{"id":338,"date":"2024-08-13T11:36:30","date_gmt":"2024-08-13T03:36:30","guid":{"rendered":"https:\/\/www.xuzhe.tj.cn\/?p=338"},"modified":"2025-05-03T09:17:31","modified_gmt":"2025-05-03T01:17:31","slug":"bagging-predictors-bagging","status":"publish","type":"post","link":"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/08\/13\/bagging-predictors-bagging\/","title":{"rendered":"Bagging Predictors \uff5c\u8bba\u6587\u7b14\u8bb0"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u8bba\u6587\u7b80\u4ecb<\/h2>\n\n\n<p>\u82f1\u6587\u9898\u76ee\uff1aBagging Predictors<\/p>\n\n\n<p>\u4e2d\u6587\u9898\u76ee\uff1a\u81ea\u52a9\u805a\u96c6\u9884\u6d4b\u6a21\u578b<\/p>\n\n\n<p>\u4f5c\u8005\uff1aLeo Breiman<\/p>\n\n\n<p>\u53d1\u8868\u671f\u520a \u6216 \u4f1a\u8bae\uff1aMachine Learning<\/p>\n\n\n<p>\u53d1\u8868\u65e5\u671f\uff1a1996\u5e74<\/p>\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1a<\/p>\n\n\n<pre class=\"wp-block-code\"><code>https:\/\/www.jianguoyun.com\/p\/Dd5_s68Qmdv9CBiBqtIFIAA\n<\/code><\/pre>\n\n\n<p>\u4ee5\u4e0b\u662f\u5bf9\u8bba\u6587\u300aBagging Predictors\u300b\u7684\u603b\u7ed3\uff1a<\/p>\n\n\n<p>\u5728\u5f53\u4eca\u6570\u636e\u9a71\u52a8\u7684\u4e16\u754c\u4e2d\uff0c\u51c6\u786e\u9884\u6d4b\u548c\u5206\u7c7b\u53d8\u5f97\u5c24\u4e3a\u5173\u952e\u3002\u7ecf\u5178\u7684\u673a\u5668\u5b66\u4e60\u6280\u672f\uff0c\u5982\u5206\u7c7b\u548c\u56de\u5f52\u6811\uff0c\u5c3d\u7ba1\u5728\u67d0\u4e9b\u9886\u57df\u8868\u73b0\u51fa\u8272\uff0c\u4f46\u5728\u9762\u5bf9\u4e0d\u7a33\u5b9a\u7684\u6570\u636e\u96c6\u65f6\u5e38\u5e38\u8868\u73b0\u4e0d\u4f73\u3002\u7136\u800c\uff0c\u4e00\u79cd\u540d\u4e3aBagging\uff08\u81ea\u52a9\u805a\u96c6\uff09\u7684\u6280\u672f\u4e3a\u8fd9\u4e00\u96be\u9898\u63d0\u4f9b\u4e86\u7a81\u7834\u6027\u7684\u89e3\u51b3\u65b9\u6848\u3002\u901a\u8fc7\u5bf9\u540c\u4e00\u6570\u636e\u96c6\u8fdb\u884c\u591a\u6b21\u81ea\u52a9\u62bd\u6837\u5e76\u7ed3\u5408\u591a\u4e2a\u9884\u6d4b\u6a21\u578b\uff0cBagging\u80fd\u591f\u663e\u8457\u63d0\u5347\u6a21\u578b\u7684\u51c6\u786e\u6027\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u65b9\u6cd5\u65f6\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u7b80\u5355\u6027\u548c\u5f3a\u5927\u7684\u6548\u679c\u4f7f\u5176\u6210\u4e3a\u8bb8\u591a\u9886\u57df\u7684\u9996\u9009\uff0c\u800c\u672c\u8bba\u6587\u6b63\u662f\u63ed\u793a\u4e86Bagging\u6280\u672f\u7684\u6f5c\u529b\u4e0e\u5e94\u7528\uff0c\u5e26\u9886\u8bfb\u8005\u63a2\u7d22\u5176\u5728\u4e0d\u540c\u6570\u636e\u96c6\u4e0a\u7684\u51fa\u8272\u8868\u73b0\u3002\u65e0\u8bba\u662f\u7406\u8bba\u57fa\u7840\u8fd8\u662f\u5b9e\u9a8c\u8bc1\u636e\uff0c\u90fd\u8868\u660eBagging\u80fd\u591f\u5c06\u4e00\u4e2a\u826f\u597d\u7684\u4f46\u4e0d\u7a33\u5b9a\u7684\u6a21\u578b\u63a8\u5411\u66f4\u63a5\u8fd1\u6700\u4f18\u7684\u8868\u73b0\u3002\u8fd9\u4e0d\u4ec5\u662f\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u4e00\u4e2a\u91cc\u7a0b\u7891\uff0c\u66f4\u662f\u6bcf\u4e00\u4e2a\u8ffd\u6c42\u5353\u8d8a\u9884\u6d4b\u80fd\u529b\u7684\u7814\u7a76\u8005\u4e0d\u53ef\u5ffd\u89c6\u7684\u91cd\u8981\u5de5\u5177\u3002<\/p>\n\n<!--more-->\n\n<p><strong>\u7814\u7a76\u80cc\u666f\u4e0e\u76ee\u7684<\/strong><\/p>\n\n\n<p>Bagging\uff08\u81ea\u52a9\u805a\u96c6\uff09\u662f\u4e00\u79cd\u65e8\u5728\u63d0\u9ad8\u9884\u6d4b\u6a21\u578b\u51c6\u786e\u6027\u7684\u65b9\u6cd5\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u65b9\u6cd5\u65f6\u3002\u7814\u7a76\u7684\u76ee\u7684\u5728\u4e8e\u63a2\u7d22\u5982\u4f55\u901a\u8fc7\u751f\u6210\u591a\u4e2a\u9884\u6d4b\u6a21\u578b\u7248\u672c\uff0c\u5e76\u5c06\u5176\u7ec4\u5408\uff0c\u4ee5\u63d0\u9ad8\u5206\u7c7b\u548c\u56de\u5f52\u6811\u7b49\u6a21\u578b\u5728\u5404\u79cd\u6570\u636e\u96c6\u4e0a\u7684\u51c6\u786e\u6027\u3002\u901a\u8fc7\u5bf9\u5b9e\u9645\u6570\u636e\u548c\u6a21\u62df\u6570\u636e\u7684\u5b9e\u9a8c\uff0c\u9a8c\u8bc1Bagging\u6280\u672f\u7684\u6709\u6548\u6027\uff0c\u5e76\u5206\u6790\u5176\u5728\u4e0d\u540c\u60c5\u51b5\u4e0b\u7684\u8868\u73b0\u3002<\/p>\n\n\n<p><strong>\u521b\u65b0\u70b9<\/strong><\/p>\n\n\n<p>Bagging\u7684\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u4f7f\u7528\u81ea\u52a9\u62bd\u6837\uff08bootstrap sampling\uff09\u6765\u751f\u6210\u591a\u4e2a\u5b66\u4e60\u96c6\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c\u805a\u5408\u3002\u805a\u5408\u7684\u65b9\u5f0f\u5305\u62ec\u5bf9\u6570\u503c\u578b\u8f93\u51fa\u53d6\u5e73\u5747\u503c\uff0c\u5bf9\u5206\u7c7b\u95ee\u9898\u8fdb\u884c\u6295\u7968\u3002\u6b64\u6280\u672f\u7279\u522b\u9002\u7528\u4e8e\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\uff0c\u5f53\u6570\u636e\u96c6\u7684\u8f7b\u5fae\u6270\u52a8\u53ef\u80fd\u5bfc\u81f4\u9884\u6d4b\u7ed3\u679c\u663e\u8457\u53d8\u5316\u65f6\uff0cBagging\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002<\/p>\n\n\n<p><strong>\u7ed3\u8bba<\/strong><\/p>\n\n\n<p>\u7814\u7a76\u8868\u660e\uff0cBagging\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u65b9\u6cd5\u65f6\u80fd\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002\u5728\u591a\u79cd\u5206\u7c7b\u548c\u56de\u5f52\u95ee\u9898\u4e2d\uff0cBagging\u663e\u8457\u964d\u4f4e\u4e86\u6d4b\u8bd5\u8bef\u5dee\u7387\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u7a33\u5b9a\u7684\u9884\u6d4b\u65b9\u6cd5\uff0cBagging\u7684\u6548\u679c\u8f83\u5dee\uff0c\u751a\u81f3\u53ef\u80fd\u7565\u5fae\u964d\u4f4e\u6a21\u578b\u7684\u8868\u73b0\u3002\u6b64\u5916\uff0cBagging\u65e0\u6cd5\u65e0\u9650\u5236\u5730\u63d0\u9ad8\u51c6\u786e\u6027\uff0c\u5c24\u5176\u662f\u5728\u6a21\u578b\u5df2\u63a5\u8fd1\u6700\u4f18\u72b6\u6001\u65f6\u3002<\/p>\n\n\n<p><strong>\u5b9e\u9a8c\u5185\u5bb9<\/strong><\/p>\n\n\n<p>\u8bba\u6587\u901a\u8fc7\u591a\u4e2a\u5b9e\u9a8c\u9a8c\u8bc1\u4e86Bagging\u6280\u672f\u7684\u6709\u6548\u6027\u3002\u5b9e\u9a8c\u5305\u62ec\u5bf9\u5206\u7c7b\u6811\u548c\u56de\u5f52\u6811\u7684Bagging\u5904\u7406\uff0c\u6d4b\u8bd5\u6570\u636e\u96c6\u5305\u62ec\u771f\u5b9e\u6570\u636e\u96c6\uff08\u5982\u5fc3\u810f\u75c5\u3001\u4e73\u817a\u764c\u6570\u636e\u96c6\uff09\u548c\u6a21\u62df\u6570\u636e\u96c6\uff08\u5982\u6ce2\u5f62\u6570\u636e\u96c6\uff09\u3002\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cBagging\u80fd\u591f\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\u663e\u8457\u964d\u4f4e\u8bef\u5206\u7c7b\u7387\u548c\u5747\u65b9\u8bef\u5dee\uff0c\u9a8c\u8bc1\u4e86\u5176\u5728\u63d0\u9ad8\u6a21\u578b\u7a33\u5b9a\u6027\u548c\u51c6\u786e\u6027\u65b9\u9762\u7684\u4f18\u8d8a\u6027\u3002<\/p>\n\n\n<p><strong>\u5bf9\u672c\u9886\u57df\u7684\u8d21\u732e<\/strong><\/p>\n\n\n<p>\u8bba\u6587\u901a\u8fc7\u7cfb\u7edf\u6027\u5730\u9a8c\u8bc1\u548c\u5206\u6790\uff0c\u786e\u7acb\u4e86Bagging\u4f5c\u4e3a\u4e00\u79cd\u91cd\u8981\u7684\u6a21\u578b\u63d0\u5347\u6280\u672f\u7684\u5730\u4f4d\u3002Bagging\u4e0d\u4ec5\u5728\u7406\u8bba\u4e0a\u5f97\u5230\u4e86\u8bc1\u660e\uff0c\u5728\u5b9e\u8df5\u4e2d\u4e5f\u5c55\u793a\u4e86\u5176\u5e7f\u6cdb\u7684\u9002\u7528\u6027\u3002\u6b64\u7814\u7a76\u4e3a\u673a\u5668\u5b66\u4e60\u9886\u57df\u63d0\u4f9b\u4e86\u4e00\u79cd\u6709\u6548\u7684\u5de5\u5177\uff0c\u7528\u4ee5\u5e94\u5bf9\u6a21\u578b\u4e0d\u7a33\u5b9a\u6027\u95ee\u9898\uff0c\u540c\u65f6\u4e5f\u4e3a\u540e\u7eed\u7684\u96c6\u6210\u5b66\u4e60\u65b9\u6cd5\u7684\u53d1\u5c55\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n\n\n<p><strong>\u4e3b\u8981\u5b9a\u7406<\/strong><\/p>\n\n\n<p>\u8bba\u6587\u4e2d\u63a2\u8ba8\u4e86Bagging\u5728\u6570\u503c\u9884\u6d4b\u548c\u5206\u7c7b\u4e2d\u7684\u6709\u6548\u6027\uff0c\u901a\u8fc7\u7406\u8bba\u5206\u6790\u548c\u4e0d\u7b49\u5f0f\u63a8\u5bfc\uff0c\u8bc1\u660e\u4e86\u5728\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\u4e2d\uff0cBagging\u80fd\u591f\u901a\u8fc7\u805a\u5408\u591a\u4e2a\u6a21\u578b\u7248\u672c\u6765\u964d\u4f4e\u603b\u4f53\u9884\u6d4b\u8bef\u5dee\u3002\u6b64\u5916\uff0c\u8bba\u6587\u8fd8\u63a2\u8ba8\u4e86\u6a21\u578b\u7a33\u5b9a\u6027\u5bf9Bagging\u6548\u679c\u7684\u5f71\u54cd\u3002<\/p>\n\n\n<p><strong>\u5b58\u5728\u7684\u4e0d\u8db3<\/strong><\/p>\n\n\n<p>Bagging\u5bf9\u4e8e\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\u6548\u679c\u8f83\u5dee\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u9884\u6d4b\u51c6\u786e\u6027\u4e0b\u964d\u3002\u6b64\u5916\uff0cBagging\u5728\u63a5\u8fd1\u6a21\u578b\u6700\u4f18\u72b6\u6001\u65f6\uff0c\u5176\u63d0\u5347\u6548\u679c\u6709\u9650\uff0c\u65e0\u6cd5\u8fdb\u4e00\u6b65\u663e\u8457\u63d0\u9ad8\u51c6\u786e\u6027\u3002\u7814\u7a76\u4e2d\u5bf9Bagging\u4e0e\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u7684\u6bd4\u8f83\u8f83\u5c11\uff0c\u53ef\u80fd\u9650\u5236\u4e86\u5bf9\u5176\u4f18\u7f3a\u70b9\u7684\u5168\u9762\u7406\u89e3\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">\u7ae0\u8282\u68b3\u7406<\/h2>\n\n\n<h3 class=\"wp-block-heading\">1. \u5f15\u8a00\uff08Introduction\uff09<\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u4ecb\u7ecd\u4e86\u5b66\u4e60\u96c6\u7684\u57fa\u672c\u6982\u5ff5\uff0c\u63d0\u51fa\u4e86\u5728\u4e0d\u7a33\u5b9a\u9884\u6d4b\u6a21\u578b\u4e2d\u63d0\u9ad8\u51c6\u786e\u6027\u7684\u9700\u6c42\u3002\u5f15\u51faBagging\uff08\u81ea\u52a9\u805a\u96c6\uff09\u4f5c\u4e3a\u4e00\u79cd\u901a\u8fc7\u805a\u5408\u591a\u4e2a\u9884\u6d4b\u6a21\u578b\u7248\u672c\u6765\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed by making bootstrap replicates of the learning set and using these as new learning sets.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u5f15\u8a00\u6e05\u695a\u5730\u6982\u8ff0\u4e86Bagging\u7684\u6838\u5fc3\u673a\u5236\uff1a\u901a\u8fc7\u81ea\u52a9\u62bd\u6837\u751f\u6210\u591a\u4e2a\u5b66\u4e60\u96c6\uff0c\u4ece\u800c\u521b\u5efa\u591a\u4e2a\u9884\u6d4b\u6a21\u578b\uff0c\u5e76\u5c06\u8fd9\u4e9b\u6a21\u578b\u7684\u8f93\u51fa\u805a\u5408\u4ee5\u63d0\u9ad8\u6574\u4f53\u9884\u6d4b\u6027\u80fd\u3002\u5bf9\u4e8e\u6570\u503c\u9884\u6d4b\uff0c\u805a\u5408\u65b9\u5f0f\u662f\u53d6\u5e73\u5747\u503c\uff0c\u800c\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u5219\u91c7\u7528\u591a\u6570\u6295\u7968\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u521b\u65b0\u4e4b\u5904\u5728\u4e8e\u901a\u8fc7\u591a\u6b21\u62bd\u6837\u6765\u51cf\u5c11\u5355\u4e2a\u6a21\u578b\u7684\u4e0d\u7a33\u5b9a\u6027\uff0c\u4ece\u800c\u63d0\u9ad8\u9884\u6d4b\u7684\u51c6\u786e\u6027\u3002\u5f15\u8a00\u90e8\u5206\u901a\u8fc7\u7b80\u6d01\u7684\u63cf\u8ff0\uff0c\u6982\u62ec\u4e86Bagging\u7684\u539f\u7406\uff0c\u4e3a\u540e\u7eed\u7684\u8be6\u7ec6\u8ba8\u8bba\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cThe vital element is the instability of the prediction method. If perturbing the learning set can cause significant changes in the predictor constructed, then bagging can improve accuracy.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u70b9\u660e\u4e86Bagging\u6280\u672f\u7684\u5e94\u7528\u573a\u666f\uff1a\u5b83\u7279\u522b\u9002\u7528\u4e8e\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\uff0c\u5373\u5f53\u8bad\u7ec3\u6570\u636e\u7684\u8f7b\u5fae\u53d8\u5316\u53ef\u80fd\u5bfc\u81f4\u9884\u6d4b\u7ed3\u679c\u53d1\u751f\u663e\u8457\u53d8\u5316\u65f6\u3002\u901a\u8fc7\u591a\u6b21\u62bd\u6837\u5e76\u805a\u5408\u7ed3\u679c\uff0cBagging\u80fd\u591f\u663e\u8457\u51cf\u5c11\u8fd9\u79cd\u4e0d\u7a33\u5b9a\u6027\u5e26\u6765\u7684\u8bef\u5dee\u3002\u8fd9\u4e00\u5173\u952e\u5185\u5bb9\u4e3a\u8bfb\u8005\u63d0\u4f9b\u4e86\u5224\u65adBagging\u9002\u7528\u6027\u7684\u6807\u51c6\uff0c\u5e76\u7a81\u51fa\u4e86Bagging\u5728\u63d0\u5347\u6a21\u578b\u7a33\u5b9a\u6027\u65b9\u9762\u7684\u72ec\u7279\u4ef7\u503c\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cTests on real and simulated data sets using classification and regression trees and subset selection in linear regression show that bagging can give substantial gains in accuracy. The vital element is the instability of the prediction method.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u5f15\u8a00\u4e2d\u8fd8\u63d0\u5230\uff0cBagging\u5728\u5206\u7c7b\u6811\u3001\u56de\u5f52\u6811\u4ee5\u53ca\u7ebf\u6027\u56de\u5f52\u7684\u5b50\u96c6\u9009\u62e9\u4e2d\uff0c\u901a\u8fc7\u5b9e\u9a8c\u8bc1\u660e\u4e86\u5176\u5728\u771f\u5b9e\u6570\u636e\u548c\u6a21\u62df\u6570\u636e\u96c6\u4e0a\u7684\u663e\u8457\u6548\u679c\u3002\u8fd9\u4e00\u4fe1\u606f\u589e\u5f3a\u4e86Bagging\u7684\u5b9e\u7528\u6027\u548c\u5e7f\u6cdb\u9002\u7528\u6027\uff0c\u8868\u660e\u8be5\u6280\u672f\u4e0d\u4ec5\u5728\u7406\u8bba\u4e0a\u6709\u610f\u4e49\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u4e5f\u80fd\u53d6\u5f97\u660e\u663e\u7684\u6548\u679c\u3002\u901a\u8fc7\u5b9e\u9a8c\u9a8c\u8bc1\u7684\u65b9\u5f0f\uff0c\u4f5c\u8005\u8fdb\u4e00\u6b65\u5f3a\u5316\u4e86Bagging\u4f5c\u4e3a\u4e00\u79cd\u6709\u6548\u7684\u6a21\u578b\u63d0\u5347\u6280\u672f\u7684\u53ef\u4fe1\u5ea6\u3002<\/p>\n\n\n<p>\u8fd9\u4e9b\u5173\u952e\u5185\u5bb9\u548c\u8bc4\u8bba\u5e2e\u52a9\u660e\u786e\u4e86Bagging\u7684\u57fa\u672c\u539f\u7406\u3001\u5e94\u7528\u573a\u666f\u548c\u5b9e\u9645\u6548\u679c\uff0c\u4e3a\u7406\u89e3\u8bba\u6587\u7684\u6838\u5fc3\u8d21\u732e\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">2. Bagging\u5206\u7c7b\u6811\uff08Bagging Classification Trees\uff09<\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u8be6\u7ec6\u63cf\u8ff0\u4e86Bagging\u5728\u5206\u7c7b\u6811\u4e0a\u7684\u5e94\u7528\uff0c\u5305\u62ec\u5177\u4f53\u7684\u5b9e\u9a8c\u8fc7\u7a0b\u548c\u7ed3\u679c\u3002\u5217\u51fa\u4e86\u591a\u4e2a\u6570\u636e\u96c6\uff08\u5982\u6ce2\u5f62\u6570\u636e\u3001\u5fc3\u810f\u75c5\u6570\u636e\u7b49\uff09\u4e0a\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c\u5c55\u793a\u4e86Bagging\u5982\u4f55\u663e\u8457\u964d\u4f4e\u5206\u7c7b\u9519\u8bef\u7387\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging was applied to classification trees using the following data sets: waveform (simulated), heart, breast cancer (Wisconsin), ionosphere, diabetes, glass, soybean.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u5217\u4e3e\u4e86\u8bba\u6587\u4e2d\u7528\u4e8e\u6d4b\u8bd5Bagging\u5728\u5206\u7c7b\u6811\u4e0a\u8868\u73b0\u7684\u5177\u4f53\u6570\u636e\u96c6\uff0c\u5305\u62ec\u6a21\u62df\u6570\u636e\u96c6\uff08\u5982\u6ce2\u5f62\u6570\u636e\u96c6\uff09\u548c\u591a\u4e2a\u771f\u5b9e\u6570\u636e\u96c6\uff08\u5982\u5fc3\u810f\u75c5\u3001\u4e73\u817a\u764c\u6570\u636e\u96c6\u7b49\uff09\u3002\u901a\u8fc7\u5bf9\u8fd9\u4e9b\u6570\u636e\u96c6\u7684\u6d4b\u8bd5\uff0c\u4f5c\u8005\u5c55\u793a\u4e86Bagging\u7684\u5e7f\u6cdb\u9002\u7528\u6027\uff0c\u6db5\u76d6\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u5206\u7c7b\u95ee\u9898\u3002\u8fd9\u4e3a\u540e\u7eed\u5b9e\u9a8c\u7ed3\u679c\u7684\u8ba8\u8bba\u63d0\u4f9b\u4e86\u80cc\u666f\uff0c\u4e5f\u5c55\u793a\u4e86Bagging\u5728\u5404\u79cd\u6570\u636e\u96c6\u4e0a\u7684\u901a\u7528\u6027\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p>*<em>\u201cIn all runs the following procedure was used: i) The data set is randomly divided into a test set T and a learning set L. ii) A classification tree is constructed from L using 10-fold cross-validation. iii) A bootstrap sample L<\/em> is selected from L, and a tree grown using L<em>. iv) The original learning set L is used as a test set to select the best pruned subtree. v) The random division of the data into L and T is repeated 100 times and the reported es, eB are the averages over the 100 iterations.\u201d<\/em>*<\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u8be6\u7ec6\u63cf\u8ff0\u4e86Bagging\u5728\u5206\u7c7b\u6811\u4e0a\u7684\u5177\u4f53\u5b9e\u9a8c\u8fc7\u7a0b\uff0c\u5305\u62ec\u5982\u4f55\u8fdb\u884c\u6570\u636e\u96c6\u5212\u5206\u3001\u6a21\u578b\u6784\u5efa\u3001Bootstrap\u62bd\u6837\u3001\u4ee5\u53ca\u6700\u7ec8\u7684\u7ed3\u679c\u8ba1\u7b97\u65b9\u6cd5\u3002\u901a\u8fc710\u6298\u4ea4\u53c9\u9a8c\u8bc1\u548c\u591a\u6b21\u91cd\u590d\u5b9e\u9a8c\uff0c\u786e\u4fdd\u4e86\u5b9e\u9a8c\u7ed3\u679c\u7684\u53ef\u9760\u6027\u3002\u8fd9\u79cd\u8be6\u5c3d\u7684\u5b9e\u9a8c\u6d41\u7a0b\u63cf\u8ff0\uff0c\u4e0d\u4ec5\u6709\u52a9\u4e8e\u7406\u89e3Bagging\u7684\u5b9e\u9645\u64cd\u4f5c\u6b65\u9aa4\uff0c\u8fd8\u4e3a\u5176\u4ed6\u7814\u7a76\u8005\u63d0\u4f9b\u4e86\u53ef\u590d\u73b0\u7684\u5b9e\u9a8c\u65b9\u6cd5\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging was applied to classification trees with a reduction in test set misclassification rates ranging from 6% to 77%.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u603b\u7ed3\u4e86Bagging\u5728\u5206\u7c7b\u6811\u5b9e\u9a8c\u4e2d\u7684\u6548\u679c\uff0c\u6307\u51fa\u4e86\u6d4b\u8bd5\u96c6\u9519\u8bef\u7387\u7684\u964d\u4f4e\u5e45\u5ea6\u57286%\u523077%\u4e4b\u95f4\u3002\u8fd9\u4e2a\u7ed3\u679c\u8868\u660e\uff0cBagging\u5bf9\u4e0d\u7a33\u5b9a\u6a21\u578b\u7684\u63d0\u5347\u6548\u679c\u975e\u5e38\u663e\u8457\uff0c\u7279\u522b\u662f\u5728\u9519\u8bef\u7387\u8f83\u9ad8\u7684\u573a\u666f\u4e0b\uff0cBagging\u80fd\u591f\u5927\u5e45\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002\u8fd9\u4e2a\u7ed3\u8bba\u5f3a\u5316\u4e86Bagging\u4f5c\u4e3a\u4e00\u79cd\u6709\u6548\u7684\u63d0\u5347\u5206\u7c7b\u6811\u6027\u80fd\u7684\u65b9\u6cd5\u7684\u89c2\u70b9\uff0c\u5e76\u4e14\u6570\u636e\u4e0a\u4e5f\u652f\u6301\u4e86\u7406\u8bba\u5206\u6790\u7684\u7ed3\u679c\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cCompared to the 22 classifiers in the Statlog Project, bagged trees ranked 2nd in accuracy on the DNA data set, 1st on the shuttle, 2nd on the satellite and 1st on letters.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u5bf9\u6bd4\u4e86Bagging\u5206\u7c7b\u6811\u4e0e\u5176\u4ed622\u79cd\u5206\u7c7b\u7b97\u6cd5\u5728Statlog\u9879\u76ee\u4e2d\u7684\u8868\u73b0\uff0c\u6307\u51faBagging\u5206\u7c7b\u6811\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\u7684\u51c6\u786e\u6027\u6392\u540d\u975e\u5e38\u9760\u524d\u3002\u8fd9\u8868\u660eBagging\u4e0d\u4ec5\u80fd\u663e\u8457\u63d0\u5347\u5206\u7c7b\u6811\u7684\u6027\u80fd\uff0c\u8fd8\u80fd\u591f\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u4e0e\u5176\u4ed6\u6d41\u884c\u7684\u5206\u7c7b\u7b97\u6cd5\u7ade\u4e89\u751a\u81f3\u8d85\u8d8a\u5b83\u4eec\u3002\u8fd9\u79cd\u6bd4\u8f83\u8fdb\u4e00\u6b65\u8bc1\u660e\u4e86Bagging\u7684\u5b9e\u7528\u4ef7\u503c\u548c\u5728\u5e7f\u6cdb\u9886\u57df\u4e2d\u7684\u7ade\u4e89\u529b\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">3. <strong>Bagging\u56de\u5f52\u6811\uff08Bagging Regression Trees\uff09<\/strong><\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u63a2\u8ba8\u4e86Bagging\u5728\u56de\u5f52\u6811\u4e2d\u7684\u5e94\u7528\u3002\u901a\u8fc7\u5728\u591a\u4e2a\u56de\u5f52\u6570\u636e\u96c6\u4e0a\u7684\u5b9e\u9a8c\uff0c\u8bf4\u660e\u4e86Bagging\u5728\u51cf\u5c11\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u65b9\u9762\u7684\u6548\u679c\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging trees was used on five data sets with numerical responses: Boston Housing, Ozone, Friedman #1 (simulated), Friedman #2 (simulated), Friedman #3 (simulated).\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u5217\u4e3e\u4e86\u8bba\u6587\u4e2d\u7528\u4e8e\u6d4b\u8bd5Bagging\u5728\u56de\u5f52\u6811\u4e0a\u8868\u73b0\u7684\u5177\u4f53\u6570\u636e\u96c6\uff0c\u5305\u62ec\u771f\u5b9e\u6570\u636e\u96c6\uff08\u5982\u6ce2\u58eb\u987f\u623f\u4ef7\u3001\u81ed\u6c27\u6d53\u5ea6\uff09\u548c\u6a21\u62df\u6570\u636e\u96c6\uff08Friedman #1, #2, #3\uff09\u3002\u901a\u8fc7\u5bf9\u8fd9\u4e9b\u6570\u636e\u96c6\u7684\u5b9e\u9a8c\uff0c\u4f5c\u8005\u65e8\u5728\u5c55\u793aBagging\u5728\u56de\u5f52\u95ee\u9898\u4e0a\u7684\u9002\u7528\u6027\u548c\u6548\u679c\uff0c\u6db5\u76d6\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u56de\u5f52\u4efb\u52a1\u3002\u8fd9\u4e3a\u540e\u7eed\u5bf9\u5b9e\u9a8c\u7ed3\u679c\u7684\u8ba8\u8bba\u63d0\u4f9b\u4e86\u91cd\u8981\u80cc\u666f\u4fe1\u606f\uff0c\u5e76\u5c55\u793a\u4e86Bagging\u5728\u56de\u5f52\u5206\u6790\u4e2d\u7684\u5e7f\u6cdb\u5e94\u7528\u573a\u666f\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cFor (yi, xi) \u2208 T, the bagged predictor is \\(\\hat{f}_B(x_i)\\) = (1\/B) \u2211(from b=1 to B) \\(\\hat{f}^{(b)}(x_i)\\), and the squared error \\(e_B(L, T)\\) is avgi(yi &#8211; \\(\\hat{f}_B(x_i)\\))^2.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u63cf\u8ff0\u4e86Bagging\u5728\u56de\u5f52\u6811\u4e2d\u7684\u5177\u4f53\u64cd\u4f5c\u65b9\u5f0f\uff0c\u5373\u901a\u8fc7Bootstrap\u62bd\u6837\u751f\u6210\u591a\u4e2a\u56de\u5f52\u6811\uff0c\u7136\u540e\u5bf9\u8fd9\u4e9b\u6811\u7684\u9884\u6d4b\u7ed3\u679c\u53d6\u5e73\u5747\u503c\u4f5c\u4e3a\u6700\u7ec8\u7684\u9884\u6d4b\u503c\u3002\u540c\u65f6\uff0c\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u88ab\u7528\u4f5c\u8bc4\u4ef7\u6307\u6807\u3002\u8fd9\u79cd\u65b9\u6cd5\u901a\u8fc7\u5e73\u5747\u591a\u4e2a\u6a21\u578b\u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u51cf\u5c11\u4e86\u5355\u4e00\u6a21\u578b\u7684\u8bef\u5dee\uff0c\u5c24\u5176\u662f\u5728\u57fa\u7840\u6a21\u578b\u4e0d\u7a33\u5b9a\u7684\u60c5\u51b5\u4e0b\u3002\u8fd9\u79cd\u805a\u5408\u7b56\u7565\u662fBagging\u7684\u6838\u5fc3\uff0c\u4e5f\u662f\u5176\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u6709\u6548\u6027\u7684\u5173\u952e\u6240\u5728\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cThe reduction in test set mean squared error on data sets ranging from 21% to 46%.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u603b\u7ed3\u4e86Bagging\u5728\u56de\u5f52\u6811\u5b9e\u9a8c\u4e2d\u7684\u6548\u679c\uff0c\u6307\u51fa\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\uff0cBagging\u4f7f\u6d4b\u8bd5\u96c6\u4e0a\u7684\u5747\u65b9\u8bef\u5dee\u51cf\u5c11\u4e8621%\u523046%\u3002\u8fd9\u4e2a\u7ed3\u679c\u8868\u660e\uff0cBagging\u5728\u56de\u5f52\u95ee\u9898\u4e2d\u540c\u6837\u5177\u6709\u663e\u8457\u7684\u63d0\u5347\u6548\u679c\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u7684\u56de\u5f52\u6a21\u578b\u65f6\uff0c\u53ef\u4ee5\u5927\u5e45\u63d0\u9ad8\u9884\u6d4b\u7684\u51c6\u786e\u6027\u3002\u8fd9\u4e00\u6570\u636e\u652f\u6301\u4e86Bagging\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u6709\u6548\u6027\uff0c\u5e76\u5c55\u793a\u4e86\u5176\u5728\u964d\u4f4e\u9884\u6d4b\u8bef\u5dee\u65b9\u9762\u7684\u80fd\u529b\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging can improve only if the unbagged is not optimal. &#8230; Bagging can improve only if the unbagged predictor is unstable.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u5f3a\u8c03\u4e86Bagging\u7684\u5c40\u9650\u6027\uff1a\u53ea\u6709\u5728\u672a\u7ecf\u8fc7Bagging\u5904\u7406\u7684\u6a21\u578b\uff08\u5373\u5355\u4e00\u6a21\u578b\uff09\u8868\u73b0\u4e0d\u4f73\u4e14\u4e0d\u7a33\u5b9a\u65f6\uff0cBagging\u624d\u80fd\u663e\u8457\u63d0\u9ad8\u5176\u6027\u80fd\u3002\u8fd9\u4e00\u89c2\u70b9\u63d0\u9192\u6211\u4eec\uff0cBagging\u5e76\u4e0d\u662f\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u90fd\u6709\u6548\uff0c\u7279\u522b\u662f\u5728\u6a21\u578b\u5df2\u7ecf\u7a33\u5b9a\u4e14\u63a5\u8fd1\u6700\u4f18\u65f6\uff0cBagging\u7684\u6548\u679c\u53ef\u80fd\u6709\u9650\u3002\u8fd9\u4e3a\u7406\u89e3Bagging\u7684\u9002\u7528\u6761\u4ef6\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u7406\u8bba\u4f9d\u636e\uff0c\u907f\u514d\u4e86\u76f2\u76ee\u4f7f\u7528\u8be5\u65b9\u6cd5\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging trees was used on five data sets with numerical responses. &#8230; Improvement will occur for unstable procedures where a small change in L can result in large changes in \\(\\hat{f}\\). Instability was studied in Breiman <a href=\"#\">1994<\/a> where it was pointed out that neural nets, classification and regression trees, and subset selection in linear regression were unstable, while k-nearest neighbor methods were stable.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u8fdb\u4e00\u6b65\u63a2\u8ba8\u4e86\u6a21\u578b\u4e0d\u7a33\u5b9a\u6027\u5728Bagging\u6548\u679c\u4e2d\u7684\u91cd\u8981\u6027\uff0c\u5f15\u7528\u4e86\u4e4b\u524d\u7684\u7814\u7a76\u6765\u652f\u6301\u8fd9\u4e00\u70b9\uff0c\u5f3a\u8c03\u4e86Bagging\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u6a21\u578b\u65f6\u7684\u4f18\u8d8a\u6027\u3002\u8fd9\u6bb5\u8ba8\u8bba\u4e0d\u4ec5\u5f3a\u5316\u4e86Bagging\u5728\u4e0d\u7a33\u5b9a\u6a21\u578b\u4e2d\u7684\u6709\u6548\u6027\uff0c\u8fd8\u5bf9\u8bfb\u8005\u7406\u89e3\u54ea\u4e9b\u6a21\u578b\u7c7b\u578b\u66f4\u9002\u5408\u5e94\u7528Bagging\u63d0\u4f9b\u4e86\u7406\u8bba\u80cc\u666f\uff0c\u7279\u522b\u662f\u5728\u9009\u62e9\u662f\u5426\u5e94\u7528Bagging\u65f6\u63d0\u4f9b\u4e86\u91cd\u8981\u53c2\u8003\u3002<\/p>\n\n\n<p>\u8fd9\u4e9b\u6458\u5f55\u548c\u8bc4\u8bba\u63ed\u793a\u4e86Bagging\u5728\u56de\u5f52\u6811\u90e8\u5206\u7684\u6838\u5fc3\u5185\u5bb9\uff0c\u8ba8\u8bba\u4e86\u5177\u4f53\u7684\u5b9e\u9a8c\u65b9\u6cd5\u3001\u6548\u679c\u8bc4\u4f30\u548cBagging\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u9002\u7528\u6027\u53ca\u5c40\u9650\u6027\uff0c\u4e3a\u7406\u89e3Bagging\u5728\u56de\u5f52\u95ee\u9898\u4e2d\u7684\u5e94\u7528\u6548\u679c\u63d0\u4f9b\u4e86\u6df1\u523b\u7684\u89c1\u89e3\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">4. Bagging\u7684\u5de5\u4f5c\u539f\u7406\uff08Why Bagging Works\uff09<\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u4ece\u7406\u8bba\u4e0a\u5206\u6790\u4e86Bagging\u5728\u6570\u503c\u9884\u6d4b\u548c\u5206\u7c7b\u4e2d\u7684\u6709\u6548\u6027\u3002\u8ba8\u8bba\u4e86\u6a21\u578b\u7684\u4e0d\u7a33\u5b9a\u6027\u5982\u4f55\u5f71\u54cdBagging\u7684\u6548\u679c\uff0c\u5e76\u89e3\u91ca\u4e86Bagging\u5728\u7a33\u5b9a\u6a21\u578b\u4e2d\u53ef\u80fd\u4f1a\u964d\u4f4e\u6027\u80fd\u7684\u539f\u56e0\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cThe aggregated predictor is the average over \\(L^*\\) of \\(\\hat{f}(x, L^*)\\), i.e. \\(\\hat{f}_A(x) = E_{L^*}[\\hat{f}(x, L^*)]\\).\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u7b80\u8981\u63cf\u8ff0\u4e86Bagging\u7684\u6838\u5fc3\u5de5\u4f5c\u539f\u7406\uff0c\u5373\u901a\u8fc7\u5728\u4e0d\u540c\u7684\u81ea\u52a9\u62bd\u6837\u6570\u636e\u96c6 \\(L^*\\) \u4e0a\u6784\u5efa\u9884\u6d4b\u6a21\u578b \\(\\hat{f}(x, L^*)\\)\uff0c\u5e76\u5bf9\u8fd9\u4e9b\u6a21\u578b\u7684\u9884\u6d4b\u7ed3\u679c\u8fdb\u884c\u5e73\u5747\uff0c\u5f62\u6210\u4e00\u4e2a\u805a\u5408\u9884\u6d4b\u5668 \\(\\hat{f}_A(x)\\)\u3002\u8fd9\u4e00\u805a\u5408\u8fc7\u7a0b\u51cf\u5c11\u4e86\u5355\u4e2a\u6a21\u578b\u7531\u4e8e\u6570\u636e\u6ce2\u52a8\u5e26\u6765\u7684\u4e0d\u7a33\u5b9a\u6027\uff0c\u4f7f\u5f97\u6700\u7ec8\u9884\u6d4b\u7ed3\u679c\u66f4\u52a0\u7a33\u5065\u3002Bagging\u901a\u8fc7\u8fd9\u79cd\u7b80\u5355\u4f46\u6709\u6548\u7684\u5e73\u5747\u7b56\u7565\uff0c\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u4e0d\u7a33\u5b9a\u6a21\u578b\u7684\u8868\u73b0\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cIf \\(L^*\\) does not change too much with replicate \\(L\\), the two sides will be nearly equal, and aggregation will not help. The more highly variable the \\(\\hat{f}(x, L)\\) is, the more improvement aggregation may produce.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u5f3a\u8c03\u4e86\u6a21\u578b\u4e0d\u7a33\u5b9a\u6027\u5bf9\u4e8eBagging\u6548\u679c\u7684\u5f71\u54cd\u3002\u5982\u679c\u5728\u4e0d\u540c\u7684\u81ea\u52a9\u62bd\u6837\u6570\u636e\u96c6 \\(L^*\\) \u4e0a\u6784\u5efa\u7684\u6a21\u578b \\(\\hat{f}(x, L)\\) \u53d8\u5316\u4e0d\u5927\uff0c\u90a3\u4e48\u805a\u5408\uff08\u5373Bagging\uff09\u5e26\u6765\u7684\u63d0\u5347\u5c31\u975e\u5e38\u6709\u9650\u3002\u7136\u800c\uff0c\u5982\u679c \\(\\hat{f}(x, L)\\) \u968f\u7740\u6570\u636e\u96c6\u7684\u53d8\u5316\u6709\u8f83\u5927\u6ce2\u52a8\uff0cBagging\u53ef\u4ee5\u663e\u8457\u51cf\u5c11\u8fd9\u79cd\u6ce2\u52a8\u5e26\u6765\u7684\u8bef\u5dee\uff0c\u4ece\u800c\u663e\u8457\u63d0\u5347\u6a21\u578b\u6027\u80fd\u3002\u8fd9\u8fdb\u4e00\u6b65\u89e3\u91ca\u4e86\u4e3a\u4f55Bagging\u5728\u4e0d\u7a33\u5b9a\u6a21\u578b\u4e2d\u8868\u73b0\u826f\u597d\uff0c\u800c\u5728\u7a33\u5b9a\u6a21\u578b\u4e2d\u6548\u679c\u5e73\u5e73\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cThere is a cross-over point between instability and stability at which \\(\\hat{f}_B\\) stops improving on \\(\\hat{f}(x, L)\\) and does worse.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u6307\u51fa\u4e86Bagging\u7684\u4e00\u4e2a\u5173\u952e\u70b9\uff0c\u5373\u5f53\u6a21\u578b\u9010\u6e10\u4ece\u4e0d\u7a33\u5b9a\u5411\u7a33\u5b9a\u8f6c\u53d8\u65f6\uff0cBagging\u7684\u6548\u679c\u4f1a\u8fbe\u5230\u4e00\u4e2a\u4e34\u754c\u70b9\uff0c\u8d85\u8fc7\u8fd9\u4e2a\u70b9\u540e\uff0cBagging\u7684\u6548\u679c\u4e0d\u4ec5\u4e0d\u518d\u63d0\u5347\uff0c\u751a\u81f3\u53ef\u80fd\u4f7f\u6a21\u578b\u8868\u73b0\u53d8\u5dee\u3002\u8fd9\u4e00\u89c2\u5bdf\u63d0\u9192\u6211\u4eec\uff0cBagging\u5e76\u4e0d\u662f\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u90fd\u9002\u7528\uff0c\u7279\u522b\u662f\u5728\u57fa\u7840\u6a21\u578b\u5df2\u7ecf\u8f83\u4e3a\u7a33\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0cBagging\u53ef\u80fd\u53cd\u800c\u4f1a\u5bfc\u81f4\u6027\u80fd\u4e0b\u964d\u3002\u8fd9\u4e00\u7406\u8bba\u70b9\u4e3a\u9009\u62e9\u662f\u5426\u5e94\u7528Bagging\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u53c2\u8003\u4f9d\u636e\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBut the bagged estimate is not \\(\\hat{f}_A(x, P)\\), but rather \\(\\hat{f}_B(x, P_L)\\), where \\(P_L\\) is the distribution that concentrates mass \\(1\/N\\) at each point \\((y_n, x_n) \\in L\\).\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u89e3\u91ca\u4e86Bagging\u7684\u7edf\u8ba1\u6027\u8d28\uff0c\u6307\u51faBagging\u7684\u805a\u5408\u4f30\u8ba1 \\(\\hat{f}_B(x, P_L)\\) \u4e0d\u662f\u76f4\u63a5\u5bf9\u76ee\u6807\u5206\u5e03 \\(P\\) \u8fdb\u884c\u805a\u5408\uff0c\u800c\u662f\u57fa\u4e8e\u81ea\u52a9\u62bd\u6837\u751f\u6210\u7684 \\(P_L\\) \u5206\u5e03\u3002\u7531\u4e8e \\(P_L\\) \u662f\u5bf9 \\(P\\) \u7684\u4e00\u79cd\u8fd1\u4f3c\uff0c\u8fd9\u610f\u5473\u7740Bagging\u5b9e\u9645\u4e0a\u662f\u5728\u4e00\u4e2a\u903c\u8fd1\u7684\u6982\u7387\u5206\u5e03\u4e0a\u8fdb\u884c\u4f30\u8ba1\u3002\u8fd9\u79cd\u8fd1\u4f3c\u5e26\u6765\u7684\u504f\u5dee\u53ef\u80fd\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5bfc\u81f4Bagging\u6548\u679c\u4e0d\u5982\u9884\u671f\uff0c\u7279\u522b\u662f\u5728\u6570\u636e\u5206\u5e03\u590d\u6742\u6216\u6a21\u578b\u975e\u5e38\u7a33\u5b9a\u65f6\u3002\u8fd9\u4e3a\u7406\u89e3Bagging\u7684\u5c40\u9650\u6027\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u7406\u8bba\u57fa\u7840\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging unstable classifiers usually improves them. Bagging stable classifiers is not a good idea.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u660e\u786e\u603b\u7ed3\u4e86Bagging\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d\u7684\u9002\u7528\u6027\uff1a\u5bf9\u4e0d\u7a33\u5b9a\u7684\u5206\u7c7b\u5668\uff0cBagging\u901a\u5e38\u80fd\u591f\u663e\u8457\u6539\u5584\u5176\u6027\u80fd\uff1b\u800c\u5bf9\u5df2\u7ecf\u7a33\u5b9a\u7684\u5206\u7c7b\u5668\uff0c\u5e94\u7528Bagging\u53ef\u80fd\u4e0d\u662f\u4e00\u4e2a\u597d\u4e3b\u610f\uff0c\u751a\u81f3\u53ef\u80fd\u964d\u4f4e\u6027\u80fd\u3002\u8fd9\u4e00\u603b\u7ed3\u975e\u5e38\u76f4\u63a5\u5730\u6307\u51fa\u4e86Bagging\u7684\u4f7f\u7528\u6761\u4ef6\uff0c\u5e2e\u52a9\u7814\u7a76\u8005\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u505a\u51fa\u66f4\u660e\u667a\u7684\u51b3\u7b56\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">5. \u7ebf\u6027\u56de\u5f52\u4e2d\u7684Bagging\u793a\u4f8b\uff08A Linear Regression Illustration\uff09<\/h3>\n\n\n<p><strong>\u4f4d\u7f6e<\/strong>\uff1a\u8bba\u6587\u7b2c5\u8282<\/p>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u901a\u8fc7\u7ebf\u6027\u56de\u5f52\u5b50\u96c6\u9009\u62e9\u7684\u793a\u4f8b\uff0c\u8fdb\u4e00\u6b65\u8bf4\u660e\u4e86Bagging\u7684\u6548\u679c\u3002\u901a\u8fc7\u6a21\u62df\u6570\u636e\u5c55\u793a\u4e86Bagging\u5728\u53d8\u91cf\u9009\u62e9\u8fc7\u7a0b\u4e2d\u5bf9\u6a21\u578b\u51c6\u786e\u6027\u7684\u5f71\u54cd\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cSubset selection in linear regression gives an illustration of the points made in the previous section. &#8230; The variables are competing for inclusion in the \\(\\{\\hat{f}_m\\}\\) and small changes in the data can cause large changes in the \\(\\{\\hat{f}_m\\}\\).\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u4ecb\u7ecd\u4e86\u7ebf\u6027\u56de\u5f52\u4e2d\u5b50\u96c6\u9009\u62e9\u7684\u793a\u4f8b\uff0c\u5f3a\u8c03\u4e86\u6a21\u578b\u4e0d\u7a33\u5b9a\u6027\u5bf9\u53d8\u91cf\u9009\u62e9\u7684\u5f71\u54cd\u3002\u5728\u5b50\u96c6\u9009\u62e9\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u540c\u53d8\u91cf\u4e4b\u95f4\u7684\u7ade\u4e89\u4f1a\u5bfc\u81f4\u5373\u4f7f\u662f\u6570\u636e\u7684\u5fae\u5c0f\u53d8\u5316\uff0c\u4e5f\u53ef\u80fd\u5bfc\u81f4\u6a21\u578b\u53d1\u751f\u663e\u8457\u53d8\u5316\u3002\u8fd9\u6b63\u662fBagging\u6280\u672f\u53ef\u4ee5\u6d3e\u4e0a\u7528\u573a\u7684\u573a\u666f\uff0c\u901a\u8fc7\u5bf9\u591a\u4e2a\u5b50\u96c6\u9009\u62e9\u7ed3\u679c\u8fdb\u884c\u805a\u5408\uff0cBagging\u53ef\u4ee5\u51cf\u5c11\u8fd9\u79cd\u4e0d\u7a33\u5b9a\u6027\u5e26\u6765\u7684\u8bef\u5dee\u3002\u8fd9\u4e00\u793a\u4f8b\u8fdb\u4e00\u6b65\u5f3a\u8c03\u4e86Bagging\u5728\u5e94\u5bf9\u4e0d\u7a33\u5b9a\u6027\u65b9\u9762\u7684\u72ec\u7279\u4f18\u52bf\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cAn obvious result is that the most accurate bagged predictor is at least as good as the most accurate subset predictor. When \\(h = 1\\) and subset selection is nearly optimal, there is no improvement. For \\(h = 3\\) and \\(h = 5\\), there is substantial improvement.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u603b\u7ed3\u4e86\u7ebf\u6027\u56de\u5f52\u4e2dBagging\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c\u6307\u51fa\u5f53\u5b50\u96c6\u9009\u62e9\u672c\u8eab\u5df2\u7ecf\u63a5\u8fd1\u6700\u4f18\uff08\u5373 \\(h = 1\\) \u65f6\uff09\uff0cBagging\u51e0\u4e4e\u6ca1\u6709\u63d0\u5347\u6548\u679c\uff1b\u7136\u800c\uff0c\u5f53\u6a21\u578b\u4e0d\u592a\u7a33\u5b9a\uff08\u5373 \\(h = 3\\) \u548c \\(h = 5\\) \u65f6\uff09\uff0cBagging\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u3002\u8fd9\u8868\u660eBagging\u5728\u6a21\u578b\u4e0d\u7a33\u5b9a\u65f6\u5177\u6709\u66f4\u5927\u7684\u63d0\u5347\u6f5c\u529b\uff0c\u800c\u5f53\u6a21\u578b\u5df2\u7ecf\u63a5\u8fd1\u6700\u4f18\u65f6\uff0cBagging\u7684\u6548\u679c\u53ef\u80fd\u6709\u9650\u3002\u8fd9\u4e00\u53d1\u73b0\u4e3aBagging\u7684\u9002\u7528\u6027\u63d0\u4f9b\u4e86\u66f4\u5177\u4f53\u7684\u6848\u4f8b\u652f\u6301\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cNote that in all three graphs there is a point past which the bagged predictors have larger prediction error than the unbagged.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u6307\u51fa\u4e86\u4e00\u4e2a\u5173\u952e\u89c2\u5bdf\uff1a\u5728\u5b9e\u9a8c\u7684\u56fe\u8868\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u968f\u7740\u53d8\u91cf\u6570\u91cf\u7684\u589e\u52a0\uff0cBagging\u7684\u9884\u6d4b\u8bef\u5dee\u5728\u67d0\u4e2a\u70b9\u4e4b\u540e\u53cd\u800c\u8d85\u8fc7\u4e86\u672a\u7ecf\u8fc7Bagging\u5904\u7406\u7684\u9884\u6d4b\u8bef\u5dee\u3002\u8fd9\u8bf4\u660e\uff0c\u5f53\u6a21\u578b\u4ece\u4e0d\u7a33\u5b9a\u8f6c\u5411\u7a33\u5b9a\u65f6\uff0cBagging\u53ef\u80fd\u4e0d\u518d\u6709\u4f18\u52bf\uff0c\u751a\u81f3\u53ef\u80fd\u5f15\u5165\u989d\u5916\u7684\u8bef\u5dee\u3002\u8fd9\u4e00\u89c2\u5bdf\u63ed\u793a\u4e86Bagging\u5728\u5904\u7406\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u65f6\u7684\u5c40\u9650\u6027\uff0c\u5f3a\u8c03\u4e86\u9009\u62e9Bagging\u65f6\u9700\u8981\u8003\u8651\u6a21\u578b\u7684\u590d\u6742\u6027\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cLinear regression using all variables is a fairly stable procedure. The stability decreases as the number of variables used in the predictor decreases. &#8230; The higher values of \\(\\hat{e}(m)\\) for large \\(m\\) reflect this fact.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u89e3\u91ca\u4e86\u7ebf\u6027\u56de\u5f52\u4e2d\u6a21\u578b\u7a33\u5b9a\u6027\u4e0e\u53d8\u91cf\u6570\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4f7f\u7528\u6240\u6709\u53d8\u91cf\u65f6\uff0c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u76f8\u5bf9\u7a33\u5b9a\uff0c\u4f46\u968f\u7740\u4f7f\u7528\u7684\u53d8\u91cf\u6570\u91cf\u51cf\u5c11\uff0c\u6a21\u578b\u7684\u7a33\u5b9a\u6027\u4e5f\u4f1a\u4e0b\u964d\u3002\u8fd9\u610f\u5473\u7740\uff0c\u968f\u7740\u53d8\u91cf\u6570\u91cf\u51cf\u5c11\uff0cBagging\u7684\u6548\u679c\u4f1a\u6709\u6240\u63d0\u5347\uff0c\u4f46\u5728\u53d8\u91cf\u8f83\u591a\u4e14\u6a21\u578b\u8f83\u4e3a\u7a33\u5b9a\u65f6\uff0cBagging\u53ef\u80fd\u53cd\u800c\u4e0d\u5229\u3002\u8fd9\u8fdb\u4e00\u6b65\u8bf4\u660e\u4e86Bagging\u5728\u7ebf\u6027\u56de\u5f52\u4e2d\u7684\u9002\u7528\u6027\u4f9d\u8d56\u4e8e\u6a21\u578b\u7684\u7a33\u5b9a\u6027\uff0c\u8fd9\u5bf9\u4e8e\u9009\u62e9\u662f\u5426\u5e94\u7528Bagging\u5177\u6709\u6307\u5bfc\u610f\u4e49\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cWhen \\(h = 1\\) and subset selection is nearly optimal, there is no improvement, For \\(h = 3\\) and 5 there is substantial improvement. This illustrates the obvious: bagging can improve only if the unbagged is not optimal.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u518d\u6b21\u5f3a\u8c03\u4e86Bagging\u7684\u5c40\u9650\u6027\uff0c\u5373\u53ea\u6709\u5728\u539f\u59cb\u6a21\u578b\u4e0d\u7a33\u5b9a\u6216\u672a\u8fbe\u5230\u6700\u4f18\u72b6\u6001\u65f6\uff0cBagging\u624d\u80fd\u5e26\u6765\u663e\u8457\u63d0\u5347\u3002\u5bf9\u4e8e\u5df2\u7ecf\u63a5\u8fd1\u6700\u4f18\u7684\u6a21\u578b\uff08\u5982 \\(h = 1\\) \u7684\u60c5\u51b5\uff09\uff0cBagging\u65e0\u6cd5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u6027\u80fd\u3002\u8fd9\u4e00\u89c2\u70b9\u4e0e\u524d\u9762\u63d0\u5230\u7684Bagging\u5728\u7a33\u5b9a\u6a21\u578b\u4e2d\u6548\u679c\u6709\u9650\u7684\u7ed3\u8bba\u76f8\u547c\u5e94\uff0c\u8fdb\u4e00\u6b65\u5f3a\u8c03\u4e86\u5728\u4f7f\u7528Bagging\u4e4b\u524d\u8bc4\u4f30\u6a21\u578b\u521d\u59cb\u72b6\u6001\u7684\u91cd\u8981\u6027\u3002<\/p>\n\n\n<p>\u8fd9\u4e9b\u6458\u5f55\u548c\u8bc4\u8bba\u6df1\u5165\u5206\u6790\u4e86\u7ebf\u6027\u56de\u5f52\u4e2dBagging\u7684\u5e94\u7528\u793a\u4f8b\uff0c\u8ba8\u8bba\u4e86Bagging\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u6a21\u578b\u65f6\u7684\u4f18\u52bf\u4ee5\u53ca\u5176\u5728\u6a21\u578b\u63a5\u8fd1\u6700\u4f18\u72b6\u6001\u65f6\u7684\u5c40\u9650\u6027\u3002\u8fd9\u4e9b\u5185\u5bb9\u4e3a\u7406\u89e3Bagging\u5728\u4e0d\u540c\u7c7b\u578b\u56de\u5f52\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u6548\u679c\u63d0\u4f9b\u4e86\u5177\u4f53\u7684\u5b9e\u9a8c\u652f\u6301\u548c\u7406\u8bba\u4f9d\u636e\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">6. <strong>\u7ed3\u8bba\uff08Concluding Remarks\uff09<\/strong><\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u603b\u7ed3\u4e86Bagging\u7684\u4f18\u70b9\u548c\u5c40\u9650\u6027\uff0c\u63a2\u8ba8\u4e86\u5728\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\u548c\u95ee\u9898\u4e0aBagging\u7684\u9002\u7528\u6027\u3002\u8fd8\u8ba8\u8bba\u4e86\u4e0eBagging\u76f8\u5173\u7684\u4e00\u4e9b\u6280\u672f\u95ee\u9898\uff0c\u5982\u81ea\u52a9\u5b66\u4e60\u96c6\u7684\u5927\u5c0f\u548c\u8ba1\u7b97\u8d44\u6e90\u7684\u9700\u6c42\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging goes a ways toward making a silk purse out of a sow&#8217;s ear, especially if the sow&#8217;s ear is twitchy. It is a relatively easy way to improve an existing method, since all that needs adding is a loop in front that selects the bootstrap sample and sends it to the procedure and a back end that does the aggregation.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u4f7f\u7528\u4e86\u5f62\u8c61\u7684\u6bd4\u55bb\u6765\u63cf\u8ff0Bagging\u7684\u6548\u679c\uff0c\u5373\u5c06\u4e00\u4e2a\u4e0d\u4f73\u4e14\u4e0d\u7a33\u5b9a\u7684\u6a21\u578b\uff08\u201csow&#8217;s ear\u201d\uff09\u8f6c\u5316\u4e3a\u4e00\u4e2a\u66f4\u597d\u7684\u6a21\u578b\uff08\u201csilk purse\u201d\uff09\uff0c\u7279\u522b\u662f\u5f53\u6a21\u578b\u8868\u73b0\u4e0d\u7a33\u5b9a\u65f6\uff08\u201ctwitchy\u201d\uff09\u3002\u4f5c\u8005\u5f3a\u8c03\u4e86Bagging\u6280\u672f\u7684\u6613\u7528\u6027\uff0c\u901a\u8fc7\u7b80\u5355\u5730\u5728\u5df2\u6709\u65b9\u6cd5\u524d\u540e\u6dfb\u52a0\u81ea\u52a9\u62bd\u6837\u548c\u805a\u5408\u6b65\u9aa4\uff0c\u5c31\u53ef\u4ee5\u663e\u8457\u6539\u5584\u6a21\u578b\u7684\u8868\u73b0\u3002\u8fd9\u79cd\u63cf\u8ff0\u4e0d\u4ec5\u751f\u52a8\uff0c\u8fd8\u7a81\u51fa\u4e86Bagging\u4f5c\u4e3a\u4e00\u79cd\u6709\u6548\u4e14\u5bb9\u6613\u5b9e\u73b0\u7684\u63d0\u5347\u6a21\u578b\u6027\u80fd\u7684\u5de5\u5177\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cWhat one loses, with the trees, is a simple and interpretable structure. What one gains is increased accuracy.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u6307\u51fa\u4e86Bagging\u7684\u4e00\u4e2a\u5173\u952e\u6743\u8861\u95ee\u9898\uff1a\u867d\u7136Bagging\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\uff0c\u4f46\u5b83\u4f1a\u4f7f\u6a21\u578b\u53d8\u5f97\u66f4\u52a0\u590d\u6742\uff0c\u96be\u4ee5\u89e3\u91ca\u3002\u5bf9\u4e8e\u6811\u6a21\u578b\u800c\u8a00\uff0c\u539f\u672c\u7b80\u5355\u3001\u6613\u89e3\u91ca\u7684\u7ed3\u6784\u53ef\u80fd\u56e0\u4e3aBagging\u7684\u805a\u5408\u800c\u53d8\u5f97\u4e0d\u518d\u76f4\u89c2\u3002\u8fd9\u79cd\u590d\u6742\u6027\u589e\u52a0\u4e86\u6a21\u578b\u7684\u201c\u9ed1\u7bb1\u201d\u7279\u6027\uff0c\u4f7f\u5f97\u7406\u89e3\u548c\u89e3\u91ca\u6a21\u578b\u53d8\u5f97\u66f4\u52a0\u56f0\u96be\u3002\u8fd9\u63d0\u9192\u6211\u4eec\uff0c\u5728\u8ffd\u6c42\u66f4\u9ad8\u7684\u51c6\u786e\u6027\u65f6\uff0c\u9700\u8981\u6743\u8861\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging can push a good but unstable procedure a significant step towards optimality. On the other hand, it can slightly degrade the performance of stable procedures.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u603b\u7ed3\u4e86Bagging\u7684\u6548\u679c\uff1a\u5b83\u80fd\u591f\u663e\u8457\u63d0\u5347\u90a3\u4e9b\u4e0d\u7a33\u5b9a\u4f46\u8868\u73b0\u826f\u597d\u7684\u6a21\u578b\uff0c\u4f7f\u5176\u66f4\u63a5\u8fd1\u6700\u4f18\u72b6\u6001\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u90a3\u4e9b\u5df2\u7ecf\u7a33\u5b9a\u7684\u6a21\u578b\uff0cBagging\u53ef\u80fd\u4f1a\u7565\u5fae\u964d\u4f4e\u5176\u6027\u80fd\u3002\u8fd9\u518d\u6b21\u5f3a\u8c03\u4e86Bagging\u7684\u9002\u7528\u6027\uff0c\u5373\u5b83\u5728\u4e0d\u7a33\u5b9a\u6a21\u578b\u4e2d\u8868\u73b0\u51fa\u8272\uff0c\u4f46\u5728\u7a33\u5b9a\u6a21\u578b\u4e2d\u6548\u679c\u6709\u9650\uff0c\u751a\u81f3\u53ef\u80fd\u5e26\u6765\u8d1f\u9762\u5f71\u54cd\u3002\u8fd9\u4e00\u7ed3\u8bba\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u9009\u62e9Bagging\u6280\u672f\u65f6\u7684\u5173\u952e\u8003\u8651\u56e0\u7d20\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cThe evidence, both experimental and theoretical, is that bagging can push a good but unstable procedure a significant step towards optimality.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u53e5\u8bdd\u8fdb\u4e00\u6b65\u5de9\u56fa\u4e86Bagging\u7684\u4f18\u52bf\uff0c\u7ed3\u5408\u5b9e\u9a8c\u7ed3\u679c\u548c\u7406\u8bba\u5206\u6790\uff0c\u8bc1\u660e\u4e86Bagging\u5728\u4e0d\u7a33\u5b9a\u6a21\u578b\u4e2d\u7684\u6709\u6548\u6027\u3002\u901a\u8fc7Bagging\uff0c\u539f\u672c\u4e0d\u7a33\u5b9a\u7684\u6a21\u578b\u80fd\u591f\u5927\u5e45\u5ea6\u63d0\u5347\u6027\u80fd\uff0c\u63a5\u8fd1\u6700\u4f18\u3002\u8fd9\u4e3aBagging\u5728\u5404\u79cd\u673a\u5668\u5b66\u4e60\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u548c\u5b9e\u8df5\u652f\u6301\uff0c\u4e5f\u51f8\u663e\u4e86\u5176\u5728\u5e94\u5bf9\u6a21\u578b\u4e0d\u7a33\u5b9a\u6027\u65b9\u9762\u7684\u5353\u8d8a\u6548\u679c\u3002<\/p>\n\n\n<h4 class=\"wp-block-heading\">\u6458\u5f55\uff1a<\/h4>\n\n\n<p><strong>\u201cBagging can improve accuracy in many situations, but not all. It is particularly effective for unstable predictors but less so for stable ones.\u201d<\/strong><\/p>\n\n\n<p><strong>\u8bc4\u8bba\uff1a<\/strong><\/p>\n\n\n<p>\u8fd9\u6bb5\u8bdd\u7b80\u6d01\u5730\u603b\u7ed3\u4e86Bagging\u7684\u603b\u4f53\u6548\u679c\uff0c\u660e\u786e\u6307\u51faBagging\u5728\u8bb8\u591a\u60c5\u51b5\u4e0b\u80fd\u591f\u63d0\u5347\u6a21\u578b\u51c6\u786e\u6027\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u4e0d\u7a33\u5b9a\u9884\u6d4b\u5668\u65f6\u6548\u679c\u663e\u8457\u3002\u7136\u800c\uff0c\u5b83\u5728\u5df2\u7ecf\u7a33\u5b9a\u7684\u9884\u6d4b\u5668\u4e2d\u6548\u679c\u6709\u9650\u3002\u8fd9\u79cd\u603b\u7ed3\u4e3a\u8bfb\u8005\u63d0\u4f9b\u4e86\u6e05\u6670\u7684\u6307\u5f15\uff0c\u5373\u5728\u5e94\u7528Bagging\u65f6\u9700\u8981\u8003\u8651\u57fa\u7840\u6a21\u578b\u7684\u7279\u6027\uff0c\u800c\u975e\u76f2\u76ee\u5730\u8ffd\u6c42\u63d0\u5347\u3002<\/p>\n\n\n<p>\u8fd9\u4e9b\u6458\u5f55\u548c\u8bc4\u8bba\u8be6\u7ec6\u63a2\u8ba8\u4e86Bagging\u6280\u672f\u7684\u4f18\u70b9\u3001\u5c40\u9650\u6027\u4ee5\u53ca\u5e94\u7528\u65f6\u7684\u6743\u8861\uff0c\u5f3a\u8c03\u4e86Bagging\u5728\u63d0\u5347\u4e0d\u7a33\u5b9a\u6a21\u578b\u8868\u73b0\u65f6\u7684\u663e\u8457\u6548\u679c\uff0c\u540c\u65f6\u4e5f\u6307\u51fa\u4e86\u5b83\u53ef\u80fd\u5e26\u6765\u7684\u590d\u6742\u6027\u548c\u5bf9\u7a33\u5b9a\u6a21\u578b\u7684\u8d1f\u9762\u5f71\u54cd\u3002\u8fd9\u4e9b\u7ed3\u8bba\u4e3a\u7406\u89e3Bagging\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u4ef7\u503c\u548c\u5c40\u9650\u6027\u63d0\u4f9b\u4e86\u91cd\u8981\u7684\u53c2\u8003\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">7. <strong>\u9644\u5f55\uff08Appendix\uff09<\/strong><\/h3>\n\n\n<p><strong>\u5185\u5bb9\u6982\u8ff0<\/strong>\uff1a\u63d0\u4f9b\u4e86\u8bba\u6587\u4e2d\u4f7f\u7528\u7684\u5206\u7c7b\u548c\u56de\u5f52\u6570\u636e\u96c6\u7684\u8be6\u7ec6\u63cf\u8ff0\uff0c\u5e2e\u52a9\u8bfb\u8005\u7406\u89e3\u5b9e\u9a8c\u80cc\u666f\u548c\u6570\u636e\u96c6\u7279\u5f81\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u4e9b\u95ee\u9898<\/h2>\n\n\n<p>\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5173\u952e\u6027\u7684\u95ee\u9898\uff0c\u7528\u4ee5\u5e2e\u52a9\u5b66\u4e60Bagging\u65b9\u6cd5\u7684\u4eba\u66f4\u597d\u5730\u7406\u89e3\u548c\u638c\u63e1\u8fd9\u4e00\u6280\u672f\uff1a<\/p>\n\n\n<h3 class=\"wp-block-heading\">Bagging\u7684\u6838\u5fc3\u539f\u7406\u662f\u4ec0\u4e48\uff1f\u5b83\u662f\u5982\u4f55\u901a\u8fc7\u81ea\u52a9\u62bd\u6837\u548c\u805a\u5408\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u7684\uff1f<\/h3>\n\n\n<p><strong>Bagging\u7684\u6838\u5fc3\u539f\u7406<\/strong>\u5728\u4e8e\u901a\u8fc7\u81ea\u52a9\u62bd\u6837\uff08Bootstrap Sampling\uff09\u751f\u6210\u591a\u4e2a\u4e0d\u540c\u7684\u8bad\u7ec3\u96c6\uff0c\u5e76\u5bf9\u6bcf\u4e2a\u8bad\u7ec3\u96c6\u5206\u522b\u8bad\u7ec3\u6a21\u578b\uff0c\u4ece\u800c\u4ea7\u751f\u591a\u4e2a\u6a21\u578b\u7248\u672c\u3002\u6700\u7ec8\u7684\u9884\u6d4b\u7ed3\u679c\u662f\u8fd9\u4e9b\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u7684\u805a\u5408\u3002\u5bf9\u4e8e\u6570\u503c\u578b\u8f93\u51fa\uff0c\u805a\u5408\u901a\u5e38\u901a\u8fc7\u53d6\u5e73\u5747\u503c\u5b9e\u73b0\uff1b\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u805a\u5408\u5219\u901a\u8fc7\u591a\u6570\u6295\u7968\u51b3\u5b9a\u6700\u7ec8\u7684\u5206\u7c7b\u3002<\/p>\n\n\n<p><strong>Bagging\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u7684\u65b9\u5f0f<\/strong>\u4e3b\u8981\u901a\u8fc7\u4ee5\u4e0b\u4e24\u70b9\u5b9e\u73b0\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u964d\u4f4e\u6a21\u578b\u7684\u4e0d\u786e\u5b9a\u6027<\/strong>\uff1a\u5728\u4e0d\u7a33\u5b9a\u7684\u6a21\u578b\uff08\u5373\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u53d8\u5316\u975e\u5e38\u654f\u611f\u7684\u6a21\u578b\uff09\u4e2d\uff0c\u8f7b\u5fae\u7684\u6570\u636e\u53d8\u52a8\u53ef\u80fd\u4f1a\u5bfc\u81f4\u9884\u6d4b\u7ed3\u679c\u7684\u5927\u5e45\u6ce2\u52a8\u3002Bagging\u901a\u8fc7\u5728\u4e0d\u540c\u7684\u81ea\u52a9\u62bd\u6837\u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u591a\u4e2a\u6a21\u578b\uff0c\u5e76\u5bf9\u7ed3\u679c\u8fdb\u884c\u5e73\u5747\u6216\u6295\u7968\uff0c\u4ece\u800c\u51cf\u5c11\u4e86\u5355\u4e00\u6a21\u578b\u56e0\u6570\u636e\u53d8\u5316\u5e26\u6765\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u8fd9\u79cd\u591a\u6a21\u578b\u7684\u805a\u5408\u6709\u6548\u5730\u5e73\u6ed1\u4e86\u9884\u6d4b\u7ed3\u679c\uff0c\u4f7f\u5f97\u6700\u7ec8\u6a21\u578b\u66f4\u7a33\u5065\uff0c\u8bef\u5dee\u66f4\u5c0f\u3002<br><\/li>\n    <li><strong>\u51cf\u5c11\u8fc7\u62df\u5408<\/strong>\uff1aBagging\u901a\u8fc7\u5bf9\u8bad\u7ec3\u6570\u636e\u96c6\u7684\u968f\u673a\u91c7\u6837\uff0c\u751f\u6210\u591a\u4e2a\u7565\u6709\u5dee\u5f02\u7684\u8bad\u7ec3\u96c6\u3002\u8fd9\u4e9b\u8bad\u7ec3\u96c6\u4e2d\u7684\u6bcf\u4e00\u4e2a\u90fd\u53ef\u80fd\u9057\u6f0f\u4e00\u4e9b\u539f\u59cb\u6570\u636e\u4e2d\u7684\u6837\u672c\uff0c\u4ece\u800c\u907f\u514d\u4e86\u6a21\u578b\u8fc7\u4e8e\u4f9d\u8d56\u67d0\u4e9b\u7279\u5b9a\u6570\u636e\u70b9\u3002\u8fd9\u79cd\u591a\u6837\u5316\u7684\u8bad\u7ec3\u96c6\u51cf\u5c11\u4e86\u6a21\u578b\u5bf9\u566a\u58f0\u7684\u654f\u611f\u6027\uff0c\u964d\u4f4e\u4e86\u8fc7\u62df\u5408\u7684\u98ce\u9669\uff0c\u4ece\u800c\u63d0\u9ad8\u4e86\u6a21\u578b\u5728\u6d4b\u8bd5\u96c6\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u3002<br><\/li>\n<\/ol>\n\n\n<p>\u901a\u8fc7\u4ee5\u4e0a\u4e24\u79cd\u65b9\u5f0f\uff0cBagging\u80fd\u591f\u663e\u8457\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\uff0c\u5c24\u5176\u662f\u5728\u9762\u5bf9\u4e0d\u7a33\u5b9a\u548c\u6613\u8fc7\u62df\u5408\u7684\u57fa\u7840\u6a21\u578b\u65f6\u8868\u73b0\u5c24\u4e3a\u51fa\u8272\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5728\u6709\u653e\u56de\u7684\u62bd\u6837\u4e2d\uff0c\u6837\u672c\u53ef\u80fd\u4f1a\u88ab\u591a\u6b21\u62bd\u4e2d\uff0c\u5bfc\u81f4\u8bad\u7ec3\u96c6\u4e2d\u51fa\u73b0\u91cd\u590d\u6837\u672c\u3002\u8fd9\u6837\u4f1a\u5bf9\u5f31\u5b66\u4e60\u5668\u7684\u5efa\u7acb\u4f1a\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u5417\uff1f<\/h3>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u5f71\u54cd\u6a21\u578b\u7684\u8bad\u7ec3\u6548\u7387<br><\/li>\n<\/ol>\n\n\n<p>\u8d1f\u9762\u5f71\u54cd\uff1a\u91cd\u590d\u6837\u672c\u53ef\u80fd\u5bfc\u81f4\u8bad\u7ec3\u6548\u7387\u4e0b\u964d\uff0c\u56e0\u4e3a\u6a21\u578b\u5728\u8bad\u7ec3\u65f6\u4f1a\u591a\u6b21\u5904\u7406\u76f8\u540c\u7684\u6837\u672c\u4fe1\u606f\uff0c\u53ef\u80fd\u6d6a\u8d39\u8ba1\u7b97\u8d44\u6e90\u3002\u7136\u800c\uff0c\u5728\u73b0\u4ee3\u8ba1\u7b97\u73af\u5883\u4e0b\uff0c\u8fd9\u4e2a\u95ee\u9898\u901a\u5e38\u4e0d\u662f\u4e3b\u8981\u7684\u74f6\u9888\uff0c\u56e0\u4e3a\u8ba1\u7b97\u8d44\u6e90\u7684\u6d6a\u8d39\u76f8\u5bf9\u8f83\u5c0f\uff0c\u5e76\u4e14\u901a\u8fc7Bagging\u83b7\u5f97\u7684\u591a\u6837\u6027\u548c\u7a33\u5b9a\u6027\u901a\u5e38\u8fdc\u8d85\u8fc7\u8fd9\u79cd\u8ba1\u7b97\u4e0a\u7684\u5f00\u9500\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\u6837\u672c\u4ee3\u8868\u6027\u7684\u5e73\u8861<br><\/li>\n<\/ol>\n\n\n<p>\u8d1f\u9762\u5f71\u54cd\uff1a\u91cd\u590d\u6837\u672c\u53ef\u80fd\u4f7f\u5f97\u67d0\u4e9b\u6837\u672c\u5728\u591a\u4e2aBootstrap\u6837\u672c\u96c6\u4e2d\u88ab\u8fc7\u5ea6\u4ee3\u8868\uff0c\u800c\u5176\u4ed6\u6837\u672c\u5219\u88ab\u4f4e\u4f30\u6216\u5b8c\u5168\u5ffd\u7565\u3002\u8fd9\u53ef\u80fd\u5bfc\u81f4\u67d0\u4e9b\u5f31\u5b66\u4e60\u5668\u5bf9\u91cd\u590d\u6837\u672c\u7684\u8fc7\u5ea6\u62df\u5408\uff0c\u5c24\u5176\u662f\u5728\u6837\u672c\u91cf\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u79cd\u73b0\u8c61\u53ef\u80fd\u66f4\u4e3a\u663e\u8457\u3002\u7136\u800c\uff0cBagging\u901a\u8fc7\u805a\u5408\u591a\u4e2a\u5f31\u5b66\u4e60\u5668\u7684\u8f93\u51fa\uff0c\u53ef\u4ee5\u90e8\u5206\u62b5\u6d88\u8fd9\u79cd\u5f71\u54cd\uff0c\u4f7f\u5f97\u6700\u7ec8\u7684\u96c6\u6210\u6a21\u578b\u80fd\u591f\u66f4\u5747\u8861\u5730\u53cd\u6620\u603b\u4f53\u6570\u636e\u7684\u5206\u5e03\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5f71\u54cdBagging\u7b97\u6cd5\u6548\u679c\u7684\u56e0\u7d20\u6709\u54ea\u4e9b\uff1f<\/h3>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u5bf9\u5c0f\u6570\u636e\u96c6\u66f4\u6709\u6548:<br><\/li>\n<\/ol>\n\n\n<p>Bagging\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u901a\u5e38\u66f4\u6709\u6548\u3002\u5bf9\u4e8e\u5c0f\u6570\u636e\u96c6,Bagging\u53ef\u4ee5\u901a\u8fc7\u521b\u5efa\u591a\u4e2a\u4e0d\u540c\u7684\u8bad\u7ec3\u5b50\u96c6\u6765\u589e\u52a0\u6a21\u578b\u7684\u591a\u6837\u6027,\u4ece\u800c\u63d0\u9ad8\u6574\u4f53\u6027\u80fd\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\u5927\u6570\u636e\u96c6\u4e0a\u7684\u6548\u679c:<br><\/li>\n<\/ol>\n\n\n<p>\u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\u636e\u96c6,\u7b80\u5355\u5730\u5c06\u6570\u636e\u5206\u5272\u6210\u4e0d\u76f8\u4ea4\u7684\u5b50\u96c6\u53ef\u80fd\u6bd4Bagging\u66f4\u6709\u6548\u3002\u7814\u7a76\u8868\u660e,\u5728\u5927\u6570\u636e\u96c6\u4e0a,\u4f7f\u7528\u4e0d\u76f8\u4ea4\u7684\u6570\u636e\u5206\u533a\u8bad\u7ec3\u591a\u4e2a\u5206\u7c7b\u5668,\u6bd4\u4f7f\u7528\u76f8\u540c\u5927\u5c0f\u7684bootstrap\u6837\u672c(bags)\u6548\u679c\u66f4\u597d\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li>\u6570\u636e\u5bc6\u5ea6\u7684\u5f71\u54cd:<br><\/li>\n<\/ol>\n\n\n<p>\u6570\u636e\u96c6\u7684\u5927\u5c0f\u4e0d\u5e94\u7b80\u5355\u5730\u4ee5\u6837\u672c\u6570\u91cf\u6765\u8861\u91cf,\u800c\u5e94\u8003\u8651\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684\u6570\u636e\u5bc6\u5ea6\u3002\u5373\u4f7f\u5bf9\u4e8e\u770b\u4f3c&#8221;\u5927&#8221;\u7684\u6570\u636e\u96c6,\u5982\u679c\u7279\u5f81\u7a7a\u95f4\u7ef4\u5ea6\u5f88\u9ad8,\u6570\u636e\u4ecd\u53ef\u80fd\u662f&#8221;\u7a00\u758f&#8221;\u7684\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b,Bagging\u4ecd\u53ef\u80fd\u6709\u6548\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li>\u8ba1\u7b97\u8d44\u6e90\u9650\u5236:<br><\/li>\n<\/ol>\n\n\n<p>\u5bf9\u4e8e\u8d85\u5927\u6570\u636e\u96c6,Bagging\u53ef\u80fd\u4f1a\u53d7\u5230\u8ba1\u7b97\u8d44\u6e90\u7684\u9650\u5236\u3002\u751f\u6210\u591a\u4e2abootstrap\u6837\u672c\u548c\u5b58\u50a8\u591a\u4e2a\u6a21\u578b\u4f1a\u589e\u52a0\u5185\u5b58\u4f7f\u7528\u548c\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n    <li>\u57fa\u7840\u6a21\u578b\u7684\u7a33\u5b9a\u6027:<br><\/li>\n<\/ol>\n\n\n<p>\u5bf9\u4e8e\u5df2\u7ecf\u76f8\u5f53\u7a33\u5b9a\u7684\u6a21\u578b,\u589e\u52a0\u8bad\u7ec3\u6570\u636e\u7684\u5927\u5c0f\u53ef\u80fd\u4e0d\u4f1a\u901a\u8fc7Bagging\u83b7\u5f97\u663e\u8457\u7684\u6027\u80fd\u63d0\u5347\u3002Bagging\u5bf9\u4e0d\u7a33\u5b9a\u7684\u9ad8\u65b9\u5dee\u6a21\u578b\u66f4\u6709\u6548\u3002<\/p>\n\n\n<p>\u603b\u7684\u6765\u8bf4,Bagging\u5728\u5c0f\u5230\u4e2d\u7b49\u5927\u5c0f\u7684\u6570\u636e\u96c6\u4e0a\u901a\u5e38\u66f4\u6709\u6548\u3002\u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\u636e\u96c6,\u7b80\u5355\u7684\u6570\u636e\u5206\u533a\u65b9\u6cd5\u53ef\u80fd\u66f4\u4e3a\u5b9e\u7528\u548c\u6709\u6548\u3002\u7136\u800c,\u5177\u4f53\u6548\u679c\u8fd8\u53d6\u51b3\u4e8e\u6570\u636e\u7684\u7279\u5f81\u3001\u57fa\u7840\u6a21\u578b\u7684\u6027\u8d28\u4ee5\u53ca\u53ef\u7528\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u5728\u5b9e\u8df5\u4e2d,\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u8fdb\u884c\u5b9e\u9a8c\u548c\u8c03\u6574,\u4ee5\u627e\u5230\u6700\u4f73\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48Bagging\u5bf9\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\u7279\u522b\u6709\u6548\uff1f\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0cBagging\u5982\u4f55\u964d\u4f4e\u6a21\u578b\u7684\u4e0d\u786e\u5b9a\u6027\uff1f<\/h3>\n\n\n<p>Bagging\u5bf9\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\u7279\u522b\u6709\u6548\u7684\u539f\u56e0\u5728\u4e8e\u5b83\u80fd\u591f\u663e\u8457\u964d\u4f4e\u8fd9\u4e9b\u6a21\u578b\u7684\u9884\u6d4b\u4e0d\u786e\u5b9a\u6027\u3002\u4e0b\u9762\u662fBagging\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u7684\u5177\u4f53\u4f5c\u7528<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u4ec0\u4e48\u662f\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\uff1f<\/strong><br><\/li>\n<\/ol>\n\n\n<p>\u4e0d\u7a33\u5b9a\u7684\u9884\u6d4b\u6a21\u578b\u662f\u6307\u5bf9\u8bad\u7ec3\u6570\u636e\u7684\u53d8\u5316\u975e\u5e38\u654f\u611f\u7684\u6a21\u578b\u3002\u5373\u4f7f\u8bad\u7ec3\u6570\u636e\u7a0d\u6709\u6539\u53d8\uff08\u4f8b\u5982\u589e\u52a0\u6216\u5220\u9664\u4e00\u4e2a\u6837\u672c\uff09\uff0c\u6a21\u578b\u7684\u9884\u6d4b\u7ed3\u679c\u4e5f\u53ef\u80fd\u53d1\u751f\u663e\u8457\u53d8\u5316\u3002\u51b3\u7b56\u6811\u5c31\u662f\u4e00\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\uff0c\u56e0\u4e3a\u5b83\u5bf9\u6570\u636e\u7684\u5206\u88c2\u8fc7\u7a0b\u9ad8\u5ea6\u4f9d\u8d56\uff0c\u8f7b\u5fae\u7684\u6570\u636e\u53d8\u52a8\u53ef\u80fd\u5bfc\u81f4\u6811\u7684\u7ed3\u6784\u53d1\u751f\u91cd\u5927\u53d8\u5316\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li><strong>Bagging\u5982\u4f55\u964d\u4f4e\u4e0d\u7a33\u5b9a\u6a21\u578b\u7684\u4e0d\u786e\u5b9a\u6027\uff1f<\/strong><\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u901a\u8fc7\u591a\u6b21\u62bd\u6837\u751f\u6210\u591a\u6837\u5316\u7684\u6a21\u578b<\/strong>\uff1a<br><ul>\n            <li>Bagging\u4f7f\u7528Bootstrap\u6709\u653e\u56de\u62bd\u6837\u7684\u65b9\u6cd5\u4ece\u539f\u59cb\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u751f\u6210\u591a\u4e2a\u4e0d\u540c\u7684\u5b50\u96c6\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5b50\u96c6\uff0c\u8bad\u7ec3\u4e00\u4e2a\u72ec\u7acb\u7684\u6a21\u578b\uff08\u5373\u5f31\u5b66\u4e60\u5668\uff09\u3002\u7531\u4e8e\u8fd9\u4e9b\u5b50\u96c6\u7565\u6709\u4e0d\u540c\uff0c\u6bcf\u4e2a\u6a21\u578b\u5728\u67d0\u4e9b\u6837\u672c\u4e0a\u7684\u8868\u73b0\u53ef\u80fd\u6709\u6240\u4e0d\u540c\uff0c\u8fd9\u6837\u5c31\u5f62\u6210\u4e86\u4e00\u7ec4\u5177\u6709\u4e0d\u540c\u504f\u5dee\u548c\u566a\u58f0\u7684\u6a21\u578b\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u805a\u5408\u51cf\u5c11\u6ce2\u52a8\u548c\u8bef\u5dee<\/strong>\uff1a<br><ul>\n            <li>\u901a\u8fc7\u5bf9\u591a\u4e2a\u6a21\u578b\u7684\u9884\u6d4b\u7ed3\u679c\u8fdb\u884c\u805a\u5408\uff08\u4f8b\u5982\u5bf9\u6570\u503c\u9884\u6d4b\u53d6\u5e73\u5747\uff0c\u5bf9\u5206\u7c7b\u95ee\u9898\u8fdb\u884c\u591a\u6570\u6295\u7968\uff09\uff0cBagging\u80fd\u591f\u5e73\u6ed1\u6389\u5355\u4e2a\u6a21\u578b\u7684\u968f\u673a\u6ce2\u52a8\u548c\u8bef\u5dee\u3002\u7531\u4e8e\u6bcf\u4e2a\u6a21\u578b\u7684\u9884\u6d4b\u9519\u8bef\u662f\u968f\u673a\u4e14\u4e0d\u5b8c\u5168\u76f8\u5173\u7684\uff0c\u805a\u5408\u7684\u7ed3\u679c\u80fd\u591f\u51cf\u5c11\u8fd9\u4e9b\u9519\u8bef\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u964d\u4f4e\u6574\u4f53\u6a21\u578b\u7684\u4e0d\u786e\u5b9a\u6027\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u51cf\u5c11\u8fc7\u62df\u5408\u7684\u98ce\u9669<\/strong>\uff1a<br><ul>\n            <li>\u4e0d\u7a33\u5b9a\u6a21\u578b\u5bb9\u6613\u8fc7\u62df\u5408\u5230\u8bad\u7ec3\u6570\u636e\u7684\u566a\u58f0\u6216\u5f02\u5e38\u503c\u3002Bagging\u901a\u8fc7\u5728\u4e0d\u540c\u7684\u5b50\u96c6\u4e0a\u8bad\u7ec3\u6a21\u578b\uff0c\u5e76\u5bf9\u7ed3\u679c\u8fdb\u884c\u805a\u5408\uff0c\u6709\u6548\u5730\u51cf\u5c11\u4e86\u6a21\u578b\u8fc7\u5ea6\u62df\u5408\u5355\u4e2a\u8bad\u7ec3\u96c6\u7684\u98ce\u9669\u3002\u8fd9\u4f7f\u5f97\u6700\u7ec8\u7684\u96c6\u6210\u6a21\u578b\u66f4\u5177\u6cdb\u5316\u80fd\u529b\uff0c\u5728\u672a\u89c1\u6570\u636e\u4e0a\u7684\u8868\u73b0\u66f4\u52a0\u7a33\u5065\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ul>\n\n\n<p><strong>\u603b\u7ed3<\/strong><\/p>\n\n\n<p>Bagging\u901a\u8fc7\u5f15\u5165\u6837\u672c\u591a\u6837\u6027\u5e76\u5bf9\u591a\u4e2a\u6a21\u578b\u7684\u7ed3\u679c\u8fdb\u884c\u805a\u5408\uff0c\u80fd\u591f\u663e\u8457\u964d\u4f4e\u4e0d\u7a33\u5b9a\u6a21\u578b\u7684\u9884\u6d4b\u4e0d\u786e\u5b9a\u6027\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u51cf\u5c11\u4e86\u5355\u4e2a\u6a21\u578b\u7684\u6ce2\u52a8\uff0c\u8fd8\u63d0\u9ad8\u4e86\u6574\u4f53\u6a21\u578b\u7684\u7a33\u5b9a\u6027\u548c\u6cdb\u5316\u80fd\u529b\uff0c\u5c24\u5176\u5728\u5e94\u5bf9\u590d\u6742\u4e14\u566a\u58f0\u8f83\u591a\u7684\u6570\u636e\u65f6\u8868\u73b0\u5c24\u4e3a\u51fa\u8272\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">Bagging\u5904\u7406\u5f02\u5e38\u503c\u7684\u5c40\u9650\u6027\uff0c\u4ee5\u53ca\u5e94\u5bf9\u5f02\u5e38\u503c\u7684\u7b56\u7565<\/h3>\n\n\n<p>Bagging\u5728\u5904\u7406\u5f02\u5e38\u503c\uff08outliers\uff09\u5b58\u5728\u4e00\u4e9b\u9700\u8981\u6ce8\u610f\u7684\u95ee\u9898\u3002<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>Bagging\u5904\u7406\u5f02\u5e38\u503c\u7684\u5c40\u9650\u6027<\/strong><\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u5f02\u5e38\u503c\u7684\u653e\u5927\u6548\u5e94<\/strong>\uff1a\u867d\u7136Bagging\u80fd\u591f\u901a\u8fc7\u805a\u5408\u4e0d\u540c\u6a21\u578b\u6765\u51cf\u8f7b\u5f02\u5e38\u503c\u7684\u5f71\u54cd\uff0c\u4f46\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5f02\u5e38\u503c\u53ef\u80fd\u4f1a\u5728\u591a\u4e2aBootstrap\u6837\u672c\u96c6\u4e2d\u88ab\u591a\u6b21\u62bd\u5230\uff0c\u4ece\u800c\u5bf9\u6700\u7ec8\u6a21\u578b\u4ea7\u751f\u8f83\u5927\u7684\u5f71\u54cd\u3002\u5982\u679c\u6570\u636e\u4e2d\u5b58\u5728\u5927\u91cf\u5f02\u5e38\u503c\uff0c\u8fd9\u4e9b\u5f02\u5e38\u503c\u53ef\u80fd\u4f1a\u5728\u591a\u4e2a\u6a21\u578b\u4e2d\u91cd\u590d\u51fa\u73b0\uff0c\u8fdb\u800c\u5f71\u54cdBagging\u7684\u6574\u4f53\u6548\u679c\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li><strong>\u5e94\u5bf9\u5f02\u5e38\u503c\u7684\u7b56\u7565<\/strong><\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u5f02\u5e38\u503c\u68c0\u6d4b\u548c\u5904\u7406<\/strong>\uff1a\u5728\u4f7f\u7528Bagging\u4e4b\u524d\uff0c\u53ef\u4ee5\u5148\u8fdb\u884c\u5f02\u5e38\u503c\u68c0\u6d4b\uff0c\u5e76\u5bf9\u68c0\u6d4b\u51fa\u7684\u5f02\u5e38\u503c\u8fdb\u884c\u5904\u7406\uff08\u5982\u79fb\u9664\u3001\u4fee\u6b63\u6216\u964d\u4f4e\u5176\u6743\u91cd\uff09\u3002\u8fd9\u6709\u52a9\u4e8e\u51cf\u5c11\u5f02\u5e38\u503c\u5bf9Bagging\u6a21\u578b\u7684\u8d1f\u9762\u5f71\u54cd\u3002<\/li>\n    <li><strong>\u52a0\u6743Bagging<\/strong>\uff1a\u4e3a\u6bcf\u4e2a\u6837\u672c\u8d4b\u4e88\u4e0d\u540c\u7684\u6743\u91cd\uff0c\u4f7f\u5f97\u5f02\u5e38\u503c\u5728\u6a21\u578b\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5f71\u54cd\u8f83\u5c0f\u3002\u901a\u8fc7\u964d\u4f4e\u5f02\u5e38\u503c\u7684\u6743\u91cd\uff0c\u53ef\u4ee5\u51cf\u5c11\u5b83\u4eec\u5bf9\u6700\u7ec8\u9884\u6d4b\u7ed3\u679c\u7684\u5f71\u54cd\u3002<\/li>\n    <li><strong>\u9c81\u68d2\u6a21\u578b<\/strong>\uff1a\u9009\u62e9\u5bf9\u5f02\u5e38\u503c\u4e0d\u654f\u611f\u7684\u57fa\u7840\u6a21\u578b\uff08\u5982\u51b3\u7b56\u6811\u7684\u9c81\u68d2\u53d8\u4f53\u6216\u4e2d\u4f4d\u6570\u56de\u5f52\uff09\uff0c\u7136\u540e\u5728\u6b64\u57fa\u7840\u4e0a\u5e94\u7528Bagging\u3002\u8fd9\u6837\u53ef\u4ee5\u51cf\u5c11\u5f02\u5e38\u503c\u5bf9\u6bcf\u4e2a\u5f31\u5b66\u4e60\u5668\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u63d0\u9ad8\u6574\u4f53\u6a21\u578b\u7684\u7a33\u5065\u6027\u3002<\/li>\n    <li><strong>\u81ea\u9002\u5e94\u65b9\u6cd5<\/strong>\uff1a\u7ed3\u5408\u81ea\u9002\u5e94\u91c7\u6837\u6216\u8c03\u6574Bagging\u65b9\u6cd5\uff0c\u4f7f\u5f97\u5728\u81ea\u52a9\u62bd\u6837\u8fc7\u7a0b\u4e2d\u51cf\u5c11\u5bf9\u5f02\u5e38\u503c\u7684\u4f9d\u8d56\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u901a\u8fc7\u51cf\u5c11\u5f02\u5e38\u503c\u88ab\u9009\u4e2d\u7684\u6982\u7387\u6765\u964d\u4f4e\u5b83\u4eec\u5728Bootstrap\u6837\u672c\u96c6\u4e2d\u51fa\u73b0\u7684\u9891\u7387\u3002<br><\/li>\n<\/ul>\n\n\n<p><strong>\u603b\u7ed3<\/strong><\/p>\n\n\n<p>Bagging\u901a\u8fc7\u591a\u6b21\u91c7\u6837\u548c\u7ed3\u679c\u805a\u5408\uff0c\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u7f13\u89e3\u5f02\u5e38\u503c\u7684\u5f71\u54cd\uff0c\u4f46\u5b83\u5e76\u4e0d\u662f\u5bf9\u5f02\u5e38\u503c\u5b8c\u5168\u514d\u75ab\u7684\u3002\u4e3a\u4e86\u89e3\u51b3Bagging\u4e2d\u53ef\u80fd\u5b58\u5728\u7684\u5f02\u5e38\u503c\u653e\u5927\u6548\u5e94\uff0c\u53ef\u4ee5\u91c7\u53d6\u5f02\u5e38\u503c\u68c0\u6d4b\u3001\u52a0\u6743Bagging\u3001\u9009\u62e9\u9c81\u68d2\u6a21\u578b\u7b49\u7b56\u7565\uff0c\u4ee5\u589e\u5f3a\u6a21\u578b\u7684\u7a33\u5065\u6027\uff0c\u8fdb\u4e00\u6b65\u63d0\u5347Bagging\u5728\u5904\u7406\u5f02\u5e38\u503c\u65f6\u7684\u6548\u679c\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5982\u4f55\u786e\u5b9aBagging\u4e2d\u57fa\u5b66\u4e60\u6a21\u578b\u7684\u6570\u91cf<\/h3>\n\n\n<p>\u8981\u786e\u5b9aBagging\u96c6\u6210\u6a21\u578b\u4e2d\u57fa\u5b66\u4e60\u5668\u7684\u6700\u4f73\u6570\u91cf\uff0c\u901a\u5e38\u91c7\u7528\u4ea4\u53c9\u9a8c\u8bc1\u3001\u6027\u80fd\u6536\u655b\u5206\u6790\u3001\u8ba1\u7b97\u6210\u672c\u4e0e\u6027\u80fd\u7684\u6743\u8861\u7b49\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u53ef\u4ee5\u7ed3\u5408\u7ecf\u9a8c\u6cd5\u5219\u548c\u95ee\u9898\u7684\u590d\u6742\u6027\u8fdb\u884c\u8c03\u6574\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">Bagging\u53ef\u4ee5\u4e0e\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u5982Boosting\u6216Stacking\u7ed3\u5408\u4f7f\u7528\u5417\uff1f<\/h3>\n\n\n<p>Bagging\u786e\u5b9e\u53ef\u4ee5\u4e0e\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u5982Boosting\u548cStacking\u7ed3\u5408\u4f7f\u7528\u3002\u8fd9\u79cd\u7ec4\u5408\u53ef\u4ee5\u5145\u5206\u5229\u7528\u5404\u79cd\u65b9\u6cd5\u7684\u4f18\u52bf\uff0c\u521b\u9020\u51fa\u66f4\u5f3a\u5927\u3001\u66f4\u7075\u6d3b\u7684\u6a21\u578b\u3002\u4ee5\u4e0b\u662f\u5173\u4e8eBagging\u4e0e\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u7ed3\u5408\u4f7f\u7528\u7684\u8be6\u7ec6\u89e3\u91ca\uff1a<\/p>\n\n\n<h4 class=\"wp-block-heading\">Bagging\u4e0eBoosting\u7684\u7ed3\u5408<\/h4>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u4e92\u8865\u6027\uff1a<\/li>\n<\/ol>\n\n\n<p>Bagging\u4e3b\u8981\u901a\u8fc7\u964d\u4f4e\u65b9\u5dee\u6765\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u3002<\/p>\n\n\n<p>Boosting\u4e3b\u8981\u901a\u8fc7\u964d\u4f4e\u504f\u5dee\u6765\u63d0\u9ad8\u6a21\u578b\u6027\u80fd\u3002<\/p>\n\n\n<p>\u7ed3\u5408\u4e24\u8005\u53ef\u4ee5\u540c\u65f6\u964d\u4f4e\u504f\u5dee\u548c\u65b9\u5dee\uff0c\u5219\u53ef\u4ee5\u63d0\u4f9b\u66f4\u597d\u7684\u6574\u4f53\u6027\u80fd\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\u5b9e\u73b0\u65b9\u5f0f\uff1a<\/li>\n<\/ol>\n\n\n<p>\u4f7f\u7528Bagging\u4f5c\u4e3aBoosting\u7684\u57fa\u5b66\u4e60\u5668\u3002<\/p>\n\n\n<p>\u4f8b\u5982\uff0c\u53ef\u4ee5\u7528Random Forest\uff08\u57fa\u4e8eBagging\u7684\u65b9\u6cd5\uff09\u4f5c\u4e3aGradient Boosting\u7684\u57fa\u5b66\u4e60\u5668\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li>\u4ee3\u7801\u793a\u4f8b\uff1a<\/li>\n<\/ol>\n\n\n<pre class=\"wp-block-code\"><code>from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier\nfrom sklearn.datasets import make_classification\nfrom sklearn.model_selection import cross_val_score\n\nX, y = make_classification(n_samples=1000, n_features=20, random_state=42)\n\nrf = RandomForestClassifier(n_estimators=10, random_state=42)\ngb = GradientBoostingClassifier(n_estimators=100, learning_rate=0.1, random_state=42)\n\ngb_rf = GradientBoostingClassifier(n_estimators=10, learning_rate=0.1, random_state=42,\n                                   base_estimator=rf)\n\nprint(\"RF Score:\", cross_val_score(rf, X, y, cv=5).mean())\nprint(\"GB Score:\", cross_val_score(gb, X, y, cv=5).mean())\nprint(\"GB with RF Score:\", cross_val_score(gb_rf, X, y, cv=5).mean())\n<\/code><\/pre>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li>\u4f18\u52bf\uff1a<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/li>\n    <li>\u53ef\u80fd\u6bd4\u5355\u72ec\u4f7f\u7528Bagging\u6216Boosting\u83b7\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002<br><\/li>\n<\/ul>\n\n\n<h4 class=\"wp-block-heading\">Bagging\u4e0eStacking\u7684\u7ed3\u5408<\/h4>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u4e92\u8865\u6027\uff1a<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li>Bagging\u53ef\u4ee5\u4f5c\u4e3aStacking\u4e2d\u7684\u57fa\u5b66\u4e60\u5668\u4e4b\u4e00\u3002<\/li>\n    <li>Stacking\u53ef\u4ee5\u5229\u7528Bagging\u7684\u8f93\u51fa\u4f5c\u4e3a\u65b0\u7279\u5f81\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\u5b9e\u73b0\u65b9\u5f0f\uff1a<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u5728Stacking\u7684\u7b2c\u4e00\u5c42\u4f7f\u7528Bagging\u6a21\u578b\uff08\u5982Random Forest\uff09\u3002<\/li>\n    <li>\u5c06Bagging\u6a21\u578b\u7684\u9884\u6d4b\u7ed3\u679c\u4f5c\u4e3aStacking\u7684\u7b2c\u4e8c\u5c42\u8f93\u5165\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li>\u4ee3\u7801\u793a\u4f8b\uff1a<\/li>\n<\/ol>\n\n\n<pre class=\"wp-block-code\"><code>from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier\nfrom sklearn.linear_model import LogisticRegression\nfrom sklearn.model_selection import cross_val_predict\nimport numpy as np\n\nX, y = make_classification(n_samples=1000, n_features=20, random_state=42)\n\nrf = RandomForestClassifier(n_estimators=10, random_state=42)\ngb = GradientBoostingClassifier(n_estimators=100, learning_rate=0.1, random_state=42)\n\nrf_pred = cross_val_predict(rf, X, y, cv=5, method='predict_proba')\ngb_pred = cross_val_predict(gb, X, y, cv=5, method='predict_proba')\n\nX_stack = np.hstack((rf_pred, gb_pred, X))\n\nlr = LogisticRegression(random_state=42)\nprint(\"Stacked Model Score:\", cross_val_score(lr, X_stack, y, cv=5).mean())\n<\/code><\/pre>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li>\u4f18\u52bf\uff1a<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u53ef\u4ee5\u5904\u7406\u66f4\u590d\u6742\u7684\u6570\u636e\u6a21\u5f0f\u3002<\/li>\n    <li>\u6f5c\u5728\u5730\u63d0\u9ad8\u6a21\u578b\u7684\u6574\u4f53\u6027\u80fd\u3002<br><\/li>\n<\/ul>\n\n\n<h4 class=\"wp-block-heading\">\u6ce8\u610f\u4e8b\u9879<\/h4>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u8ba1\u7b97\u590d\u6742\u5ea6\uff1a\u7ed3\u5408\u591a\u79cd\u96c6\u6210\u65b9\u6cd5\u53ef\u80fd\u4f1a\u663e\u8457\u589e\u52a0\u8ba1\u7b97\u65f6\u95f4\u548c\u8d44\u6e90\u9700\u6c42\u3002<br><\/li>\n    <li>\u8fc7\u62df\u5408\u98ce\u9669\uff1a\u9700\u8981\u8c28\u614e\u5904\u7406\uff0c\u4ee5\u907f\u514d\u6a21\u578b\u53d8\u5f97\u8fc7\u4e8e\u590d\u6742\u800c\u5bfc\u81f4\u8fc7\u62df\u5408\u3002<br><\/li>\n    <li>\u53c2\u6570\u8c03\u4f18\uff1a\u7ec4\u5408\u4f7f\u7528\u65f6\uff0c\u53c2\u6570\u8c03\u4f18\u53d8\u5f97\u66f4\u52a0\u590d\u6742\uff0c\u53ef\u80fd\u9700\u8981\u66f4\u591a\u7684\u5b9e\u9a8c\u548c\u8c03\u6574\u3002<br><\/li>\n    <li>\u89e3\u91ca\u6027\uff1a\u968f\u7740\u6a21\u578b\u590d\u6742\u5ea6\u7684\u589e\u52a0\uff0c\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\u53ef\u80fd\u4f1a\u964d\u4f4e\u3002<br><\/li>\n<\/ol>\n\n\n<h4 class=\"wp-block-heading\">\u603b\u7ed3<\/h4>\n\n\n<p>Bagging\u53ef\u4ee5\u6709\u6548\u5730\u4e0eBoosting\u548cStacking\u7b49\u5176\u4ed6\u96c6\u6210\u65b9\u6cd5\u7ed3\u5408\u4f7f\u7528\u3002\u8fd9\u79cd\u7ec4\u5408\u5229\u7528\u4e86\u5404\u79cd\u65b9\u6cd5\u7684\u4f18\u52bf\uff0c\u53ef\u4ee5\u521b\u5efa\u66f4\u5f3a\u5927\u3001\u66f4\u7075\u6d3b\u7684\u6a21\u578b\u3002\u901a\u8fc7\u964d\u4f4e\u504f\u5dee\u548c\u65b9\u5dee\uff0c\u5904\u7406\u590d\u6742\u7684\u6570\u636e\u6a21\u5f0f\uff0c\u8fd9\u4e9b\u7ec4\u5408\u65b9\u6cd5\u6709\u6f5c\u529b\u63d0\u4f9b\u4f18\u4e8e\u5355\u4e00\u65b9\u6cd5\u7684\u6027\u80fd\u3002<\/p>\n\n\n<p>\u7136\u800c\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u6743\u8861\u6a21\u578b\u6027\u80fd\u3001\u8ba1\u7b97\u590d\u6742\u5ea6\u548c\u53ef\u89e3\u91ca\u6027\u3002\u9009\u62e9\u5408\u9002\u7684\u7ec4\u5408\u65b9\u6cd5\u5e94\u57fa\u4e8e\u5177\u4f53\u95ee\u9898\u3001\u53ef\u7528\u8d44\u6e90\u548c\u6027\u80fd\u8981\u6c42\u3002\u540c\u65f6\uff0c\u8981\u6ce8\u610f\u907f\u514d\u8fc7\u62df\u5408\uff0c\u5e76\u8003\u8651\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\u9700\u6c42\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8bba\u6587\u7b80\u4ecb \u82f1\u6587\u9898\u76ee\uff1aBagging Predictors \u4e2d&#8230;<\/p>\n","protected":false},"author":1,"featured_media":509,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[27],"class_list":["post-338","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-26","tag-ensemble-learning"],"_links":{"self":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/comments?post=338"}],"version-history":[{"count":3,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/338\/revisions"}],"predecessor-version":[{"id":510,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/338\/revisions\/510"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media\/509"}],"wp:attachment":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media?parent=338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/categories?post=338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/tags?post=338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}