{"id":73088,"date":"2026-02-07T00:33:06","date_gmt":"2026-02-06T16:33:06","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/73088.html"},"modified":"2026-02-07T00:33:06","modified_gmt":"2026-02-06T16:33:06","slug":"%e4%bf%a1%e8%80%8c%e6%9c%89%e5%be%81-%e6%a8%a1%e5%9e%8b%e8%af%84%e4%bc%b0%e3%80%81%e9%aa%8c%e8%af%81%e4%b8%8e%e5%8f%af%e4%bf%a1%e9%83%a8%e7%bd%b2%e7%9a%84%e5%ae%8c%e6%95%b4%e4%bd%93","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/73088.html","title":{"rendered":"\u4fe1\u800c\u6709\u5f81\u2014\u2014\u6a21\u578b\u8bc4\u4f30\u3001\u9a8c\u8bc1\u4e0e\u53ef\u4fe1\u90e8\u7f72\u7684\u5b8c\u6574\u4f53\u7cfb"},"content":{"rendered":"<p>\u201c\u4e00\u4e2a\u672a\u7ecf\u9a8c\u8bc1\u7684\u6a21\u578b&#xff0c;\u65e0\u8bba\u591a\u4e48\u7cbe\u5de7&#xff0c;\u90fd\u53ea\u662f\u7a7a\u4e2d\u697c\u9601\u3002 \u771f\u6b63\u7684\u667a\u80fd&#xff0c;\u4e0d\u5728\u4e8e\u9884\u6d4b\u672c\u8eab&#xff0c;\u800c\u5728\u4e8e\u5bf9\u9884\u6d4b\u4e0d\u786e\u5b9a\u6027\u7684\u8bda\u5b9e\u3002\u201d \u2014\u2014\u673a\u5668\u5b66\u4e60\u5de5\u7a0b\u7684\u6838\u5fc3\u4fe1\u6761<\/p>\n<hr \/>\n<h3>\u4e00\u3001\u4e3a\u4ec0\u4e48\u6a21\u578b\u8bc4\u4f30\u81f3\u5173\u91cd\u8981&#xff1f;<\/h3>\n<p>\u5728\u524d\u516b\u7ae0\u4e2d&#xff0c;\u6211\u4eec\u7cfb\u7edf\u6784\u5efa\u4e86\u4ece\u7ebf\u6027\u6a21\u578b\u5230\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3001\u4ece\u76d1\u7763\u5b66\u4e60\u5230\u65e0\u76d1\u7763\u63a2\u7d22\u7684\u5b8c\u6574\u5de5\u5177\u7bb1\u3002\u7136\u800c&#xff0c;\u6a21\u578b\u4e00\u65e6\u79bb\u5f00\u8bad\u7ec3\u73af\u5883&#xff0c;\u4fbf\u9762\u4e34\u771f\u5b9e\u4e16\u754c\u7684\u4e25\u82db\u8003\u9a8c&#xff1a;<\/p>\n<ul>\n<li>\u8bad\u7ec3\u96c6\u4e0a\u7684\u9ad8\u51c6\u786e\u7387&#xff0c;\u5728\u6d4b\u8bd5\u96c6\u4e0a\u53ef\u80fd\u5927\u5e45\u4e0b\u964d&#xff1b;<\/li>\n<li>\u6a21\u578b\u5bf9\u67d0\u4e9b\u7fa4\u4f53\u5b58\u5728\u7cfb\u7edf\u6027\u504f\u89c1&#xff08;\u5982\u4eba\u8138\u8bc6\u522b\u5bf9\u6df1\u80a4\u8272\u4eba\u7fa4\u9519\u8bef\u7387\u66f4\u9ad8&#xff09;&#xff1b;<\/li>\n<li>\u6570\u636e\u5206\u5e03\u968f\u65f6\u95f4\u6f02\u79fb&#xff08;\u5982\u75ab\u60c5\u540e\u7528\u6237\u6d88\u8d39\u884c\u4e3a\u5267\u53d8&#xff09;&#xff1b;<\/li>\n<li>\u90e8\u7f72\u540e\u7f3a\u4e4f\u76d1\u63a7&#xff0c;\u5bfc\u81f4\u201c\u9759\u9ed8\u5931\u6548\u201d\u3002<\/li>\n<\/ul>\n<p>&#x1f3af; \u672c\u7ae0\u76ee\u6807&#xff1a;<\/p>\n<ul>\n<li>\u6df1\u5165\u7406\u89e3\u504f\u5dee-\u65b9\u5dee\u6743\u8861&#xff08;Bias-Variance Tradeoff&#xff09;\u8fd9\u4e00\u6839\u672c\u77db\u76fe&#xff1b;<\/li>\n<li>\u638c\u63e1\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Cross-Validation&#xff09;\u3001\u81ea\u52a9\u6cd5&#xff08;Bootstrap&#xff09;\u7b49\u53ef\u9760\u8bc4\u4f30\u6280\u672f&#xff1b;<\/li>\n<li>\u5b66\u4f1a\u9488\u5bf9\u4e0d\u540c\u4efb\u52a1&#xff08;\u5206\u7c7b\/\u56de\u5f52\/\u6392\u5e8f&#xff09;\u9009\u62e9\u5408\u9002\u7684\u8bc4\u4f30\u6307\u6807&#xff1b;<\/li>\n<li>\u6784\u5efa\u6a21\u578b\u76d1\u63a7\u4e0e\u6f02\u79fb\u68c0\u6d4b\u673a\u5236&#xff1b;<\/li>\n<li>\u63a2\u8ba8\u516c\u5e73\u6027\u3001\u53ef\u89e3\u91ca\u6027\u4e0e\u4e0d\u786e\u5b9a\u6027\u91cf\u5316\u7b49\u53ef\u4fe1 AI \u8981\u7d20&#xff1b;<\/li>\n<li>\u8bbe\u8ba1\u7aef\u5230\u7aef\u7684\u6a21\u578b\u9a8c\u8bc1\u4e0e\u90e8\u7f72\u6d41\u6c34\u7ebf\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u4e8c\u3001\u504f\u5dee-\u65b9\u5dee\u5206\u89e3&#xff1a;\u7406\u89e3\u6cdb\u5316\u8bef\u5dee\u7684\u6839\u6e90<\/h3>\n<p>\u4efb\u4f55\u76d1\u7763\u5b66\u4e60\u6a21\u578b\u7684\u6cdb\u5316\u8bef\u5dee&#xff08;Generalization Error&#xff09;\u53ef\u5206\u89e3\u4e3a\u4e09\u90e8\u5206&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         Error<\/p>\n<p>         &#061;<\/p>\n<p>          Bias<\/p>\n<p>          2<\/p>\n<p>         &#043;<\/p>\n<p>         Variance<\/p>\n<p>         &#043;<\/p>\n<p>         Irreducible\u00a0Error<\/p>\n<p>         \\\\text{Error} &#061; \\\\text{Bias}^2 &#043; \\\\text{Variance} &#043; \\\\text{Irreducible Error} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Error<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9707em;vertical-align: -0.0833em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">Bias<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8873em\"><span class=\"\" style=\"top: -3.1362em;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: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Variance<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Irreducible\u00a0Error<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>2.1 \u5b9a\u4e49\u4e0e\u76f4\u89c2\u89e3\u91ca<\/h4>\n<p>\u8bbe\u771f\u5b9e\u51fd\u6570\u4e3a $ f(\\\\mathbf{x}) $&#xff0c;\u6a21\u578b\u9884\u6d4b\u4e3a $ \\\\hat{f}(\\\\mathbf{x}) $&#xff0c;\u5219\u5bf9\u4efb\u610f\u8f93\u5165 $ \\\\mathbf{x} $&#xff0c;\u671f\u671b\u9884\u6d4b\u8bef\u5dee\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         E<\/p>\n<p>          [<\/p>\n<p>          (<\/p>\n<p>          y<\/p>\n<p>          \u2212<\/p>\n<p>           f<\/p>\n<p>           ^<\/p>\n<p>          (<\/p>\n<p>          x<\/p>\n<p>          )<\/p>\n<p>           )<\/p>\n<p>           2<\/p>\n<p>          ]<\/p>\n<p>         &#061;<\/p>\n<p>             (<\/p>\n<p>             E<\/p>\n<p>             [<\/p>\n<p>              f<\/p>\n<p>              ^<\/p>\n<p>             (<\/p>\n<p>             x<\/p>\n<p>             )<\/p>\n<p>             ]<\/p>\n<p>             \u2212<\/p>\n<p>             f<\/p>\n<p>             (<\/p>\n<p>             x<\/p>\n<p>             )<\/p>\n<p>             )<\/p>\n<p>            2<\/p>\n<p>           \u23df<\/p>\n<p>           Bias<\/p>\n<p>           2<\/p>\n<p>         &#043;<\/p>\n<p>            E<\/p>\n<p>             [<\/p>\n<p>             (<\/p>\n<p>              f<\/p>\n<p>              ^<\/p>\n<p>             (<\/p>\n<p>             x<\/p>\n<p>             )<\/p>\n<p>             \u2212<\/p>\n<p>             E<\/p>\n<p>             [<\/p>\n<p>              f<\/p>\n<p>              ^<\/p>\n<p>             (<\/p>\n<p>             x<\/p>\n<p>             )<\/p>\n<p>             ]<\/p>\n<p>              )<\/p>\n<p>              2<\/p>\n<p>             ]<\/p>\n<p>           \u23df<\/p>\n<p>          Variance<\/p>\n<p>         &#043;<\/p>\n<p>            \u03c3<\/p>\n<p>            2<\/p>\n<p>           \u23df<\/p>\n<p>          Irreducible<\/p>\n<p>         \\\\mathbb{E}\\\\left[ (y &#8211; \\\\hat{f}(\\\\mathbf{x}))^2 \\\\right] &#061; \\\\underbrace{\\\\left( \\\\mathbb{E}[\\\\hat{f}(\\\\mathbf{x})] &#8211; f(\\\\mathbf{x}) \\\\right)^2}_{\\\\text{Bias}^2} &#043; \\\\underbrace{\\\\mathbb{E}\\\\left[ (\\\\hat{f}(\\\\mathbf{x}) &#8211; \\\\mathbb{E}[\\\\hat{f}(\\\\mathbf{x})])^2 \\\\right]}_{\\\\text{Variance}} &#043; \\\\underbrace{\\\\sigma^2}_{\\\\text{Irreducible}} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.8em;vertical-align: -0.65em\"><\/span><span class=\"mord mathbb\">E<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0833em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.4056em;vertical-align: -2.0516em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.354em\"><span class=\"\" style=\"top: -1.3024em\"><span class=\"pstrut\" style=\"height: 3.354em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Bias<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7908em\"><span class=\"\" style=\"top: -2.8305em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.354em\"><span class=\"pstrut\" style=\"height: 3.354em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.354em\"><span class=\"svg-align\" style=\"top: -2.056em\"><span class=\"pstrut\" style=\"height: 3.354em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3.354em\"><span class=\"pstrut\" style=\"height: 3.354em\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0833em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)]<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.354em\"><span class=\"\" style=\"top: -3.6029em;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><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.298em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.0516em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1264em;vertical-align: -1.9764em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"\" style=\"top: -1.1736em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">Variance<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.15em\"><span class=\"svg-align\" style=\"top: -1.852em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3.15em\"><span class=\"pstrut\" style=\"height: 3.15em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">E<\/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=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0833em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9579em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><span class=\"\" style=\"top: -3.2634em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.0833em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mclose\">)]<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.298em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.9764em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1982em;vertical-align: -1.3341em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -1.6659em\"><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\">Irreducible<\/span><\/span><\/span><\/span><\/span><span class=\"\" 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: 0.8641em\"><span class=\"svg-align\" style=\"top: -2.352em\"><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\"><\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.648em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3341em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>\u504f\u5dee&#xff08;Bias&#xff09;&#xff1a;\u6a21\u578b\u9884\u6d4b\u7684\u671f\u671b\u4e0e\u771f\u5b9e\u503c\u4e4b\u5dee&#xff0c;\u53cd\u6620\u6b20\u62df\u5408&#xff08;Underfitting&#xff09;&#xff1b;<\/li>\n<li>\u65b9\u5dee&#xff08;Variance&#xff09;&#xff1a;\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u6270\u52a8\u7684\u654f\u611f\u5ea6&#xff0c;\u53cd\u6620\u8fc7\u62df\u5408&#xff08;Overfitting&#xff09;&#xff1b;<\/li>\n<li>\u4e0d\u53ef\u7ea6\u8bef\u5dee&#xff08;Irreducible Error&#xff09;&#xff1a;\u7531\u566a\u58f0 $ \\\\epsilon $ \u5f15\u8d77&#xff0c;\u65e0\u6cd5\u901a\u8fc7\u6a21\u578b\u6d88\u9664\u3002<\/li>\n<\/ul>\n<h4>2.2 \u504f\u5dee-\u65b9\u5dee\u6743\u8861\u7684\u53ef\u89c6\u5316<\/h4>\n<ul>\n<li>\u9ad8\u504f\u5dee\u6a21\u578b&#xff08;\u5982\u7ebf\u6027\u56de\u5f52\u62df\u5408\u975e\u7ebf\u6027\u6570\u636e&#xff09;&#xff1a;\u7b80\u5355\u3001\u7a33\u5b9a&#xff0c;\u4f46\u7cfb\u7edf\u6027\u504f\u79bb\u771f\u76f8&#xff1b;<\/li>\n<li>\u9ad8\u65b9\u5dee\u6a21\u578b&#xff08;\u5982\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5728\u5c0f\u6570\u636e\u4e0a&#xff09;&#xff1a;\u590d\u6742\u3001\u7075\u6d3b&#xff0c;\u4f46\u5bf9\u8bad\u7ec3\u6837\u672c\u8fc7\u5ea6\u654f\u611f\u3002<\/li>\n<\/ul>\n<p>\u2705 \u7406\u60f3\u6a21\u578b&#xff1a;\u5728\u504f\u5dee\u4e0e\u65b9\u5dee\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861&#xff0c;\u4f7f\u603b\u8bef\u5dee\u6700\u5c0f\u3002<\/p>\n<h4>2.3 \u5982\u4f55\u8bca\u65ad&#xff1f;<\/h4>\n<table>\n<tr>\u73b0\u8c61\u53ef\u80fd\u539f\u56e0\u89e3\u51b3\u65b9\u6848<\/tr>\n<tbody>\n<tr>\n<td>\u8bad\u7ec3\u8bef\u5dee\u9ad8&#xff0c;\u9a8c\u8bc1\u8bef\u5dee\u9ad8<\/td>\n<td>\u9ad8\u504f\u5dee&#xff08;\u6b20\u62df\u5408&#xff09;<\/td>\n<td>\u589e\u52a0\u6a21\u578b\u590d\u6742\u5ea6\u3001\u6dfb\u52a0\u7279\u5f81\u3001\u51cf\u5c11\u6b63\u5219\u5316<\/td>\n<\/tr>\n<tr>\n<td>\u8bad\u7ec3\u8bef\u5dee\u4f4e&#xff0c;\u9a8c\u8bc1\u8bef\u5dee\u9ad8<\/td>\n<td>\u9ad8\u65b9\u5dee&#xff08;\u8fc7\u62df\u5408&#xff09;<\/td>\n<td>\u589e\u52a0\u6570\u636e\u3001\u6b63\u5219\u5316\u3001\u7b80\u5316\u6a21\u578b\u3001\u65e9\u505c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u4e09\u3001\u6570\u636e\u5212\u5206\u7b56\u7565&#xff1a;\u907f\u514d\u8bc4\u4f30\u9677\u9631<\/h3>\n<h4>3.1 \u7b80\u5355\u5212\u5206&#xff1a;\u8bad\u7ec3\u96c6\/\u9a8c\u8bc1\u96c6\/\u6d4b\u8bd5\u96c6<\/h4>\n<p>\u6700\u57fa\u7840\u7684\u5212\u5206\u65b9\u5f0f&#xff1a;<\/p>\n<ul>\n<li>\u8bad\u7ec3\u96c6&#xff08;Training Set&#xff09;&#xff1a;\u7528\u4e8e\u62df\u5408\u6a21\u578b\u53c2\u6570&#xff1b;<\/li>\n<li>\u9a8c\u8bc1\u96c6&#xff08;Validation Set&#xff09;&#xff1a;\u7528\u4e8e\u8c03\u53c2\u3001\u6a21\u578b\u9009\u62e9&#xff1b;<\/li>\n<li>\u6d4b\u8bd5\u96c6&#xff08;Test Set&#xff09;&#xff1a;\u4ec5\u7528\u4e8e\u6700\u7ec8\u8bc4\u4f30&#xff0c;\u6a21\u62df\u672a\u77e5\u6570\u636e\u3002<\/li>\n<\/ul>\n<p>\u5178\u578b\u6bd4\u4f8b&#xff1a;70%\/15%\/15% \u6216 80%\/10%\/10%\u3002<\/p>\n<p>\u26a0\ufe0f \u5173\u952e\u539f\u5219&#xff1a;\u6d4b\u8bd5\u96c6\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21&#xff01;\u591a\u6b21\u4f7f\u7528\u4f1a\u5bfc\u81f4\u4fe1\u606f\u6cc4\u9732&#xff0c;\u8bc4\u4f30\u7ed3\u679c\u8fc7\u4e8e\u4e50\u89c2\u3002<\/p>\n<h4>3.2 \u65f6\u95f4\u5e8f\u5217\u6570\u636e\u7684\u7279\u6b8a\u5904\u7406<\/h4>\n<p>\u5bf9\u4e8e\u65f6\u5e8f\u6570\u636e&#xff08;\u5982\u80a1\u4ef7\u3001\u9500\u91cf&#xff09;&#xff0c;\u4e0d\u80fd\u968f\u673a\u6253\u4e71\u5212\u5206&#xff0c;\u5426\u5219\u4f1a\u5f15\u5165\u672a\u6765\u4fe1\u606f&#xff08;Look-ahead Bias&#xff09;\u3002<\/p>\n<p>\u6b63\u786e\u505a\u6cd5&#xff1a;\u6309\u65f6\u95f4\u987a\u5e8f\u5212\u5206<\/p>\n<p><span class=\"token comment\"># \u9519\u8bef&#xff1a;\u968f\u673a\u5212\u5206<\/span><br \/>\nX_train<span class=\"token punctuation\">,<\/span> X_test<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6b63\u786e&#xff1a;\u65f6\u95f4\u5e8f\u5217\u5212\u5206<\/span><br \/>\nsplit_idx <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0.8<\/span> <span class=\"token operator\">*<\/span> <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\nX_train<span class=\"token punctuation\">,<\/span> X_test <span class=\"token operator\">&#061;<\/span> X<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span>split_idx<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">[<\/span>split_idx<span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span><br \/>\ny_train<span class=\"token punctuation\">,<\/span> y_test <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span>split_idx<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">[<\/span>split_idx<span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<h4>3.3 \u5206\u5c42\u62bd\u6837&#xff08;Stratified Sampling&#xff09;<\/h4>\n<p>\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d&#xff0c;\u4e3a\u4fdd\u8bc1\u5404\u7c7b\u522b\u5728\u5404\u96c6\u5408\u4e2d\u6bd4\u4f8b\u4e00\u81f4&#xff0c;\u4f7f\u7528\u5206\u5c42\u62bd\u6837&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<\/p>\n<p>X_train<span class=\"token punctuation\">,<\/span> X_test<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span><br \/>\n    X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> stratify<span class=\"token operator\">&#061;<\/span>y<span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<hr \/>\n<h3>\u56db\u3001\u4ea4\u53c9\u9a8c\u8bc1&#xff1a;\u66f4\u7a33\u5065\u7684\u6a21\u578b\u8bc4\u4f30<\/h3>\n<p>\u5f53\u6570\u636e\u91cf\u6709\u9650\u65f6&#xff0c;\u7b80\u5355\u5212\u5206\u53ef\u80fd\u5bfc\u81f4\u8bc4\u4f30\u4e0d\u7a33\u5b9a&#xff08;\u56e0\u67d0\u6b21\u5212\u5206\u8fd0\u6c14\u597d\/\u574f&#xff09;\u3002\u4ea4\u53c9\u9a8c\u8bc1&#xff08;Cross-Validation, CV&#xff09;\u901a\u8fc7\u591a\u6b21\u5212\u5206\u53d6\u5e73\u5747&#xff0c;\u63d0\u4f9b\u66f4\u53ef\u9760\u7684\u6027\u80fd\u4f30\u8ba1\u3002<\/p>\n<h4>4.1 K \u6298\u4ea4\u53c9\u9a8c\u8bc1&#xff08;K-Fold CV&#xff09;<\/h4>\n<p>\u5c06\u8bad\u7ec3\u96c6\u5212\u5206\u4e3a $ K $ \u4e2a\u4e92\u65a5\u5b50\u96c6&#xff08;folds&#xff09;&#xff0c;\u8f6e\u6d41\u7528 $ K-1 $ \u4e2a fold \u8bad\u7ec3&#xff0c;1 \u4e2a fold \u9a8c\u8bc1&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         CV\u00a0Score<\/p>\n<p>         &#061;<\/p>\n<p>          1<\/p>\n<p>          K<\/p>\n<p>          \u2211<\/p>\n<p>           k<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          K<\/p>\n<p>          Score<\/p>\n<p>          k<\/p>\n<p>         \\\\text{CV Score} &#061; \\\\frac{1}{K} \\\\sum_{k&#061;1}^{K} \\\\text{Score}_k <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">CV\u00a0Score<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.1304em;vertical-align: -1.3021em\"><\/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 class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/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: 1.8283em\"><span class=\"\" style=\"top: -1.8479em;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\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;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\" style=\"margin-right: 0.0715em\">K<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3021em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">Score<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5e38\u7528 $ K &#061; 5 $ \u6216 $ 10 $\u3002<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> cross_val_score<\/p>\n<p>scores <span class=\"token operator\">&#061;<\/span> cross_val_score<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">,<\/span> X_train<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> cv<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> scoring<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;accuracy&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;Accuracy: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>scores<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> (&#043;\/- <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>scores<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">)&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>4.2 \u5206\u5c42 K \u6298&#xff08;Stratified K-Fold&#xff09;<\/h4>\n<p>\u786e\u4fdd\u6bcf\u4e00\u6298\u4e2d\u7c7b\u522b\u6bd4\u4f8b\u4e0e\u6574\u4f53\u4e00\u81f4&#xff0c;\u9002\u7528\u4e8e\u4e0d\u5e73\u8861\u5206\u7c7b\u3002<\/p>\n<h4>4.3 \u7559\u4e00\u6cd5&#xff08;LOO-CV&#xff09;\u4e0e\u7559 P \u6cd5&#xff08;LPO-CV&#xff09;<\/h4>\n<ul>\n<li>LOO-CV&#xff1a;$ K &#061; n $&#xff0c;\u6bcf\u6298\u7559\u4e00\u4e2a\u6837\u672c\u3002\u8ba1\u7b97\u6602\u8d35&#xff0c;\u4f46\u65e0\u504f\u3002<\/li>\n<li>LPO-CV&#xff1a;\u6bcf\u6298\u7559 $ p $ \u4e2a\u6837\u672c&#xff0c;\u6298\u8877\u65b9\u6848\u3002<\/li>\n<\/ul>\n<h4>4.4 \u65f6\u95f4\u5e8f\u5217\u4ea4\u53c9\u9a8c\u8bc1&#xff08;TimeSeriesSplit&#xff09;<\/h4>\n<p>\u4e13\u4e3a\u65f6\u5e8f\u6570\u636e\u8bbe\u8ba1&#xff0c;\u786e\u4fdd\u8bad\u7ec3\u96c6\u59cb\u7ec8\u5728\u9a8c\u8bc1\u96c6\u4e4b\u524d&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> TimeSeriesSplit<\/p>\n<p>tscv <span class=\"token operator\">&#061;<\/span> TimeSeriesSplit<span class=\"token punctuation\">(<\/span>n_splits<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">for<\/span> train_index<span class=\"token punctuation\">,<\/span> test_index <span class=\"token keyword\">in<\/span> tscv<span class=\"token punctuation\">.<\/span>split<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    X_train<span class=\"token punctuation\">,<\/span> X_test <span class=\"token operator\">&#061;<\/span> X<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    y_train<span class=\"token punctuation\">,<\/span> y_test <span class=\"token operator\">&#061;<\/span> y<span class=\"token punctuation\">[<\/span>train_index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">[<\/span>test_index<span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token comment\"># \u8bad\u7ec3\u5e76\u8bc4\u4f30<\/span><\/p>\n<hr \/>\n<h3>\u4e94\u3001\u8bc4\u4f30\u6307\u6807&#xff1a;\u5ea6\u91cf\u6a21\u578b\u6027\u80fd\u7684\u6807\u5c3a<\/h3>\n<p>\u6307\u6807\u9009\u62e9\u5fc5\u987b\u4e0e\u4e1a\u52a1\u76ee\u6807\u5bf9\u9f50\u3002<\/p>\n<h4>5.1 \u5206\u7c7b\u4efb\u52a1\u6307\u6807<\/h4>\n<h5>5.1.1 \u6df7\u6dc6\u77e9\u9635&#xff08;Confusion Matrix&#xff09;<\/h5>\n<table>\n<tr>\u9884\u6d4b\u4e3a\u6b63\u9884\u6d4b\u4e3a\u8d1f<\/tr>\n<tbody>\n<tr>\n<td>\u771f\u5b9e\u4e3a\u6b63<\/td>\n<td>TP<\/td>\n<td>FN<\/td>\n<\/tr>\n<tr>\n<td>\u771f\u5b9e\u4e3a\u8d1f<\/td>\n<td>FP<\/td>\n<td>TN<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>TP&#xff1a;\u771f\u6b63\u4f8b&#xff08;True Positive&#xff09;<\/li>\n<li>FN&#xff1a;\u5047\u8d1f\u4f8b&#xff08;False Negative&#xff09;<\/li>\n<li>FP&#xff1a;\u5047\u6b63\u4f8b&#xff08;False Positive&#xff09;<\/li>\n<li>TN&#xff1a;\u771f\u8d1f\u4f8b&#xff08;True Negative&#xff09;<\/li>\n<\/ul>\n<h5>5.1.2 \u5e38\u7528\u6307\u6807<\/h5>\n<ul>\n<li>\n<p>\u51c6\u786e\u7387&#xff08;Accuracy&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           Acc<\/p>\n<p>           &#061;<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             &#043;<\/p>\n<p>             T<\/p>\n<p>             N<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             &#043;<\/p>\n<p>             T<\/p>\n<p>             N<\/p>\n<p>             &#043;<\/p>\n<p>             F<\/p>\n<p>             P<\/p>\n<p>             &#043;<\/p>\n<p>             F<\/p>\n<p>             N<\/p>\n<p>           \\\\text{Acc} &#061; \\\\frac{TP &#043; TN}{TP &#043; TN &#043; FP &#043; FN} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Acc<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;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: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">TN<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">FP<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">FN<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">TN<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u9002\u7528\u4e8e\u7c7b\u522b\u5e73\u8861\u573a\u666f\u3002<\/p>\n<\/li>\n<li>\n<p>\u7cbe\u786e\u7387&#xff08;Precision&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           Prec<\/p>\n<p>           &#061;<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             &#043;<\/p>\n<p>             F<\/p>\n<p>             P<\/p>\n<p>           \\\\text{Prec} &#061; \\\\frac{TP}{TP &#043; FP} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Prec<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;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: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">FP<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5173\u6ce8\u201c\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\u6709\u591a\u5c11\u662f\u771f\u7684\u6b63\u201d\u3002<\/p>\n<\/li>\n<li>\n<p>\u53ec\u56de\u7387&#xff08;Recall \/ Sensitivity&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           Rec<\/p>\n<p>           &#061;<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             T<\/p>\n<p>             P<\/p>\n<p>             &#043;<\/p>\n<p>             F<\/p>\n<p>             N<\/p>\n<p>           \\\\text{Rec} &#061; \\\\frac{TP}{TP &#043; FN} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">Rec<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;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: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">FN<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">TP<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5173\u6ce8\u201c\u6240\u6709\u771f\u5b9e\u6b63\u4f8b\u4e2d\u6709\u591a\u5c11\u88ab\u627e\u51fa\u6765\u4e86\u201d\u3002<\/p>\n<\/li>\n<li>\n<p>F1 \u5206\u6570&#xff08;F1-Score&#xff09;&#xff1a;\u7cbe\u786e\u7387\u4e0e\u53ec\u56de\u7387\u7684\u8c03\u548c\u5e73\u5747 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            F<\/p>\n<p>            1<\/p>\n<p>           &#061;<\/p>\n<p>           2<\/p>\n<p>           \u22c5<\/p>\n<p>             Prec<\/p>\n<p>             \u22c5<\/p>\n<p>             Rec<\/p>\n<p>             Prec<\/p>\n<p>             &#043;<\/p>\n<p>             Rec<\/p>\n<p>           F_1 &#061; 2 \\\\cdot \\\\frac{\\\\text{Prec} \\\\cdot \\\\text{Rec}}{\\\\text{Prec} &#043; \\\\text{Rec}} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" 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\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;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: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">Prec<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord\">Rec<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">Prec<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord\">Rec<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u7279\u5f02\u6027&#xff08;Specificity&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           Spec<\/p>\n<p>           &#061;<\/p>\n<p>             T<\/p>\n<p>             N<\/p>\n<p>             T<\/p>\n<p>             N<\/p>\n<p>             &#043;<\/p>\n<p>             F<\/p>\n<p>             P<\/p>\n<p>           \\\\text{Spec} &#061; \\\\frac{TN}{TN &#043; FP} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord text\"><span class=\"mord\">Spec<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;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: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">TN<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">FP<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">TN<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<h5>5.1.3 ROC \u4e0e AUC<\/h5>\n<ul>\n<li>ROC \u66f2\u7ebf&#xff1a;\u4ee5\u5047\u6b63\u7387&#xff08;FPR &#061; $ \\\\frac{FP}{FP &#043; TN} $&#xff09;\u4e3a\u6a2a\u8f74&#xff0c;\u771f\u6b63\u7387&#xff08;TPR &#061; Recall&#xff09;\u4e3a\u7eb5\u8f74&#xff0c;\u7ed8\u5236\u4e0d\u540c\u9608\u503c\u4e0b\u7684\u70b9\u3002<\/li>\n<li>AUC&#xff08;Area Under Curve&#xff09;&#xff1a;ROC \u66f2\u7ebf\u4e0b\u9762\u79ef&#xff0c;\u8861\u91cf\u6a21\u578b\u6392\u5e8f\u80fd\u529b\u3002AUC &#061; 0.5 \u4e3a\u968f\u673a&#xff0c;1.0 \u4e3a\u5b8c\u7f8e\u3002<\/li>\n<\/ul>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> roc_auc_score<span class=\"token punctuation\">,<\/span> roc_curve<\/p>\n<p>auc <span class=\"token operator\">&#061;<\/span> roc_auc_score<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_proba<span class=\"token punctuation\">)<\/span><br \/>\nfpr<span class=\"token punctuation\">,<\/span> tpr<span class=\"token punctuation\">,<\/span> _ <span class=\"token operator\">&#061;<\/span> roc_curve<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_proba<span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>fpr<span class=\"token punctuation\">,<\/span> tpr<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;AUC &#061; <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>auc<span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.2f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;k&#8211;&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;False Positive Rate&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;True Positive Rate&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>legend<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h5>5.1.4 PR \u66f2\u7ebf&#xff08;Precision-Recall Curve&#xff09;<\/h5>\n<p>\u5728\u6b63\u4f8b\u7a00\u758f&#xff08;\u5982\u6b3a\u8bc8\u68c0\u6d4b&#xff09;\u65f6&#xff0c;PR \u66f2\u7ebf\u6bd4 ROC \u66f4\u5177\u4fe1\u606f\u91cf\u3002<\/p>\n<h4>5.2 \u56de\u5f52\u4efb\u52a1\u6307\u6807<\/h4>\n<ul>\n<li>\n<p>\u5747\u65b9\u8bef\u5dee&#xff08;MSE&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           MSE<\/p>\n<p>           &#061;<\/p>\n<p>            1<\/p>\n<p>            n<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           (<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>             y<\/p>\n<p>             ^<\/p>\n<p>            i<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>           \\\\text{MSE} &#061; \\\\frac{1}{n} \\\\sum_{i&#061;1}^{n} (y_i &#8211; \\\\hat{y}_i)^2 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">MSE<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/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 class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/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 class=\"\" 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\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;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\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/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 class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" 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\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/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 class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u5747\u65b9\u6839\u8bef\u5dee&#xff08;RMSE&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           RMSE<\/p>\n<p>           &#061;<\/p>\n<p>            MSE<\/p>\n<p>           \\\\text{RMSE} &#061; \\\\sqrt{\\\\text{MSE}} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">RMSE<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.0645em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9755em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord text\"><span class=\"mord\">MSE<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.9355em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>              <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.0645em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee&#xff08;MAE&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           MAE<\/p>\n<p>           &#061;<\/p>\n<p>            1<\/p>\n<p>            n<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           \u2223<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>             y<\/p>\n<p>             ^<\/p>\n<p>            i<\/p>\n<p>           \u2223<\/p>\n<p>           \\\\text{MAE} &#061; \\\\frac{1}{n} \\\\sum_{i&#061;1}^{n} |y_i &#8211; \\\\hat{y}_i| <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord\">MAE<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.9291em;vertical-align: -1.2777em\"><\/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 class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/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 class=\"\" 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\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;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\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/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\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" 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\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/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 class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u51b3\u5b9a\u7cfb\u6570&#xff08;$ R^2 $&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>            R<\/p>\n<p>            2<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           \u2212<\/p>\n<p>             \u2211<\/p>\n<p>             (<\/p>\n<p>              y<\/p>\n<p>              i<\/p>\n<p>             \u2212<\/p>\n<p>               y<\/p>\n<p>               ^<\/p>\n<p>              i<\/p>\n<p>              )<\/p>\n<p>              2<\/p>\n<p>             \u2211<\/p>\n<p>             (<\/p>\n<p>              y<\/p>\n<p>              i<\/p>\n<p>             \u2212<\/p>\n<p>              y<\/p>\n<p>              \u02c9<\/p>\n<p>              )<\/p>\n<p>              2<\/p>\n<p>           R^2 &#061; 1 &#8211; \\\\frac{\\\\sum (y_i &#8211; \\\\hat{y}_i)^2}{\\\\sum (y_i &#8211; \\\\bar{y})^2} <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8641em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4271em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4911em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" 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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/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 class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" 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\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/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 class=\"\" 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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8861\u91cf\u6a21\u578b\u89e3\u91ca\u7684\u65b9\u5dee\u6bd4\u4f8b\u3002$ R^2 &#061; 1 $ \u4e3a\u5b8c\u7f8e&#xff0c;0 \u4e3a\u5e38\u6570\u9884\u6d4b&#xff0c;\u8d1f\u503c\u8868\u793a\u6bd4\u5747\u503c\u8fd8\u5dee\u3002<\/p>\n<\/li>\n<\/ul>\n<h4>5.3 \u6392\u5e8f\u4e0e\u63a8\u8350\u6307\u6807<\/h4>\n<ul>\n<li>NDCG&#xff08;Normalized Discounted Cumulative Gain&#xff09;&#xff1a;\u8861\u91cf\u6392\u5e8f\u8d28\u91cf&#xff1b;<\/li>\n<li>MAP&#xff08;Mean Average Precision&#xff09;&#xff1a;\u4fe1\u606f\u68c0\u7d22\u5e38\u7528\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u516d\u3001\u6a21\u578b\u9009\u62e9\u4e0e\u8d85\u53c2\u8c03\u4f18<\/h3>\n<h4>6.1 \u7f51\u683c\u641c\u7d22&#xff08;Grid Search&#xff09;<\/h4>\n<p>\u904d\u5386\u9884\u5b9a\u4e49\u7684\u8d85\u53c2\u7ec4\u5408&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> GridSearchCV<\/p>\n<p>param_grid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token string\">&#039;C&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;kernel&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;rbf&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;linear&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><br \/>\ngrid <span class=\"token operator\">&#061;<\/span> GridSearchCV<span class=\"token punctuation\">(<\/span>SVC<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> param_grid<span class=\"token punctuation\">,<\/span> cv<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> scoring<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;accuracy&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\ngrid<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X_train<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Best params:&#034;<\/span><span class=\"token punctuation\">,<\/span> grid<span class=\"token punctuation\">.<\/span>best_params_<span class=\"token punctuation\">)<\/span><\/p>\n<h4>6.2 \u968f\u673a\u641c\u7d22&#xff08;Random Search&#xff09;<\/h4>\n<p>\u5728\u8d85\u53c2\u7a7a\u95f4\u968f\u673a\u91c7\u6837&#xff0c;\u901a\u5e38\u6bd4\u7f51\u683c\u641c\u7d22\u66f4\u9ad8\u6548&#xff08;\u5c24\u5176\u5f53\u67d0\u4e9b\u53c2\u6570\u5f71\u54cd\u66f4\u5927\u65f6&#xff09;\u3002<\/p>\n<h4>6.3 \u8d1d\u53f6\u65af\u4f18\u5316&#xff08;Bayesian Optimization&#xff09;<\/h4>\n<p>\u4f7f\u7528\u6982\u7387\u6a21\u578b&#xff08;\u5982\u9ad8\u65af\u8fc7\u7a0b&#xff09;\u5efa\u6a21\u201c\u8d85\u53c2 \u2192 \u6027\u80fd\u201d\u6620\u5c04&#xff0c;\u667a\u80fd\u9009\u62e9\u4e0b\u4e00\u4e2a\u8bc4\u4f30\u70b9&#xff0c;\u6781\u5927\u51cf\u5c11\u8c03\u4f18\u6b21\u6570\u3002<\/p>\n<p>\u2705 \u5b9e\u8df5\u5efa\u8bae&#xff1a;\u5c0f\u6570\u636e\u7528 Grid Search&#xff0c;\u5927\u6570\u636e\u7528 Random\/Bayesian Search\u3002<\/p>\n<hr \/>\n<h3>\u4e03\u3001\u6a21\u578b\u76d1\u63a7\u4e0e\u6982\u5ff5\u6f02\u79fb\u68c0\u6d4b<\/h3>\n<p>\u6a21\u578b\u90e8\u7f72\u540e&#xff0c;\u6570\u636e\u5206\u5e03\u53ef\u80fd\u968f\u65f6\u95f4\u53d8\u5316&#xff08;\u6982\u5ff5\u6f02\u79fb&#xff0c;Concept Drift&#xff09;&#xff0c;\u5bfc\u81f4\u6027\u80fd\u4e0b\u964d\u3002<\/p>\n<h4>7.1 \u6f02\u79fb\u7c7b\u578b<\/h4>\n<ul>\n<li>\u7a81\u53d1\u6f02\u79fb&#xff08;Sudden Drift&#xff09;&#xff1a;\u5206\u5e03\u7a81\u53d8&#xff08;\u5982\u653f\u7b56\u53d8\u5316&#xff09;&#xff1b;<\/li>\n<li>\u6e10\u8fdb\u6f02\u79fb&#xff08;Gradual Drift&#xff09;&#xff1a;\u7f13\u6162\u53d8\u5316&#xff08;\u5982\u7528\u6237\u504f\u597d\u6f14\u53d8&#xff09;&#xff1b;<\/li>\n<li>\u5468\u671f\u6027\u6f02\u79fb&#xff08;Recurring Drift&#xff09;&#xff1a;\u5b63\u8282\u6027\u6a21\u5f0f\u3002<\/li>\n<\/ul>\n<h4>7.2 \u68c0\u6d4b\u65b9\u6cd5<\/h4>\n<h5>7.2.1 \u7edf\u8ba1\u68c0\u9a8c<\/h5>\n<ul>\n<li>KS \u68c0\u9a8c&#xff08;Kolmogorov-Smirnov&#xff09;&#xff1a;\u6bd4\u8f83\u4e24\u6837\u672c\u5206\u5e03\u662f\u5426\u76f8\u540c&#xff1b;<\/li>\n<li>\u5361\u65b9\u68c0\u9a8c&#xff1a;\u7528\u4e8e\u5206\u7c7b\u7279\u5f81\u3002<\/li>\n<\/ul>\n<h5>7.2.2 \u57fa\u4e8e\u6a21\u578b\u7684\u65b9\u6cd5<\/h5>\n<ul>\n<li>\u6f02\u79fb\u68c0\u6d4b\u5668&#xff08;\u5982 ADWIN\u3001DDM&#xff09;&#xff1a;\u76d1\u63a7\u9884\u6d4b\u8bef\u5dee&#xff0c;\u82e5\u663e\u8457\u4e0a\u5347\u5219\u62a5\u8b66&#xff1b;<\/li>\n<li>\u53cc\u6a21\u578b\u6cd5&#xff1a;\u8bad\u7ec3\u4e24\u4e2a\u6a21\u578b&#xff08;\u65e7 vs \u65b0&#xff09;&#xff0c;\u82e5\u65b0\u6a21\u578b\u663e\u8457\u66f4\u597d&#xff0c;\u5219\u5b58\u5728\u6f02\u79fb\u3002<\/li>\n<\/ul>\n<h5>7.2.3 \u7279\u5f81\u5206\u5e03\u76d1\u63a7<\/h5>\n<p>\u5b9a\u671f\u8ba1\u7b97\u7279\u5f81\u7684\u5747\u503c\u3001\u65b9\u5dee\u3001\u76f4\u65b9\u56fe&#xff0c;\u4e0e\u57fa\u7ebf\u6bd4\u8f83\u3002<\/p>\n<p><span class=\"token comment\"># \u76d1\u63a7\u6570\u503c\u7279\u5f81\u5747\u503c\u6f02\u79fb<\/span><br \/>\nbaseline_mean <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>X_train<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\ncurrent_mean <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span>X_current_batch<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token builtin\">abs<\/span><span class=\"token punctuation\">(<\/span>current_mean <span class=\"token operator\">&#8211;<\/span> baseline_mean<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&gt;<\/span> threshold<span class=\"token punctuation\">:<\/span><br \/>\n    alert<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Feature drift detected!&#034;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<hr \/>\n<h3>\u516b\u3001\u53ef\u4fe1 AI&#xff1a;\u516c\u5e73\u6027\u3001\u53ef\u89e3\u91ca\u6027\u4e0e\u4e0d\u786e\u5b9a\u6027<\/h3>\n<h4>8.1 \u516c\u5e73\u6027&#xff08;Fairness&#xff09;<\/h4>\n<p>\u6a21\u578b\u4e0d\u5e94\u56e0\u654f\u611f\u5c5e\u6027&#xff08;\u5982\u6027\u522b\u3001\u79cd\u65cf&#xff09;\u4ea7\u751f\u6b67\u89c6\u6027\u7ed3\u679c\u3002<\/p>\n<h5>\u5e38\u89c1\u516c\u5e73\u6027\u5b9a\u4e49<\/h5>\n<ul>\n<li>\n<p>\u4eba\u53e3\u5747\u7b49&#xff08;Demographic Parity&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>            Y<\/p>\n<p>            ^<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           &#061;<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>           &#061;<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>            Y<\/p>\n<p>            ^<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           &#061;<\/p>\n<p>           b<\/p>\n<p>           )<\/p>\n<p>           P(\\\\hat{Y}&#061;1 \\\\mid A&#061;a) &#061; P(\\\\hat{Y}&#061;1 \\\\mid A&#061;b) <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1968em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9468em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">\u2223<\/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\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1968em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9468em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">\u2223<\/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\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">b<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u5404\u7fa4\u4f53\u9884\u6d4b\u4e3a\u6b63\u7684\u6bd4\u4f8b\u76f8\u540c\u3002<\/p>\n<\/li>\n<li>\n<p>\u673a\u4f1a\u5747\u7b49&#xff08;Equal Opportunity&#xff09;&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>            Y<\/p>\n<p>            ^<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           \u2223<\/p>\n<p>           Y<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           ,<\/p>\n<p>           A<\/p>\n<p>           &#061;<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>           &#061;<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>            Y<\/p>\n<p>            ^<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           \u2223<\/p>\n<p>           Y<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>           ,<\/p>\n<p>           A<\/p>\n<p>           &#061;<\/p>\n<p>           b<\/p>\n<p>           )<\/p>\n<p>           P(\\\\hat{Y}&#061;1 \\\\mid Y&#061;1, A&#061;a) &#061; P(\\\\hat{Y}&#061;1 \\\\mid Y&#061;1, A&#061;b) <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1968em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9468em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">\u2223<\/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: 0.2222em\">Y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1968em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9468em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">\u2223<\/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: 0.2222em\">Y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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\">b<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span> \u5404\u7fa4\u4f53\u4e2d\u771f\u5b9e\u6b63\u4f8b\u88ab\u6b63\u786e\u8bc6\u522b\u7684\u6bd4\u4f8b\u76f8\u540c\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u2705 \u5de5\u5177&#xff1a;IBM AI Fairness 360\u3001Google What-If Tool\u3002<\/p>\n<h4>8.2 \u53ef\u89e3\u91ca\u6027&#xff08;Interpretability&#xff09;<\/h4>\n<ul>\n<li>\u5168\u5c40\u89e3\u91ca&#xff1a;\u7406\u89e3\u6a21\u578b\u6574\u4f53\u884c\u4e3a&#xff08;\u5982\u7279\u5f81\u91cd\u8981\u6027&#xff09;&#xff1b;<\/li>\n<li>\u5c40\u90e8\u89e3\u91ca&#xff1a;\u89e3\u91ca\u5355\u4e2a\u9884\u6d4b&#xff08;\u5982 LIME\u3001SHAP&#xff09;\u3002<\/li>\n<\/ul>\n<p><span class=\"token keyword\">import<\/span> shap<\/p>\n<p>explainer <span class=\"token operator\">&#061;<\/span> shap<span class=\"token punctuation\">.<\/span>TreeExplainer<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">)<\/span><br \/>\nshap_values <span class=\"token operator\">&#061;<\/span> explainer<span class=\"token punctuation\">.<\/span>shap_values<span class=\"token punctuation\">(<\/span>X_test<span class=\"token punctuation\">)<\/span><br \/>\nshap<span class=\"token punctuation\">.<\/span>summary_plot<span class=\"token punctuation\">(<\/span>shap_values<span class=\"token punctuation\">,<\/span> X_test<span class=\"token punctuation\">)<\/span><\/p>\n<h4>8.3 \u4e0d\u786e\u5b9a\u6027\u91cf\u5316&#xff08;Uncertainty Quantification&#xff09;<\/h4>\n<p>\u6a21\u578b\u5e94\u8f93\u51fa\u9884\u6d4b\u7684\u7f6e\u4fe1\u5ea6\u3002<\/p>\n<ul>\n<li>\u8d1d\u53f6\u65af\u65b9\u6cd5&#xff1a;\u901a\u8fc7\u540e\u9a8c\u5206\u5e03\u91cf\u5316\u4e0d\u786e\u5b9a\u6027&#xff1b;<\/li>\n<li>\u96c6\u6210\u65b9\u6cd5&#xff1a;\u591a\u4e2a\u6a21\u578b\u9884\u6d4b\u7684\u65b9\u5dee\u53cd\u6620\u4e0d\u786e\u5b9a\u6027&#xff1b;<\/li>\n<li>\u8499\u7279\u5361\u6d1b Dropout&#xff1a;\u5728\u63a8\u7406\u65f6\u542f\u7528 Dropout \u591a\u6b21\u91c7\u6837\u3002<\/li>\n<\/ul>\n<p>\u2705 \u5e94\u7528&#xff1a;\u9ad8\u4e0d\u786e\u5b9a\u6027\u6837\u672c\u53ef\u8f6c\u4eba\u5de5\u5ba1\u6838\u3002<\/p>\n<hr \/>\n<h3>\u4e5d\u3001\u52a8\u624b\u5b9e\u6218&#xff1a;\u6784\u5efa\u7aef\u5230\u7aef\u8bc4\u4f30\u6d41\u6c34\u7ebf<\/h3>\n<p>\u6211\u4eec\u5c06\u4ee5\u4fe1\u7528\u5361\u6b3a\u8bc8\u68c0\u6d4b\u4e3a\u4f8b&#xff0c;\u6f14\u793a\u5b8c\u6574\u6d41\u7a0b\u3002<\/p>\n<p><span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<br \/>\n<span class=\"token keyword\">import<\/span> pandas <span class=\"token keyword\">as<\/span> pd<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>ensemble <span class=\"token keyword\">import<\/span> RandomForestClassifier<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> StratifiedKFold<span class=\"token punctuation\">,<\/span> cross_validate<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> classification_report<span class=\"token punctuation\">,<\/span> roc_auc_score<span class=\"token punctuation\">,<\/span> precision_recall_curve<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>preprocessing <span class=\"token keyword\">import<\/span> StandardScaler<br \/>\n<span class=\"token keyword\">import<\/span> matplotlib<span class=\"token punctuation\">.<\/span>pyplot <span class=\"token keyword\">as<\/span> plt<\/p>\n<p><span class=\"token comment\"># 1. \u52a0\u8f7d\u6570\u636e&#xff08;\u6a21\u62df&#xff09;<\/span><br \/>\n<span class=\"token comment\"># \u5047\u8bbe df \u5305\u542b features \u548c target &#039;is_fraud&#039;<\/span><br \/>\n<span class=\"token comment\"># X, y &#061; df.drop(&#039;is_fraud&#039;, axis&#061;1), df[&#039;is_fraud&#039;]<\/span><\/p>\n<p><span class=\"token comment\"># 2. \u5206\u5c42\u5212\u5206&#xff08;\u56e0\u6b3a\u8bc8\u6837\u672c\u7a00\u758f&#xff09;<\/span><br \/>\nskf <span class=\"token operator\">&#061;<\/span> StratifiedKFold<span class=\"token punctuation\">(<\/span>n_splits<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span> shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 3. \u5b9a\u4e49\u6a21\u578b\u4e0e\u9884\u5904\u7406\u5668<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> RandomForestClassifier<span class=\"token punctuation\">(<\/span>n_estimators<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><br \/>\nscaler <span class=\"token operator\">&#061;<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 4. \u4ea4\u53c9\u9a8c\u8bc1\u8bc4\u4f30&#xff08;\u591a\u6307\u6807&#xff09;<\/span><br \/>\nscoring <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;roc_auc&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;precision&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;recall&#039;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;f1&#039;<\/span><span class=\"token punctuation\">]<\/span><br \/>\ncv_results <span class=\"token operator\">&#061;<\/span> cross_validate<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">,<\/span> X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> cv<span class=\"token operator\">&#061;<\/span>skf<span class=\"token punctuation\">,<\/span> scoring<span class=\"token operator\">&#061;<\/span>scoring<span class=\"token punctuation\">,<\/span> return_train_score<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u6253\u5370\u7ed3\u679c<\/span><br \/>\n<span class=\"token keyword\">for<\/span> metric <span class=\"token keyword\">in<\/span> scoring<span class=\"token punctuation\">:<\/span><br \/>\n    scores <span class=\"token operator\">&#061;<\/span> cv_results<span class=\"token punctuation\">[<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#039;test_<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>metric<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">&#039;<\/span><\/span><span class=\"token punctuation\">]<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string-interpolation\"><span class=\"token string\">f&#034;<\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>metric<span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">: <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>scores<span class=\"token punctuation\">.<\/span>mean<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\"> (&#043;\/- <\/span><span class=\"token interpolation\"><span class=\"token punctuation\">{<\/span>scores<span class=\"token punctuation\">.<\/span>std<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">*<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">:<\/span><span class=\"token format-spec\">.3f<\/span><span class=\"token punctuation\">}<\/span><\/span><span class=\"token string\">)&#034;<\/span><\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 6. \u6700\u7ec8\u8bad\u7ec3\u4e0e\u6d4b\u8bd5<\/span><br \/>\nX_train<span class=\"token punctuation\">,<\/span> X_test<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span> stratify<span class=\"token operator\">&#061;<\/span>y<span class=\"token punctuation\">,<\/span> random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">42<\/span><span class=\"token punctuation\">)<\/span><br \/>\nX_train_scaled <span class=\"token operator\">&#061;<\/span> scaler<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>X_train<span class=\"token punctuation\">)<\/span><br \/>\nX_test_scaled <span class=\"token operator\">&#061;<\/span> scaler<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>X_test<span class=\"token punctuation\">)<\/span><\/p>\n<p>model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X_train_scaled<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">)<\/span><br \/>\ny_proba <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict_proba<span class=\"token punctuation\">(<\/span>X_test_scaled<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p><span class=\"token comment\"># 7. PR \u66f2\u7ebf&#xff08;\u56e0\u6b63\u4f8b\u7a00\u758f&#xff09;<\/span><br \/>\nprecision<span class=\"token punctuation\">,<\/span> recall<span class=\"token punctuation\">,<\/span> thresholds <span class=\"token operator\">&#061;<\/span> precision_recall_curve<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_proba<span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>plot<span class=\"token punctuation\">(<\/span>recall<span class=\"token punctuation\">,<\/span> precision<span class=\"token punctuation\">,<\/span> label<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;PR Curve&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>xlabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Recall&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>ylabel<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Precision&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;Precision-Recall Curve for Fraud Detection&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># 8. \u7279\u5f81\u91cd\u8981\u6027<\/span><br \/>\nimportances <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>feature_importances_<br \/>\nindices <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>argsort<span class=\"token punctuation\">(<\/span>importances<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">:<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>bar<span class=\"token punctuation\">(<\/span><span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> importances<span class=\"token punctuation\">[<\/span>indices<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>title<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;Top 10 Feature Importances&#034;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nplt<span class=\"token punctuation\">.<\/span>show<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>\u2705 \u5173\u952e\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u4f7f\u7528 StratifiedKFold \u5904\u7406\u4e0d\u5e73\u8861\u6570\u636e&#xff1b;<\/li>\n<li>\u8bc4\u4f30\u6307\u6807\u9009\u7528 AUC\u3001Precision\u3001Recall&#xff08;\u800c\u975e Accuracy&#xff09;&#xff1b;<\/li>\n<li>\u6700\u7ec8\u7528 PR \u66f2\u7ebf \u800c\u975e ROC&#xff08;\u56e0\u6b63\u4f8b&lt;1%&#xff09;\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u5341\u3001A\/B \u6d4b\u8bd5&#xff1a;\u7ebf\u4e0a\u9a8c\u8bc1\u7684\u9ec4\u91d1\u6807\u51c6<\/h3>\n<p>\u6a21\u578b\u79bb\u7ebf\u8bc4\u4f30\u826f\u597d&#xff0c;\u4e0d\u4ee3\u8868\u7ebf\u4e0a\u6709\u6548\u3002A\/B \u6d4b\u8bd5\u662f\u9a8c\u8bc1\u6a21\u578b\u4e1a\u52a1\u4ef7\u503c\u7684\u7ec8\u6781\u624b\u6bb5\u3002<\/p>\n<h4>10.1 \u8bbe\u8ba1\u539f\u5219<\/h4>\n<ul>\n<li>\u968f\u673a\u5206\u7ec4&#xff1a;\u7528\u6237\u968f\u673a\u5206\u914d\u5230\u5bf9\u7167\u7ec4&#xff08;\u65e7\u6a21\u578b&#xff09;\u548c\u5b9e\u9a8c\u7ec4&#xff08;\u65b0\u6a21\u578b&#xff09;&#xff1b;<\/li>\n<li>\u5355\u4e00\u53d8\u91cf&#xff1a;\u53ea\u6539\u53d8\u6a21\u578b&#xff0c;\u5176\u4ed6\u6761\u4ef6\u4e00\u81f4&#xff1b;<\/li>\n<li>\u8db3\u591f\u6837\u672c\u91cf&#xff1a;\u786e\u4fdd\u7edf\u8ba1\u663e\u8457\u6027&#xff1b;<\/li>\n<li>\u9884\u5b9a\u4e49\u6307\u6807&#xff1a;\u5982\u70b9\u51fb\u7387\u3001\u8f6c\u5316\u7387\u3001GMV\u3002<\/li>\n<\/ul>\n<h4>10.2 \u7edf\u8ba1\u663e\u8457\u6027\u68c0\u9a8c<\/h4>\n<p>\u4f7f\u7528 \u53cc\u6837\u672c t \u68c0\u9a8c \u6216 Z \u68c0\u9a8c \u5224\u65ad\u5dee\u5f02\u662f\u5426\u663e\u8457&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         Z<\/p>\n<p>         &#061;<\/p>\n<p>             X<\/p>\n<p>             \u02c9<\/p>\n<p>            1<\/p>\n<p>           \u2212<\/p>\n<p>             X<\/p>\n<p>             \u02c9<\/p>\n<p>            2<\/p>\n<p>              \u03c3<\/p>\n<p>              1<\/p>\n<p>              2<\/p>\n<p>              n<\/p>\n<p>              1<\/p>\n<p>            &#043;<\/p>\n<p>              \u03c3<\/p>\n<p>              2<\/p>\n<p>              2<\/p>\n<p>              n<\/p>\n<p>              2<\/p>\n<p>         Z &#061; \\\\frac{\\\\bar{X}_1 &#8211; \\\\bar{X}_2}{\\\\sqrt{\\\\frac{\\\\sigma_1^2}{n_1} &#043; \\\\frac{\\\\sigma_2^2}{n_2}}} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">Z<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.2271em;vertical-align: -1.73em\"><\/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: 1.4971em\"><span class=\"\" style=\"top: -2.11em\"><span class=\"pstrut\" style=\"height: 3.3083em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3083em\"><span class=\"svg-align\" style=\"top: -3.8em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/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: 1.0916em\"><span class=\"\" 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\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" 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\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5281em\"><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 mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8051em\"><span class=\"\" style=\"top: -2.1885em;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\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8448em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3115em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/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: 1.0916em\"><span class=\"\" 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\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" 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\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.5281em\"><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 mathnormal mtight\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8051em\"><span class=\"\" style=\"top: -2.1885em;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\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8448em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3115em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2683em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.88em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5317em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5383em\"><span class=\"pstrut\" style=\"height: 3.3083em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.9853em\"><span class=\"pstrut\" style=\"height: 3.3083em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8201em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0785em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8201em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><\/span><span class=\"\" style=\"top: -3.2523em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0785em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.73em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u82e5 $ |Z| &gt; 1.96 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        &#xff08;<\/p>\n<p>       &#xff08;<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord cjk_fallback\">&#xff08;<\/span><\/span><\/span><\/span><\/span> \\\\alpha &#061; 0.05 $&#xff09;&#xff0c;\u5219\u62d2\u7edd\u539f\u5047\u8bbe&#xff08;\u65e0\u5dee\u5f02&#xff09;\u3002<\/p>\n<p>\u2705 \u6ce8\u610f&#xff1a;\u907f\u514d\u201c\u91cd\u590d peeking\u201d&#xff08;\u591a\u6b21\u68c0\u67e5\u7ed3\u679c&#xff09;&#xff0c;\u5426\u5219\u4f1a 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