{"id":9836,"date":"2025-03-19T20:44:39","date_gmt":"2025-03-19T12:44:39","guid":{"rendered":"https:\/\/www.invbus.com\/blog\/?p=9836"},"modified":"2025-03-19T20:44:39","modified_gmt":"2025-03-19T12:44:39","slug":"%e9%80%9a%e9%80%8f%ef%bc%81%e8%bf%87%e6%8b%9f%e5%90%88%e6%ac%a0%e6%8b%9f%e5%90%88-%e5%85%a8%e9%9d%a2%e6%80%bb%e7%bb%93%ef%bc%81%ef%bc%81","status":"publish","type":"post","link":"https:\/\/www.invbus.com\/blog\/?p=9836","title":{"rendered":"\u901a\u900f\uff01\u8fc7\u62df\u5408&\u6b20\u62df\u5408 \u5168\u9762\u603b\u7ed3\uff01\uff01"},"content":{"rendered":"\n

\u6838\u5fc3\u70b9\uff1a<\/strong>\u8fc7\u62df\u5408&\u6b20\u62df\u5408\uff0c\u5982\u4f55\u9632\u6b62\uff01<\/strong><\/p>\n\n\n\n

\u54c8\u55bd\uff0c\u6211\u662fcos\u5927\u58ee\uff01<\/p>\n\n\n\n

\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u6709\u4e00\u9879\u5f88\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u90a3\u5c31\u662f\uff1a\u8fc7\u62df\u5408\uff08Overfitting\uff09\u548c\u6b20\u62df\u5408\uff08Underfitting\uff09\u3002<\/p>\n\n\n\n

\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\uff0c\u548c\u4e0d\u5c11\u540c\u5b66\u79c1\u4fe1\u804a\u5230\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408\u7684\u95ee\u9898\u3002\u5c24\u5176\u662f\u5bf9\u4e8e\u521d\u5b66\u8005\u6765\u8bf4\uff0c\u8fd9\u4e2a\u6709\u65f6\u5019\u611f\u89c9\u5f88\u96be\u628a\u63e1\u3002<\/p>\n\n\n\n

\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408\uff0c\u6d89\u53ca\u5230\u673a\u5668\u5b66\u4e60\u4e2d\u5e38\u89c1\u7684\u4e24\u79cd\u6a21\u578b\u6027\u80fd\u95ee\u9898\uff0c\u5206\u522b\u8868\u793a\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8868\u73b0\u5f97\u8fc7\u4e8e\u590d\u6742\u6216\u8fc7\u4e8e\u7b80\u5355\u3002<\/strong><\/p>\n\n\n\n

\u4e0b\u9762\u54b1\u4eec\u5148\u6765\u7b80\u5355\u804a\u804a\u5173\u4e8e\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408\u7684\u7279\u5f81\uff0c\u4ee5\u53ca\u9632\u6b62\u6027\u80fd\u95ee\u9898\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u8001\u89c4\u77e9<\/strong>\uff1a\u5927\u5bb6\u4f19\u5982\u679c\u89c9\u5f97\u8fd1\u671f\u6587\u7ae0\u8fd8\u4e0d\u9519\uff01\u6b22\u8fce\u5927\u5bb6<\/strong>\u70b9\u4e2a\u8d5e\u3001\u8f6c\u4e2a\u53d1~<\/strong><\/p>\n\n\n\n

\u6709\u540c\u5b66\u60f3\u8981\u83b7\u53d6 PDF \u6587\u6863\uff0c\u8bb0\u5f97\u6587\u672b\u79c1\u4fe1\u5373\u53ef\uff01<\/strong><\/p>\n\n\n\n

\"\u56fe\u7247\"\/<\/div><\/figure>\n\n\n\n

ok\uff0c\u54b1\u4eec\u4e00\u8d77\u6765\u5b66\u4e60\u4e00\u4e0b~<\/p>\n\n\n\n

\u8fc7\u62df\u5408\uff08Overfitting\uff09<\/h2>\n\n\n\n

\u57fa\u672c\u6982\u5ff5<\/h3>\n\n\n\n

\u7b80\u5355\u6765\u8bf4\uff0c\u8fc7\u62df\u5408\u5c31\u662f\u6a21\u578b\u5728\u8bad\u7ec3\u96c6\u4e0a\u5b66\u4e60\u5f97\u592a\u597d\uff0c\u4ee5\u81f3\u4e8e\u5b66\u5230\u4e86\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u566a\u58f0\u548c\u7ec6\u8282\uff0c\u5bfc\u81f4\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u5dee\uff0c\u5373\u6a21\u578b\u5728\u65b0\u7684\u3001\u672a\u89c1\u8fc7\u7684\u6570\u636e\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002<\/p>\n\n\n\n

\u901a\u5e38\u53d1\u751f\u5728\u6a21\u578b\u590d\u6742\u5ea6\u8f83\u9ad8\u65f6\uff0c\u6b64\u65f6\u6a21\u578b\u53ef\u80fd\u4f1a\u5c1d\u8bd5\u53bb\u6355\u6349\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u6bcf\u4e2a\u5c0f\u7684\u7279\u5f81\uff0c\u5305\u62ec\u90a3\u4e9b\u4e0d\u5177\u4ee3\u8868\u6027\u7684\u7279\u5f81\uff0c\u800c\u8fd9\u4e9b\u7279\u5f81\u53ef\u80fd\u4ec5\u4ec5\u662f\u7531\u4e8e\u968f\u673a\u566a\u58f0\u800c\u5b58\u5728\u3002<\/p>\n\n\n\n

\u7279\u5f81<\/h3>\n\n\n\n

\u8fd9\u91cc\u603b\u7ed3\u8fc7\u62df\u54084\u4e2a\u6700\u4e3b\u8981\u7684\u7279\u5f81~<\/p>\n\n\n\n

    \n
  1. \u8bad\u7ec3\u96c6\u8868\u73b0\u826f\u597d<\/strong>\uff1a\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u7684\u51c6\u786e\u7387\u975e\u5e38\u9ad8\uff0c\u51e0\u4e4e\u5b8c\u7f8e\u3002<\/li>\n\n\n\n
  2. \u6d4b\u8bd5\u96c6\u8868\u73b0\u5dee<\/strong>\uff1a\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u6216\u9a8c\u8bc1\u96c6\u4e0a\u7684\u8868\u73b0\u8981\u5dee\u5f97\u591a\u3002<\/li>\n\n\n\n
  3. \u6cdb\u5316\u80fd\u529b\u5f31<\/strong>\uff1a\u6a21\u578b\u5bf9\u4e8e\u65b0\u7684\u6570\u636e\u7f3a\u4e4f\u9002\u5e94\u6027\uff0c\u6cdb\u5316\u80fd\u529b\u5dee\u3002<\/li>\n\n\n\n
  4. \u5b66\u4e60\u66f2\u7ebf\u8868\u73b0<\/strong>\uff1a\u5728\u5b66\u4e60\u66f2\u7ebf\u4e0a\uff0c\u8bad\u7ec3\u8bef\u5dee\u6301\u7eed\u964d\u4f4e\uff0c\u800c\u9a8c\u8bc1\u8bef\u5dee\u964d\u4f4e\u5230\u4e00\u5b9a\u7a0b\u5ea6\u540e\u5f00\u59cb\u589e\u52a0\u3002<\/li>\n<\/ol>\n\n\n\n

    \u9632\u6b62\u8fc7\u62df\u5408\u6709\u6548\u65b9\u6cd5<\/h3>\n\n\n\n

    \u9632\u6b62\u8fc7\u62df\u5408\u7684\u65b9\u6cd5\u5f88\u591a\uff0c\u8981\u6839\u636e\u4e0d\u540c\u7684\u60c5\u51b5\u8fdb\u884c\u4e0d\u540c\u7684\u64cd\u4f5c\uff0c\u4ee5\u4e0b\u603b\u7ed3\u4e8611\u79cd\u65b9\u6cd5\u3002<\/p>\n\n\n\n

    \u76f8\u6bd4\u4e8e\u4e4b\u524d\u6587\u4e2d\u76845\u79cd\u65b9\u5f0f\uff0c\u591a\u589e\u52a0\u4e865\u79cd\uff0c\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u5927\u5bb6\u4f7f\u7528\u7684\u65b9\u5f0f~<\/p>\n\n\n\n

      \n
    1. \u6570\u636e\u589e\u5f3a<\/strong>\uff1a\u901a\u8fc7\u5bf9\u8bad\u7ec3\u6570\u636e\u8fdb\u884c\u53d8\u6362\uff0c\u6bd4\u5982\u65cb\u8f6c\u3001\u7f29\u653e\u3001\u7ffb\u8f6c\u7b49\uff0c\u53ef\u4ee5\u589e\u52a0\u6570\u636e\u7684\u591a\u6837\u6027\uff0c\u5e2e\u52a9\u6a21\u578b\u5b66\u4e60\u5230\u66f4\u4e00\u822c\u7684\u7279\u5f81\u3002<\/li>\n\n\n\n
    2. \u51cf\u5c11\u6a21\u578b\u590d\u6742\u5ea6<\/strong>\uff1a\u9009\u62e9\u66f4\u7b80\u5355\u7684\u6a21\u578b\u6216\u51cf\u5c11\u6a21\u578b\u4e2d\u7684\u53c2\u6570\u6570\u91cf\uff08\u4f8b\u5982\uff0c\u51cf\u5c11\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5c42\u6570\u6216\u6bcf\u5c42\u7684\u8282\u70b9\u6570\uff09\u53ef\u4ee5\u964d\u4f4e\u8fc7\u62df\u5408\u7684\u98ce\u9669\u3002<\/li>\n\n\n\n
    3. \u6b63\u5219\u5316(Regularization)<\/strong>\uff1a\u6dfb\u52a0\u6b63\u5219\u9879\uff08\u5982L1\u6216L2\u6b63\u5219\u5316\uff09\u5230\u635f\u5931\u51fd\u6570\u4e2d\u53ef\u4ee5\u60e9\u7f5a\u6a21\u578b\u7684\u590d\u6742\u5ea6\uff0c\u9650\u5236\u6a21\u578b\u6743\u91cd\u7684\u5927\u5c0f\uff0c\u4ece\u800c\u51cf\u5c11\u8fc7\u62df\u5408\u3002<\/li>\n\n\n\n
    4. \u63d0\u524d\u505c\u6b62(Early Stopping)<\/strong>\uff1a\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u4e00\u65e6\u9a8c\u8bc1\u8bef\u5dee\u5f00\u59cb\u589e\u52a0\uff0c\u5373\u505c\u6b62\u8fdb\u4e00\u6b65\u8bad\u7ec3\uff0c\u53ef\u4ee5\u9632\u6b62\u6a21\u578b\u8fc7\u5ea6\u62df\u5408\u8bad\u7ec3\u6570\u636e\u3002<\/li>\n\n\n\n
    5. \u4ea4\u53c9\u9a8c\u8bc1(Cross-Validation)<\/strong>\uff1a\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u53ef\u4ee5\u66f4\u597d\u5730\u4f30\u8ba1\u6a21\u578b\u5728\u672a\u89c1\u6570\u636e\u4e0a\u7684\u8868\u73b0\uff0c\u5e76\u9009\u62e9\u8868\u73b0\u6700\u597d\u7684\u6a21\u578b\u53c2\u6570\u3002<\/li>\n\n\n\n
    6. Dropout<\/strong>\uff1a\u5728\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u65f6\uff0c\u968f\u673a\u4e22\u5f03\uff08\u5373\u6682\u65f6\u79fb\u9664\uff09\u7f51\u7edc\u4e2d\u7684\u4e00\u4e9b\u8282\u70b9\uff0c\u53ef\u4ee5\u9632\u6b62\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u540c\u65f6\u5171\u540c\u9002\u5e94\u8bad\u7ec3\u6570\u636e\u3002<\/li>\n\n\n\n
    7. \u96c6\u6210\u5b66\u4e60(Ensemble Methods)<\/strong>\uff1a\u7ed3\u5408\u591a\u4e2a\u6a21\u578b\u7684\u9884\u6d4b\uff0c\u5982\u968f\u673a\u68ee\u6797\u6216\u68af\u5ea6\u63d0\u5347\u673a\uff0c\u901a\u5e38\u53ef\u4ee5\u51cf\u5c11\u8fc7\u62df\u5408\u5e76\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/li>\n\n\n\n
    8. \u9650\u5236\u53c2\u6570\u7684\u641c\u7d22\u7a7a\u95f4<\/strong>\uff1a\u5728\u8fdb\u884c\u6a21\u578b\u9009\u62e9\u548c\u8d85\u53c2\u6570\u8c03\u4f18\u65f6\uff0c\u9650\u5236\u53c2\u6570\u7684\u641c\u7d22\u7a7a\u95f4\u53ef\u4ee5\u907f\u514d\u9009\u62e9\u8fc7\u4e8e\u590d\u6742\u7684\u6a21\u578b\u3002<\/li>\n\n\n\n
    9. \u6570\u636e\u96c6\u5206\u5272<\/strong>\uff1a\u5408\u7406\u5206\u5272\u6570\u636e\u96c6\u4e3a\u8bad\u7ec3\u96c6\u3001\u9a8c\u8bc1\u96c6\u548c\u6d4b\u8bd5\u96c6\uff0c\u786e\u4fdd\u6a21\u578b\u4e0d\u662f\u7b80\u5355\u5730\u8bb0\u4f4f\u4e86\u7279\u5b9a\u6570\u636e\u96c6\u7684\u7279\u5f81\u3002<\/li>\n\n\n\n
    10. \u566a\u58f0\u6ce8\u5165<\/strong>\uff1a\u5728\u8bad\u7ec3\u6570\u636e\u4e2d\u6dfb\u52a0\u566a\u58f0\u53ef\u4ee5\u51cf\u5c11\u6a21\u578b\u5bf9\u8bad\u7ec3\u6837\u672c\u7684\u4f9d\u8d56\uff0c\u5e76\u589e\u52a0\u5176\u6cdb\u5316\u80fd\u529b\u3002<\/li>\n\n\n\n
    11. \u7279\u5f81\u9009\u62e9<\/strong>\uff1a\u51cf\u5c11\u8f93\u5165\u7279\u5f81\u7684\u6570\u91cf\uff0c\u820d\u5f03\u90a3\u4e9b\u4e0d\u76f8\u5173\u6216\u5197\u4f59\u7684\u7279\u5f81\uff0c\u53ef\u4ee5\u7b80\u5316\u6a21\u578b\u5e76\u51cf\u5c11\u8fc7\u62df\u5408\u7684\u98ce\u9669\u3002<\/li>\n<\/ol>\n\n\n\n

      \u5927\u5bb6\u5728\u5b9e\u9a8c\u4e2d\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u7684\u5e94\u7528\u548c\u7ed3\u5408\uff0c\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u907f\u514d\u8fc7\u62df\u5408\uff0c\u4ece\u800c\u63d0\u9ad8\u6a21\u578b\u5bf9\u65b0\u6570\u636e\u7684\u6cdb\u5316\u548c\u9884\u6d4b\u80fd\u529b\u3002<\/p>\n\n\n\n

      \u6b20\u62df\u5408\uff08Underfitting\uff09<\/h2>\n\n\n\n

      \u57fa\u672c\u6982\u5ff5<\/h3>\n\n\n\n

      \u6b20\u62df\u5408\u6307\u7684\u5c31\u662f\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u6ca1\u6709\u83b7\u5f97\u8db3\u591f\u7684\u5b66\u4e60\uff0c\u4ee5\u81f3\u4e8e\u65e0\u6cd5\u6355\u6349\u5230\u6570\u636e\u7684\u57fa\u672c\u7ed3\u6784\uff0c\u65e2\u4e0d\u80fd\u5728\u8bad\u7ec3\u96c6\u4e0a\u8868\u73b0\u826f\u597d\uff0c\u4e5f\u4e0d\u80fd\u5728\u65b0\u7684\u6570\u636e\u4e0a\u505a\u51fa\u51c6\u786e\u7684\u9884\u6d4b\u3002<\/p>\n\n\n\n

      \u6b20\u62df\u5408\u901a\u5e38\u662f\u56e0\u4e3a\u6a21\u578b\u8fc7\u4e8e\u7b80\u5355\uff0c\u6ca1\u6709\u8db3\u591f\u7684\u53c2\u6570\u6765\u5b66\u4e60\u6570\u636e\u7684\u590d\u6742\u6027\u3002<\/p>\n\n\n\n

      \u7279\u5f81<\/h3>\n\n\n\n

      \u8fd9\u91cc\u4e5f\u662f\u603b\u7ed3\u4e864\u70b9\uff0c\u5927\u5bb6\u53ef\u4ee5\u5927\u6982\u770b\u4e0b\uff1a<\/p>\n\n\n\n

        \n
      1. \u8bad\u7ec3\u96c6\u8868\u73b0\u4e0d\u4f73<\/strong>\uff1a\u6a21\u578b\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u7684\u51c6\u786e\u7387\u4f4e\uff0c\u65e0\u6cd5\u5f97\u5230\u4e00\u4e2a\u597d\u7684\u62df\u5408\u3002<\/li>\n\n\n\n
      2. \u6d4b\u8bd5\u96c6\u8868\u73b0\u540c\u6837\u4e0d\u4f73<\/strong>\uff1a\u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u8868\u73b0\u4e5f\u5f88\u5dee\uff0c\u56e0\u4e3a\u5b83\u8fde\u8bad\u7ec3\u6570\u636e\u90fd\u6ca1\u6709\u5b66\u4e60\u597d\u3002<\/li>\n\n\n\n
      3. \u6cdb\u5316\u80fd\u529b\u5dee<\/strong>\uff1a\u56e0\u4e3a\u6a21\u578b\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u5b66\u4e60\u4e0d\u8db3\uff0c\u6240\u4ee5\u5bf9\u65b0\u6570\u636e\u7684\u6cdb\u5316\u80fd\u529b\u4e5f\u5f88\u5dee\u3002<\/li>\n\n\n\n
      4. \u5b66\u4e60\u66f2\u7ebf\u8868\u73b0<\/strong>\uff1a\u5728\u5b66\u4e60\u66f2\u7ebf\u4e0a\uff0c\u8bad\u7ec3\u8bef\u5dee\u548c\u9a8c\u8bc1\u8bef\u5dee\u90fd\u5f88\u9ad8\uff0c\u4e14\u4e24\u8005\u53ef\u80fd\u76f8\u5dee\u4e0d\u5927\u3002<\/li>\n<\/ol>\n\n\n\n

        \u9632\u6b62\u6b20\u62df\u5408\u7684\u65b9\u6cd5<\/h3>\n\n\n\n

        \u540c\u6837\u662f11\u79cd\u6700\u5e38\u7528\u7684\u65b9\u6cd5~<\/p>\n\n\n\n

          \n
        1. \u589e\u52a0\u6a21\u578b\u590d\u6742\u5ea6<\/strong>\uff1a\u9009\u62e9\u66f4\u590d\u6742\u7684\u6a21\u578b\u6216\u589e\u52a0\u6a21\u578b\u4e2d\u7684\u53c2\u6570\u6570\u91cf\uff08\u4f8b\u5982\u589e\u52a0\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5c42\u6570\u6216\u6bcf\u5c42\u7684\u8282\u70b9\u6570\uff09\u4ee5\u4fbf\u6355\u6349\u6570\u636e\u4e2d\u66f4\u590d\u6742\u7684\u6a21\u5f0f\u3002<\/li>\n\n\n\n
        2. **\u7279\u5f81\u5de5\u7a0b(Feature Engineering)**\uff1a\u901a\u8fc7\u521b\u5efa\u66f4\u591a\u7684\u7279\u5f81\uff0c\u4f8b\u5982\u901a\u8fc7\u7ec4\u5408\u3001\u8f6c\u6362\u6216\u591a\u9879\u5f0f\u6269\u5c55\u73b0\u6709\u7279\u5f81\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6a21\u578b\u5b66\u4e60\u5230\u6570\u636e\u4e2d\u7684\u66f4\u591a\u6709\u7528\u4fe1\u606f\u3002<\/li>\n\n\n\n
        3. \u51cf\u5c11\u6b63\u5219\u5316<\/strong>\uff1a\u5982\u679c\u6a21\u578b\u8fc7\u4e8e\u7b80\u5355\uff0c\u53ef\u80fd\u9700\u8981\u51cf\u5c11\u6b63\u5219\u5316\u9879\u7684\u6743\u91cd\u6216\u5b8c\u5168\u53bb\u6389\u6b63\u5219\u5316\uff0c\u4ee5\u5141\u8bb8\u6a21\u578b\u7684\u590d\u6742\u5ea6\u589e\u52a0\u3002<\/li>\n\n\n\n
        4. \u66f4\u957f\u7684\u8bad\u7ec3\u65f6\u95f4<\/strong>\uff1a\u6709\u65f6\u6a21\u578b\u4ec5\u4ec5\u662f\u56e0\u4e3a\u6ca1\u6709\u8bad\u7ec3\u8db3\u591f\u4e45\uff0c\u56e0\u6b64\u589e\u52a0\u8bad\u7ec3\u8fed\u4ee3\u6b21\u6570\u6216\u8005\u8bad\u7ec3\u65f6\u95f4\u6709\u52a9\u4e8e\u6a21\u578b\u66f4\u597d\u5730\u5b66\u4e60\u6570\u636e\u3002<\/li>\n\n\n\n
        5. \u51cf\u5c11\u6570\u636e\u9884\u5904\u7406<\/strong>\uff1a\u5982\u679c\u6570\u636e\u9884\u5904\u7406\u8fc7\u7a0b\u8fc7\u4e8e\u7b80\u5316\uff0c\u53ef\u80fd\u4f1a\u4e22\u5931\u91cd\u8981\u4fe1\u606f\u3002\u786e\u4fdd\u6570\u636e\u5904\u7406\u4e0d\u4f1a\u5bfc\u81f4\u6709\u4ef7\u503c\u4fe1\u606f\u7684\u4e22\u5931\u3002<\/li>\n\n\n\n
        6. \u8c03\u6574\u8d85\u53c2\u6570<\/strong>\uff1a\u901a\u8fc7\u8c03\u6574\u5b66\u4e60\u7b97\u6cd5\u7684\u8d85\u53c2\u6570\uff08\u5982\u5b66\u4e60\u7387\u3001\u6811\u7684\u6df1\u5ea6\u7b49\uff09\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6a21\u578b\u66f4\u597d\u5730\u5b66\u4e60\u6570\u636e\u3002<\/li>\n\n\n\n
        7. \u66f4\u591a\u7684\u6570\u636e<\/strong>\uff1a\u5982\u679c\u53ef\u7528\uff0c\u4f7f\u7528\u66f4\u591a\u7684\u8bad\u7ec3\u6570\u636e\u53ef\u4ee5\u5e2e\u52a9\u6a21\u578b\u66f4\u597d\u5730\u6cdb\u5316\u5230\u65b0\u6570\u636e\u4e0a\u3002<\/li>\n\n\n\n
        8. \u96c6\u6210\u4e0d\u540c\u6a21\u578b<\/strong>\uff1a\u6709\u65f6\u5c06\u4e0d\u540c\u7684\u6a21\u578b\u7ec4\u5408\u8d77\u6765\uff0c\u6bd4\u5982\u4f7f\u7528\u6a21\u578b\u878d\u5408\u6216\u5806\u53e0(stacking)\uff0c\u53ef\u4ee5\u5e2e\u52a9\u63d0\u5347\u6574\u4f53\u7684\u6a21\u578b\u6027\u80fd\u3002<\/li>\n\n\n\n
        9. \u4f7f\u7528\u975e\u7ebf\u6027\u6a21\u578b<\/strong>\uff1a\u5982\u679c\u6570\u636e\u672c\u8eab\u5177\u6709\u975e\u7ebf\u6027\u5173\u7cfb\u800c\u4f7f\u7528\u4e86\u7ebf\u6027\u6a21\u578b\uff0c\u6362\u7528\u975e\u7ebf\u6027\u6a21\u578b\u53ef\u80fd\u4f1a\u5e26\u6765\u66f4\u597d\u7684\u62df\u5408\u3002<\/li>\n\n\n\n
        10. \u83b7\u53d6\u66f4\u591a\u7279\u5f81\u4fe1\u606f<\/strong>\uff1a\u5728\u53ef\u80fd\u7684\u60c5\u51b5\u4e0b\uff0c\u6536\u96c6\u66f4\u591a\u76f8\u5173\u7279\u5f81\uff0c\u589e\u52a0\u6a21\u578b\u7684\u8f93\u5165\u4fe1\u606f\u3002<\/li>\n\n\n\n
        11. \u6a21\u578b\u9009\u62e9<\/strong>\uff1a\u6709\u65f6\u9700\u8981\u91cd\u65b0\u8003\u8651\u6240\u9009\u6a21\u578b\u7684\u9002\u7528\u6027\uff0c\u5c1d\u8bd5\u4e0d\u540c\u7684\u6a21\u578b\u4ee5\u627e\u5230\u66f4\u597d\u7684\u5339\u914d\u3002<\/li>\n<\/ol>\n\n\n\n

          \u5728\u5b9e\u9a8c\u4e2d\uff0c\u5927\u5bb6\u53ef\u4ee5\u7528\u8d77\u6765~<\/p>\n\n\n\n

          \u6848\u4f8b – \u8fc7\u62df\u5408<\/h2>\n\n\n\n

          \u4e0b\u9762\uff0c\u54b1\u4eec\u901a\u8fc7\u4e00\u4e2a\u5177\u4f53\u7684\u6848\u4f8b\u6765\u8bf4\u660e\u8fc7\u62df\u5408\u73b0\u8c61\u53ca\u5176\u89e3\u51b3\u65b9\u6cd5\u3002\u4f7f\u7528\u591a\u9879\u5f0f\u7279\u5f81\u548c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u6765\u6f14\u793a\u8fc7\u62df\u5408\uff0c\u5e76\u5c55\u793a\u5982\u4f55\u901a\u8fc7\u589e\u52a0\u6b63\u5219\u5316\u6765\u51cf\u8f7b\u8fc7\u62df\u5408\u3002<\/p>\n\n\n\n

          \u5b9e\u9a8c\u8bbe\u7f6e<\/strong><\/p>\n\n\n\n

            \n
          • \u4efb\u52a1<\/strong>\uff1a\u57fa\u4e8e\u5355\u4e00\u7279\u5f81x\uff0c\u9884\u6d4b\u76ee\u6807\u53d8\u91cfy\u3002<\/li>\n\n\n\n
          • \u6570\u636e\u96c6<\/strong>\uff1a\u751f\u6210\u4e00\u4e2a\u7b80\u5355\u7684\u6570\u636e\u96c6\uff0c\u5305\u542b\u566a\u58f0\u3002<\/li>\n\n\n\n
          • \u6a21\u578b<\/strong>\uff1a\u4f7f\u7528\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u5148\u4e0d\u5e26\u6b63\u5219\u5316\uff08\u5bb9\u6613\u8fc7\u62df\u5408\uff09\uff0c\u540e\u6dfb\u52a0L2\u6b63\u5219\u5316\uff08\u5cad\u56de\u5f52\uff09\u5bf9\u6bd4\u6548\u679c\u3002<\/li>\n<\/ul>\n\n\n\n

            \u5b9e\u9a8c\u8bf4\u660e<\/strong><\/p>\n\n\n\n

              \n
            1. \u751f\u6210\u6570\u636e\u96c6\u3002<\/li>\n\n\n\n
            2. \u4f7f\u7528\u9ad8\u9636\u591a\u9879\u5f0f\u7279\u5f81\u5bf9\u6570\u636e\u8fdb\u884c\u8f6c\u6362\uff0c\u4f7f\u6a21\u578b\u66f4\u590d\u6742\uff0c\u6613\u4e8e\u51fa\u73b0\u8fc7\u62df\u5408\u3002<\/li>\n\n\n\n
            3. \u8bad\u7ec3\u4e24\u4e2a\u6a21\u578b\uff1a\u4e00\u4e2a\u662f\u666e\u901a\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u53e6\u4e00\u4e2a\u662f\u52a0\u5165L2\u6b63\u5219\u5316\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff08\u5cad\u56de\u5f52\uff09\u3002<\/li>\n\n\n\n
            4. \u53ef\u89c6\u5316\u5e76\u6bd4\u8f83\u6a21\u578b\u5728\u8bad\u7ec3\u96c6\u4e0a\u7684\u62df\u5408\u60c5\u51b5\u4ee5\u53ca\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u8868\u73b0\u3002<\/li>\n<\/ol>\n\n\n\n

              \u5b8c\u6574\u4ee3\u7801<\/strong><\/p>\n\n\n\n

              import numpy as np
              import matplotlib.pyplot as plt
              from sklearn.model_selection import train_test_split
              from sklearn.preprocessing import PolynomialFeatures
              from sklearn.linear_model import LinearRegression, Ridge
              from sklearn.metrics import mean_squared_error

              # \u751f\u6210\u6570\u636e\u96c6<\/em>
              np.random.seed(0)
              x = np.linspace(-3, 3, 100)
              y = x**2 + np.random.randn(100) * 2 + 3
              X = x[:, np.newaxis] # \u8f6c\u6362\u4e3a\u4e8c\u7ef4\u6570\u7ec4\uff0c\u7528\u4e8e\u6a21\u578b\u8bad\u7ec3<\/em>

              # \u5212\u5206\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6<\/em>
              X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

              # \u521b\u5efa\u591a\u9879\u5f0f\u7279\u5f81<\/em>
              poly = PolynomialFeatures(degree=10, include_bias=False)
              X_poly_train = poly.fit_transform(X_train)
              X_poly_test = poly.transform(X_test)

              # \u6a21\u578b\u8bad\u7ec3\uff1a\u7ebf\u6027\u56de\u5f52<\/em>
              model_lr = LinearRegression()
              model_lr.fit(X_poly_train, y_train)

              # \u6a21\u578b\u8bad\u7ec3\uff1a\u5cad\u56de\u5f52<\/em>
              model_ridge = Ridge(alpha=100)
              model_ridge.fit(X_poly_train, y_train)

              # \u9884\u6d4b\u548c\u8bc4\u4f30<\/em>
              x_range = np.linspace(X.min(), X.max(), 100).reshape(-1, 1)
              x_range_poly = poly.transform(x_range)

              y_pred_lr = model_lr.predict(x_range_poly)
              y_pred_ridge = model_ridge.predict(x_range_poly)

              print(\"Linear Regression MSE:\", mean_squared_error(y_test, model_lr.predict(X_poly_test)))
              print(\"Ridge Regression MSE:\", mean_squared_error(y_test, model_ridge.predict(X_poly_test)))

              # \u7ed8\u5236\u56fe\u5f62<\/em>
              plt.scatter(X_train, y_train, color='gray', marker='o', label='Training data')
              plt.scatter(X_test, y_test, color='gold', marker='x', label='Test data')
              plt.plot(x_range, y_pred_lr, label='Linear Regression', color='red', linewidth=2)
              plt.plot(x_range, y_pred_ridge, label='Ridge Regression', color='blue', linewidth=2)
              plt.legend()
              plt.xlabel('x')
              plt.ylabel('y')
              plt.title('Overfitting Example and Solution')
              plt.grid(True)
              plt.show()<\/code><\/pre>\n\n\n\n
              \"\u56fe\u7247\"\/<\/div><\/figure>\n\n\n\n
              \u8fc7\u62df\u5408\u7684\u60c5\u51b5<\/strong><\/p>\n\n\n\n
              \u5f88\u663e\u7136\uff0c\u5927\u5bb6\u53ef\u4ee5\u770b\u5230\u3002\u5728\u672a\u6dfb\u52a0\u6b63\u5219\u5316\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e2d\uff08\u7ea2\u8272\u66f2\u7ebf\uff09\uff0c\u4f1a\u770b\u5230\u6a21\u578b\u5c1d\u8bd5\u975e\u5e38\u7cbe\u786e\u5730\u901a\u8fc7\u6bcf\u4e2a\u8bad\u7ec3\u6570\u636e\u70b9\uff0c\u5bfc\u81f4\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u8868\u73b0\uff08\u9ec4\u8272\u70b9\uff09\u8f83\u5dee\uff0c\u8fd9\u5c31\u662f\u5178\u578b\u7684\u8fc7\u62df\u5408\u73b0\u8c61\u3002<\/p>\n\n\n\n
              \u89e3\u51b3\u8fc7\u62df\u5408\u540e\u7684\u60c5\u51b5<\/strong><\/p>\n\n\n\n
              \u5f15\u5165L2\u6b63\u5219\u5316\u7684\u5cad\u56de\u5f52\u6a21\u578b\uff08\u84dd\u8272\u66f2\u7ebf\uff09\u80fd\u591f\u6709\u6548\u964d\u4f4e\u6a21\u578b\u590d\u6742\u5ea6\uff0c\u867d\u7136\u5b83\u4e0d\u518d\u5c1d\u8bd5\u7a7f\u8fc7\u6240\u6709\u8bad\u7ec3\u6570\u636e\u70b9\uff0c\u4f46\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684MSE\uff08\u5747\u65b9\u8bef\u5dee\uff09\u6709\u663e\u8457\u964d\u4f4e\uff0c\u663e\u793a\u51fa\u4e86\u66f4\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n\n
              \u6848\u4f8b – \u6b20\u62df\u5408<\/h2>\n\n\n\n
              \u8fd9\u91cc\uff0c\u54b1\u4eec\u518d\u901a\u8fc7\u4e00\u4e2a\u6848\u4f8b\u8bf4\u660e\u6b20\u62df\u5408\u7684\u60c5\u51b5~<\/p>\n\n\n\n
              \u5b9e\u9a8c\u8bbe\u7f6e<\/strong><\/p>\n\n\n\n