{"id":47389,"date":"2025-07-30T07:36:51","date_gmt":"2025-07-29T23:36:51","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/47389.html"},"modified":"2025-07-30T07:36:51","modified_gmt":"2025-07-29T23:36:51","slug":"%e6%b7%b1%e5%85%a5%e7%90%86%e8%a7%a3%e6%ad%a3%e5%88%99%e5%8c%96%ef%bc%9a%e5%8e%9f%e7%90%86%e3%80%81%e4%bd%9c%e7%94%a8%e4%b8%8e%e5%b8%b8%e8%a7%81%e6%96%b9%e6%b3%95%e5%ae%9e%e8%b7%b5","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/47389.html","title":{"rendered":"\u6df1\u5165\u7406\u89e3\u6b63\u5219\u5316\uff1a\u539f\u7406\u3001\u4f5c\u7528\u4e0e\u5e38\u89c1\u65b9\u6cd5\u5b9e\u8df5"},"content":{"rendered":"<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\n<ul>\n<li>1. \u6b63\u5219\u5316\u6982\u8ff0<\/li>\n<li>\n<ul>\n<li>1.1 \u4e3a\u4ec0\u4e48\u9700\u8981\u6b63\u5219\u5316&#xff1f;<\/li>\n<li>1.2 \u6b63\u5219\u5316\u7684\u6570\u5b66\u672c\u8d28<\/li>\n<\/ul>\n<\/li>\n<li>2. \u6b63\u5219\u5316\u7684\u4e3b\u8981\u4f5c\u7528<\/li>\n<li>\n<ul>\n<li>2.1 \u9632\u6b62\u8fc7\u62df\u5408<\/li>\n<li>2.2 \u6539\u5584\u6a21\u578b\u6cdb\u5316\u80fd\u529b<\/li>\n<li>2.3 \u7279\u5f81\u9009\u62e9<\/li>\n<li>2.4 \u89e3\u51b3\u75c5\u6001\u95ee\u9898<\/li>\n<li>2.5 \u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6<\/li>\n<\/ul>\n<\/li>\n<li>3. \u5e38\u89c1\u6b63\u5219\u5316\u65b9\u6cd5<\/li>\n<li>\n<ul>\n<li>3.1 L1\u6b63\u5219\u5316&#xff08;Lasso\u56de\u5f52&#xff09;<\/li>\n<li>3.2 L2\u6b63\u5219\u5316&#xff08;Ridge\u56de\u5f52&#xff09;<\/li>\n<li>3.3 \u5f39\u6027\u7f51\u7edc(Elastic Net)<\/li>\n<li>3.4 Dropout&#xff08;\u795e\u7ecf\u7f51\u7edc&#xff09;<\/li>\n<li>3.5 \u65e9\u505c\u6cd5(Early Stopping)<\/li>\n<li>3.6 \u6570\u636e\u589e\u5f3a<\/li>\n<\/ul>\n<\/li>\n<li>4. \u6b63\u5219\u5316\u65b9\u6cd5\u6bd4\u8f83\u4e0e\u9009\u62e9<\/li>\n<li>\n<ul>\n<li>4.1 \u4e0d\u540c\u6b63\u5219\u5316\u65b9\u6cd5\u5bf9\u6bd4<\/li>\n<li>4.2 \u6b63\u5219\u5316\u65b9\u6cd5\u9009\u62e9\u6d41\u7a0b\u56fe<\/li>\n<\/ul>\n<\/li>\n<li>5. \u6b63\u5219\u5316\u8d85\u53c2\u6570\u8c03\u4f18<\/li>\n<li>\n<ul>\n<li>5.1 \u7f51\u683c\u641c\u7d22<\/li>\n<li>5.2 \u968f\u673a\u641c\u7d22<\/li>\n<\/ul>\n<\/li>\n<li>6. \u6b63\u5219\u5316\u5728\u5b9e\u9645\u9879\u76ee\u4e2d\u7684\u5e94\u7528\u6848\u4f8b<\/li>\n<li>\n<ul>\n<li>6.1 \u6848\u4f8b&#xff1a;\u623f\u4ef7\u9884\u6d4b<\/li>\n<li>6.2 \u6848\u4f8b&#xff1a;\u6587\u672c\u5206\u7c7b&#xff08;\u795e\u7ecf\u7f51\u7edc&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>7. \u6b63\u5219\u5316\u7684\u6ce8\u610f\u4e8b\u9879<\/li>\n<li>8. \u603b\u7ed3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>1. \u6b63\u5219\u5316\u6982\u8ff0<\/h3>\n<p>\u6b63\u5219\u5316(Regularization)\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u7528\u4e8e\u9632\u6b62\u6a21\u578b\u8fc7\u62df\u5408\u7684\u6838\u5fc3\u6280\u672f\u4e4b\u4e00\u3002\u5b83\u901a\u8fc7\u5728\u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5f15\u5165\u989d\u5916\u7684\u7ea6\u675f\u6216\u60e9\u7f5a\u9879&#xff0c;\u9650\u5236\u6a21\u578b\u590d\u6742\u5ea6&#xff0c;\u4ece\u800c\u63d0\u9ad8\u6a21\u578b\u5728\u672a\u89c1\u6570\u636e\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<h4>1.1 \u4e3a\u4ec0\u4e48\u9700\u8981\u6b63\u5219\u5316&#xff1f;<\/h4>\n<p>\u5f53\u6a21\u578b\u8fc7\u5ea6\u590d\u6742\u65f6&#xff0c;\u5b83\u53ef\u80fd\u4f1a&#034;\u8bb0\u4f4f&#034;\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u566a\u58f0\u548c\u7ec6\u8282&#xff0c;\u800c\u4e0d\u662f\u5b66\u4e60\u6570\u636e\u7684\u771f\u5b9e\u6a21\u5f0f&#xff0c;\u8fd9\u79cd\u73b0\u8c61\u79f0\u4e3a\u8fc7\u62df\u5408(Overfitting)\u3002\u6b63\u5219\u5316\u7684\u4e3b\u8981\u76ee\u7684\u5c31\u662f\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898&#xff1a;<\/p>\n<ul>\n<li>\u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6&#xff1a;\u9632\u6b62\u6a21\u578b\u53d8\u5f97\u8fc7\u4e8e\u590d\u6742<\/li>\n<li>\u63d0\u9ad8\u6cdb\u5316\u80fd\u529b&#xff1a;\u4f7f\u6a21\u578b\u5728\u65b0\u6570\u636e\u4e0a\u8868\u73b0\u66f4\u597d<\/li>\n<li>\u7279\u5f81\u9009\u62e9&#xff1a;\u67d0\u4e9b\u6b63\u5219\u5316\u65b9\u6cd5\u53ef\u4ee5\u81ea\u52a8\u9009\u62e9\u91cd\u8981\u7279\u5f81<\/li>\n<\/ul>\n<h4>1.2 \u6b63\u5219\u5316\u7684\u6570\u5b66\u672c\u8d28<\/h4>\n<p>\u4ece\u6570\u5b66\u89d2\u5ea6\u770b&#xff0c;\u6b63\u5219\u5316\u901a\u5e38\u901a\u8fc7\u5728\u635f\u5931\u51fd\u6570\u4e2d\u6dfb\u52a0\u60e9\u7f5a\u9879\u6765\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u603b\u635f\u5931<\/p>\n<p>         &#061;<\/p>\n<p>         \u539f\u59cb\u635f\u5931\u51fd\u6570<\/p>\n<p>         &#043;<\/p>\n<p>         \u03bb<\/p>\n<p>         \u00d7<\/p>\n<p>         \u6b63\u5219\u5316\u9879<\/p>\n<p>         \\\\text{\u603b\u635f\u5931} &#061; \\\\text{\u539f\u59cb\u635f\u5931\u51fd\u6570} &#043; \\\\lambda \\\\times \\\\text{\u6b63\u5219\u5316\u9879} <\/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 cjk_fallback\">\u603b\u635f\u5931<\/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: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u539f\u59cb\u635f\u5931\u51fd\u6570<\/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: 0.7778em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u6b63\u5219\u5316\u9879<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03bb<\/p>\n<p>        \\\\lambda<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><\/span><\/span><\/span><\/span> \u662f\u6b63\u5219\u5316\u5f3a\u5ea6&#xff08;\u8d85\u53c2\u6570&#xff09;<\/li>\n<li>\u6b63\u5219\u5316\u9879\u901a\u5e38\u662f\u6a21\u578b\u53c2\u6570\u7684\u51fd\u6570<\/li>\n<\/ul>\n<h3>2. \u6b63\u5219\u5316\u7684\u4e3b\u8981\u4f5c\u7528<\/h3>\n<h4>2.1 \u9632\u6b62\u8fc7\u62df\u5408<\/h4>\n<p>\u8fd9\u662f\u6b63\u5219\u5316\u7684\u6700\u4e3b\u8981\u4f5c\u7528\u3002\u901a\u8fc7\u7ea6\u675f\u6a21\u578b\u53c2\u6570\u7684\u5927\u5c0f&#xff0c;\u6b63\u5219\u5316\u53ef\u4ee5\u9650\u5236\u6a21\u578b\u7684\u5b66\u4e60\u80fd\u529b&#xff0c;\u4f7f\u5176\u65e0\u6cd5\u8fc7\u5ea6\u62df\u5408\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u566a\u58f0\u3002<\/p>\n<h4>2.2 \u6539\u5584\u6a21\u578b\u6cdb\u5316\u80fd\u529b<\/h4>\n<p>\u6b63\u5219\u5316\u540e\u7684\u6a21\u578b\u901a\u5e38\u5728\u6d4b\u8bd5\u96c6\u6216\u65b0\u6570\u636e\u4e0a\u8868\u73b0\u66f4\u597d&#xff0c;\u56e0\u4e3a\u5b83\u5b66\u4e60\u7684\u662f\u6570\u636e\u4e2d\u66f4\u4e00\u822c\u7684\u6a21\u5f0f\u800c\u4e0d\u662f\u7279\u5b9a\u6837\u672c\u7684\u7279\u6027\u3002<\/p>\n<h4>2.3 \u7279\u5f81\u9009\u62e9<\/h4>\n<p>\u67d0\u4e9b\u6b63\u5219\u5316\u65b9\u6cd5&#xff08;\u5982L1\u6b63\u5219\u5316&#xff09;\u53ef\u4ee5\u4ea7\u751f\u7a00\u758f\u89e3&#xff0c;\u81ea\u52a8\u6267\u884c\u7279\u5f81\u9009\u62e9&#xff0c;\u8bc6\u522b\u51fa\u5bf9\u9884\u6d4b\u6700\u91cd\u8981\u7684\u7279\u5f81\u3002<\/p>\n<h4>2.4 \u89e3\u51b3\u75c5\u6001\u95ee\u9898<\/h4>\n<p>\u5f53\u6570\u636e\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027\u6216\u7279\u5f81\u9ad8\u5ea6\u76f8\u5173\u65f6&#xff0c;\u6b63\u5219\u5316\u53ef\u4ee5\u5e2e\u52a9\u89e3\u51b3\u53c2\u6570\u4f30\u8ba1\u4e0d\u7a33\u5b9a\u7684\u95ee\u9898\u3002<\/p>\n<h4>2.5 \u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6<\/h4>\n<p>\u6b63\u5219\u5316\u63d0\u4f9b\u4e86\u4e00\u79cd\u660e\u786e\u7684\u65b9\u5f0f\u6765\u63a7\u5236\u6a21\u578b\u590d\u6742\u5ea6&#xff0c;\u5373\u4f7f\u5728\u4f7f\u7528\u590d\u6742\u6a21\u578b\u67b6\u6784\u65f6\u4e5f\u80fd\u4fdd\u6301\u5408\u7406\u7684\u590d\u6742\u5ea6\u3002<\/p>\n<h3>3. \u5e38\u89c1\u6b63\u5219\u5316\u65b9\u6cd5<\/h3>\n<h4>3.1 L1\u6b63\u5219\u5316&#xff08;Lasso\u56de\u5f52&#xff09;<\/h4>\n<p>L1\u6b63\u5219\u5316\u6dfb\u52a0\u6a21\u578b\u6743\u91cd\u7684\u7edd\u5bf9\u503c\u4e4b\u548c\u4f5c\u4e3a\u60e9\u7f5a\u9879&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u60e9\u7f5a\u9879<\/p>\n<p>         &#061;<\/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>          w<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>         \\\\text{\u60e9\u7f5a\u9879} &#061; \\\\sum_{i&#061;1}^{n} |w_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 cjk_fallback\">\u60e9\u7f5a\u9879<\/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=\"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: 0.0269em\">w<\/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: -0.0269em;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<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u4ea7\u751f\u7a00\u758f\u6743\u91cd\u5411\u91cf&#xff08;\u8bb8\u591a\u6743\u91cd\u6070\u597d\u4e3a0&#xff09;<\/li>\n<li>\u53ef\u7528\u4e8e\u7279\u5f81\u9009\u62e9<\/li>\n<li>\u5bf9\u5f02\u5e38\u503c\u66f4\u9c81\u68d2<\/li>\n<\/ul>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>linear_model <span class=\"token keyword\">import<\/span> Lasso<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\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>pipeline <span class=\"token keyword\">import<\/span> Pipeline<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_boston<\/p>\n<p><span class=\"token comment\"># \u52a0\u8f7d\u6570\u636e<\/span><br \/>\nX<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> load_boston<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efaL1\u6b63\u5219\u5316\u6a21\u578b\u7ba1\u9053<\/span><br \/>\nlasso_model <span class=\"token operator\">&#061;<\/span> Pipeline<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;scaler&#039;<\/span><span class=\"token punctuation\">,<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;lasso&#039;<\/span><span class=\"token punctuation\">,<\/span> Lasso<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># alpha\u662f\u6b63\u5219\u5316\u5f3a\u5ea6<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u6a21\u578b<\/span><br \/>\nlasso_model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u770b\u7cfb\u6570<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u975e\u96f6\u7279\u5f81\u6570\u91cf:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>lasso_model<span class=\"token punctuation\">.<\/span>named_steps<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;lasso&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>coef_ <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.2 L2\u6b63\u5219\u5316&#xff08;Ridge\u56de\u5f52&#xff09;<\/h4>\n<p>L2\u6b63\u5219\u5316\u6dfb\u52a0\u6a21\u578b\u6743\u91cd\u7684\u5e73\u65b9\u548c\u4f5c\u4e3a\u60e9\u7f5a\u9879&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u60e9\u7f5a\u9879<\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>          w<\/p>\n<p>          i<\/p>\n<p>          2<\/p>\n<p>         \\\\text{\u60e9\u7f5a\u9879} &#061; \\\\sum_{i&#061;1}^{n} w_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 cjk_fallback\">\u60e9\u7f5a\u9879<\/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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0269em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u4f7f\u6743\u91cd\u63a5\u8fd10\u4f46\u4e0d\u5b8c\u5168\u4e3a0<\/li>\n<li>\u5bf9\u76f8\u5173\u7279\u5f81\u7684\u5904\u7406\u66f4\u7a33\u5b9a<\/li>\n<li>\u5bf9\u5f02\u5e38\u503c\u654f\u611f<\/li>\n<\/ul>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>linear_model <span class=\"token keyword\">import<\/span> Ridge<\/p>\n<p><span class=\"token comment\"># \u521b\u5efaL2\u6b63\u5219\u5316\u6a21\u578b\u7ba1\u9053<\/span><br \/>\nridge_model <span class=\"token operator\">&#061;<\/span> Pipeline<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;scaler&#039;<\/span><span class=\"token punctuation\">,<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;ridge&#039;<\/span><span class=\"token punctuation\">,<\/span> Ridge<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># alpha\u662f\u6b63\u5219\u5316\u5f3a\u5ea6<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u6a21\u578b<\/span><br \/>\nridge_model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u770b\u7cfb\u6570<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u7cfb\u6570\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> np<span class=\"token punctuation\">.<\/span>linalg<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>ridge_model<span class=\"token punctuation\">.<\/span>named_steps<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;ridge&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>coef_<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.3 \u5f39\u6027\u7f51\u7edc(Elastic Net)<\/h4>\n<p>\u5f39\u6027\u7f51\u7edc\u7ed3\u5408\u4e86L1\u548cL2\u6b63\u5219\u5316&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u60e9\u7f5a\u9879<\/p>\n<p>         &#061;<\/p>\n<p>          \u03bb<\/p>\n<p>          1<\/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>          w<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>          \u03bb<\/p>\n<p>          2<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>          w<\/p>\n<p>          i<\/p>\n<p>          2<\/p>\n<p>         \\\\text{\u60e9\u7f5a\u9879} &#061; \\\\lambda_1 \\\\sum_{i&#061;1}^{n} |w_i| &#043; \\\\lambda_2 \\\\sum_{i&#061;1}^{n} w_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 cjk_fallback\">\u60e9\u7f5a\u9879<\/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=\"mord mathnormal\">\u03bb<\/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: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\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: 0.1667em\"><\/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: 0.0269em\">w<\/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: -0.0269em;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 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: 2.9291em;vertical-align: -1.2777em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/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: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\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: 0.1667em\"><\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0269em;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 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 class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u7ed3\u5408\u4e86L1\u548cL2\u7684\u4f18\u70b9<\/li>\n<li>\u9002\u7528\u4e8e\u7279\u5f81\u6570\u91cf\u591a\u4e8e\u6837\u672c\u6570\u7684\u60c5\u51b5<\/li>\n<li>\u53ef\u4ee5\u5904\u7406\u7279\u5f81\u95f4\u7684\u76f8\u5173\u6027<\/li>\n<\/ul>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>linear_model <span class=\"token keyword\">import<\/span> ElasticNet<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u5f39\u6027\u7f51\u7edc\u6a21\u578b<\/span><br \/>\nelastic_model <span class=\"token operator\">&#061;<\/span> Pipeline<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;scaler&#039;<\/span><span class=\"token punctuation\">,<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;elastic&#039;<\/span><span class=\"token punctuation\">,<\/span> ElasticNet<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> l1_ratio<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\"># l1_ratio\u63a7\u5236L1\/L2\u6df7\u5408\u6bd4\u4f8b<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>elastic_model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u67e5\u770b\u7ed3\u679c<\/span><br \/>\ncoef <span class=\"token operator\">&#061;<\/span> elastic_model<span class=\"token punctuation\">.<\/span>named_steps<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;elastic&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>coef_<br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u975e\u96f6\u7279\u5f81\u6570\u91cf:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>coef <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u7cfb\u6570\u8303\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> np<span class=\"token punctuation\">.<\/span>linalg<span class=\"token punctuation\">.<\/span>norm<span class=\"token punctuation\">(<\/span>coef<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.4 Dropout&#xff08;\u795e\u7ecf\u7f51\u7edc&#xff09;<\/h4>\n<p>Dropout\u662f\u795e\u7ecf\u7f51\u7edc\u7279\u6709\u7684\u6b63\u5219\u5316\u65b9\u6cd5&#xff0c;\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u968f\u673a&#034;\u4e22\u5f03&#034;&#xff08;\u5373\u6682\u65f6\u79fb\u9664&#xff09;\u4e00\u90e8\u5206\u795e\u7ecf\u5143\u3002<\/p>\n<p>\u5de5\u4f5c\u539f\u7406&#xff1a;<\/p>\n<li>\u6bcf\u4e2a\u8bad\u7ec3\u6b65\u9aa4\u4e2d&#xff0c;\u968f\u673a\u9009\u62e9\u4e00\u5b9a\u6bd4\u4f8b\u7684\u795e\u7ecf\u5143\u8bbe\u7f6e\u4e3a0<\/li>\n<li>\u524d\u5411\u4f20\u64ad\u548c\u53cd\u5411\u4f20\u64ad\u90fd\u53ea\u901a\u8fc7\u5269\u4f59\u7684\u795e\u7ecf\u5143<\/li>\n<li>\u6d4b\u8bd5\u65f6\u4f7f\u7528\u6240\u6709\u795e\u7ecf\u5143&#xff0c;\u4f46\u6743\u91cd\u6309dropout\u6bd4\u4f8b\u7f29\u653e<\/li>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>models <span class=\"token keyword\">import<\/span> Sequential<br \/>\n<span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>layers <span class=\"token keyword\">import<\/span> Dense<span class=\"token punctuation\">,<\/span> Dropout<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u5e26Dropout\u7684\u795e\u7ecf\u7f51\u7edc<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> Sequential<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> activation<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">,<\/span> input_shape<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">.<\/span>shape<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 punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dropout<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u4e22\u5f0350%\u7684\u795e\u7ecf\u5143<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span> activation<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dropout<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.3<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u4e22\u5f0330%\u7684\u795e\u7ecf\u5143<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>model<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">compile<\/span><span class=\"token punctuation\">(<\/span>optimizer<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;adam&#039;<\/span><span class=\"token punctuation\">,<\/span> loss<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;mse&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span> validation_split<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.5 \u65e9\u505c\u6cd5(Early Stopping)<\/h4>\n<p>\u65e9\u505c\u6cd5\u901a\u8fc7\u76d1\u63a7\u9a8c\u8bc1\u96c6\u6027\u80fd&#xff0c;\u5728\u6a21\u578b\u5f00\u59cb\u8fc7\u62df\u5408\u65f6\u505c\u6b62\u8bad\u7ec3\u3002<\/p>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>callbacks <span class=\"token keyword\">import<\/span> EarlyStopping<\/p>\n<p><span class=\"token comment\"># \u5b9a\u4e49\u65e9\u505c\u56de\u8c03<\/span><br \/>\nearly_stopping <span class=\"token operator\">&#061;<\/span> EarlyStopping<span class=\"token punctuation\">(<\/span><br \/>\n    monitor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;val_loss&#039;<\/span><span class=\"token punctuation\">,<\/span>  <span class=\"token comment\"># \u76d1\u63a7\u9a8c\u8bc1\u96c6\u635f\u5931<\/span><br \/>\n    patience<span class=\"token operator\">&#061;<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span>        <span class=\"token comment\"># \u5141\u8bb8\u6027\u80fd\u4e0d\u63d0\u5347\u7684epoch\u6570<\/span><br \/>\n    restore_best_weights<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span>  <span class=\"token comment\"># \u6062\u590d\u6700\u4f73\u6743\u91cd<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u6a21\u578b<\/span><br \/>\nhistory <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span><br \/>\n    X_train<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span><br \/>\n    validation_data<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>X_val<span class=\"token punctuation\">,<\/span> y_val<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1000<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    callbacks<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span>early_stopping<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    verbose<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<h4>3.6 \u6570\u636e\u589e\u5f3a<\/h4>\n<p>\u6570\u636e\u589e\u5f3a\u901a\u8fc7\u5bf9\u8bad\u7ec3\u6570\u636e\u8fdb\u884c\u968f\u673a\u53d8\u6362\u6765\u4eba\u5de5\u589e\u52a0\u6570\u636e\u591a\u6837\u6027&#xff0c;\u662f\u8ba1\u7b97\u673a\u89c6\u89c9\u4efb\u52a1\u4e2d\u5e38\u7528\u7684\u6b63\u5219\u5316\u65b9\u6cd5\u3002<\/p>\n<p>\u4ee3\u7801\u5b9e\u73b0&#xff08;\u56fe\u50cf\u5206\u7c7b&#xff09;&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>preprocessing<span class=\"token punctuation\">.<\/span>image <span class=\"token keyword\">import<\/span> ImageDataGenerator<\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u6570\u636e\u589e\u5f3a\u751f\u6210\u5668<\/span><br \/>\ndatagen <span class=\"token operator\">&#061;<\/span> ImageDataGenerator<span class=\"token punctuation\">(<\/span><br \/>\n    rotation_range<span class=\"token operator\">&#061;<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    width_shift_range<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    height_shift_range<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    shear_range<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    zoom_range<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    horizontal_flip<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    fill_mode<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;nearest&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u4f7f\u7528\u589e\u5f3a\u6570\u636e\u8bad\u7ec3\u6a21\u578b<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>datagen<span class=\"token punctuation\">.<\/span>flow<span class=\"token punctuation\">(<\/span>X_train<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span> batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n          steps_per_epoch<span class=\"token operator\">&#061;<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>X_train<span class=\"token punctuation\">)<\/span><span class=\"token operator\">\/<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">,<\/span><br \/>\n          epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<h3>4. \u6b63\u5219\u5316\u65b9\u6cd5\u6bd4\u8f83\u4e0e\u9009\u62e9<\/h3>\n<h4>4.1 \u4e0d\u540c\u6b63\u5219\u5316\u65b9\u6cd5\u5bf9\u6bd4<\/h4>\n<table>\n<tr>\u65b9\u6cd5\u7a00\u758f\u89e3\u7279\u5f81\u9009\u62e9\u5904\u7406\u76f8\u5173\u6027\u9002\u7528\u573a\u666f<\/tr>\n<tbody>\n<tr>\n<td>L1<\/td>\n<td>\u662f<\/td>\n<td>\u662f<\/td>\n<td>\u5426<\/td>\n<td>\u7279\u5f81\u9009\u62e9<\/td>\n<\/tr>\n<tr>\n<td>L2<\/td>\n<td>\u5426<\/td>\n<td>\u5426<\/td>\n<td>\u662f<\/td>\n<td>\u4e00\u822c\u56de\u5f52<\/td>\n<\/tr>\n<tr>\n<td>Elastic Net<\/td>\n<td>\u90e8\u5206<\/td>\n<td>\u662f<\/td>\n<td>\u662f<\/td>\n<td>\u9ad8\u7ef4\u6570\u636e<\/td>\n<\/tr>\n<tr>\n<td>Dropout<\/td>\n<td>\u5426<\/td>\n<td>\u5426<\/td>\n<td>&#8211;<\/td>\n<td>\u795e\u7ecf\u7f51\u7edc<\/td>\n<\/tr>\n<tr>\n<td>\u65e9\u505c\u6cd5<\/td>\n<td>\u5426<\/td>\n<td>\u5426<\/td>\n<td>&#8211;<\/td>\n<td>\u8fed\u4ee3\u8bad\u7ec3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>4.2 \u6b63\u5219\u5316\u65b9\u6cd5\u9009\u62e9\u6d41\u7a0b\u56fe<\/h4>\n<p>  #mermaid-svg-94okakTgRnLpQfYB {font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}#mermaid-svg-94okakTgRnLpQfYB .error-icon{fill:#552222;}#mermaid-svg-94okakTgRnLpQfYB .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-94okakTgRnLpQfYB .edge-thickness-normal{stroke-width:2px;}#mermaid-svg-94okakTgRnLpQfYB .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-94okakTgRnLpQfYB .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-94okakTgRnLpQfYB .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-94okakTgRnLpQfYB .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-94okakTgRnLpQfYB .marker{fill:#333333;stroke:#333333;}#mermaid-svg-94okakTgRnLpQfYB .marker.cross{stroke:#333333;}#mermaid-svg-94okakTgRnLpQfYB svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-94okakTgRnLpQfYB .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-94okakTgRnLpQfYB .cluster-label text{fill:#333;}#mermaid-svg-94okakTgRnLpQfYB .cluster-label span{color:#333;}#mermaid-svg-94okakTgRnLpQfYB .label text,#mermaid-svg-94okakTgRnLpQfYB span{fill:#333;color:#333;}#mermaid-svg-94okakTgRnLpQfYB .node rect,#mermaid-svg-94okakTgRnLpQfYB .node circle,#mermaid-svg-94okakTgRnLpQfYB .node ellipse,#mermaid-svg-94okakTgRnLpQfYB .node polygon,#mermaid-svg-94okakTgRnLpQfYB .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-94okakTgRnLpQfYB .node .label{text-align:center;}#mermaid-svg-94okakTgRnLpQfYB .node.clickable{cursor:pointer;}#mermaid-svg-94okakTgRnLpQfYB .arrowheadPath{fill:#333333;}#mermaid-svg-94okakTgRnLpQfYB .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-94okakTgRnLpQfYB .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-94okakTgRnLpQfYB .edgeLabel{background-color:#e8e8e8;text-align:center;}#mermaid-svg-94okakTgRnLpQfYB .edgeLabel rect{opacity:0.5;background-color:#e8e8e8;fill:#e8e8e8;}#mermaid-svg-94okakTgRnLpQfYB .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-94okakTgRnLpQfYB .cluster text{fill:#333;}#mermaid-svg-94okakTgRnLpQfYB .cluster span{color:#333;}#mermaid-svg-94okakTgRnLpQfYB div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-94okakTgRnLpQfYB :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}<\/p>\n<p>         <span id=\"L-L-A-B\" class=\"edgeLabel L-LS-A&#039; L-LE-B\"><\/span><\/p>\n<p>         <span id=\"L-L-B-C\" class=\"edgeLabel L-LS-B&#039; L-LE-C\">\u7ed3\u6784\u5316\u6570\u636e<\/span><\/p>\n<p>         <span id=\"L-L-B-D\" class=\"edgeLabel L-LS-B&#039; L-LE-D\">\u56fe\u50cf\/\u6587\u672c<\/span><\/p>\n<p>         <span id=\"L-L-C-E\" class=\"edgeLabel L-LS-C&#039; L-LE-E\">\u7279\u5f81\u591a\/\u9ad8\u7ef4<\/span><\/p>\n<p>         <span id=\"L-L-C-F\" class=\"edgeLabel L-LS-C&#039; L-LE-F\">\u7279\u5f81\u5c11<\/span><\/p>\n<p>         <span id=\"L-L-E-G\" class=\"edgeLabel L-LS-E&#039; L-LE-G\"><\/span><\/p>\n<p>         <span id=\"L-L-G-H\" class=\"edgeLabel L-LS-G&#039; L-LE-H\">\u662f<\/span><\/p>\n<p>         <span id=\"L-L-G-I\" class=\"edgeLabel L-LS-G&#039; L-LE-I\">\u5426<\/span><\/p>\n<p>         <span id=\"L-L-D-J\" class=\"edgeLabel L-LS-D&#039; L-LE-J\"><\/span><\/p>\n<p>         <span id=\"L-L-H-K\" class=\"edgeLabel L-LS-H&#039; L-LE-K\"><\/span><\/p>\n<p>         <span id=\"L-L-I-K\" class=\"edgeLabel L-LS-I&#039; L-LE-K\"><\/span><\/p>\n<p>         <span id=\"L-L-J-K\" class=\"edgeLabel L-LS-J&#039; L-LE-K\"><\/span><\/p>\n<p>         <span id=\"L-L-K-L\" class=\"edgeLabel L-LS-K&#039; L-LE-L\"><\/span><\/p>\n<p>         <span id=\"L-L-L-M\" class=\"edgeLabel L-LS-L&#039; L-LE-M\"><\/span><\/p>\n<p>          \u5f00\u59cb<\/p>\n<p>          \u6570\u636e\u7c7b\u578b?<\/p>\n<p>          \u7279\u5f81\u6570\u91cf?<\/p>\n<p>          \u4f7f\u7528Dropout\/\u6570\u636e\u589e\u5f3a<\/p>\n<p>          \u5c1d\u8bd5L1\u6216Elastic Net<\/p>\n<p>          \u5c1d\u8bd5L2\u6216\u65e9\u505c\u6cd5<\/p>\n<p>          \u9700\u8981\u7279\u5f81\u9009\u62e9?<\/p>\n<p>          \u9009\u62e9L1\u6216Elastic Net<\/p>\n<p>          \u9009\u62e9L2<\/p>\n<p>          \u7ed3\u5408Dropout\u548c\u6570\u636e\u589e\u5f3a<\/p>\n<p>          \u8c03\u6574\u6b63\u5219\u5316\u5f3a\u5ea6<\/p>\n<p>          \u4ea4\u53c9\u9a8c\u8bc1\u8bc4\u4f30<\/p>\n<p>          \u786e\u5b9a\u6700\u4f73\u6b63\u5219\u5316\u65b9\u6848<\/p>\n<h3>5. \u6b63\u5219\u5316\u8d85\u53c2\u6570\u8c03\u4f18<\/h3>\n<p>\u6b63\u5219\u5316\u6548\u679c\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4f9d\u8d56\u4e8e\u8d85\u53c2\u6570\u7684\u9009\u62e9&#xff08;\u5982\u03bb\u3001dropout\u7387\u7b49&#xff09;\u3002\u5e38\u7528\u7684\u8c03\u4f18\u65b9\u6cd5\u5305\u62ec&#xff1a;<\/p>\n<h4>5.1 \u7f51\u683c\u641c\u7d22<\/h4>\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><span class=\"token comment\"># \u5b9a\u4e49\u53c2\u6570\u7f51\u683c<\/span><br \/>\nparam_grid <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token string\">&#039;alpha&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">0.001<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.01<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10.0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token string\">&#039;l1_ratio&#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\">0.3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.7<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.9<\/span><span class=\"token punctuation\">]<\/span>  <span class=\"token comment\"># \u7528\u4e8eElastic Net<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\"># \u521b\u5efa\u6a21\u578b<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> ElasticNet<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u7f51\u683c\u641c\u7d22<\/span><br \/>\ngrid_search <span class=\"token operator\">&#061;<\/span> GridSearchCV<span class=\"token punctuation\">(<\/span>model<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;neg_mean_squared_error&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\ngrid_search<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u53c2\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> grid_search<span class=\"token punctuation\">.<\/span>best_params_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u5206\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span>grid_search<span class=\"token punctuation\">.<\/span>best_score_<span class=\"token punctuation\">)<\/span><\/p>\n<h4>5.2 \u968f\u673a\u641c\u7d22<\/h4>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> RandomizedSearchCV<br \/>\n<span class=\"token keyword\">from<\/span> scipy<span class=\"token punctuation\">.<\/span>stats <span class=\"token keyword\">import<\/span> loguniform<\/p>\n<p><span class=\"token comment\"># \u5b9a\u4e49\u53c2\u6570\u5206\u5e03<\/span><br \/>\nparam_dist <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token string\">&#039;alpha&#039;<\/span><span class=\"token punctuation\">:<\/span> loguniform<span class=\"token punctuation\">(<\/span><span class=\"token number\">1e<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1e2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token string\">&#039;l1_ratio&#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\">0.3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.7<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.9<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\"># \u968f\u673a\u641c\u7d22<\/span><br \/>\nrandom_search <span class=\"token operator\">&#061;<\/span> RandomizedSearchCV<span class=\"token punctuation\">(<\/span><br \/>\n    ElasticNet<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> param_dist<span class=\"token punctuation\">,<\/span> n_iter<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span> cv<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    scoring<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;neg_mean_squared_error&#039;<\/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 \/>\nrandom_search<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>X<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u6700\u4f73\u53c2\u6570:&#034;<\/span><span class=\"token punctuation\">,<\/span> random_search<span class=\"token punctuation\">.<\/span>best_params_<span class=\"token punctuation\">)<\/span><\/p>\n<h3>6. \u6b63\u5219\u5316\u5728\u5b9e\u9645\u9879\u76ee\u4e2d\u7684\u5e94\u7528\u6848\u4f8b<\/h3>\n<h4>6.1 \u6848\u4f8b&#xff1a;\u623f\u4ef7\u9884\u6d4b<\/h4>\n<p><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>model_selection <span class=\"token keyword\">import<\/span> train_test_split<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\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>linear_model <span class=\"token keyword\">import<\/span> ElasticNet<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>metrics <span class=\"token keyword\">import<\/span> mean_squared_error<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<\/p>\n<p><span class=\"token comment\"># \u52a0\u8f7d\u6570\u636e<\/span><br \/>\ndata <span class=\"token operator\">&#061;<\/span> pd<span class=\"token punctuation\">.<\/span>read_csv<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;housing.csv&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\nX <span class=\"token operator\">&#061;<\/span> data<span class=\"token punctuation\">.<\/span>drop<span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;MEDV&#039;<\/span><span class=\"token punctuation\">,<\/span> axis<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\ny <span class=\"token operator\">&#061;<\/span> data<span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;MEDV&#039;<\/span><span class=\"token punctuation\">]<\/span><\/p>\n<p><span class=\"token comment\"># \u5212\u5206\u8bad\u7ec3\u6d4b\u8bd5\u96c6<\/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> 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\"># \u6570\u636e\u6807\u51c6\u5316<\/span><br \/>\nscaler <span class=\"token operator\">&#061;<\/span> StandardScaler<span class=\"token punctuation\">(<\/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><span class=\"token comment\"># \u8bad\u7ec3\u4e0d\u540c\u6b63\u5219\u5316\u6a21\u578b<\/span><br \/>\nmodels <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token string\">&#039;Linear&#039;<\/span><span class=\"token punctuation\">:<\/span> LinearRegression<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token string\">&#039;L1(Lasso)&#039;<\/span><span class=\"token punctuation\">:<\/span> Lasso<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token string\">&#039;L2(Ridge)&#039;<\/span><span class=\"token punctuation\">:<\/span> Ridge<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token string\">&#039;ElasticNet&#039;<\/span><span class=\"token punctuation\">:<\/span> ElasticNet<span class=\"token punctuation\">(<\/span>alpha<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span> l1_ratio<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>results <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">for<\/span> name<span class=\"token punctuation\">,<\/span> model <span class=\"token keyword\">in<\/span> models<span class=\"token punctuation\">.<\/span>items<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    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 \/>\n    y_pred <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>X_test_scaled<span class=\"token punctuation\">)<\/span><br \/>\n    mse <span class=\"token operator\">&#061;<\/span> mean_squared_error<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span> y_pred<span class=\"token punctuation\">)<\/span><br \/>\n    results<span class=\"token punctuation\">[<\/span>name<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token string\">&#039;MSE&#039;<\/span><span class=\"token punctuation\">:<\/span> mse<span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#039;RMSE&#039;<\/span><span class=\"token punctuation\">:<\/span> np<span class=\"token punctuation\">.<\/span>sqrt<span class=\"token punctuation\">(<\/span>mse<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#039;\u975e\u96f6\u7cfb\u6570&#039;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>coef_ <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token builtin\">hasattr<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#039;coef_&#039;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token string\">&#039;N\/A&#039;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\"># \u663e\u793a\u7ed3\u679c<\/span><br \/>\npd<span class=\"token punctuation\">.<\/span>DataFrame<span class=\"token punctuation\">(<\/span>results<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>T<\/p>\n<h4>6.2 \u6848\u4f8b&#xff1a;\u6587\u672c\u5206\u7c7b&#xff08;\u795e\u7ecf\u7f51\u7edc&#xff09;<\/h4>\n<p><span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>models <span class=\"token keyword\">import<\/span> Sequential<br \/>\n<span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>layers <span class=\"token keyword\">import<\/span> Dense<span class=\"token punctuation\">,<\/span> Dropout<br \/>\n<span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>regularizers <span class=\"token keyword\">import<\/span> l2<br \/>\n<span class=\"token keyword\">from<\/span> tensorflow<span class=\"token punctuation\">.<\/span>keras<span class=\"token punctuation\">.<\/span>callbacks <span class=\"token keyword\">import<\/span> EarlyStopping<\/p>\n<p><span class=\"token comment\"># \u6784\u5efa\u5e26\u591a\u91cd\u6b63\u5219\u5316\u7684\u6587\u672c\u5206\u7c7b\u6a21\u578b<\/span><br \/>\nmodel <span class=\"token operator\">&#061;<\/span> Sequential<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span><span class=\"token number\">256<\/span><span class=\"token punctuation\">,<\/span> activation<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">,<\/span> input_shape<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>input_dim<span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n           kernel_regularizer<span class=\"token operator\">&#061;<\/span>l2<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dropout<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span><span class=\"token number\">128<\/span><span class=\"token punctuation\">,<\/span> activation<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;relu&#039;<\/span><span class=\"token punctuation\">,<\/span> kernel_regularizer<span class=\"token operator\">&#061;<\/span>l2<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.01<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dropout<span class=\"token punctuation\">(<\/span><span class=\"token number\">0.3<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    Dense<span class=\"token punctuation\">(<\/span>num_classes<span class=\"token punctuation\">,<\/span> activation<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;softmax&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u7f16\u8bd1\u6a21\u578b<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">compile<\/span><span class=\"token punctuation\">(<\/span>optimizer<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;adam&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n              loss<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;categorical_crossentropy&#039;<\/span><span class=\"token punctuation\">,<\/span><br \/>\n              metrics<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token string\">&#039;accuracy&#039;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u5b9a\u4e49\u65e9\u505c<\/span><br \/>\nearly_stop <span class=\"token operator\">&#061;<\/span> EarlyStopping<span class=\"token punctuation\">(<\/span>monitor<span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#039;val_loss&#039;<\/span><span class=\"token punctuation\">,<\/span> patience<span class=\"token operator\">&#061;<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u8bad\u7ec3\u6a21\u578b<\/span><br \/>\nhistory <span class=\"token operator\">&#061;<\/span> model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span><br \/>\n    X_train<span class=\"token punctuation\">,<\/span> y_train<span class=\"token punctuation\">,<\/span><br \/>\n    epochs<span class=\"token operator\">&#061;<\/span><span class=\"token number\">100<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    batch_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">64<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    validation_data<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>X_val<span class=\"token punctuation\">,<\/span> y_val<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    callbacks<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span>early_stop<span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<h3>7. 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