{"id":340,"date":"2022-07-12T15:09:35","date_gmt":"2022-07-12T07:09:35","guid":{"rendered":"https:\/\/www.lazybirds.top\/?p=340"},"modified":"2022-07-12T15:09:35","modified_gmt":"2022-07-12T07:09:35","slug":"d2l%e8%87%aa%e5%ad%a6%e7%ac%94%e8%ae%b0-4-%e5%a4%9a%e5%b1%82%e6%84%9f%e7%9f%a5%e6%9c%ba","status":"publish","type":"post","link":"https:\/\/www.lazybirds.top\/?p=340","title":{"rendered":"d2l\u81ea\u5b66\u7b14\u8bb0 &#8211; 4.\u591a\u5c42\u611f\u77e5\u673a"},"content":{"rendered":"\n<p><a href=\"https:\/\/zh.d2l.ai\/\">\u300a\u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60\u300b \u2014 \u52a8\u624b\u5b66\u6df1\u5ea6\u5b66\u4e60 2.0.0-beta0 documentation (d2l.ai)<\/a><\/p>\n\n\n\n<!--more-->\n\n\n\n      <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n      \n      <link rel=\"stylesheet\" href=\"https:\/\/www.lazybirds.top\/katex\/katex.min.css\">\n      \n      \n      \n      \n      \n      \n      \n      \n      \n      <style>\n      \/**\n * prism.js 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class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"sigmoid%E5%87%BD%E6%95%B0%E5%8F%88%E7%A7%B0squashing-function-%E6%8C%A4%E5%8E%8B%E5%87%BD%E6%95%B0\">sigmoid&#x51FD;&#x6570;&#xFF08;&#x53C8;&#x79F0;squashing function, &#x6324;&#x538B;&#x51FD;&#x6570;&#xFF09;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">sigmoid<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\operatorname{sigmoid}(x)=\\frac{1}{1+e^{-x}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\"><span class=\"mord mathrm\">sigmoid<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.0908em;vertical-align:-0.7693em;\"><\/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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6973em;\"><span style=\"top:-2.989em;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 mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"tanh%E5%87%BD%E6%95%B0%E5%8F%8C%E6%9B%B2%E6%AD%A3%E5%88%87%E5%87%BD%E6%95%B0\">tanh&#x51FD;&#x6570;&#xFF08;&#x53CC;&#x66F2;&#x6B63;&#x5207;&#x51FD;&#x6570;&#xFF09;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">tanh<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><msup><mi>e<\/mi><mi>x<\/mi><\/msup><mo>&#x2212;<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>x<\/mi><\/mrow><\/msup><\/mrow><mrow><msup><mi>e<\/mi><mi>x<\/mi><\/msup><mo>+<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>1<\/mn><mo>&#x2212;<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mn>2<\/mn><mi>x<\/mi><\/mrow><\/msup><\/mrow><mrow><mn>1<\/mn><mo>+<\/mo><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mn>2<\/mn><mi>x<\/mi><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\operatorname{tanh}(x)=\\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}=\\frac{1-e^{-2x}}{1+e^{-2x}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\"><span class=\"mord mathrm\">tanh<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.2177em;vertical-align:-0.7693em;\"><\/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:1.4483em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.5904em;\"><span style=\"top:-2.989em;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 mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6973em;\"><span style=\"top:-2.989em;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 mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6644em;\"><span 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 mtight\"><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.2604em;vertical-align:-0.7693em;\"><\/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:1.4911em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7401em;\"><span style=\"top:-2.989em;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 mtight\">&#x2212;<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">2<\/span><span class=\"mord mathnormal mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x5F62;&#x72B6;&#x7C7B;&#x4F3C;sigmoid&#x51FD;&#x6570;&#xFF0C;&#x4E0D;&#x540C;&#x7684;&#x662F;tanh&#x51FD;&#x6570;&#x5173;&#x4E8E;&#x5750;&#x6807;&#x7CFB;&#x539F;&#x70B9;&#x4E2D;&#x5FC3;&#x5BF9;&#x79F0;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E6%A8%A1%E5%9E%8B%E4%B8%8E%E6%A8%A1%E5%9E%8B%E5%8F%82%E6%95%B0%E7%9A%84%E5%88%9D%E5%A7%8B%E5%8C%96\">&#x6A21;&#x578B;&#x4E0E;&#x6A21;&#x578B;&#x53C2;&#x6570;&#x7684;&#x521D;&#x59CB;&#x5316;<\/h2>\n\n<p>&#x901A;&#x5E38;&#x9009;&#x62E9;2&#x7684;&#x6B21;&#x5E42;&#x4F5C;&#x4E3A;&#x5C42;&#x7684;&#x5BBD;&#x5EA6;&#xFF0C;&#x4EE5;&#x4FBF;&#x5185;&#x5B58;&#x5206;&#x914D;&#x4E0E;&#x5BFB;&#x5740;&#x3002;<\/p>\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">num_inputs<span class=\"token punctuation\">,<\/span> num_outputs<span class=\"token punctuation\">,<\/span> num_hiddens <span class=\"token operator\">=<\/span> <span class=\"token number\">784<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">256<\/span>\n\nW1 <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>\n    num_inputs<span class=\"token punctuation\">,<\/span> num_hiddens<span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">=<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span>\nb1 <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span>num_hiddens<span class=\"token punctuation\">,<\/span> \nrequires_grad<span class=\"token operator\">=<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>\nW2 <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>randn<span class=\"token punctuation\">(<\/span>\n    num_hiddens<span class=\"token punctuation\">,<\/span> num_outputs<span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">=<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span>\nb2 <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Parameter<span class=\"token punctuation\">(<\/span>torch<span class=\"token punctuation\">.<\/span>zeros<span class=\"token punctuation\">(<\/span>num_outputs<span class=\"token punctuation\">,<\/span> requires_grad<span class=\"token operator\">=<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>\n\n<span class=\"token keyword keyword-def\">def<\/span> <span class=\"token function\">relu<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span>\n    <span class=\"token keyword keyword-return\">return<\/span> torch<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> torch<span class=\"token punctuation\">.<\/span>zeros_like<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>\n\n<span class=\"token keyword keyword-def\">def<\/span> <span class=\"token function\">net<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span>\n    X <span class=\"token operator\">=<\/span> X<span class=\"token punctuation\">.<\/span>reshape<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> num_inputs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>\n    H <span class=\"token operator\">=<\/span> relu<span class=\"token punctuation\">(<\/span>X@W1 <span class=\"token operator\">+<\/span> b1<span class=\"token punctuation\">)<\/span>\n    <span class=\"token keyword keyword-return\">return<\/span> <span class=\"token punctuation\">(<\/span>H@W2 <span class=\"token operator\">+<\/span> b2<span class=\"token punctuation\">)<\/span>\n<\/pre><p>&#x6216;&#x8005;&#x4F7F;&#x7528;&#x9AD8;&#x7EA7;API<\/p>\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">net <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>nn<span class=\"token punctuation\">.<\/span>Flatten<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>num_inputs<span class=\"token punctuation\">,<\/span> num_hiddens<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>ReLU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span>num_hiddens<span class=\"token punctuation\">,<\/span> num_outputs<span class=\"token punctuation\">)<\/span>\n<span class=\"token punctuation\">)<\/span>\n\n<span class=\"token keyword keyword-def\">def<\/span> <span class=\"token function\">init_weights<\/span><span class=\"token punctuation\">(<\/span>m<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span>\n    <span class=\"token keyword keyword-if\">if<\/span> <span class=\"token builtin\">type<\/span><span class=\"token punctuation\">(<\/span>m<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">==<\/span> nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">:<\/span>\n        nn<span class=\"token punctuation\">.<\/span>init<span class=\"token punctuation\">.<\/span>normal_<span class=\"token punctuation\">(<\/span>m<span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> std<span class=\"token operator\">=<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span>\n\nnet<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">apply<\/span><span class=\"token punctuation\">(<\/span>init_weights<span class=\"token punctuation\">)<\/span>\n<\/pre><h1 class=\"mume-header\" id=\"%E6%A8%A1%E5%9E%8B%E9%80%89%E6%8B%A9-%E6%AC%A0%E6%8B%9F%E5%90%88%E4%B8%8E%E8%BF%87%E6%8B%9F%E5%90%88\">&#x6A21;&#x578B;&#x9009;&#x62E9;&#x3001;&#x6B20;&#x62DF;&#x5408;&#x4E0E;&#x8FC7;&#x62DF;&#x5408;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5-1\">&#x57FA;&#x672C;&#x6982;&#x5FF5;<\/h2>\n\n<ul>\n<li>&#x6A21;&#x5F0F;&#xFF08;pattern&#xFF09;<br>\n&#x76EE;&#x6807;&#xFF1A;&#x53D1;&#x73B0;&#x53CD;&#x5E94;&#x8BAD;&#x7EC3;&#x96C6;&#x6F5C;&#x5728;&#x603B;&#x4F53;&#x89C4;&#x5F8B;&#x7684;&#x6A21;&#x5F0F;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>&#x2192;<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\rightarrow<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.3669em;\"><\/span><span class=\"mrel\">&#x2192;<\/span><\/span><\/span><\/span>&#x6CDB;&#x5316;&#x80FD;&#x529B;<\/li>\n<li>&#x6B20;&#x62DF;&#x5408;&#xFF08;underfitting&#xFF09;<\/li>\n<li>&#x8FC7;&#x62DF;&#x5408;&#xFF08;overfitting&#xFF09;<br>\n&#x6B63;&#x5219;&#x5316;&#xFF08;regularization&#xFF09;&#xFF1A;&#x7528;&#x4E8E;&#x5BF9;&#x6297;&#x8FC7;&#x62DF;&#x5408;&#x7684;&#x6280;&#x672F;<\/li>\n<li>&#x8BAD;&#x7EC3;&#x8BEF;&#x5DEE;&#xFF08;training error&#xFF09;<\/li>\n<li>&#x6CDB;&#x5316;&#x8BEF;&#x5DEE;&#xFF08;generalization error&#xFF09;<\/li>\n<li>&#x8BAD;&#x7EC3;&#x96C6;&#xFF08;train&#xFF09; &#8211; &#x9A8C;&#x8BC1;&#x96C6;&#xFF08;validation&#xFF09; &#8211;  &#x6D4B;&#x8BD5;&#x96C6;&#xFF08;test&#xFF09;<\/li>\n<\/ul>\n<blockquote>\n<p>&#x8BAD;&#x7EC3;&#x96C6;&#x7528;&#x6765;&#x4F30;&#x8BA1;&#x6A21;&#x578B;&#xFF0C;<br>\n&#x9A8C;&#x8BC1;&#x96C6;&#x7528;&#x6765;&#x786E;&#x5B9A;&#x7F51;&#x7EDC;&#x7ED3;&#x6784;&#x6216;&#x8005;&#x63A7;&#x5236;&#x6A21;&#x578B;&#x590D;&#x6742;&#x7A0B;&#x5EA6;&#x7684;&#x53C2;&#x6570;&#xFF0C;<br>\n&#x6D4B;&#x8BD5;&#x96C6;&#x7528;&#x6765;&#x68C0;&#x9A8C;&#x6700;&#x7EC8;&#x9009;&#x62E9;&#x6700;&#x4F18;&#x7684;&#x6A21;&#x578B;&#x7684;&#x6027;&#x80FD;&#x5982;&#x4F55;&#x3002;<\/p>\n<\/blockquote>\n<h2 class=\"mume-header\" id=\"%E5%BD%B1%E5%93%8D%E6%A8%A1%E5%9E%8B%E6%B3%9B%E5%8C%96%E7%9A%84%E5%9B%A0%E7%B4%A0\">&#x5F71;&#x54CD;&#x6A21;&#x578B;&#x6CDB;&#x5316;&#x7684;&#x56E0;&#x7D20;<\/h2>\n\n<ol>\n<li>&#x53EF;&#x8C03;&#x6574;&#x53C2;&#x6570;&#x7684;&#x6570;&#x91CF;<\/li>\n<li>&#x53C2;&#x6570;&#x91C7;&#x7528;&#x7684;&#x503C;&#xFF08;&#x6743;&#x91CD;&#x53D6;&#x503C;&#x8303;&#x56F4;&#x8F83;&#x5927;&#x65F6;&#xFF0C;&#x6A21;&#x578B;&#x53EF;&#x80FD;&#x66F4;&#x5BB9;&#x6613;&#x8FC7;&#x62DF;&#x5408;&#xFF09;<\/li>\n<li>&#x8BAD;&#x7EC3;&#x6837;&#x672C;&#x7684;&#x6570;&#x91CF;<\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"k%E6%8A%98%E4%BA%A4%E5%8F%89%E9%AA%8C%E8%AF%81\">K&#x6298;&#x4EA4;&#x53C9;&#x9A8C;&#x8BC1;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E4%B8%BA%E4%BB%80%E4%B9%88\">&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/h3>\n\n<p>&#x6709;&#x65F6;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x7A00;&#x7F3A;&#xFF0C;&#x53EF;&#x80FD;&#x65E0;&#x6CD5;&#x63D0;&#x4F9B;&#x8DB3;&#x591F;&#x6570;&#x636E;&#x6765;&#x6784;&#x6210;&#x4E00;&#x4E2A;&#x5408;&#x9002;&#x7684;&#x9A8C;&#x8BC1;&#x96C6;&#x3002;&#x6B64;&#x65F6;&#x901A;&#x5E38;&#x4F1A;&#x4F7F;&#x7528;K&#x6298;&#x4EA4;&#x53C9;&#x9A8C;&#x8BC1;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E6%98%AF%E4%BB%80%E4%B9%88\">&#x662F;&#x4EC0;&#x4E48;&#xFF1F;<\/h3>\n\n<p>&#x5C06;&#x539F;&#x59CB;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x5206;&#x6210;K&#x4E2A;&#x65E0;&#x4EA4;&#x96C6;&#xFF0C;&#x7136;&#x540E;&#x6267;&#x884C;K&#x6B21;&#x6A21;&#x578B;&#x8BAD;&#x7EC3;&#x548C;&#x9A8C;&#x8BC1;&#x3002;&#x6BCF;&#x6B21;&#x5728;K-1&#x4E2A;&#x5B50;&#x96C6;&#x4E0A;&#x8BAD;&#x7EC3;&#xFF0C;&#x6700;&#x540E;&#x4E00;&#x4E2A;&#x5B50;&#x96C6;&#x7528;&#x6765;&#x9A8C;&#x8BC1;&#x3002;<\/p>\n<p>&#x6700;&#x540E;&#xFF0C;&#x901A;&#x8FC7;&#x5BF9;K&#x6B21;&#x5B9E;&#x9A8C;&#x7684;&#x7ED3;&#x679C;&#x53D6;&#x5E73;&#x5747;&#x6765;&#x4F30;&#x8BA1;&#x8BAD;&#x7EC3;&#x548C;&#x9A8C;&#x8BC1;&#x8BEF;&#x5DEE;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E6%9D%83%E9%87%8D%E8%A1%B0%E5%87%8Fweight-decay-l_2%E6%AD%A3%E5%88%99%E5%8C%96\">&#x6743;&#x91CD;&#x8870;&#x51CF;&#xFF08;weight decay, <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x6B63;&#x5219;&#x5316;&#xFF09;<\/h2>\n\n<p>&#x7F13;&#x89E3;&#x8FC7;&#x62DF;&#x5408;&#xFF1A;<\/p>\n<ol>\n<li>&#x9650;&#x5236;&#x7279;&#x5F81;&#x6570;&#x91CF;<\/li>\n<li>&#x9650;&#x5236;&#x6A21;&#x578B;&#x53C2;&#x6570;&#x9009;&#x62E9;&#x8303;&#x56F4;<\/li>\n<\/ol>\n<p>&#x6743;&#x91CD;&#x8870;&#x51CF;&#x662F;&#x4E00;&#x79CD;&#x5E7F;&#x6CDB;&#x4F7F;&#x7528;&#x7684;&#x6B63;&#x5219;&#x5316;&#x6280;&#x672F;&#x3002;<\/p>\n<p>&#x901A;&#x8FC7;&#x51FD;&#x6570;&#x4E0E;&#x96F6;&#x7684;&#x8DDD;&#x79BB;&#xFF08;&#x8303;&#x6570;&#xFF09;&#x6765;&#x8861;&#x91CF;&#x51FD;&#x6570;&#x7684;&#x590D;&#x6742;&#x5EA6;&#x3002;&#x5C06;&#x51FD;&#x6570;&#x590D;&#x6742;&#x5EA6;&#x4F5C;&#x4E3A;&#x60E9;&#x7F5A;&#x9879;&#x52A0;&#x5230;&#x6700;&#x5C0F;&#x5316;&#x635F;&#x5931;&#x7684;&#x95EE;&#x9898;&#x4E2D;&#xFF0C;&#x4EE5;&#x4FDD;&#x8BC1;&#x6743;&#x91CD;&#x5411;&#x91CF;&#x6BD4;&#x8F83;&#x5C11;&#x3002;&#x65B0;&#x7684;&#x635F;&#x5931;&#x51FD;&#x6570;&#x53EF;&#x4EE5;&#x5199;&#x505A;&#xFF1A;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>L<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">w<\/mi><mo separator=\"true\">,<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mfrac><mi>&#x3BB;<\/mi><mn>2<\/mn><\/mfrac><mi mathvariant=\"normal\">&#x2225;<\/mi><mi mathvariant=\"bold\">w<\/mi><msup><mi mathvariant=\"normal\">&#x2225;<\/mi><mn>2<\/mn><\/msup><mspace linebreak=\"newline\"><\/mspace><mi mathvariant=\"bold\">w<\/mi><mo>&#x2190;<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>&#x3B7;<\/mi><mi>&#x3BB;<\/mi><mo stretchy=\"false\">)<\/mo><mi mathvariant=\"bold\">w<\/mi><mo>&#x2212;<\/mo><mfrac><mi>&#x3B7;<\/mi><mrow><mi mathvariant=\"normal\">&#x2223;<\/mi><mi mathvariant=\"script\">B<\/mi><mi mathvariant=\"normal\">&#x2223;<\/mi><\/mrow><\/mfrac><munder><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>&#x2208;<\/mo><mi>B<\/mi><\/mrow><\/munder><msup><mi mathvariant=\"bold\">x<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mrow><mo fence=\"true\">(<\/mo><msup><mi mathvariant=\"bold\">w<\/mi><mi mathvariant=\"normal\">&#x22A4;<\/mi><\/msup><msup><mi mathvariant=\"bold\">x<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mo>+<\/mo><mi>b<\/mi><mo>&#x2212;<\/mo><msup><mi>y<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">L(\\mathbf{w}, b)+\\frac{\\lambda}{2}\\|\\mathbf{w}\\|^{2}\n\\\\\n\\mathbf{w} \\leftarrow(1-\\eta \\lambda) \\mathbf{w}-\\frac{\\eta}{|\\mathcal{B}|} \\sum_{i \\in B} \\mathbf{x}^{(i)}\\left(\\mathbf{w}^{\\top} \\mathbf{x}^{(i)}+b-y^{(i)}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">w<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.0574em;vertical-align:-0.686em;\"><\/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:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">&#x2225;<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">w<\/span><span class=\"mord\"><span class=\"mord\">&#x2225;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span 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 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.4444em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">w<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2190;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3B7;<\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">w<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.4717em;vertical-align:-1.3217em;\"><\/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:1.1076em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">&#x2223;<\/span><span class=\"mord mathcal\" style=\"margin-right:0.03041em;\">B<\/span><span class=\"mord\">&#x2223;<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3B7;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.05em;\"><span style=\"top:-1.8557em;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 mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#x2208;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05017em;\">B<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3217em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x22A4;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3BB;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\">&#x3BB;<\/span><\/span><\/span><\/span>&#x4E3A;&#x6B63;&#x5219;&#x5316;&#x5E38;&#x6570;&#xFF0C;&#x662F;&#x4E00;&#x4E2A;&#x975E;&#x8D1F;&#x8D85;&#x53C2;&#x6570;&#x3002;<\/p>\n<p>&#x8FD9;&#x91CC;&#x4F7F;&#x7528;&#x4E86;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x8303;&#x6570;&#xFF0C;&#x800C;&#x975E;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>1<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x8303;&#x6570;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"l_2%E6%AD%A3%E5%88%99%E5%8C%96%E7%BA%BF%E6%80%A7%E6%A8%A1%E5%9E%8B%E5%B2%AD%E5%9B%9E%E5%BD%92ridge-regression\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x6B63;&#x5219;&#x5316;&#x7EBF;&#x6027;&#x6A21;&#x578B;&#xFF1A;&#x5CAD;&#x56DE;&#x5F52;&#xFF08;ridge regression&#xFF09;<\/h3>\n\n<p><img src=\"https:\/\/i0.wp.com\/pic3.zhimg.com\/80\/v2-a13db3079fd191c00150eec088c1530e_1440w.jpg?w=840&#038;ssl=1\" alt data-recalc-dims=\"1\"><\/p>\n<ul>\n<li>&#x5BF9;&#x6743;&#x91CD;&#x5411;&#x91CF;&#x7684;&#x5927;&#x5206;&#x91CF;&#x65BD;&#x52A0;&#x4E86;&#x5DE8;&#x5927;&#x7684;&#x4E58;&#x6CD5;<\/li>\n<li>&#x504F;&#x5411;&#x4E8E;&#x5728;&#x5927;&#x91CF;&#x7279;&#x5F81;&#x4E0A;&#x5747;&#x5300;&#x5206;&#x5E03;&#x6743;&#x91CD;&#x7684;&#x6A21;&#x578B;<\/li>\n<li>&#x53EF;&#x80FD;&#x4F7F;&#x5BF9;&#x5355;&#x4E2A;&#x53D8;&#x91CF;&#x7684;&#x89C2;&#x6D4B;&#x8BEF;&#x5DEE;&#x66F4;&#x7A33;&#x5B9A;&#xFF08;<mark>&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/mark>&#xFF09;<\/li>\n<\/ul>\n<h3 class=\"mume-header\" id=\"l_1%E6%AD%A3%E5%88%99%E5%8C%96%E7%BA%BF%E6%80%A7%E6%A8%A1%E5%9E%8B%E5%A5%97%E7%B4%A2%E5%9B%9E%E5%BD%92lasso-regression\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>1<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x6B63;&#x5219;&#x5316;&#x7EBF;&#x6027;&#x6A21;&#x578B;&#xFF1A;&#x5957;&#x7D22;&#x56DE;&#x5F52;&#xFF08;lasso regression&#xFF09;<\/h3>\n\n<p><img src=\"https:\/\/i0.wp.com\/pic2.zhimg.com\/80\/v2-e16c01b5088ed0e6dc37833002e7b769_1440w.jpg?w=840&#038;ssl=1\" alt data-recalc-dims=\"1\"><\/p>\n<ul>\n<li>&#x6743;&#x91CD;&#x96C6;&#x4E2D;&#x4E8E;&#x4E00;&#x5C0F;&#x90E8;&#x5206;&#x7279;&#x5F81;<\/li>\n<li>&#x5176;&#x4ED6;&#x6743;&#x91CD;&#x6E05;&#x96F6;&#xFF08;&#x53EF;&#x4EE5;&#x4ECE;&#x56FE;&#x4E2D;&#x84DD;&#x8272;&#x65B9;&#x5F62;&#x4E0E;&#x7EA2;&#x8272;&#x692D;&#x5706;&#x7684;&#x4EA4;&#x70B9;&#x770B;&#x51FA;&#xFF09;<\/li>\n<li>&#x5177;&#x6709;&#x7279;&#x5F81;&#x9009;&#x62E9;&#xFF08;feature selection&#xFF09;&#x7684;&#x80FD;&#x529B;<\/li>\n<\/ul>\n<p>&#x56FE;&#x7247;&#x6765;&#x6E90;&#x53CA;&#x8BE6;&#x7EC6;&#x89E3;&#x91CA;&#x53C2;&#x89C1;<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/30535220\">&#x673A;&#x5668;&#x5B66;&#x4E60;&#x7B97;&#x6CD5;&#x5B9E;&#x8DF5;-&#x5CAD;&#x56DE;&#x5F52;&#x548C;LASSO &#8211; &#x77E5;&#x4E4E;<\/a><\/p>\n<h3 class=\"mume-header\" id=\"%E6%9D%83%E9%87%8D%E8%A1%B0%E5%87%8F%E7%9A%84%E5%AE%9E%E7%8E%B0\">&#x6743;&#x91CD;&#x8870;&#x51CF;&#x7684;&#x5B9E;&#x73B0;<\/h3>\n\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">trainer <span class=\"token operator\">=<\/span> torch<span class=\"token punctuation\">.<\/span>optim<span class=\"token punctuation\">.<\/span>SGD<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span>\n    <span class=\"token punctuation\">{<\/span><span class=\"token string\">&apos;params&apos;<\/span><span class=\"token punctuation\">:<\/span> net<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>weight<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&apos;weight_decay&apos;<\/span><span class=\"token punctuation\">:<\/span> wd<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span>\n    <span class=\"token punctuation\">{<\/span><span class=\"token string\">&apos;params&apos;<\/span><span class=\"token punctuation\">:<\/span> net<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>bias<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> lr<span class=\"token operator\">=<\/span>lr<span class=\"token punctuation\">)<\/span>\n<\/pre><h2 class=\"mume-header\" id=\"%E6%9A%82%E9%80%80%E6%B3%95dropout\">&#x6682;&#x9000;&#x6CD5;&#xFF08;Dropout&#xFF09;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E4%B8%BA%E4%BB%80%E4%B9%88-1\">&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/h3>\n\n<p>&#x907F;&#x514D;&#x8FC7;&#x62DF;&#x5408;<\/p>\n<h3 class=\"mume-header\" id=\"%E6%98%AF%E4%BB%80%E4%B9%88-1\">&#x662F;&#x4EC0;&#x4E48;&#xFF1F;<\/h3>\n\n<p>&#x5728;&#x524D;&#x9879;&#x4F20;&#x64AD;&#x8FC7;&#x7A0B;&#x4E2D;&#xFF0C;&#x8BA1;&#x7B97;&#x6BCF;&#x4E00;&#x5185;&#x90E8;&#x5C42;&#x7684;&#x540C;&#x65F6;&#x6CE8;&#x5165;&#x566A;&#x58F0;&#x3002;&#x4ECE;&#x8868;&#x9762;&#x4E0A;&#x770B;&#x662F;&#x5728;&#x8BAD;&#x7EC3;&#x8FC7;&#x7A0B;&#x4E2D;&#x4E22;&#x5F03;&#xFF08;dropout&#xFF09;&#x4E00;&#x4E9B;&#x795E;&#x7ECF;&#x5143;&#x3002;<\/p>\n<p>&#x5728;&#x6807;&#x51C6;&#x6682;&#x9000;&#x6CD5;&#x6B63;&#x5219;&#x5316;&#x4E2D;&#xFF0C;&#x6BCF;&#x4E2A;&#x4E2D;&#x95F4;&#x6D3B;&#x6027;&#x503C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">h<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><\/span><\/span>&#x4EE5;&#x6682;&#x9000;&#x6982;&#x7387;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>&#x7531;&#x968F;&#x673A;&#x53D8;&#x91CF;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>h<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">h&apos;<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.7519em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x66FF;&#x6362;&#xFF0C;&#x540C;&#x65F6;&#x671F;&#x671B;&#x503C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo stretchy=\"false\">[<\/mo><msup><mi>h<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo stretchy=\"false\">]<\/mo><mo>=<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E[h&apos;]=h<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.0019em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7519em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><\/span><\/span>&#x4FDD;&#x6301;&#x4E0D;&#x53D8;&#x3002;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>h<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">&#x2032;<\/mo><\/msup><mo>=<\/mo><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.36em\" columnalign=\"left left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>0<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mtext>&#xA0;&#x6982;&#x7387;&#x4E3A;&#xA0;<\/mtext><mi>p<\/mi><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mfrac><mi>h<\/mi><mrow><mn>1<\/mn><mo>&#x2212;<\/mo><mi>p<\/mi><\/mrow><\/mfrac><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>&#xA0;&#x5176;&#x4ED6;&#x60C5;&#x51B5;&#xA0;<\/mtext><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">h^{\\prime}= \\begin{cases}0 &amp; \\text { &#x6982;&#x7387;&#x4E3A; } p \\\\ \\frac{h}{1-p} &amp; \\text { &#x5176;&#x4ED6;&#x60C5;&#x51B5; }\\end{cases}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8019em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8019em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2032;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:3em;vertical-align:-1.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7146em;\"><span style=\"top:-3.7146em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span style=\"top:-2.2746em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><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:0.8801em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.4811em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2146em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width:1em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7146em;\"><span style=\"top:-3.7146em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">&#xA0;<\/span><span class=\"mord cjk_fallback\">&#x6982;&#x7387;&#x4E3A;<\/span><span class=\"mord\">&#xA0;<\/span><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><span style=\"top:-2.2746em;\"><span class=\"pstrut\" style=\"height:3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">&#xA0;<\/span><span class=\"mord cjk_fallback\">&#x5176;&#x4ED6;&#x60C5;&#x51B5;<\/span><span class=\"mord\">&#xA0;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2146em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<blockquote>\n<p>&#x9700;&#x8981;&#x8BF4;&#x660E;&#x7684;&#x662F;&#xFF0C;&#x6682;&#x9000;&#x6CD5;&#x7684;&#x539F;&#x59CB;&#x8BBA;&#x6587;&#x63D0;&#x5230;&#x4E86;&#x4E00;&#x4E2A;&#x5173;&#x4E8E;&#x6709;&#x6027;&#x7E41;&#x6B96;&#x7684;&#x7C7B;&#x6BD4;&#xFF1A;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x8FC7;&#x62DF;&#x5408;&#x4E0E;&#x6BCF;&#x4E00;&#x5C42;&#x90FD;&#x4F9D;&#x8D56;&#x4E8E;&#x524D;&#x4E00;&#x5C42;&#x6FC0;&#x6D3B;&#x503C;&#x76F8;&#x5173;&#xFF0C;&#x79F0;&#x8FD9;&#x79CD;&#x60C5;&#x51B5;&#x4E3A;&#x201C;&#x5171;&#x9002;&#x5E94;&#x6027;&#x201D;&#x3002;&#x4F5C;&#x8005;&#x8BA4;&#x4E3A;&#xFF0C;&#x6682;&#x9000;&#x6CD5;&#x4F1A;&#x7834;&#x574F;&#x5171;&#x9002;&#x5E94;&#x6027;&#xFF0C;&#x5C31;&#x50CF;&#x6709;&#x6027;&#x751F;&#x6B96;&#x4F1A;&#x7834;&#x574F;&#x5171;&#x9002;&#x5E94;&#x7684;&#x57FA;&#x56E0;&#x4E00;&#x6837;&#x3002;&#xFF08;<mark>&#x6CA1;&#x770B;&#x61C2;&#x3002;&#x3002;<\/mark>&#xFF09;<\/p>\n<\/blockquote>\n<p>&#x5E38;&#x89C1;&#x6280;&#x5DE7;&#xFF1A;&#x5728;&#x9760;&#x8FD1;&#x8F93;&#x5165;&#x5C42;&#x7684;&#x5730;&#x65B9;&#x8BBE;&#x7F6E;&#x8F83;&#x4F4E;&#x7684;&#x6682;&#x9000;&#x6982;&#x7387;&#x3002;&#xFF08;<mark>&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/mark>&#xFF09;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%AE%9E%E7%8E%B0\">&#x5B9E;&#x73B0;<\/h3>\n\n<pre data-role=\"codeBlock\" data-info=\"python\" class=\"language-python\">net <span class=\"token operator\">=<\/span> nn<span class=\"token punctuation\">.<\/span>Sequential<span class=\"token punctuation\">(<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">784<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">256<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>ReLU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Dropout<span class=\"token punctuation\">(<\/span>dropout1<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">256<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">256<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>ReLU<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Dropout<span class=\"token punctuation\">(<\/span>dropout2<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>\n    nn<span class=\"token punctuation\">.<\/span>Linear<span class=\"token punctuation\">(<\/span><span class=\"token number\">256<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span>\n<span class=\"token punctuation\">)<\/span>\n<\/pre><h1 class=\"mume-header\" id=\"%E5%89%8D%E5%90%91%E4%BC%A0%E6%92%AD-%E5%8F%8D%E5%90%91%E4%BC%A0%E6%92%AD%E5%92%8C%E8%AE%A1%E7%AE%97%E5%9B%BE\">&#x524D;&#x5411;&#x4F20;&#x64AD;&#x3001;&#x53CD;&#x5411;&#x4F20;&#x64AD;&#x548C;&#x8BA1;&#x7B97;&#x56FE;<\/h1>\n\n<ul>\n<li>&#x524D;&#x5411;&#x4F20;&#x64AD;&#xFF08;forward propagation &#x6216; forward pass&#xFF09;<\/li>\n<li>&#x77E9;&#x9635;&#x7684;Frobenius&#x8303;&#x6570;&#xFF1A;&#x5C06;&#x77E9;&#x9635;&#x5C55;&#x5E73;&#x4E3A;&#x5411;&#x91CF;&#x540E;&#x5E94;&#x7528;&#x7684;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>L<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x8303;&#x6570;<\/li>\n<li>&#x53CD;&#x5411;&#x4F20;&#x64AD;&#xFF08;backward propagation &#x6216; backpropagation&#xFF09;<\/li>\n<\/ul>\n<p>&#x53CD;&#x5411;&#x4F20;&#x64AD;&#x91CD;&#x590D;&#x5229;&#x7528;&#x524D;&#x5411;&#x4F20;&#x64AD;&#x4E2D;&#x5B58;&#x50A8;&#x7684;&#x4E2D;&#x95F4;&#x503C;&#xFF0C;&#x4EE5;&#x907F;&#x514D;&#x91CD;&#x590D;&#x8BA1;&#x7B97;&#x3002;&#x6211;&#x4EEC;&#x9700;&#x8981;&#x4FDD;&#x7559;&#x4E2D;&#x95F4;&#x503C;&#xFF0C;&#x76F4;&#x5230;&#x53CD;&#x5411;&#x4F20;&#x64AD;&#x5B8C;&#x6210;&#x3002;<\/p>\n<p>&#x8FD9;&#x4E5F;&#x662F;&#x8BAD;&#x7EC3;&#x6BD4;&#x5355;&#x7EAF;&#x9884;&#x6D4B;&#x9700;&#x8981;&#x66F4;&#x591A;&#x5185;&#x5B58;&#xFF08;&#x663E;&#x5B58;&#xFF09;&#x7684;&#x539F;&#x56E0;&#x4E4B;&#x4E00;&#x3002;<\/p>\n<p>&#x4F7F;&#x7528;&#x66F4;&#x5927;&#x6279;&#x91CF;&#x6765;&#x8BAD;&#x7EC3;&#x66F4;&#x6DF1;&#x5C42;&#x6B21;&#x7684;&#x7F51;&#x7EDC;&#x66F4;&#x5BB9;&#x6613;&#x5BFC;&#x81F4;&#x5185;&#x5B58;&#x4E0D;&#x8DB3;&#x9519;&#x8BEF;&#x3002;<\/p>\n<h1 class=\"mume-header\" id=\"%E6%95%B0%E5%80%BC%E7%A8%B3%E5%AE%9A%E6%80%A7%E5%92%8C%E6%A8%A1%E5%9E%8B%E5%88%9D%E5%A7%8B%E5%8C%96\">&#x6570;&#x503C;&#x7A33;&#x5B9A;&#x6027;&#x548C;&#x6A21;&#x578B;&#x521D;&#x59CB;&#x5316;<\/h1>\n\n<p>&#x8F93;&#x51FA;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"bold\">o<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{o}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4444em;\"><\/span><span class=\"mord mathbf\">o<\/span><\/span><\/span><\/span>&#x5173;&#x4E8E;&#x4EFB;&#x4F55;&#x4E00;&#x7EC4;&#x53C2;&#x6570;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi mathvariant=\"bold\">W<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{W}^{(l)}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.888em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.888em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x7684;&#x68AF;&#x5EA6;&#x4E3A;&#xFF1A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi mathvariant=\"normal\">&#x2202;<\/mi><msup><mi mathvariant=\"bold\">W<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/msub><mi mathvariant=\"bold\">o<\/mi><mo>=<\/mo><munder><munder><mrow><msub><mi mathvariant=\"normal\">&#x2202;<\/mi><msup><mi mathvariant=\"bold\">h<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>L<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/msub><msup><mi mathvariant=\"bold\">h<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>L<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/mrow><mo stretchy=\"true\">&#x23DF;<\/mo><\/munder><mrow><msup><mi mathvariant=\"bold\">M<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>L<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mo><mover><mo><mo>=<\/mo><\/mo><mtext>&#xA0;def&#xA0;<\/mtext><\/mover><\/mo><\/mrow><\/munder><mo>&#x22C5;<\/mo><mo>&#x2026;<\/mo><mo>&#x22C5;<\/mo><munder><munder><mrow><msub><mi mathvariant=\"normal\">&#x2202;<\/mi><msup><mi mathvariant=\"bold\">h<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/msub><msup><mi mathvariant=\"bold\">h<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/mrow><mo stretchy=\"true\">&#x23DF;<\/mo><\/munder><mrow><msup><mi mathvariant=\"bold\">M<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mtext>&#xA0;def&#xA0;<\/mtext><\/mrow><\/msup><mo>=<\/mo><\/mrow><\/munder><munder><munder><mrow><msub><mi mathvariant=\"normal\">&#x2202;<\/mi><msup><mi mathvariant=\"bold\">W<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/msub><msup><mi mathvariant=\"bold\">h<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><\/mrow><mo stretchy=\"true\">&#x23DF;<\/mo><\/munder><mrow><msup><mi mathvariant=\"bold\">v<\/mi><mrow><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mo><mover><mo><mo>=<\/mo><\/mo><mtext>&#xA0;def&#xA0;<\/mtext><\/mover><\/mo><\/mrow><\/munder><\/mrow><annotation encoding=\"application\/x-tex\">\\partial_{\\mathbf{W}^{(l)}} \\mathbf{o}=\\underbrace{\\partial_{\\mathbf{h}^{(L-1)}} \\mathbf{h}^{(L)}}_{\\mathbf{M}^{(L)} \\stackrel{\\text { def }}{=}} \\cdot \\ldots \\cdot \\underbrace{\\partial_{\\mathbf{h}^{(l)}} \\mathbf{h}^{(l+1)}}_{\\mathbf{M}^{(l+1) \\text { def }}=} \\underbrace{\\partial_{\\mathbf{W}^{(l)}} \\mathbf{h}^{(l)}}_{\\mathbf{v}^{(l)} \\stackrel{\\text { def }}{=}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9251em;vertical-align:-0.2306em;\"><\/span><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.4694em;margin-left:-0.0556em;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 mtight\"><span class=\"mord mathbf mtight\" style=\"margin-right:0.01597em;\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2306em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathbf\">o<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.8608em;vertical-align:-1.9228em;\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span style=\"top:-1.0772em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">L<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\"><span class=\"mop op-limits mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2059em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span><span class=\"mop mtight\">=<\/span><\/span><\/span><span style=\"top:-3.2669em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">&#xA0;def&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span class=\"svg-align\" style=\"top:-2.1214em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"stretchy\" style=\"height:0.548em;min-width:1.6em;\"><span class=\"brace-left\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z\"\/><\/svg><\/span><span class=\"brace-center\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMidYMin slice\"><path d=\"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z\"\/><\/svg><\/span><span class=\"brace-right\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMaxYMin slice\"><path d=\"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z\"\/><\/svg><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.4694em;margin-left:-0.0556em;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 mtight\"><span class=\"mord mathbf mtight\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">L<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2306em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">L<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8786em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.9228em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x22C5;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.4445em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x22C5;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.8608em;vertical-align:-1.9228em;\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span style=\"top:-1.346em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">M<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">&#xA0;def&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\">=<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span class=\"svg-align\" style=\"top:-2.1214em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"stretchy\" style=\"height:0.548em;min-width:1.6em;\"><span class=\"brace-left\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z\"\/><\/svg><\/span><span class=\"brace-center\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMidYMin slice\"><path d=\"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z\"\/><\/svg><\/span><span class=\"brace-right\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMaxYMin slice\"><path d=\"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z\"\/><\/svg><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.4694em;margin-left:-0.0556em;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 mtight\"><span class=\"mord mathbf mtight\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2306em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8786em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.654em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span style=\"top:-1.0772em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\" style=\"margin-right:0.01597em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel mtight\"><span class=\"mop op-limits mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2059em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span><span class=\"mop mtight\">=<\/span><\/span><\/span><span style=\"top:-3.2669em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">&#xA0;def&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span class=\"svg-align\" style=\"top:-2.1214em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"stretchy\" style=\"height:0.548em;min-width:1.6em;\"><span class=\"brace-left\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z\"\/><\/svg><\/span><span class=\"brace-center\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMidYMin slice\"><path d=\"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z\"\/><\/svg><\/span><span class=\"brace-right\" style=\"height:0.548em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"0.548em\" viewBox=\"0 0 400000 548\" preserveAspectRatio=\"xMaxYMin slice\"><path d=\"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z\"\/><\/svg><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\" style=\"margin-right:0.05556em;\">&#x2202;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.4694em;margin-left:-0.0556em;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 mtight\"><span class=\"mord mathbf mtight\" style=\"margin-right:0.01597em;\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.822em;\"><span style=\"top:-2.822em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5357em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2306em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathbf\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.938em;\"><span 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 mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8786em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.9228em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x4E3A;&#x907F;&#x514D;&#x6570;&#x503C;&#x4E0B;&#x6EA2;&#x5F71;&#x54CD;&#xFF0C;&#x4E00;&#x4E2A;&#x5E38;&#x89C1;&#x6280;&#x5DE7;&#x662F;&#x5207;&#x6362;&#x5230;&#x5BF9;&#x6570;&#x7A7A;&#x95F4;&#xFF0C;&#x5373;&#x5C06;&#x6570;&#x503C;&#x8868;&#x793A;&#x7684;&#x538B;&#x529B;&#x4ECE;&#x5C3E;&#x6570;&#x8F6C;&#x79FB;&#x5230;&#x6307;&#x6570;&#x3002;<\/p>\n<h2 class=\"mume-header\" id=\"%E6%A2%AF%E5%BA%A6%E6%B6%88%E5%A4%B1gradient-vanishing\">&#x68AF;&#x5EA6;&#x6D88;&#x5931;&#xFF08;gradient vanishing&#xFF09;<\/h2>\n\n<ul>\n<li>&#x53C2;&#x6570;&#x66F4;&#x65B0;&#x8FC7;&#x5C0F;&#xFF0C;&#x5728;&#x6BCF;&#x6B21;&#x66F4;&#x65B0;&#x65F6;&#x51E0;&#x4E4E;&#x4E0D;&#x4F1A;&#x79FB;&#x52A8;&#xFF0C;&#x5BFC;&#x81F4;&#x6A21;&#x578B;&#x65E0;&#x6CD5;&#x5B66;&#x4E60;&#x3002;<\/li>\n<li>&#x4F8B;&#x5982;sigmoid&#x51FD;&#x6570;&#xFF0C;&#x5728;&#x8F93;&#x5165;&#x5F88;&#x5927;&#x6216;&#x5F88;&#x5C0F;&#x65F6;&#xFF0C;&#x68AF;&#x5EA6;&#x90FD;&#x4F1A;&#x6D88;&#x5931;&#x3002;<br>\n&#x76F8;&#x6BD4;&#x4E4B;&#x4E0B;&#xFF0C;ReLU&#x6FC0;&#x6D3B;&#x51FD;&#x6570;&#x7F13;&#x89E3;&#x4E86;&#x68AF;&#x5EA6;&#x6D88;&#x5931;&#x95EE;&#x9898;&#xFF0C;&#x52A0;&#x901F;&#x6536;&#x655B;&#x3002;<\/li>\n<li>&#x7F51;&#x7EDC;&#x8F83;&#x6DF1;&#x65F6;&#xFF0C;&#x5BB9;&#x6613;&#x5728;&#x67D0;&#x4E00;&#x5C42;&#x5207;&#x65AD;&#x68AF;&#x5EA6;&#x3002;<\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E6%A2%AF%E5%BA%A6%E7%88%86%E7%82%B8gradient-explosion\">&#x68AF;&#x5EA6;&#x7206;&#x70B8;&#xFF08;gradient explosion&#xFF09;<\/h2>\n\n<ul>\n<li>&#x53C2;&#x6570;&#x66F4;&#x65B0;&#x8FC7;&#x5927;&#xFF0C;&#x7834;&#x574F;&#x4E86;&#x6A21;&#x578B;&#x7684;&#x7A33;&#x5B9A;&#x6536;&#x655B;&#x3002;<\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E6%89%93%E7%A0%B4%E5%AF%B9%E7%A7%B0%E6%80%A7\">&#x6253;&#x7834;&#x5BF9;&#x79F0;&#x6027;<\/h2>\n\n<p>&#x9690;&#x85CF;&#x5C42;&#x53C2;&#x6570;&#x4E0D;&#x80FD;&#x521D;&#x59CB;&#x5316;&#x4E3A;&#x76F8;&#x540C;&#x503C;&#xFF0C;&#x56E0;&#x4E3A;&#x5C0F;&#x6279;&#x91CF;&#x968F;&#x673A;&#x68AF;&#x5EA6;&#x4E0B;&#x964D;&#x4E0D;&#x4F1A;&#x7834;&#x574F;&#x5BF9;&#x79F0;&#x6027;&#xFF08;&#x5C3D;&#x7BA1;&#x6682;&#x9000;&#x6CD5;&#x6B63;&#x5219;&#x5316;&#x53EF;&#x4EE5;&#xFF09;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E9%9A%8F%E6%9C%BA%E5%88%9D%E5%A7%8B%E5%8C%96\">&#x968F;&#x673A;&#x521D;&#x59CB;&#x5316;<\/h3>\n\n<h3 class=\"mume-header\" id=\"xavier%E5%8F%82%E6%95%B0%E5%88%9D%E5%A7%8B%E5%8C%96\">Xavier&#x53C2;&#x6570;&#x521D;&#x59CB;&#x5316;<\/h3>\n\n<p>&#x5728;&#x7EBF;&#x6027;&#x5168;&#x8FDE;&#x63A5;&#x5C42;&#x4E2D;&#xFF0C;&#x5F53;&#x6B63;&#x5411;&#x4F20;&#x64AD;&#x65F6;&#xFF0C;&#x82E5;&#x8981;&#x4ECE;&#x8F93;&#x5165;&#x5230;&#x8F93;&#x51FA;&#x65B9;&#x5DEE;&#x4FDD;&#x6301;&#x4E0D;&#x53D8;&#xFF08;<mark>&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/mark>&#xFF09;&#xFF0C;&#x5219;&#x9700;&#x8981;&#x6743;&#x91CD;&#x6807;&#x51C6;&#x5DEE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3C3;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><\/span><\/span><\/span>&#x6EE1;&#x8DB3;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>n<\/mi><mtext>in<\/mtext><\/msub><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n_{\\text{in}}\\sigma^2=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9641em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3175em;\"><span 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 text mtight\"><span class=\"mord mtight\">in<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span 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 mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span>&#xFF1B;&#x5F53;&#x53CD;&#x5411;&#x4F20;&#x64AD;&#x65F6;&#xFF0C;&#x540C;&#x7406;&#x9700;&#x8981;&#x6743;&#x91CD;&#x6807;&#x51C6;&#x5DEE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3C3;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><\/span><\/span><\/span>&#x6EE1;&#x8DB3;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>n<\/mi><mtext>out<\/mtext><\/msub><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n_{\\text{out}}\\sigma^2=1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.9641em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span 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 text mtight\"><span class=\"mord mtight\">out<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span 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 mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span>&#xFF08;<mark>&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/mark>&#xFF09;&#x3002;<\/p>\n<p>&#x4E3A;&#x4E86;&#x5E73;&#x8861;&#x4E8C;&#x8005;&#x9700;&#x6C42;&#xFF0C;&#x53D6;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mrow><mo fence=\"true\">(<\/mo><msub><mi>n<\/mi><mtext>in&#xA0;<\/mtext><\/msub><mo>+<\/mo><msub><mi>n<\/mi><mtext>out&#xA0;<\/mtext><\/msub><mo fence=\"true\">)<\/mo><\/mrow><msup><mi>&#x3C3;<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><mtext>&#xA0;&#x6216;&#x7B49;&#x4EF7;&#x4E8E;&#xA0;<\/mtext><mi>&#x3C3;<\/mi><mo>=<\/mo><msqrt><mfrac><mn>2<\/mn><mrow><msub><mi>n<\/mi><mtext>in&#xA0;<\/mtext><\/msub><mo>+<\/mo><msub><mi>n<\/mi><mtext>out&#xA0;<\/mtext><\/msub><\/mrow><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2}\\left(n_{\\text {in }}+n_{\\text {out }}\\right) \\sigma^{2}=1 \\text { &#x6216;&#x7B49;&#x4EF7;&#x4E8E; } \\sigma=\\sqrt{\\frac{2}{n_{\\text {in }}+n_{\\text {out }}}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.0074em;vertical-align:-0.686em;\"><\/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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3175em;\"><span 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 text mtight\"><span class=\"mord mtight\">in&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span 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 text mtight\"><span class=\"mord mtight\">out&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span 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 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord text\"><span class=\"mord\">&#xA0;<\/span><span class=\"mord cjk_fallback\">&#x6216;&#x7B49;&#x4EF7;&#x4E8E;<\/span><span class=\"mord\">&#xA0;<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">&#x3C3;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.44em;vertical-align:-0.8634em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.5766em;\"><span class=\"svg-align\" style=\"top:-4.4em;\"><span class=\"pstrut\" style=\"height:4.4em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3175em;\"><span 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 text mtight\"><span class=\"mord mtight\">in&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span 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 text mtight\"><span class=\"mord mtight\">out&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-3.5366em;\"><span class=\"pstrut\" style=\"height:4.4em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:2.48em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"2.48em\" viewBox=\"0 0 400000 2592\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8634em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x6743;&#x91CD;&#x53EF;&#x4EE5;&#x6309;&#x9AD8;&#x65AF;&#x5206;&#x5E03;&#x521D;&#x59CB;&#x5316;&#xFF0C;&#x4E5F;&#x53EF;&#x4EE5;&#x6309;&#x5747;&#x5300;&#x5206;&#x5E03;&#x521D;&#x59CB;&#x5316;&#xFF0C;&#x4F46;&#x65B9;&#x5DEE;&#x5747;&#x5982;&#x4E0A;&#x5F0F;&#x63CF;&#x8FF0;&#x3002;<\/p>\n<h1 class=\"mume-header\" id=\"%E7%8E%AF%E5%A2%83%E5%92%8C%E5%88%86%E5%B8%83%E5%81%8F%E7%A7%BB\">&#x73AF;&#x5883;&#x548C;&#x5206;&#x5E03;&#x504F;&#x79FB;<\/h1>\n\n<p>&#x673A;&#x5668;&#x5B66;&#x4E60;&#x8BB8;&#x591A;&#x5E94;&#x7528;&#x5B58;&#x5728;&#x7684;&#x95EE;&#x9898;&#xFF1A;<strong>&#x901A;&#x8FC7;&#x5C06;&#x57FA;&#x4E8E;&#x6A21;&#x578B;&#x7684;&#x51B3;&#x7B56;&#x5F15;&#x5165;&#x73AF;&#x5883;&#xFF0C;&#x6211;&#x4EEC;&#x53EF;&#x80FD;&#x4F1A;&#x7834;&#x574F;&#x6A21;&#x578B;&#x3002;<\/strong><\/p>\n<p>&#x5728;&#x5F88;&#x591A;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;<strong>&#x8BAD;&#x7EC3;&#x96C6;&#x548C;&#x6D4B;&#x8BD5;&#x96C6;&#x5E76;&#x4E0D;&#x6765;&#x81EA;&#x540C;&#x4E2A;&#x5206;&#x5E03;<\/strong>&#xFF0C;&#x8FD9;&#x5C31;&#x662F;&#x6240;&#x8C13;&#x7684;&#x5206;&#x5E03;&#x504F;&#x79FB;&#x3002;&#x5047;&#x8BBE;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x96C6;&#x5206;&#x5E03;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text{tra}}(x,y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF0C;&#x6D4B;&#x8BD5;&#x6570;&#x636E;&#x96C6;&#x5206;&#x5E03;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text{tst}}(x,y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E7%BB%8F%E9%AA%8C%E9%A3%8E%E9%99%A9%E4%B8%8E%E5%AE%9E%E9%99%85%E9%A3%8E%E9%99%A9\">&#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#x4E0E;&#x5B9E;&#x9645;&#x98CE;&#x9669;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E7%BB%8F%E9%AA%8C%E9%A3%8E%E9%99%A9empirical-risk%E6%9C%80%E5%B0%8F%E5%8C%96\">&#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#xFF08;empirical risk&#xFF09;&#x6700;&#x5C0F;&#x5316;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi><munder><mo><mi mathvariant=\"normal\">minimize<\/mi><mo>&#x2061;<\/mo><\/mo><mi>f<\/mi><\/munder><\/mi><mfrac><mn>1<\/mn><mi>n<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><mi>l<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\underset{f}{\\operatorname{minimize}} \\frac{1}{n} \\sum_{i=1}^{n} l\\left(f\\left(\\mathbf{x}_{i}\\right), y_{i}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\"><\/span><span class=\"mord\"><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6679em;\"><span style=\"top:-2.3479em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10764em;\">f<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\"><span class=\"mop\"><span class=\"mord mathrm\">minimize<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8882em;\"><span><\/span><\/span><\/span><\/span><\/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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6514em;\"><span style=\"top:-1.8723em;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 mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2777em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E7%9C%9F%E5%AE%9E%E9%A3%8E%E9%99%A9true-risk\">&#x771F;&#x5B9E;&#x98CE;&#x9669;&#xFF08;true risk&#xFF09;<\/h3>\n\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>E<\/mi><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/msub><mo stretchy=\"false\">[<\/mo><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">]<\/mo><mo>=<\/mo><mo>&#x222C;<\/mo><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi mathvariant=\"bold\">x<\/mi><mi>d<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E_{p(\\mathbf{x}, y)}[l(f(\\mathbf{x}), y)]=\\iint l(f(\\mathbf{x}), y) p(\\mathbf{x}, y) d \\mathbf{x} d y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1052em;vertical-align:-0.3552em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.5198em;margin-left:-0.0576em;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 mathnormal mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3552em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)]<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.222em;vertical-align:-0.862em;\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.001em;\">&#x222C;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><br>\n&#x7531;&#x4E8E;&#x901A;&#x5E38;&#x65E0;&#x6CD5;&#x83B7;&#x53D6;&#x771F;&#x5B9E;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">p(\\mathbf{x},y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF0C;&#x4E00;&#x822C;&#x901A;&#x8FC7;<strong>&#x6700;&#x5C0F;&#x5316;&#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#x6765;&#x8FD1;&#x4F3C;&#x6700;&#x5C0F;&#x5316;&#x771F;&#x5B9E;&#x98CE;&#x9669;<\/strong>&#x3002;<\/p>\n<p>&#x4E0B;&#x8FF0;&#x5B9A;&#x4E49;&#x90E8;&#x5206;&#x6458;&#x81EA;<br>\n<a href=\"https:\/\/towardsdatascience.com\/understanding-dataset-shift-f2a5a262a766\">Understanding Dataset Shift. How to make sure your models are not&#x2026; | by Matthew Stewart | Towards Data Science<\/a><\/p>\n<h2 class=\"mume-header\" id=\"%E5%8D%8F%E5%8F%98%E9%87%8F%E5%81%8F%E7%A7%BBcovariate-shift\">&#x534F;&#x53D8;&#x91CF;&#x504F;&#x79FB;&#xFF08;covariate shift&#xFF09;<\/h2>\n\n<p>Covariate shift appears only in <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><mo>&#x2192;<\/mo><mi>Y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X \\rightarrow Y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2192;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span> problems, and is defined as the case where <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(y \\mid x)=P_{\\text{tst}}(y \\mid x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo mathvariant=\"normal\">&#x2260;<\/mo><msub><mi>P<\/mi><mrow><mi mathvariant=\"normal\">t<\/mi><mi mathvariant=\"normal\">s<\/mi><mi mathvariant=\"normal\">t<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\neq P_{\\mathrm{tst}}(\\mathrm{x})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">&#xE020;<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 mtight\"><span class=\"mord mathrm mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathrm\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E5%8D%8F%E5%8F%98%E9%87%8F%E5%81%8F%E7%A7%BB%E7%BA%A0%E6%AD%A3\">&#x534F;&#x53D8;&#x91CF;&#x504F;&#x79FB;&#x7EA0;&#x6B63;<\/h3>\n\n<p>&#x8BBE;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x96C6;&#x7684;&#x89C2;&#x6D4B;&#x503C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"bold\">x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{x}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4444em;\"><\/span><span class=\"mord mathbf\">x<\/span><\/span><\/span><\/span>&#x6765;&#x81EA;&#x4E8E;&#x67D0;&#x4E9B;&#x6E90;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">q(\\mathbf{x})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x800C;&#x975E;&#x76EE;&#x6807;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">p(\\mathbf{x})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF0C;&#x5219;&#x6709;&#xFF1A;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>&#x222C;<\/mo><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mi>d<\/mi><mi mathvariant=\"bold\">x<\/mi><mi>d<\/mi><mi>y<\/mi><mo>=<\/mo><mo>&#x222C;<\/mo><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mfrac><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mi>d<\/mi><mi mathvariant=\"bold\">x<\/mi><mi>d<\/mi><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\iint l(f(\\mathbf{x}), y) p(y \\mid \\mathbf{x}) p(\\mathbf{x}) d \\mathbf{x} d y=\\iint l(f(\\mathbf{x}), y) q(y \\mid \\mathbf{x}) q(\\mathbf{x}) \\frac{p(\\mathbf{x})}{q(\\mathbf{x})} d \\mathbf{x} d y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.222em;vertical-align:-0.862em;\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.001em;\">&#x222C;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.222em;vertical-align:-0.862em;\"><\/span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;position:relative;top:-0.001em;\">&#x222C;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/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 style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x82E5;&#x4EE4;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><mo><mover><mo><mo>=<\/mo><\/mo><mtext>&#xA0;def&#xA0;<\/mtext><\/mover><\/mo><mfrac><mrow><mi>p<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi>q<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{i} \\stackrel{\\text { def }}{=} \\frac{p\\left(\\mathbf{x}_{i}\\right)}{q\\left(\\mathbf{x}_{i}\\right)}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.3474em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\"><span class=\"mop op-limits\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.153em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">=<\/span><\/span><\/span><span style=\"top:-3.5669em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">&#xA0;def&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.53em;vertical-align:-0.52em;\"><\/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:1.01em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.485em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x5219;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x201C;<strong>&#x52A0;&#x6743;&#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#x6700;&#x5C0F;&#x5316;<\/strong>&#x201D;&#x6765;&#x8BAD;&#x7EC3;&#x6A21;&#x578B;&#xFF1A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi><munder><mo><mi mathvariant=\"normal\">minimize<\/mi><mo>&#x2061;<\/mo><\/mo><mi>f<\/mi><\/munder><\/mi><mfrac><mn>1<\/mn><mi>n<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><mi>l<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>f<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\underset{f}{\\operatorname{minimize}} \\frac{1}{n} \\sum_{i=1}^{n} \\beta_{i} l\\left(f\\left(\\mathbf{x}_{i}\\right), y_{i}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\"><\/span><span class=\"mord\"><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6679em;\"><span style=\"top:-2.3479em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.10764em;\">f<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\"><span class=\"mop\"><span class=\"mord mathrm\">minimize<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8882em;\"><span><\/span><\/span><\/span><\/span><\/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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6514em;\"><span style=\"top:-1.8723em;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 mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2777em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10764em;\">f<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x5176;&#x4E2D;&#x201C;&#x771F;&#x5B9E;&#x201D;&#x7684;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x8BBF;&#x95EE;&#x6D4B;&#x8BD5;&#x6570;&#x636E;&#x83B7;&#x53D6;&#x3002;<\/p>\n<p>&#x73B0;&#x5047;&#x8BBE;&#x6709;&#x4E00;&#x4E2A;&#x8BAD;&#x7EC3;&#x96C6;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>n<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\left(\\mathbf{x}_{1}, y_{1}\\right), \\ldots,\\left(\\mathbf{x}_{n}, y_{n}\\right)\\right\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">{<\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span 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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">}<\/span><\/span><\/span><\/span><\/span>&#x548C;&#x4E00;&#x4E2A;&#x672A;&#x6807;&#x8BB0;&#x7684;&#x6D4B;&#x8BD5;&#x96C6;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><msub><mi mathvariant=\"bold\">u<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><msub><mi mathvariant=\"bold\">u<\/mi><mi>m<\/mi><\/msub><mo fence=\"true\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{m}\\right\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">{<\/span><span class=\"mord\"><span class=\"mord mathbf\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span 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 mathnormal mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">}<\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x6211;&#x4EEC;&#x9884;&#x5148;&#x5B66;&#x4E60;&#x4E00;&#x4E2A;&#x5206;&#x7C7B;&#x5668;&#x6765;&#x533A;&#x5206;&#x4ECE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">p(\\mathbf{x})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x62BD;&#x53D6;&#x7684;&#x6570;&#x636E;&#x548C;&#x4ECE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">q(\\mathbf{x})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#x62BD;&#x53D6;&#x7684;&#x6570;&#x636E;&#x3002;&#x6574;&#x4E2A;&#x7B97;&#x6CD5;&#x5305;&#x62EC;&#x4EE5;&#x4E0B;&#x51E0;&#x4E2A;&#x6B65;&#x9AA4;&#xFF1A;<\/p>\n<ol>\n<li>&#x751F;&#x6210;&#x4E00;&#x4E2A;&#x4E8C;&#x5143;&#x5206;&#x7C7B;&#x6570;&#x636E;&#x96C6;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2212;<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>n<\/mi><\/msub><mo separator=\"true\">,<\/mo><mo>&#x2212;<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">u<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">u<\/mi><mi>m<\/mi><\/msub><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\left(\\mathbf{x}_{1},-1\\right), \\ldots,\\left(\\mathbf{x}_{n},-1\\right),\\left(\\mathbf{u}_{1}, 1\\right), \\ldots,\\left(\\mathbf{u}_{m}, 1\\right)\\right\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">{<\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span 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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">&#x2212;<\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span 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 mathnormal mtight\">m<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">}<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>&#x7528;<strong>&#x5BF9;&#x6570;&#x51E0;&#x7387;&#x56DE;&#x5F52;&#xFF08;logistic regression&#xFF0C;softmax&#x56DE;&#x5F52;&#x7684;&#x4E8C;&#x5143;&#x5206;&#x7C7B;&#x7279;&#x4F8B;&#xFF09;<\/strong> &#x8BAD;&#x7EC3;<strong>&#x4E8C;&#x5143;&#x5206;&#x7C7B;&#x5668;<\/strong>&#x5F97;&#x5230;&#x51FD;&#x6570;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">h<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><\/span><\/span><br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo>=<\/mo><mn>1<\/mn><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mtext>&#xA0;and&#xA0;hence&#xA0;<\/mtext><mfrac><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo>=<\/mo><mn>1<\/mn><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo>=<\/mo><mo>&#x2212;<\/mo><mn>1<\/mn><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mspace linebreak=\"newline\"><\/mspace><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo>=<\/mo><mn>1<\/mn><mo>&#x2223;<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mi>exp<\/mi><mo>&#x2061;<\/mo><mo stretchy=\"false\">(<\/mo><mo>&#x2212;<\/mo><mi>h<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">x<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(z=1 \\mid \\mathbf{x})=\\frac{p(\\mathbf{x})}{p(\\mathbf{x})+q(\\mathbf{x})} \\text { and hence } \\frac{P(z=1 \\mid \\mathbf{x})}{P(z=-1 \\mid \\mathbf{x})}=\\frac{p(\\mathbf{x})}{q(\\mathbf{x})}\\\\\nP(z=1 \\mid \\mathbf{x})=\\frac{1}{1+\\exp (-h(\\mathbf{x}))}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.53em;vertical-align:-0.52em;\"><\/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:1.01em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.485em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord text\"><span class=\"mord\">&#xA0;and&#xA0;hence&#xA0;<\/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:1.01em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">&#x2223;<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.485em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><span class=\"mrel mtight\">&#x2223;<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.53em;vertical-align:-0.52em;\"><\/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:1.01em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.485em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.04398em;\">z<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.3651em;vertical-align:-0.52em;\"><\/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:0.8451em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mop mtight\"><span class=\"mtight\">e<\/span><span class=\"mtight\">x<\/span><span class=\"mtight\">p<\/span><\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mclose mtight\">))<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>&#x4F7F;&#x7528; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mi>exp<\/mi><mo>&#x2061;<\/mo><mrow><mo fence=\"true\">(<\/mo><mi>h<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{i}=\\exp \\left(h\\left(\\mathbf{x}_{i}\\right)\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span> &#x6216;&#x66F4;&#x597D;&#x7684; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mi>min<\/mi><mo>&#x2061;<\/mo><mrow><mo fence=\"true\">(<\/mo><mi>exp<\/mi><mo>&#x2061;<\/mo><mrow><mo fence=\"true\">(<\/mo><mi>h<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mi>c<\/mi><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{i}=\\min \\left(\\exp \\left(h\\left(\\mathbf{x}_{i}\\right)\\right), c\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">min<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span> (c&#x4E3A;&#x5E38;&#x91CF;) &#x5BF9;&#x8BAD;&#x7EC3;&#x6570;&#x636E;&#x8FDB;&#x884C;&#x52A0;&#x6743;<\/li>\n<li>&#x4F7F;&#x7528;&#x6743;&#x91CD; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{i}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#x8FDB;&#x884C; <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mo>&#x2026;<\/mo><mo separator=\"true\">,<\/mo><mrow><mo fence=\"true\">(<\/mo><msub><mi mathvariant=\"bold\">x<\/mi><mi>n<\/mi><\/msub><mo separator=\"true\">,<\/mo><msub><mi>y<\/mi><mi>n<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo fence=\"true\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\left(\\mathbf{x}_{1}, y_{1}\\right), \\ldots,\\left(\\mathbf{x}_{n}, y_{n}\\right)\\right\\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">{<\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span 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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">&#x2026;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathbf\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span 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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">}<\/span><\/span><\/span><\/span><\/span> &#x7684;&#x8BAD;&#x7EC3;<\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"%E6%A0%87%E7%AD%BE%E5%81%8F%E7%A7%BBlabel-shift-prior-probability-shift\">&#x6807;&#x7B7E;&#x504F;&#x79FB;&#xFF08;label shift, prior probability shift&#xFF09;<\/h2>\n\n<p>Prior probability shift appears only in <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Y<\/mi><mo>&#x2192;<\/mo><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Y \\rightarrow X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2192;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span> problems, and is defined as the case where <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&#x2223;<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&#x2223;<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(x \\mid y)=P_{\\text {tst}}(x \\mid y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\">&#x2260;<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(y) \\neq P_{\\text{tst}}(y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">&#xE020;<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"%E6%A0%87%E7%AD%BE%E5%81%8F%E7%A7%BB%E7%BA%A0%E6%AD%A3\">&#x6807;&#x7B7E;&#x504F;&#x79FB;&#x7EA0;&#x6B63;<\/h3>\n\n<p>&#x540C;&#x6837;&#x5730;&#x53EF;&#x4EE5;&#x5B9A;&#x4E49;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3B2;<\/mi><mi>i<\/mi><\/msub><mo><mover><mo><mo>=<\/mo><\/mo><mtext>&#xA0;def&#xA0;<\/mtext><\/mover><\/mo><mfrac><mrow><mi>p<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>y<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><mrow><mi>q<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>y<\/mi><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\beta_{i} \\stackrel{\\text { def }}{=} \\frac{p\\left(y_{i}\\right)}{q\\left(y_{i}\\right)}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.3474em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.05278em;\">&#x3B2;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0528em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\"><span class=\"mop op-limits\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.153em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">=<\/span><\/span><\/span><span style=\"top:-3.5669em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">&#xA0;def&#xA0;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.53em;vertical-align:-0.52em;\"><\/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:1.01em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">q<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.485em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">p<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight delimcenter\" style=\"top:0em;\"><span class=\"mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.52em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x6839;&#x636E;&#x52A0;&#x6743;&#x7ECF;&#x9A8C;&#x98CE;&#x9669;&#x6700;&#x5C0F;&#x5316;&#x6765;&#x8BAD;&#x7EC3;&#x6A21;&#x578B;&#x3002;<\/p>\n<p>&#x4E0B;&#x9762;&#x7ED9;&#x51FA;&#x4F30;&#x7B97;&#x76EE;&#x6807;&#x6807;&#x7B7E;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>&#x7684;&#x4E00;&#x79CD;&#x65B9;&#x6CD5;&#xFF1A;<\/p>\n<ol>\n<li>\n<p>&#x8BA1;&#x7B97;&#x9A8C;&#x8BC1;&#x96C6;&#xFF08;<mark>&#x4E3A;&#x4EC0;&#x4E48;&#xFF1F;<\/mark>&#xFF09;&#x7684;&#x6DF7;&#x6DC6;&#x77E9;&#x9635;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"bold\">C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{C}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6861em;\"><\/span><span class=\"mord mathbf\">C<\/span><\/span><\/span><\/span>&#x3002;&#x8BE5;&#x77E9;&#x9635;&#x4E2D;&#x6BCF;&#x4E2A;&#x5355;&#x5143;&#x683C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>c<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">c_{ij}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.7167em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\" style=\"margin-right:0.05724em;\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x7684;&#x503C;&#x8868;&#x793A;&#x9A8C;&#x8BC1;&#x96C6;&#x4E2D;&#x771F;&#x5B9E;&#x6807;&#x7B7E;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>j<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">j<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.854em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span>&#xFF0C;&#x6A21;&#x578B;&#x9884;&#x6D4B;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>i<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6595em;\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span>&#x7684;&#x6837;&#x672C;&#x5360;&#x6BD4;&#x3002;<\/p>\n<\/li>\n<li>\n<p>&#x5C06;&#x6240;&#x6709;&#x6A21;&#x578B;&#x5728;&#x6D4B;&#x8BD5;&#x65F6;&#x7684;&#x9884;&#x6D4B;&#x53D6;&#x5E73;&#x5747;&#x6570;&#xFF0C;&#x5F97;&#x5230;&#x5E73;&#x5747;&#x6A21;&#x578B;&#x8F93;&#x51FA;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>&#x3BC;<\/mi><mo stretchy=\"false\">(<\/mo><mover accent=\"true\"><mi mathvariant=\"bold\">y<\/mi><mo>^<\/mo><\/mover><mo stretchy=\"false\">)<\/mo><mo>&#x2208;<\/mo><msup><mi mathvariant=\"double-struck\">R<\/mi><mi>k<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\mu(\\hat{\\mathbf{y}}) \\in \\mathbb{R}^{k}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7079em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">y<\/span><\/span><span style=\"top:-3.0134em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2208;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8491em;\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491em;\"><span 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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x6C42;&#x89E3;&#x4E00;&#x4E2A;&#x7B80;&#x5355;&#x7EBF;&#x6027;&#x7CFB;&#x7EDF;&#x6765;&#x4F30;&#x7B97;&#x6D4B;&#x8BD5;&#x96C6;&#x7684;&#x6807;&#x7B7E;&#x5206;&#x5E03;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi mathvariant=\"bold\">C<\/mi><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"bold\">y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>&#x3BC;<\/mi><mo stretchy=\"false\">(<\/mo><mover accent=\"true\"><mi mathvariant=\"bold\">y<\/mi><mo>^<\/mo><\/mover><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\mathbf{C} p(\\mathbf{y})=\\mu(\\hat{\\mathbf{y}})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbf\">C<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7079em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathbf\" style=\"margin-right:0.01597em;\">y<\/span><\/span><span style=\"top:-3.0134em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mo>&#x2211;<\/mo><mrow><mi>j<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>k<\/mi><\/msubsup><msub><mi>c<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><mi>p<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mi>y<\/mi><mi>j<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mi>&#x3BC;<\/mi><mrow><mo fence=\"true\">(<\/mo><msub><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\sum_{j=1}^{k} c_{i j} p\\left(y_{j}\\right)=\\mu\\left(\\hat{y}_{i}\\right)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.4248em;vertical-align:-0.4358em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position:relative;top:0em;\">&#x2211;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.989em;\"><span style=\"top:-2.4003em;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 mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span 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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.4358em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span 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 mathnormal mtight\" style=\"margin-right:0.05724em;\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">&#x3BC;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<h2 class=\"mume-header\" id=\"%E6%A6%82%E5%BF%B5%E5%81%8F%E7%A7%BBconcept-shift\">&#x6982;&#x5FF5;&#x504F;&#x79FB;&#xFF08;concept shift&#xFF09;<\/h2>\n\n<p>Concept shift is defined as<\/p>\n<ul>\n<li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\">&#x2260;<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>&#x2223;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(y \\mid x) \\neq P_{\\text{tst}}(y \\mid x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">&#xE020;<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(x)=P_{\\text{tst}}(x)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> in <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>X<\/mi><mo>&#x2192;<\/mo><mi>Y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">X \\rightarrow Y<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2192;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><\/span><\/span><\/span> problems.<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&#x2223;<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\">&#x2260;<\/mo><msub><mi>P<\/mi><mtext>tst<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&#x2223;<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text {tra}}(x \\mid y) \\neq P_{\\text{tst}}(x \\mid y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">&#xE020;<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tst<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> and <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>P<\/mi><mtext>tra<\/mtext><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mi>P<\/mi><mrow><mi>t<\/mi><mi>s<\/mi><mi>t<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P_{\\text{tra}}(y)=P_{tst}(y)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 text mtight\"><span class=\"mord mtight\">tra<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;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 mathnormal mtight\">t<\/span><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> in <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Y<\/mi><mo>&#x2192;<\/mo><mi>X<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Y \\rightarrow X<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.22222em;\">Y<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2192;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.07847em;\">X<\/span><\/span><\/span><\/span> problems.<\/li>\n<\/ul>\n<h3 class=\"mume-header\" id=\"%E6%A6%82%E5%BF%B5%E5%81%8F%E7%A7%BB%E7%BA%A0%E6%AD%A3\">&#x6982;&#x5FF5;&#x504F;&#x79FB;&#x7EA0;&#x6B63;<\/h3>\n\n<p>&#x6982;&#x5FF5;&#x7684;&#x53D8;&#x5316;&#x603B;&#x662F;&#x7F13;&#x6162;&#x7684;&#x3002;&#x6211;&#x4EEC;&#x4F7F;&#x7528;&#x65B0;&#x6570;&#x636E;&#x66F4;&#x65B0;&#x73B0;&#x6709;&#x7F51;&#x7EDC;&#x6743;&#x91CD;&#xFF0C;&#x800C;&#x4E0D;&#x662F;&#x4ECE;&#x5934;&#x5F00;&#x59CB;&#x8BAD;&#x7EC3;&#x3002;<\/p>\n<h1 class=\"mume-header\" id=\"%E4%B8%80%E4%BA%9B%E5%AE%9E%E6%88%98%E7%BB%8F%E9%AA%8C\">&#x4E00;&#x4E9B;&#x5B9E;&#x6218;&#x7ECF;&#x9A8C;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E6%95%B0%E6%8D%AE%E9%A2%84%E5%A4%84%E7%90%86\">&#x6570;&#x636E;&#x9884;&#x5904;&#x7406;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E7%89%B9%E5%BE%81%E6%95%B0%E6%8D%AE%E6%A0%87%E5%87%86%E5%8C%96\">&#x7279;&#x5F81;&#x6570;&#x636E;&#x6807;&#x51C6;&#x5316;<\/h3>\n\n<p>&#x56E0;&#x4E3A;&#x6211;&#x4EEC;&#x4E0D;&#x77E5;&#x9053;&#x54EA;&#x4E9B;&#x7279;&#x5F81;&#x662F;&#x76F8;&#x5173;&#x7684;&#xFF0C;&#x4E0D;&#x60F3;&#x8BA9;&#x60E9;&#x7F5A;&#x5206;&#x914D;&#x7ED9;&#x4E00;&#x4E2A;&#x7279;&#x5F81;&#x7684;&#x7CFB;&#x6570;&#x6BD4;&#x5206;&#x914D;&#x7ED9;&#x5176;&#x4ED6;&#x7279;&#x5F81;&#x7684;&#x7CFB;&#x6570;&#x66F4;&#x5927;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%B0%86%E7%A6%BB%E6%95%A3%E7%89%B9%E5%BE%81%E8%BD%AC%E5%8C%96%E4%B8%BA%E7%8B%AC%E7%83%AD%E5%90%91%E9%87%8F\">&#x5C06;&#x79BB;&#x6563;&#x7279;&#x5F81;&#x8F6C;&#x5316;&#x4E3A;&#x72EC;&#x70ED;&#x5411;&#x91CF;<\/h3>\n\n<h2 class=\"mume-header\" id=\"%E5%AF%B9%E6%95%B0%E5%B7%AE%E5%BC%82\">&#x5BF9;&#x6570;&#x5DEE;&#x5F02;<\/h2>\n\n<p>&#x4E00;&#x4E9B;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;&#x6211;&#x4EEC;&#x5173;&#x5FC3;&#x76F8;&#x5BF9;&#x8BEF;&#x5DEE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mrow><mi>y<\/mi><mo>&#x2212;<\/mo><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><\/mrow><mi>y<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{y-\\hat{y}}{y}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.4133em;vertical-align:-0.4811em;\"><\/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:0.9322em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.4461em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord accent mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.4811em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x800C;&#x975E;&#x7EDD;&#x5BF9;&#x8BEF;&#x5DEE;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>&#x2212;<\/mo><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><\/mrow><annotation encoding=\"application\/x-tex\">y-\\hat{y}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.7778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xFF0C;&#x56E0;&#x6B64;&#x4F7F;&#x7528;&#x5BF9;&#x6570;&#x6765;&#x8861;&#x91CF;&#x5DEE;&#x5F02;&#x3002;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>e<\/mi><mrow><mo>&#x2212;<\/mo><mi>&#x3B4;<\/mi><\/mrow><\/msup><mo>&#x2264;<\/mo><mfrac><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><mi>y<\/mi><\/mfrac><mo>&#x2264;<\/mo><msup><mi>e<\/mi><mi>&#x3B4;<\/mi><\/msup><mo>&#x21D4;<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><mi>log<\/mi><mo>&#x2061;<\/mo><mi>y<\/mi><mo>&#x2212;<\/mo><mi>log<\/mi><mo>&#x2061;<\/mo><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><mi mathvariant=\"normal\">&#x2223;<\/mi><mo>&#x2264;<\/mo><mi>&#x3B4;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">e^{-\\delta} \\leq \\frac{\\hat{y}}{y} \\leq e^{\\delta}\\Leftrightarrow |\\log y-\\log \\hat{y}| \\leq \\delta<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.0351em;vertical-align:-0.136em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991em;\"><span 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 mtight\"><span class=\"mord mtight\">&#x2212;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03785em;\">&#x3B4;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.2519em;vertical-align:-0.8804em;\"><\/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:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8804em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.8991em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991em;\"><span 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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03785em;\">&#x3B4;<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x21D4;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&#x2264;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03785em;\">&#x3B4;<\/span><\/span><\/span><\/span><\/span><br>\n&#x8BEF;&#x5DEE;&#x51FD;&#x6570;&#x4E3A;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mfrac><mn>1<\/mn><mi>n<\/mi><\/mfrac><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msup><mrow><mo fence=\"true\">(<\/mo><mi>log<\/mi><mo>&#x2061;<\/mo><msub><mi>y<\/mi><mi>i<\/mi><\/msub><mo>&#x2212;<\/mo><mi>log<\/mi><mo>&#x2061;<\/mo><msub><mover accent=\"true\"><mi>y<\/mi><mo>^<\/mo><\/mover><mi>i<\/mi><\/msub><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{\\frac{1}{n} \\sum_{i=1}^{n}\\left(\\log y_{i}-\\log \\hat{y}_{i}\\right)^{2}}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:3.1568em;vertical-align:-1.2777em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8791em;\"><span class=\"svg-align\" style=\"top:-5.1168em;\"><span class=\"pstrut\" style=\"height:5.1168em;\"><\/span><span class=\"mord\" style=\"padding-left:1.056em;\"><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:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6514em;\"><span style=\"top:-1.8723em;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 mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;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 mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2777em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\">(<\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.954em;\"><span 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 mtight\"><span class=\"mord 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(d2l.ai)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[31,20],"tags":[32,33,26,25],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/340"}],"collection":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=340"}],"version-history":[{"count":1,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/340\/revisions"}],"predecessor-version":[{"id":341,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=\/wp\/v2\/posts\/340\/revisions\/341"}],"wp:attachment":[{"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lazybirds.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}