><\/span><\/span><\/span>\uff0c\u5219<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( E ) = \u2211 i = 0 n P ( E B i ) = \u2211 i = 0 n P ( B i ) P ( E \u2223 B i ) P(E)=\\sum_{i=0} ^nP(EB_i)\\\\=\\sum_{i=0} ^nP(B_i)P(E|B_i) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.92907em; vertical-align: -1.27767em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em;\"><span class=\"\" style=\"top: -1.87233em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.92907em; vertical-align: -1.27767em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6514em;\"><span class=\"\" style=\"top: -1.87233em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u4e2a\u4e5f\u53eb\u4f5c\u5168\u6982\u7387\u516c\u5f0f<\/li>\n<li>\u7efc\u4e0a\u6240\u8ff0\uff0cboss\u7ea7\u522b\u7684\u8d1d\u53f6\u65af\u516c\u5f0f\uff08\u5b9a\u7406\uff09\u9a6c\u4e0a\u5c31\u6210\u578b\u4e86\uff0c\u5176\u5b9e\u8d1d\u53f6\u65af\u5b9a\u7406\u5c31\u662f\u5168\u6982\u7387\u516c\u5f0f\u7684\u4e00\u4e2a\u53d8\u5f62\uff0c\u524d\u9762\u7684\u516c\u5f0f\u6c42\u5f97\u6240\u6709\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\uff0c\u90a3\u4e48\u5982\u679c\u8fd9\u4e2a\u5168\u6982\u7387\u6211\u77e5\u9053\u4e86\uff0c\u60f3\u77e5\u9053\u5177\u4f53\u67d0\u4e2aB\u4e8b\u4ef6\u7684\u6982\u7387\u600e\u4e48\u529e\u5462\uff1f <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( B i \u2223 E ) = P ( B i E ) P ( E ) = P ( E B i ) \u2211 i = 0 n P ( B i ) P ( E \u2223 B i ) = P ( E \u2223 B i ) P ( B i ) \u2211 i = 0 n P ( B i ) P ( E \u2223 B i ) P(B_i|E)=\\frac{P(B_iE)}{P(E)}=\\frac{P(EB_i)}{\\sum_{i=0} ^nP(B_i)P(E|B_i)}=\\frac{P(E|B_i)P(B_i)}{\\sum_{i=0} ^nP(B_i)P(E|B_i)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em; vertical-align: -0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.421em; vertical-align: -0.994002em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.30571em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.994002em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.421em; vertical-align: -0.994002em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.30571em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05764em;\" class=\"mord mathdefault\">E<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span style=\"margin-right: 0.05017em;\" class=\"mord mathdefault\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.05017em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.994002em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<p>\u5728\u7f51\u4e0a\u5bf9\u8fd9\u4e2a\u795e\u5947\u516c\u5f0f\u5404\u79cd\u89e3\u91ca\u6587\u7ae0\u592a\u591a\uff0c\u4ece\u8054\u5408\u5206\u5e03 & \u6761\u4ef6\u5206\u5e03 & \u8fb9\u7f18\u5206\u5e03\u501f\u56fe\u6765\u5bf9\u8fd9\u4e2a\u62bd\u8c61\u7684\u516c\u5f0f\u505a\u4e00\u4e2a\u6ce8\u89e3\uff0c\u52a0\u6df1\u7406\u89e3\u5427\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/d1e1b404e74a4569967c50aa0719434b.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u901a\u4fd7\uff08\u4e0d\u4e25\u8c28\u4e0d\u4fdd\u8bc1\u51c6\u786e\uff09\u7684\u8bb2\uff1aEF\u7684\u5c31\u662f\u8054\u5408\u5206\u5e03\uff0c\u5355\u72ec\u770b\u4e00\u4e2a\u7684\u5206\u5e03\u5c31\u662f\u8fb9\u7f18\u5206\u5e03\uff0c\u628a\u4e00\u4e2a\u5b9a\u4e0b\u6765\u770b\u53e6\u5916\u4e00\u4e2a\u7684\u5c31\u662f\u6761\u4ef6\u5206\u5e03\u3002<\/p>\n<h3>EM Expectation Maximum\u7b97\u6cd5<\/h3>\n<p>EM\u7b97\u6cd5\u662f\u8fed\u4ee3\u6c42\u89e3\u6700\u5927\u503c\u7684\u7b97\u6cd5\uff0c\u540c\u65f6\u7b97\u6cd5\u5728\u6bcf\u4e00\u6b21\u8fed\u4ee3\u65f6\u5206\u4e3a\u4e24\u6b65\uff0cE\u6b65\u548cM\u6b65\u3002\u4e00\u8f6e\u8f6e\u8fed\u4ee3\u66f4\u65b0\u9690\u542b\u6570\u636e\u548c\u6a21\u578b\u5206\u5e03\u53c2\u6570\uff0c\u76f4\u5230\u6536\u655b\uff0c\u5373\u5f97\u5230\u6211\u4eec\u9700\u8981\u7684\u6a21\u578b\u53c2\u6570\u3002\u53c2\u8003\u6587\u6863\u91cc\u6709\u8be6\u7ec6\u4ecb\u7ecd\u3002<\/p>\n<h3>MIX\u6240\u6307\u7684\u5c31\u662f\u9ad8\u65af\u6df7\u5408\u6a21\u578b<\/h3>\n<p>\u7ecf\u8fc7\u4e86\u90a3\u4e48\u591a\u94fa\u57ab\uff0c\u8fd9\u91cc\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\u5c31\u662f\u60f3\u529e\u6cd5\u8ba9\u8bed\u97f3\u7ecf\u8fc7\u77e2\u91cf\u91cf\u5316\u540e\u6210\u4e3a\u4e00\u4e2a\u6df7\u5408\u9ad8\u65af\u6a21\u578b\uff0c\u8fd9\u5c31\u7ed3\u4e86\u3002\u4f46\u60f3\u5b9e\u73b0\u8fd9\u4e2a\u76ee\u6807\u8fd8\u662f\u5f88\u66f2\u6298\u7684\uff0c\u4e5f\u6709\u5c06\u8fd9\u4e2a\u6a21\u578b\u53eb\u505a\u6807\u7b7e\u6a21\u578b\uff08labeling model\uff09\uff0c\u5728\u30106\u3011\u4e2d\u7528\u4e86K-MEANS\u805a\u7c7b\uff0c\u30107\u3011\u7528\u7684Bootstrapping or Clustering, \u30108\u3011\u7528\u7684EM\u3002\u5f53\u7136\u8fd8\u6709\u5f88\u591a\u522b\u7684\u65b9\u6cd5\u5c31\u4e0d\u4e00\u4e00\u5217\u4e3e\u4e86\uff0c\u8981\u770b\u7ed3\u679c\u8c01\u6700\u9ad8\u65af\uff0c\u8c01\u6700\u7b26\u5408\u5047\u8bbe\u3002<\/p>\n<h3>MAX\u5c31\u662f\u8c01\u5927\u5c31\u7528\u8c01<\/h3>\n<p>\u8fd9\u4e2a\u6a21\u578b\u5728\u30106\u3011\u4e2d\u88ab\u8bbe\u8ba1\u51fa\u6765\uff0c\u8bde\u751f\u4e8eIBM\u534e\u751f\u7814\u7a76\u4e2d\u5fc3\u3002\u6700\u521d\u7684\u60f3\u6cd5\u662f\u7528\u6765\u505a\u8bed\u97f3\u8bc6\u522b\uff0c\u8fd9\u4e2a\u6a21\u578b\u7684\u63d0\u51fa\u7684\u76ee\u7684\u662f\u60f3\u6839\u636e\u89c2\u6d4b\u4fe1\u53f7\u5f97\u51fa\u67d0\u4e2a\u5177\u4f53\u6807\u7b7e\u51fa\u73b0\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3002\u600e\u4e48\u89c2\u5bdf\u5462\uff0c\u4e14\u770b\u4e0b\u9762\u5bf9\u6570\u8c31\u7ebf\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y = l o g \uff08 X 1 + X 2 \uff09 Y=log\uff08X_1+X_2\uff09 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.88888em; vertical-align: -0.19444em;\"><\/span><span style=\"margin-right: 0.01968em;\" class=\"mord mathdefault\">l<\/span><span class=\"mord mathdefault\">o<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord cjk_fallback\">\uff09<\/span><\/span><\/span><\/span><\/span>,<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X 1 X_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X 2 X_2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8d8a\u5927\u7684\u503c\u5bf9log\u7ed3\u679c\u5f71\u54cd\u8d8a\u5927\uff0c\u5c24\u5176\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \uff08 X 1 + X 2 \uff09 \uff08X_1+X_2\uff09 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.07847em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord cjk_fallback\">\uff09<\/span><\/span><\/span><\/span><\/span>\u7ed3\u679c\u5927\u4e8e10\u4e4b\u540e\uff0c\u5728\u589e\u957f\u4e00\u70b9\u5bf9\u7eb5\u8f74\u7684\u8d21\u732e\u4f1a\u5f88\u5c0f\u3002<br \/> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/6843efe14f1543bc9ade0ae03e8faf37.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21 (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u5728\u8bba\u6587\u30108\u3011\u4e2d\u7ed9\u51fa\u4e86\u6bd4\u8f83\u76f4\u89c2\u7684\u63a8\u5bfc\u3002\u8fd9\u4e2a\u7b97\u6cd5\u662f\u57fa\u4e8e\u5bf9\u6570\u8c31\u7684\uff0c\u524d\u7aef\u7684\u6846\u56fe\u5982\u4e0b\uff1a<br \/> <img decoding=\"async\" src=\"https:\/\/img.mushiming.top\/app\/mushiming_com\/3da79104cad84eda878103a1fe43c844.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6211\u4eec\u53ea\u8bb0\u4f4f\u7ed3\u679c<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> Z \u2248 m a x ( X , Y ) Z\\approx max(X,Y) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2>Bayesian\u6982\u7387\u6a21\u578b<\/h2>\n<p>\u5bf9\u8d1d\u53f6\u65af\u7684\u7406\u89e3\u8fd8\u505c\u7559\u5728\u5927\u5b66\u7684\u8d1d\u53f6\u65af\u516c\u5f0f\u5c42\u9762\u4e0a\uff0c\u968f\u4fbf\u641c\u4e86\u4e00\u4e0b\uff0c\u4eff\u4f5b\u6253\u5f00\u4e86\u6f58\u591a\u62c9\u7684\u58a8\u76d2\uff0cbayesian statistics\u3001bayesian inference\u3001bayesian probability \u8fd8\u6709bayesian theorem\u7b49\u7b49\u6982\u5ff5\u5192\u51fa\u6765\uff0c\u5c31\u8fde\u8d1d\u53f6\u65af\u516c\u5f0f\u90fd\u8fd8\u6ca1\u641e\u660e\u767d\uff0c\u8fd9\u4e9b\u4e1c\u897f\u662f\u5565\u66f4\u52a0\u61f5\u903c\u4e86\u3002\u8bf4\u7b80\u5355\u70b9\u662f\u57fa\u4e8ebayesian\u6761\u4ef6\u6982\u7387\u516c\u5f0f\uff0c\u5f15\u5165\u7684\u4e00\u79cd\u5efa\u6a21\u5206\u6790\u65b9\u6cd5\uff0c\u5373\u5229\u7528\u5148\u9a8c\u77e5\u8bc6\uff0c\u907f\u514d\u968f\u4fbf\u778e\u731c\uff0c\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u5c31\u597d\u7406\u89e3\u4e3a\u4ec0\u4e48paper\u90fd\u8bf4GMM\u662fbayesian\u6982\u7387\u6a21\u578b\u4e86\uff0c\u5c31\u662f\u56e0\u4e3a\u4eba\u4eec\u5148\u9a8c\u5047\u8bbe\u4e86\u968f\u673a\u53d8\u91cf\u7b26\u5408\u6df7\u5408\u9ad8\u65af\u5206\u5e03\u7684\u7279\u70b9\uff0c\u8be6\u7ec6\u7684\u53c2\u8003\u6587\u6863\u6709\u5f88\u591a\u4ecb\u7ecd\uff0c\u5728\u566a\u58f0\u81ea\u9002\u5e94\u7684\u7b97\u6cd5\u91cc\uff0c\u8bed\u97f3\u7ecf\u8fc7\u77e2\u91cf\u91cf\u5316\uff0c\u5f97\u51fa\u7684\u9ad8\u7ef4\u6570\u636e\u901a\u8fc7\u8bad\u7ec3\uff08EM\/KNN\uff09\u6216\u8005\u901a\u8fc7\u5176\u4ed6\u624b\u6bb5\uff0c\u88abclassify\u6210\u4e3a\u6df7\u5408\u7684\u9ad8\u65af\u6a21\u578b\uff0c\u800c\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u7406\u89e3\u6210\u4e3a\u8d1d\u53f6\u65af\u65b9\u6cd5\uff0c\u6682\u65f6\u7406\u89e3\u8fd9\u4e48\u591a\u5c31\u591f\u4e86\u3002\u4e0a\u56fe\u7684\u6ce8\u811a\u4e5f\u6709\u6bd4\u8f83\u76f4\u89c2\u7684\u8bf4\u660e\u3002\u90a3\u5728\u8bed\u97f3\u8bc6\u522b\u6a21\u578b\u4e2d\u5982\u4f55\u548cbayesian\u6982\u7387\u6a21\u578b\u8054\u7cfb\u7684\u5462\uff1f\u6211\u4eec\u8ddf\u7740\u8bba\u6587\u30106\u3011\u7684\u8db3\u8ff9\u53bb\u63e3\u6d4b\u4e00\u4e0b\u4f5c\u8005\u7684\u5efa\u6a21\u601d\u8def\uff0c\u5728\u7406\u89e3\u8bba\u6587\u4e4b\u524d\uff0c\u5148\u5bf9\u6240\u8c13\u7684\u6807\u7b7e\u5668\uff08labeler\uff09\u505a\u4e9b\u94fa\u57ab\uff1a<\/p>\n<ul>\n<li>\u5047\u8bbe\u7ed9\u4f60\u4e00\u5f20\u5c0f\u72d7\u7684\u56fe\u7247\uff0c\u7ed9\u8fd9\u4e2a\u56fe\u7247\u6253\u4e2a\u201c\u5c0f\u72d7\u201d\u7684\u6807\u7b7e\u5f88\u5bb9\u6613\uff1b<\/li>\n<li>\u5982\u679c\u8ba9\u4f60\u6253\u4e2a\u662f\u201c\u67ef\u57fa\u72d7\u201d\u8fd8\u662f\u201c\u96ea\u6a47\u72ac\u201d\u7684\u6807\u7b7e\uff0c\u5c31\u9700\u8981\u4e00\u4e9b\u989d\u5916\u7684\u77e5\u8bc6\u4e86\uff0c\u800c\u5bf9\u4e8e\u54c1\u79cd\u76f8\u8fd1\u7684\u72d7\u72d7\uff0c\u4ece\u4e00\u5f20\u7167\u7247\u4e0a\u8bf4\u4ed6\u60f3\u8c01\u7684\u6982\u7387\u5927\u4e00\u4e9b\uff0c\u53ef\u80fd\u66f4\u5408\u9002\u3002\u8fd9\u65f6\u5019\u6807\u7b7e\u548c\u72d7\u72d7\u7684\u79cd\u7c7b\u5c31\u4e0d\u662f\u771f\u5b9e\u7684\u4e00\u4e00\u5bf9\u5e94\u4e86\uff0c\u4f1a\u51fa\u73b0\u504f\u5dee\uff1b<\/li>\n<li>\u5982\u679c\u51fa\u73b0100\u4e07\u5f20\u72d7\u72d7\u7684\u7167\u7247\uff08\u7167\u7247\u91cc\u8fd8\u6709\u732b\u548c\u9e2d\u5b50\u6ee5\u7afd\u5145\u6570\uff09\uff0c\u6309\u7167\u54c1\u79cd\u5206\u7c7b\u7684\u6807\u7b7e\u4f1a\u548c\u72d7\u72d7\u771f\u5b9e\u7684\u54c1\u79cd\u4e4b\u95f4\u5b58\u5728\u504f\u5dee\uff0c\u52a0\u5165\u6211\u628a\u7167\u7247\u63a8\u5411\u6d77\u91cf\u65e0\u7a77\u5927\uff0c\u8ba4\u4e3a\u7167\u7247\u4e2d\u6807\u7b7e\u51fa\u73b0\u7684\u6b21\u6570\u548c\u72d7\u72d7\u54c1\u79cd\u5728\u81ea\u7136\u754c\u4e2d\u5b58\u5728\u6570\u91cf\u7684\u6bd4\u91cd\u4f1a\u5448\u73b0\u4e00\u4e2a\u8054\u7cfb\uff0cok\u90a3\u4e48\u8fd9\u65f6\u5019\u5c31\u53ef\u4ee5\u8003\u8651\u4e24\u4e2a\u4e8b\u4ef6\u7684\u6709\u8da3\u5173\u7cfb\u4e86\uff1b<\/li>\n<li>\u901a\u5e38\u6807\u7b7e\u51fa\u73b0\u7684\u6b21\u6570\u4f5c\u4e3a\u7edf\u8ba1\u5b66\u610f\u4e49\u7684\u6982\u7387\uff0c\u6211\u4eec\u8bb0\u505a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i p_i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u4e3a\u67d0\u79cd\u72d7\u72d7\u7684\u54c1\u79cd\u3002<\/li>\n<li>\u72d7\u72d7\u771f\u5b9e\u7684\u5c5e\u4e8e\u54ea\u4e00\u4e2a\u7c7b\u522b\u65e0\u6cd5\u77e5\u9053\uff0c\u5c24\u5176\u5404\u79cd\u72d7\u72d7\u6742\u5c45\u5728\u4e00\u8d77\uff0c\u540e\u4ee3\u4eec\u4f60\u4e2d\u6709\u6211\uff0c\u6211\u4e2d\u6709\u4f60\u7684\uff0c\u600e\u4e48\u5b9a\u4e0b\u6765\u5462\uff1f\u4e8e\u662f\u62bd\u8840\u63d0\u53d6DNA\uff0c\u5229\u7528DNA\uff08\u5411\u91cf\uff09\u7247\u6bb5\u6765\u505a\u68c0\u9a8c\uff0c\u53ef\u4ee5\u628aDNA\u7247\u6bb5\u505a\u4e2a\u805a\u7c7b\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u7b97\u51fa\u67d0\u6bb5DNA\u548c\u54ea\u7c7bDNA\u7684\u76f8\u4f3c\u5ea6(\u6982\u7387)\uff0c\u6211\u4eec\u7528<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><\/span><\/span><\/span><\/span>\u8868\u793aDNA\u7279\u5f81\u5411\u91cf\uff0c\u800c\u5bf9\u6bcf\u4e00\u4e2a\u72d7\u72d7\u7684\u5177\u4f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x x <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">x<\/span><\/span><\/span><\/span><\/span>\u62bd\u517b\u503c\uff0c\u90fd\u9488\u5bf9\u4e8e\u6bcf\u4e00\u7c7b\u54c1\u79cd\uff0c\u6709\u4e00\u4e2a\u6982\u7387\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570\uff08\u8fd9\u4e2a\u53ef\u4e0d\u4e00\u5b9a\u662f\u9ad8\u65af\u7684\uff09<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> f i ( x ) f_i(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u7b80\u5355\u7684\u5224\u65ad\u662f\uff0c\u4e00\u7ef4\u9ad8\u65af\u60c5\u51b5\u4e0b\uff0c\u91c7\u6837\u503c\u79bb\u76f4\u65b9\u56fe\u5c16\u5cf0\u8d8a\u8fd1\uff0c\u5c31\u8d8a\u63a5\u8fd1\u8fd9\u4e2a\u7c7b\u522b\u3002<\/li>\n<li>\u6211\u4eec\u5e0c\u671b\u5229\u7528\u4e4b\u524d\u7167\u7247\u4e0a\u7684\u6807\u7b7e\uff08\u5916\u89c2\u7279\u5f81\uff09\u548c\u72d7\u72d7DNA\u7247\u6bb5\u6765\u7efc\u5408\u8bc4\u5b9a\u4e00\u4e0b\uff0c\u4e8e\u662f\u4e4e\u5c31\u5b9a\u4e49\u4e86\u8fd9\u4e2a\u8054\u5408\u5206\u5e03\u51fd\u6570<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> f ( x ) = \u2211 i = 1 k p i f i ( x ) f(x)=\\sum_{i=1}^kp_if_i(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.11378em; vertical-align: -1.27767em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.83611em;\"><span class=\"\" style=\"top: -1.87233em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p>\u6709\u4e86\u4e0a\u8ff0\u6807\u7b7e\u5668\u7684\u4e00\u4e9b\u80a4\u6d45\u7406\u89e3\uff0c\u6211\u4eec\u5728\u987a\u7740\u8bba\u6587\u7684\u601d\u8def\u6bd4\u8f83\u4e00\u4e0b\u3002<\/p>\n<ol>\n<li>\u9996\u5148\u5728\u7406\u60f3\u65e0\u566a\u58f0\u7684\u60c5\u51b5\u4e0b\uff0c\u5047\u8bbe\u8bed\u97f3\u7684\u539f\u578b\u5df2\u7ecf\u4e0d\u662f\u4e00\u4e2ad\u7ef4\u7b80\u5355\u7684\u77e2\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><\/span><\/span><\/span><\/span>\uff0c\u800c\u662f\u4e00\u4e2ad\u7ef4\u7a7a\u95f4\u5b9a\u4e49\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u539f\u59cb\u5e8f\u5217\u4e0d\u80fd\u89c2\u5bdf\uff0c\u6240\u4ee5\u4e00\u822c\u8ba4\u4e3a\u662f\u9690\u53d8\u91cf\u30106\u3011\uff0c\u8fd9\u91cc\u5b9a\u4e49\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I I <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><\/span><\/span><\/span><\/span>\uff0c\u53ef\u80fd\u503c\u4e3a\u4e00\u4e2a\u7f16\u7801\u7d22\u5f15\uff0c\u8fd9\u4e2a\u7f16\u7801\u7d22\u5f15\u4f5c\u4e3a\u539f\u578b\u5e8f\u5217\u7684\u6620\u5c04\u3002\u5373<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I = i I=i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\uff0c\u610f\u5473\u7740<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X = x X=x <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">x<\/span><\/span><\/span><\/span><\/span>\uff0c\u90a3\u4e48\u8fd9\u79cd\u6df7\u5408\u6a21\u578b\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><\/span><\/span><\/span><\/span>\u7684\u8fb9\u7f18\u5206\u5e03\u6765\u8868\u793a\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> f ( x ) = \u2211 i = 1 k p i f i ( x ) f(x)=\\sum_{i=1}^kp_if_i(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.11378em; vertical-align: -1.27767em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.83611em;\"><span class=\"\" style=\"top: -1.87233em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u5728\u7406\u60f3\u7684\u65e0\u566a\u58f0\u73af\u5883\u4e0b\uff0c\u9009\u5b9a\u6807\u7b7e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7b49\u4ef7\u4e8e\u6700\u5927\u5316\u6761\u4ef6\u6982\u7387<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( i \u2223 x ) p(i|x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u5f53\u9009\u5b9a\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X = x X=x <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">x<\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\uff0c\u8fd9\u5c31\u662f\u6240\u8c13\u7684MAP\u89e3\u7801<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> i = a r g m a x &nbsp; p ( j \u2223 x ) i=argmax\\ p(j|x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">a<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mspace\">&nbsp;<\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault\">j<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u91cc\u5176\u5b9e\u5df2\u7ecf\u544a\u8bc9\u8bfb\u8005\uff0c\u5efa\u6a21\u7684\u65b9\u6cd5\u5c31\u662f\u6784\u5efa\u4e00\u4e2a\u5f3a\u76f8\u5173\u7684\u6761\u4ef6\u6982\u7387\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> f i ( x ) f_i(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u6839\u636e\u8054\u5408\u6982\u7387\u8868\u793a\u7684\u6761\u4ef6\u6982\u7387\u5f62\u5f0f\uff0c<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> p ( i \u2223 x ) = p i f i ( x ) \u2211 j = 1 k p j f j ( x ) p(i|x)=\\frac{p_if_i(x)}{\\sum_{j=1}^kp_jf_j(x)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.74183em; vertical-align: -1.31483em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.12099em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.989008em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.435818em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.31483em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u4e2a\u5c31\u662f\u5728\u89c2\u6d4b\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x x <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">x<\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c\u5bf9\u5e94\u662f\u6807\u7b7e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7684\u6982\u7387<\/li>\n<li>\u5728\u6709\u566a\u58f0\u7684\u60c5\u51b5\u4e0b\uff0c\u51fa\u73b0\u4e86\u566a\u58f0\u53d8\u91cf\uff0c\u7528\u540c\u7ef4\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><\/span><\/span><\/span><\/span>\u6765\u8868\u793a\uff0c\u4f46\u662f\u6839\u636eHMM\u7406\u8bba\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \uff08 I , X , Y \uff09 \uff08I,X,Y\uff09 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mord cjk_fallback\">\uff09<\/span><\/span><\/span><\/span><\/span>\u90fd\u662f\u9690\u53d8\u91cf\uff0c\u662f\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5230\u7684\uff0c\u53ea\u80fd\u901a\u8fc7\u5e26\u566a\u7684\u89c2\u6d4b\u5411\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Z = \u03a8 ( X , Y ) Z=\\Psi(X,Y) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">\u03a8<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8fdb\u884c\u63a8\u7b97\u3002\u5982\u679c\u662f\u964d\u566a\uff0c\u4fa7\u91cd\u70b9\u5728\u4e8e\u5206\u5f00<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X , Y X,Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><\/span><\/span><\/span><\/span>\uff0c\u5982\u679c\u662f\u8bc6\u522b\u4fa7\u91cd\u70b9\u662f\u6c42\u51fa\u6700\u5927\u6982\u7387\u4e0b\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I I <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><\/span><\/span><\/span><\/span>\u503c\u3002\u6700\u5927\u6807\u7b7e\u5668\u65b9\u6cd5\u5c31\u662f\u901a\u8fc7\u89c2\u5bdf\uff0c\u5f97\u51fa<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a8 = M A X \\Psi=MAX <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u03a8<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.10903em;\" class=\"mord mathdefault\">M<\/span><span class=\"mord mathdefault\">A<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><\/span><\/span><\/span><\/span>\uff0c\u5728\u635f\u5931\u7cbe\u5ea6\u7684\u60c5\u51b5\u4e0b\uff08\u6982\u7387\u4ea7\u751f\u504f\u5dee\uff09\uff0c\u8ba9\u8fd0\u7b97\u53d8\u5f97\u975e\u5e38\u7b80\u5355\u3002<\/li>\n<li>\u4e0a\u9762\u8fd9\u6b65\u5316\u89e3\u4e86\u4e09\u4e2a\u9690\u53d8\u91cf\u7684\u590d\u6742\u5ea6\uff0c\u53ea\u7528<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \uff08 I , Z \uff09 \uff08I,Z\uff09 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mord cjk_fallback\">\uff09<\/span><\/span><\/span><\/span><\/span>\u6a21\u578b\u6765\u8bbe\u8ba1\u6761\u4ef6\u6982\u7387\u6a21\u578b\uff0c\u4eff\u7167\u7b2c\u4e00\u6b65\u518d\u6765\u4e00\u904d\uff0c\u9009\u5b9a\u6807\u7b7e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7b49\u4ef7\u4e8e\u6700\u5927\u5316\u6761\u4ef6\u6982\u7387<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q ( i \u2223 z ) q(i|z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u5f53\u9009\u5b9a\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X = z X=z <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\uff0c\u8fd9\u5c31\u662f\u6240\u8c13\u7684MAP\u89e3\u7801<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> i = a r g m a x &nbsp; q ( j \u2223 z ) i=argmax\\ q(j|z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">a<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord mathdefault\">a<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mspace\">&nbsp;<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault\">j<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q ( i \u2223 z ) q(i|z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4f5c\u4e3a\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Z = z Z=z <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><\/span><\/span><\/span><\/span>\u65f6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I = i I=i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\u6982\u7387\u516c\u5f0f<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> q ( i \u2223 z ) = p i h i ( z ) \u2211 j = 1 k p j h j ( z ) q(i|z)=\\frac{p_ih_i(z)}{\\sum_{j=1}^kp_jh_j(z)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.74183em; vertical-align: -1.31483em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em;\"><span class=\"\" style=\"top: -2.12099em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -0.000005em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.989008em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.03148em;\" class=\"mord mathdefault mtight\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.435818em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.05724em;\" class=\"mord mathdefault mtight\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.31483em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0a\u6587\u5173\u952e\u5c31\u662f\u8bbe\u8ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> h ( x ) h(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u76f8\u5bf9\u4e8e\u4e4b\u524d\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> f ( x ) f(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u8fd9\u4e2a\u66f4\u52a0\u96be\u4ee5\u6c42\u53d6\uff0c\u4f46\u6240\u6b32\u7684\u7b97\u6cd5\u90fd\u662f\u969c\u773c\u6cd5\uff0c\u94fa\u57ab\u4e86\u8fd9\u4e48\u591a\uff0c\u5c31\u662f\u4e3a\u4e86\u8ba9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> h ( x ) h(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e56\u4e56\u7684\u73b0\u5f62\u3002\u76f8\u5bf9\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> h ( x ) h(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">h<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8fd9\u79cd\u540e\u9a8c\u4fe1\u606f\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> f ( x ) f(x) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4f5c\u4e3a\u5148\u9a8c\u77e5\u8bc6\u53ef\u4ee5\u5229\u7528\u7edf\u8ba1\u6982\u7387\uff0c\u673a\u5668\u5b66\u4e60\u7b49\u65b9\u6cd5\u8fd1\u4f3c\u6c42\u5f97\uff08EM\/K-MEANS\uff09\uff0c\u5047\u8bbe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> d d <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">d<\/span><\/span><\/span><\/span><\/span>\u7ef4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><\/span><\/span><\/span><\/span>\u53d8\u91cf\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> f i ( x ) = \u220f m = 1 d f i , m ( x ( m ) ) f_i(x)=\\prod_{m=1}^d f_{i,m}(x(m)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.10323em; vertical-align: -1.26711em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.83611em;\"><span class=\"\" style=\"top: -1.88289em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u220f<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.26711em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u6309\u7167\u7c7b\u4f3c\u7684\u65b9\u6cd5\u5b9a\u4e49\u566a\u58f0\u7684\u8be5V\u9886\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> g ( x ) = \u220f m = 1 d g m ( y ( m ) ) g(x)=\\prod_{m=1}^d g_{m}(y(m)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.10323em; vertical-align: -1.26711em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.83611em;\"><span class=\"\" style=\"top: -1.88289em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u220f<\/span><\/span><\/span><span class=\"\" style=\"top: -4.30001em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.26711em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u8fdb\u4e00\u6b65\u7684\u5b9a\u4e49\u4e00\u4e2a\u5173\u4e8eX\u6982\u7387\u5206\u5e03\u51fd\u6570<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> F i , m ( x ) = P r o b { X ( m ) \u2a7d x \u2223 I = i } F_{i,m}(x)=Prob\\{X(m) \\leqslant x |I=i\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.13889em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span class=\"mord mathdefault\">o<\/span><span class=\"mord mathdefault\">b<\/span><span class=\"mopen\">{<br \/>\n        <!-- --><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">x<\/span><span class=\"mord\">\u2223<\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u662f\u4e00\u4e2a\u6761\u4ef6\u6982\u7387\uff0c\u5373<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I = i I=i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7684\u6761\u4ef6\u4e0b\uff0c\u53e6\u5916\u5173\u4e8e\u566a\u58f0Y\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> G m ( y ) = P r o b { Y ( m ) \u2a7d y } G_{m}(y)=Prob\\{Y(m) \\leqslant y\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span class=\"mord mathdefault\">o<\/span><span class=\"mord mathdefault\">b<\/span><span class=\"mopen\">{<br \/>\n        <!-- --><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">y<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/span>\u4ee5\u53ca\u53d7\u566a\u8bed\u97f3Z\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> H i , m ( z ) = P r o b { Z ( m ) \u2a7d z } H_{i,m}(z)=Prob\\{Z(m) \\leqslant z\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.08125em;\" class=\"mord mathdefault\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.08125em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span class=\"mord mathdefault\">o<\/span><span class=\"mord mathdefault\">b<\/span><span class=\"mopen\">{<br \/>\n        <!-- --><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/span>\u8fd9\u91cc\u7528X\u7684\u7d2f\u8ba1\u8fb9\u7f18\u5206\u5e03\u8fd8\u662f\u6709\u5f85\u63a8\u6572\uff0c\u5047\u5b9a\u8fd9\u4e2a\u7406\u8bba\u6b63\u786e\u7684\u524d\u63d0\u4e0b\uff0c\u7ee7\u7eed\u8003\u8651\u6761\u4ef6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> I = i I=i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">I<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\u63a8\u5bfc\u5982\u4e0b\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> H i , m ( z ) = P r o b { Z ( m ) \u2a7d z } = P r o b { X ( m ) \u2a7d z , Y ( m ) \u2a7d z } = F i , m ( z ) G m ( z ) H_{i,m}(z)=Prob\\{Z(m) \\leqslant z\\}\\\\=Prob\\{X(m) \\leqslant z,Y(m) \\leqslant z \\}\\\\=F_{i,m}(z)G_{m}(z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.08125em;\" class=\"mord mathdefault\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.08125em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span class=\"mord mathdefault\">o<\/span><span class=\"mord mathdefault\">b<\/span><span class=\"mopen\">{<br \/>\n        <!-- --><\/span><span style=\"margin-right: 0.07153em;\" class=\"mord mathdefault\">Z<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">P<\/span><span style=\"margin-right: 0.02778em;\" class=\"mord mathdefault\">r<\/span><span class=\"mord mathdefault\">o<\/span><span class=\"mord mathdefault\">b<\/span><span class=\"mopen\">{<br \/>\n        <!-- --><\/span><span style=\"margin-right: 0.07847em;\" class=\"mord mathdefault\">X<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span style=\"margin-right: 0.22222em;\" class=\"mord mathdefault\">Y<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.13889em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5bf9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> H i , m ( z ) H_{i,m}(z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.08125em;\" class=\"mord mathdefault\">H<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.08125em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u6c42<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> z z <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><\/span><\/span><\/span><\/span>\u7684\u504f\u5bfc\u6570\uff0c\u6700\u540e\u56de\u63a8\u51fa\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u4e2a\u6807\u7b7e\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> h i , m ( z ) = f i , m ( z ) G m ( z ) + F i , m ( z ) g m ( z ) h_{i,m}(z)=f_{i,m}(z)G_m(z)+F_{i,m}(z)g_m(z) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.10764em;\" class=\"mord mathdefault\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.10764em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.13889em;\" class=\"mord mathdefault\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.13889em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span style=\"margin-right: 0.03588em;\" class=\"mord mathdefault\">g<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span style=\"margin-right: 0.04398em;\" class=\"mord mathdefault\">z<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u540e\u9a8c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u5c31\u8fd9\u6837\u88ab\u5148\u9a8c\u7684\u65b9\u6cd5\u6c42\u5f97\u4e86\uff0c\u800c\u5148\u9a8c\u7684\u5bc6\u5ea6\u51fd\u6570\u901a\u5e38\u6309\u7167\u7edf\u8ba1\u65b9\u6cd5\uff0c\u5047\u8bbe\u4e3a\u6df7\u5408\u9ad8\u65af\u6a21\u578b\u3002<\/li>\n<\/ol>\n<h2>\u7ed3\u8bed<\/h2>\n<p>\u81f3\u6b64\uff0cMIXMAX\u6982\u7387\u6a21\u578b\u63a8\u5bfc\u89e3\u6790\u5b8c\u6bd5\uff0c\u8fd9\u4e2a\u6a21\u578b\u5177\u6709\u566a\u58f0\u81ea\u9002\u5e94\u7684\u7279\u70b9\uff0c\u8fd0\u7b97\u590d\u6742\u5ea6\u4e5f\u4e0d\u9ad8\uff0c\u8fd8\u662f\u5f88\u6709\u4ef7\u503c\u7684\u3002\u6709\u5174\u8da3\u7684\u53ef\u4ee5\u60f3\u8c61\u8fd9\u4e9b\u63a8\u5bfc\u5982\u4f55\u4e0e\u90a3\u5f20beyasian\u7684\u6807\u6ce8\u6765\u5bf9\u5e94\u3002<\/p>\n<h2>\u53c2\u8003\u6587\u6863<\/h2>\n<p>1.\u8d1d\u53f6\u65af\u65b9\u6cd5\u6982\u8981\u4e0e\u53d8\u5206\u63a8\u65ad<br \/> 2.\u77e5\u8bc6\u5206\u4eab-\u8d1d\u53f6\u65af\u6a21\u578b\u601d\u60f3\u4e0e\u5b9e\u6218<br \/> 3.\u53c2\u6570\u4f30\u8ba1\u65b9\u6cd5\u7b80\u8bba\uff08\u8d1d\u53f6\u65af\u4f30\u8ba1\u3001\u6700\u5927\u540e\u9a8c\u6982\u7387\u4f30\u8ba1\u3001\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\uff09<br \/> 4.Materials of the Summer school on Deep learning and Bayesian methods 2019<br \/> 5.EM\u7b97\u6cd5\u8be6\u89e3<br \/> 6.SPEECH RECOGNITION USING NOISE-ADAPTIVE PROTOTYPES\uff0c Arthur Nadas,<br \/> 7.Continuous Speech Recognition with Autolnaticdly Selected Acoustic Prototypes Obtained by either Bootstrapping or Clustering, Nadas,<br \/> 8.Speech Enhancement Using a Mixture Maximum Model\uff0cDavid Burshtein,<\/p>\n","protected":false},"excerpt":{"rendered":"\u600e\u4e48\u5efa\u6a21_3dmax\u5efa\u6a21MIXMAX\u6982\u7387\u6a21\u578b\u7406\u89e3\u50a8\u5907\u77e5\u8bc6HMM-\u9690\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff08HiddenMarkovModel\uff09GMM-\u6df7\u5408\u9ad8\u65af\u6a21\u578b\u591a\u5143\u9ad8\u65af\u5206\u5e03\uff08TheM...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8529"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=8529"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/8529\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=8529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=8529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=8529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}