{"id":326,"date":"2024-08-11T10:07:23","date_gmt":"2024-08-11T02:07:23","guid":{"rendered":"https:\/\/www.xuzhe.tj.cn\/?p=326"},"modified":"2025-05-03T09:19:49","modified_gmt":"2025-05-03T01:19:49","slug":"adaboost-a-decision-theoretic-generalization-of-on-line-learning-and-an-application-to-boosting","status":"publish","type":"post","link":"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/08\/11\/adaboost-a-decision-theoretic-generalization-of-on-line-learning-and-an-application-to-boosting\/","title":{"rendered":"A decision-theoretic generalization of on-line learning and an application to boosting \uff5c AdaBoost  |  \u8bba\u6587\u7b14\u8bb0"},"content":{"rendered":"\n<p>\u82f1\u6587\u9898\u76ee\uff1aA decision-theoretic generalization of on-line learning and an application to boosting<\/p>\n\n\n<p>\u4e2d\u6587\u9898\u76ee\uff1a\u5728\u7ebf\u5b66\u4e60\u7684\u51b3\u7b56\u7406\u8bba\u63a8\u5e7f\u53ca\u5176\u5728Boosting\u4e2d\u7684\u5e94\u7528<\/p>\n\n\n<p>\u4f5c\u8005\uff1aYoav Freund, Robert E. Schapire<\/p>\n\n\n<p>\u53d1\u8868\u671f\u520a \u6216 \u4f1a\u8bae\uff1aJournal of Computer and System Sciences<\/p>\n\n\n<p>\u53d1\u8868\u65e5\u671f\uff1aSeptember 20, 1995<\/p>\n\n\n<p>AdaBoost\u53ef\u5c06\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u9884\u6d4b\u7cbe\u5ea6\u63d0\u5347\u5230\u4efb\u610f\u9ad8\u7684\u6c34\u5e73\uff01\u8fd9\u9879\u7814\u7a76\u4e0d\u4ec5\u4e3a\u5728\u7ebf\u8d44\u6e90\u5206\u914d\u95ee\u9898\u63d0\u4f9b\u4e86\u4e00\u4e2a\u66f4\u901a\u7528\u7684\u6846\u67b6\uff0c\u8fd8\u4e3a\u673a\u5668\u5b66\u4e60\u9886\u57df\u5e26\u6765\u4e86\u65b0\u7684\u601d\u8def\u3002AdaBoost\u65e0\u9700\u4e8b\u5148\u4e86\u89e3\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\uff0c\u5c31\u80fd\u81ea\u9002\u5e94\u5730\u8c03\u6574\u53c2\u6570\uff0c\u6700\u5927\u7a0b\u5ea6\u5730\u5229\u7528\u5f31\u5b66\u4e60\u7b97\u6cd5\u751f\u6210\u7684\u5047\u8bbe\uff0c\u4ece\u800c\u83b7\u5f97\u60ca\u4eba\u7684\u9884\u6d4b\u7cbe\u5ea6\u3002<\/p>\n\n<!--more-->\n\n<p><strong>&lt;\u7814\u7a76\u80cc\u666f\u4e0e\u76ee\u7684&gt;<\/strong><\/p>\n\n\n<p>\u5728 1990 \u5e74\uff0cSchapire \u63d0\u51fa\u4e86\u6700\u521d\u7684 Boosting \u7b97\u6cd5\uff0c\u5c55\u793a\u4e86\u5982\u4f55\u5c06\u591a\u4e2a\u5f31\u5b66\u4e60\u5668\u7ec4\u5408\u6210\u4e00\u4e2a\u5f3a\u5b66\u4e60\u5668\u3002<\/p>\n\n\n<p>1993 \u5e74\uff0cDrunker \u548c Schapire \u5c06 Boosting \u7b97\u6cd5\u5e94\u7528\u4e8e OCR \u95ee\u9898\uff0c\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u5f31\u5b66\u4e60\u5668\u3002<\/p>\n\n\n<p>1995 \u5e74\uff0cFreund \u548c Schapire \u5728\u6b64\u8bba\u6587\u4e2d\u63d0\u51fa\u4e86 AdaBoost \u7b97\u6cd5\uff0c\u8fdb\u4e00\u6b65\u53d1\u5c55\u4e86 Boosting \u6280\u672f\u3002<\/p>\n\n\n<p>\u8fd9\u7bc7\u8bba\u6587\u7814\u7a76\u4e86\u5728\u7ebf\u8d44\u6e90\u5206\u914d\u95ee\u9898\uff0c\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u63d0\u5347\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\u3002\u5728\u7ebf\u8d44\u6e90\u5206\u914d\u95ee\u9898\u65e8\u5728\u52a8\u6001\u5730\u5c06\u8d44\u6e90\u5206\u914d\u7ed9\u4e00\u7ec4\u9009\u9879\uff0c\u76ee\u6807\u662f\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u6700\u5c0f\u5316\u7d2f\u8ba1\u635f\u5931\uff0c\u5e76\u4e0e\u6700\u4f73\u9009\u9879\u7684\u635f\u5931\u76f8\u6bd4\u3002\u4f20\u7edf\u7684\u5728\u7ebf\u9884\u6d4b\u6a21\u578b\u4e3b\u8981\u5173\u6ce8\u4e8c\u5143\u51b3\u7b56\u548c\u7ed3\u679c\u7a7a\u95f4\uff08\u610f\u5473\u7740\u6a21\u578b\u53ea\u80fd\u9884\u6d4b\u4e24\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff0c\u4f8b\u5982\u201c\u662f\u201d\u6216\u201c\u5426\u201d\uff09\uff0c\u800c\u8fd9\u7bc7\u8bba\u6587\u5c06\u5176\u6269\u5c55\u5230\u66f4\u4e00\u822c\u7684\u51b3\u7b56\u7406\u8bba\u6846\u67b6\uff08\u610f\u5473\u7740\u6a21\u578b\u53ef\u4ee5\u5904\u7406\u66f4\u591a\u79cd\u7c7b\u7684\u7ed3\u679c\u7a7a\u95f4\uff0c\u5305\u62ec\u591a\u7c7b\u522b\u7ed3\u679c\u7a7a\u95f4\u548c\u8fde\u7eed\u7ed3\u679c\u7a7a\u95f4\uff09\uff0c\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u63d0\u5347\u5f31\u5b66\u4e60\u7b97\u6cd5\uff0c\u4f7f\u5176\u80fd\u591f\u5904\u7406\u66f4\u5e7f\u6cdb\u7684\u5b66\u4e60\u95ee\u9898\u3002<\/p>\n\n\n<p><strong>&lt;\u521b\u65b0\u70b9&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u5c06Littlestone\u548cWarmuth\u7684\u4e58\u6cd5\u6743\u91cd\u66f4\u65b0\u89c4\u5219\u5e94\u7528\u4e8e\u5728\u7ebf\u8d44\u6e90\u5206\u914d\u6a21\u578b\uff0c\u5e76\u63a8\u5bfc\u51fa\u66f4\u901a\u7528\u7684\u8fb9\u754c\u3002<\/strong> \u8fd9\u4f7f\u5f97\u7b97\u6cd5\u80fd\u591f\u5904\u7406\u66f4\u5e7f\u6cdb\u7684\u5b66\u4e60\u95ee\u9898\uff0c\u5305\u62ec\u591a\u7ed3\u679c\u9884\u6d4b\u3001\u91cd\u590d\u535a\u5f08\u548c\u9884\u6d4bR^n\u4e2d\u7684\u70b9\u3002<\/li>\n    <li><strong>\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684Boosting\u7b97\u6cd5AdaBoost\uff0c\u8be5\u7b97\u6cd5\u65e0\u9700\u4e8b\u5148\u4e86\u89e3\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\u3002<\/strong> AdaBoost\u80fd\u81ea\u9002\u5e94\u5730\u8c03\u6574\u53c2\u6570\uff0c\u4ee5\u6700\u5927\u7a0b\u5ea6\u5730\u5229\u7528\u5f31\u5b66\u4e60\u7b97\u6cd5\u751f\u6210\u7684\u5047\u8bbe\u3002<\/li>\n    <li><strong>\u5c06AdaBoost\u6269\u5c55\u5230\u591a\u7c7b\u522b\u9884\u6d4b\u95ee\u9898\uff0c\u63d0\u51fa\u4e86AdaBoost.M1\u548cAdaBoost.M2\u4e24\u79cd\u7b97\u6cd5\u3002<\/strong> AdaBoost.M1\u8981\u6c42\u5f31\u5047\u8bbe\u7684\u9884\u6d4b\u8bef\u5dee\u5c0f\u4e8e1\/2\uff0c\u800cAdaBoost.M2\u5219\u4f7f\u7528\u66f4\u7075\u6d3b\u7684\u4f2a\u635f\u5931\u5ea6\u91cf\uff0c\u5141\u8bb8\u5f31\u5b66\u4e60\u5668\u5373\u4f7f\u9884\u6d4b\u8bef\u5dee\u5927\u4e8e1\/2\u4e5f\u80fd\u505a\u51fa\u8d21\u732e\u3002<\/li>\n    <li><strong>\u5c06AdaBoost\u6269\u5c55\u5230\u56de\u5f52\u95ee\u9898\uff0c\u63d0\u51fa\u4e86AdaBoost.R\u7b97\u6cd5\u3002<\/strong> \u8be5\u7b97\u6cd5\u5c06\u56de\u5f52\u95ee\u9898\u7b80\u5316\u4e3a\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\uff0c\u5e76\u5229\u7528AdaBoost\u6765\u63d0\u5347\u5f31\u56de\u5f52\u7b97\u6cd5\u7684\u6027\u80fd\u3002<br><\/li>\n<\/ol>\n\n\n<p><strong>&lt;\u7ed3\u8bba&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u5728\u7ebf\u8d44\u6e90\u5206\u914d\u7b97\u6cd5Hedge(\u03b2)\u7684\u6027\u80fd\u53ef\u4ee5\u63a5\u8fd1\u6700\u4f73\u7b56\u7565\u7684\u6027\u80fd\uff0c\u4e14\u8bef\u5dee\u7387\u968f\u65f6\u95f4\u51cf\u5c11\u3002<\/strong><\/li>\n    <li><strong>AdaBoost\u80fd\u591f\u5c06\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\u63d0\u5347\u5230\u4efb\u610f\u9ad8\u7684\u7cbe\u5ea6\uff0c\u5176\u6700\u7ec8\u5047\u8bbe\u7684\u8bef\u5dee\u4ee5\u6307\u6570\u901f\u5ea6\u4e0b\u964d\u3002<\/strong><\/li>\n    <li><strong>AdaBoost\u53ef\u4ee5\u6269\u5c55\u5230\u591a\u7c7b\u522b\u9884\u6d4b\u548c\u56de\u5f52\u95ee\u9898\u3002<\/strong><br><\/li>\n<\/ol>\n\n\n<p><strong>&lt;\u5b9e\u9a8c\u5185\u5bb9&gt;<\/strong><\/p>\n\n\n<p>\u8bba\u6587\u4e2d\u6ca1\u6709\u5305\u542b\u5b9e\u9a8c\u5185\u5bb9\uff0c\u4f46\u63d0\u5230\u4e86Drucker, Schapire and Simard [7]\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c\u8868\u660e\u65b0\u7b97\u6cd5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u53ef\u80fd\u5177\u6709\u4f18\u52bf\u3002<\/p>\n\n\n<p><strong>&lt;\u5bf9\u672c\u9886\u57df\u7684\u8d21\u732e&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u5c06\u5728\u7ebf\u9884\u6d4b\u6a21\u578b\u63a8\u5e7f\u5230\u66f4\u4e00\u822c\u7684\u51b3\u7b56\u7406\u8bba\u6846\u67b6\uff0c\u5e76\u8bc1\u660e\u4e86\u4e58\u6cd5\u6743\u91cd\u66f4\u65b0\u89c4\u5219\u7684\u5e7f\u6cdb\u9002\u7528\u6027\u3002<\/strong><\/li>\n    <li><strong>\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u81ea\u9002\u5e94Boosting\u7b97\u6cd5AdaBoost\uff0c\u8be5\u7b97\u6cd5\u65e0\u9700\u4e8b\u5148\u4e86\u89e3\u5f31\u5b66\u4e60\u7b97\u6cd5\u7684\u6027\u80fd\uff0c\u5e76\u5728\u7406\u8bba\u4e0a\u8bc1\u660e\u4e86\u5176\u6709\u6548\u6027\u3002<\/strong><\/li>\n    <li><strong>\u4e3a\u591a\u7c7b\u522b\u9884\u6d4b\u548c\u56de\u5f52\u95ee\u9898\u63d0\u4f9b\u4e86\u65b0\u7684Boosting\u7b97\u6cd5\u3002<\/strong><br><\/li>\n<\/ol>\n\n\n<p><strong>&lt;\u4e3b\u8981\u5b9a\u7406&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u5b9a\u74062\uff1a<\/strong> \u7ed9\u51fa\u4e86Hedge(\u03b2)\u7b97\u6cd5\u51c0\u635f\u5931\u7684\u4e0a\u754c\uff0c\u8bc1\u660e\u5176\u6027\u80fd\u63a5\u8fd1\u6700\u4f73\u7b56\u7565\u3002<\/li>\n    <li><strong>\u5b9a\u74066\uff1a<\/strong> \u7ed9\u51fa\u4e86AdaBoost\u7b97\u6cd5\u6700\u7ec8\u5047\u8bbe\u8bef\u5dee\u7684\u4e0a\u754c\uff0c\u8bc1\u660e\u5176\u8bef\u5dee\u4ee5\u6307\u6570\u901f\u5ea6\u4e0b\u964d\u3002<\/li>\n    <li><strong>\u5b9a\u740610\u548c\u5b9a\u740611\uff1a<\/strong> \u5206\u522b\u7ed9\u51fa\u4e86AdaBoost.M1\u548cAdaBoost.M2\u7b97\u6cd5\u7684\u8bef\u5dee\u4e0a\u754c\uff0c\u8bc1\u660e\u5176\u53ef\u7528\u4e8e\u591a\u7c7b\u522b\u9884\u6d4b\u95ee\u9898\u3002<\/li>\n    <li><strong>\u5b9a\u740612\uff1a<\/strong> \u7ed9\u51fa\u4e86AdaBoost.R\u7b97\u6cd5\u7684\u5747\u65b9\u8bef\u5dee\u4e0a\u754c\uff0c\u8bc1\u660e\u5176\u53ef\u7528\u4e8e\u56de\u5f52\u95ee\u9898\u3002<br><\/li>\n<\/ol>\n\n\n<p><strong>&lt;\u5b58\u5728\u7684\u4e0d\u8db3&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u8bba\u6587\u4e2d\u6ca1\u6709\u5305\u542b\u5b9e\u9a8c\u7ed3\u679c\u6765\u9a8c\u8bc1\u65b0\u7b97\u6cd5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u6027\u80fd\u3002<\/li>\n    <li>\u5bf9\u4e8e\u591a\u7c7b\u522b\u9884\u6d4b\u95ee\u9898\uff0cAdaBoost.M1\u548cAdaBoost.M2\u7684\u6027\u80fd\u9700\u8981\u8fdb\u4e00\u6b65\u7684\u5b9e\u8bc1\u7814\u7a76\u6765\u6bd4\u8f83\u3002<\/li>\n    <li>\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u9700\u8981\u8fdb\u4e00\u6b65\u7814\u7a76\u5982\u4f55\u627e\u5230\u5177\u67091\/2\u635f\u5931\u7684\u5f31\u5047\u8bbe\uff0c\u4ee5\u6539\u8fdbAdaBoost.R\u7b97\u6cd5\u3002<br><\/li>\n<\/ol>\n\n\n<p><strong>&lt;\u672a\u6765\u7684\u5de5\u4f5c&gt;<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u5c06AdaBoost\u6269\u5c55\u5230\u66f4\u590d\u6742\u7684\u5b66\u4e60\u95ee\u9898\uff0c\u4f8b\u5982\u7ed3\u6784\u5316\u9884\u6d4b\u548c\u5f3a\u5316\u5b66\u4e60\u3002 <br><\/li>\n<\/ol>\n\n\n<h2 class=\"wp-block-heading\">2.AdaBoost.M1\u7b97\u6cd5<\/h2>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"1616\" height=\"1232\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage.png\" class=\"wp-image-319\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage.png 1616w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage-300x229.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage-1024x781.png 1024w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage-768x586.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage-1536x1171.png 1536w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/DraggedImage-624x476.png 624w\" sizes=\"auto, (max-width: 1616px) 100vw, 1616px\" \/><\/figure><\/div>\n\n\n<p>AdaBoost.M1 \u7b97\u6cd5\u662f\u4e00\u4e2a\u7528\u4e8e\u89e3\u51b3\u591a\u7c7b\u522b\u5206\u7c7b\u95ee\u9898\u7684 boosting \u7b97\u6cd5\uff0c\u5b83\u901a\u8fc7\u7ec4\u5408\u591a\u4e2a\u5f31\u5b66\u4e60\u5668\u6765\u6784\u5efa\u4e00\u4e2a\u5f3a\u5b66\u4e60\u5668\u3002 \u5f31\u5b66\u4e60\u5668\u6307\u7684\u662f\u6027\u80fd\u7565\u597d\u4e8e\u968f\u673a\u731c\u6d4b\u7684\u5206\u7c7b\u5668\uff0c\u800c\u5f3a\u5b66\u4e60\u5668\u5219\u53ef\u4ee5\u8fbe\u5230\u5f88\u9ad8\u7684\u5206\u7c7b\u7cbe\u5ea6\u3002<\/p>\n\n\n<p><strong>\u4e0b\u9762\u662f\u7b97\u6cd5\u7684\u6b65\u9aa4\u8be6\u89e3\uff1a<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u8f93\u5165\uff1a<\/strong> \u7b97\u6cd5\u7684\u8f93\u5165\u5305\u62ec N \u4e2a\u5e26\u6807\u7b7e\u7684\u8bad\u7ec3\u6837\u672c\u3001\u6837\u672c\u5206\u5e03 D\u3001\u5f31\u5b66\u4e60\u7b97\u6cd5 WeakLearn \u4ee5\u53ca\u8fed\u4ee3\u6b21\u6570 T\u3002 \u6bcf\u4e2a\u6837\u672c\u662f\u4e00\u4e2a\u4e8c\u5143\u7ec4 (x\u1d62, y\u1d62)\uff0c\u5176\u4e2d x\u1d62 \u662f\u4e00\u4e2a\u5b9e\u4f8b\uff0cy\u1d62 \u662f\u5b83\u7684\u6807\u7b7e\u3002\u6807\u7b7e y\u1d62 \u6765\u81ea\u4e8e\u4e00\u4e2a\u5305\u542b k \u4e2a\u53ef\u80fd\u6807\u7b7e\u7684\u96c6\u5408 Y = {1, &#8230;, k}\u3002<br><\/li>\n    <li><strong>\u521d\u59cb\u5316\uff1a<\/strong> \u7b97\u6cd5\u5c06\u6743\u91cd\u5411\u91cf w\u00b9 \u521d\u59cb\u5316\u4e3a\u5206\u5e03 D\uff0c\u8fd9\u4e2a\u6743\u91cd\u5411\u91cf\u4e3a\u6bcf\u4e2a\u8bad\u7ec3\u6837\u672c\u5206\u914d\u4e00\u4e2a\u6743\u91cd\u3002\u521d\u59cb\u65f6\uff0c\u53ef\u4ee4\u6240\u6709\u6837\u672c\u7684\u6743\u91cd\u90fd\u76f8\u7b49\u3002<br><\/li>\n    <li><strong>\u8fed\u4ee3\uff1a<\/strong> \u7b97\u6cd5\u8fdb\u884c T \u8f6e\u8fed\u4ee3\uff0c\u6bcf\u8f6e\u8fed\u4ee3\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<br><br>a. <strong>\u8ba1\u7b97\u6837\u672c\u5206\u5e03\uff1a<\/strong> \u6839\u636e\u5f53\u524d\u7684\u6743\u91cd\u5411\u91cf w\u1d57 \u8ba1\u7b97\u6837\u672c\u5206\u5e03 p\u1d57\uff0c\u4e5f\u5c31\u662f\u5c06\u6bcf\u4e2a\u6837\u672c\u7684\u6743\u91cd\u9664\u4ee5\u6240\u6709\u6837\u672c\u6743\u91cd\u4e4b\u548c\u3002<br><br>b. <strong>\u8c03\u7528\u5f31\u5b66\u4e60\u5668\uff1a<\/strong> \u4f7f\u7528\u5206\u5e03 p\u1d57 \u8c03\u7528\u5f31\u5b66\u4e60\u7b97\u6cd5 WeakLearn\uff0c\u5f97\u5230\u4e00\u4e2a\u5f31\u5047\u8bbe h\u209c: X \u2192 Y\u3002\uff08\u5b66\u4e60\u51fa\u4e00\u4e2a\u5206\u7c7b\u5668 h\u209c\uff09<br><br>c. <strong>\u8ba1\u7b97\u5047\u8bbe\u8bef\u5dee\uff1a<\/strong> \u8ba1\u7b97\u5f31\u5047\u8bbe h\u209c \u5728\u5f53\u524d\u6837\u672c\u5206\u5e03 p\u1d57 \u4e0b\u7684\u8bef\u5dee \u03b5\u209c\uff0c\u4e5f\u5c31\u662f h\u209c \u5206\u7c7b\u9519\u8bef\u7684\u6837\u672c\u6743\u91cd\u4e4b\u548c\u3002\u5982\u679c \u03b5\u209c \u2265 1\/2\uff0c\u8bf4\u660e\u8fd9\u4e2a\u5f31\u5047\u8bbe\u7684\u6027\u80fd\u751a\u81f3\u4e0d\u5982\u968f\u673a\u731c\u6d4b\uff0c\u6b64\u65f6\u8bbe\u7f6e T = t &#8211; 1 \u5e76\u505c\u6b62\u8fed\u4ee3\u3002<br><br>d. <strong>\u8ba1\u7b97\u66f4\u65b0\u53c2\u6570\uff1a<\/strong> \u6839\u636e\u8bef\u5dee \u03b5\u209c \u8ba1\u7b97\u66f4\u65b0\u53c2\u6570 \u03b2\u209c = \u03b5\u209c \/ (1 &#8211; \u03b5\u209c)\u3002<br><br>e. <strong>\u66f4\u65b0\u6743\u91cd\u5411\u91cf\uff1a<\/strong> \u4f7f\u7528\u66f4\u65b0\u53c2\u6570 \u03b2\u209c \u66f4\u65b0\u6837\u672c\u6743\u91cd\u5411\u91cf w\u1d57\u207a\u00b9\u3002\u66f4\u65b0\u89c4\u5219\u662f\uff1a\u5982\u679c\u5f31\u5047\u8bbe h\u209c \u5728\u6837\u672c x\u1d62 \u4e0a\u5206\u7c7b\u9519\u8bef\uff0c\u5219\u589e\u52a0 x\u1d62 \u7684\u6743\u91cd\uff1b\u5426\u5219\uff0c\u51cf\u5c11 x\u1d62 \u7684\u6743\u91cd\u3002\u5177\u4f53\u6765\u8bf4\uff0cw\u1d57\u207a\u00b9\u1d62 = w\u1d57\u1d62 \u03b2\u209c ^(1-[h\u209c(x\u1d62) \u2260 y\u1d62])\uff0c\u5176\u4e2d [h\u209c(x\u1d62) \u2260 y\u1d62] \u8868\u793a\u5f53 h\u209c \u5728\u6837\u672c x\u1d62 \u4e0a\u5206\u7c7b\u9519\u8bef\u65f6\u4e3a 1\uff0c\u5426\u5219\u4e3a 0\u3002<br><\/li>\n    <li><strong>\u8f93\u51fa\uff1a<\/strong> \u8fed\u4ee3\u7ed3\u675f\u540e\uff0c\u7b97\u6cd5\u8f93\u51fa\u6700\u7ec8\u5047\u8bbe h\ua730\uff0c\u8be5\u5047\u8bbe\u5bf9\u65b0\u7684\u6837\u672c x \u7684\u9884\u6d4b\u7ed3\u679c\u662f arg max\u1d67\u2208Y \u03a3\u209c (log 1\/\u03b2\u209c) [h\u209c(x) = y]\uff0c\u4e5f\u5c31\u662f\u6240\u6709\u5f31\u5047\u8bbe\u7684\u52a0\u6743\u6295\u7968\u7ed3\u679c\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5f31\u5047\u8bbe\u7684\u6743\u91cd\u7531\u66f4\u65b0\u53c2\u6570 \u03b2 \u51b3\u5b9a\u3002<br><\/li>\n<\/ol>\n\n\n<p><strong>\u7b80\u800c\u8a00\u4e4b\uff0cAdaBoost.M1 \u7b97\u6cd5\u901a\u8fc7\u8fed\u4ee3\u5730\u8bad\u7ec3\u5f31\u5b66\u4e60\u5668\uff0c\u5e76\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u6027\u80fd\u8c03\u6574\u6837\u672c\u6743\u91cd\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u5f3a\u5b66\u4e60\u5668\u3002<\/strong> <\/p>\n\n\n<h3 class=\"wp-block-heading\">AdaBoost.M1\u7b97\u6cd5\u4e2d\u7684\u6743\u91cd\u7c7b\u578b\u53ca\u7528\u6cd5<\/h3>\n\n\n<p>\u5728AdaBoost.M1\u7b97\u6cd5\u4e2d\uff0c\u6d89\u53ca\u7684\u6743\u91cd\u7c7b\u578b\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u6837\u672c\u6743\u91cd \\(w^t\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u7c7b\u578b<\/strong>\uff1a\u521d\u59cb\u6743\u91cd\u548c\u66f4\u65b0\u6743\u91cd<\/li>\n    <li><strong>\u521d\u59cb\u5316<\/strong>\uff1a \\(w^1_i = D(i)\\) \u5bf9\u4e8e\u6bcf\u4e2a\u6837\u672c \\(i\\) \u6765\u8bf4\uff0c\u5176\u4e2d \\(D(i)\\) \u8868\u793a\u6837\u672c\u7684\u521d\u59cb\u6743\u91cd\u3002<\/li>\n    <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u5728\u6bcf\u6b21\u8fed\u4ee3\u7ed3\u675f\u540e\uff0c\u6743\u91cd \\(w^t\\) \u4f1a\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u9519\u8bef\u7387 \\(\\epsilon_t\\) \u8fdb\u884c\u66f4\u65b0\uff1a<br>\n        <p class=\"has-text-align-center\">\\(\\displaystyle w^{t+1}_i = w^t_i \\beta_t^{1 &#8211; [h_t(x_i) \\neq y_i]}\\)<\/p>\n        \n         \u5176\u4e2d\uff0c \\(\\beta_t = \\frac{\\epsilon_t}{1 &#8211; \\epsilon_t}\\)<\/li>\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u521d\u59cb\u5316\u65f6\u8868\u793a\u6bcf\u4e2a\u6837\u672c\u7684\u521d\u59cb\u91cd\u8981\u6027\uff0c\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u8868\u73b0\u8c03\u6574\u6837\u672c\u7684\u6743\u91cd\uff0c\u4f7f\u5f97\u9519\u8bef\u5206\u7c7b\u7684\u6837\u672c\u5728\u540e\u7eed\u8fed\u4ee3\u4e2d\u5f97\u5230\u66f4\u5927\u7684\u5173\u6ce8\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li><strong>\u5f52\u4e00\u5316\u6743\u91cd \\(p^t\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u7c7b\u578b<\/strong>\uff1a\u5f52\u4e00\u5316\u6743\u91cd<\/li>\n    <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a <\/li>\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle p^t_i = \\frac{w^t_i}{\\sum_{j=1}^N w^t_j}\\)<\/p>\n        <\/li>\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5c06\u5f53\u524d\u8fed\u4ee3\u7684\u6743\u91cd \\(w^t\\) \u5f52\u4e00\u5316\u4e3a\u6982\u7387\u5206\u5e03\uff0c\u4ee5\u4fbf\u63d0\u4f9b\u7ed9\u5f31\u5b66\u4e60\u5668 WeakLearn\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li><strong>\u9519\u8bef\u7387 \\(\\epsilon_t\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u7c7b\u578b<\/strong>\uff1a\u8ba1\u7b97\u8f85\u52a9\u6743\u91cd<\/li>\n    <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a <\/li>\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle \\epsilon_t = \\sum_{i=1}^N p^t_i [h_t(x_i) \\neq y_i]\\)<\/p>\n        <\/li>\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u8861\u91cf\u5f31\u5b66\u4e60\u5668\u5728\u5f53\u524d\u8fed\u4ee3\u4e2d\u7684\u9519\u8bef\u7387\uff0c\u6307\u5bfc\u4e0b\u4e00\u6b65\u7684\u6743\u91cd\u66f4\u65b0\u3002<br><\/li>\n<\/ul>\n\n\n<p>\u901a\u8fc7\u4ee5\u4e0a\u51e0\u79cd\u6743\u91cd\u7684\u76f8\u4e92\u4f5c\u7528\uff0cAdaBoost.M1\u7b97\u6cd5\u80fd\u591f\u9010\u6b65\u63d0\u5347\u6574\u4f53\u5206\u7c7b\u5668\u7684\u6027\u80fd\uff0c\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u6837\u672c\u7684\u6743\u91cd\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u8868\u73b0\u8fdb\u884c\u8c03\u6574\uff0c\u4f7f\u5f97\u96be\u5206\u7c7b\u7684\u6837\u672c\u5f97\u5230\u66f4\u591a\u7684\u5173\u6ce8\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5f31\u5b66\u4e60\u7b97\u6cd5\u662f\u5982\u4f55\u4f7f\u7528\u5206\u5e03 p\u1d57 \u7684\uff1f<\/h3>\n\n\n<p>\u5f31\u5b66\u4e60\u7b97\u6cd5\u4f7f\u7528\u5206\u5e03 p\u1d57 \u7684\u65b9\u5f0f\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u7b97\u6cd5\u5b9e\u73b0\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u6709\u4e24\u79cd\u4e3b\u8981\u7684\u65b9\u5f0f\uff1a<\/p>\n\n\n<p><strong>1.  \u91cd\u65b0\u91c7\u6837\u8bad\u7ec3\u6837\u672c\uff1a<\/strong><\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li> \u6839\u636e\u5206\u5e03 p\u1d57 \u5bf9\u539f\u59cb\u8bad\u7ec3\u6837\u672c\u8fdb\u884c\u91cd\u65b0\u91c7\u6837\uff0c\u751f\u6210\u4e00\u4e2a\u65b0\u7684\u8bad\u7ec3\u96c6\u3002\u65b0\u7684\u8bad\u7ec3\u96c6\u4e2d\uff0c\u90a3\u4e9b\u5728 p\u1d57 \u4e2d\u6743\u91cd\u8f83\u9ad8\u7684\u6837\u672c\u51fa\u73b0\u7684\u6b21\u6570\u66f4\u591a\uff0c\u800c\u6743\u91cd\u8f83\u4f4e\u7684\u6837\u672c\u51fa\u73b0\u7684\u6b21\u6570\u66f4\u5c11\u3002<\/li>\n    <li> \u4f7f\u7528\u65b0\u7684\u8bad\u7ec3\u96c6\u6765\u8bad\u7ec3\u5f31\u5b66\u4e60\u7b97\u6cd5\uff0c\u5f97\u5230\u65b0\u7684\u5f31\u5047\u8bbe\u3002<br><\/li>\n<\/ul>\n\n\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u662f\u7b80\u5355\u6613\u61c2\uff0c\u5e76\u4e14\u9002\u7528\u4e8e\u5927\u591a\u6570\u5f31\u5b66\u4e60\u7b97\u6cd5\u3002\u7f3a\u70b9\u662f\u91cd\u65b0\u91c7\u6837\u53ef\u80fd\u4f1a\u4e22\u5931\u4e00\u4e9b\u4fe1\u606f\uff0c\u5e76\u4e14\u53ef\u80fd\u4f1a\u5bfc\u81f4\u8bad\u7ec3\u96c6\u89c4\u6a21\u53d1\u751f\u53d8\u5316\u3002<\/p>\n\n\n<p><strong>2.  \u76f4\u63a5\u4fee\u6539\u7b97\u6cd5\u7684\u76ee\u6807\u51fd\u6570\uff1a<\/strong><\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li> \u4e00\u4e9b\u5f31\u5b66\u4e60\u7b97\u6cd5\uff0c\u4f8b\u5982\u57fa\u4e8e\u68af\u5ea6\u4e0b\u964d\u7684\u7b97\u6cd5\uff0c\u5176\u76ee\u6807\u51fd\u6570\u901a\u5e38\u5305\u542b\u4e00\u4e2a\u635f\u5931\u51fd\u6570\u9879\uff0c\u7528\u4e8e\u8861\u91cf\u6a21\u578b\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/li>\n    <li> \u53ef\u4ee5\u901a\u8fc7\u5c06\u635f\u5931\u51fd\u6570\u4e58\u4ee5\u6837\u672c\u6743\u91cd p\u1d57\u1d62 \u6765\u4fee\u6539\u76ee\u6807\u51fd\u6570\uff0c\u4f7f\u5f97\u7b97\u6cd5\u66f4\u52a0\u5173\u6ce8\u6743\u91cd\u8f83\u9ad8\u7684\u6837\u672c\u3002<\/li>\n    <li> \u4f7f\u7528\u4fee\u6539\u540e\u7684\u76ee\u6807\u51fd\u6570\u6765\u8bad\u7ec3\u5f31\u5b66\u4e60\u7b97\u6cd5\uff0c\u5f97\u5230\u65b0\u7684\u5f31\u5047\u8bbe\u3002<br><\/li>\n<\/ul>\n\n\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u662f\u80fd\u591f\u66f4\u76f4\u63a5\u5730\u5229\u7528\u6837\u672c\u6743\u91cd\u4fe1\u606f\uff0c\u5e76\u4e14\u4e0d\u4f1a\u6539\u53d8\u8bad\u7ec3\u96c6\u89c4\u6a21\u3002\u7f3a\u70b9\u662f\u9700\u8981\u5bf9\u5f31\u5b66\u4e60\u7b97\u6cd5\u8fdb\u884c\u4fee\u6539\uff0c\u5e76\u4e14\u53ea\u9002\u7528\u4e8e\u90e8\u5206\u5f31\u5b66\u4e60\u7b97\u6cd5\u3002<\/p>\n\n\n<p><strong>\u4e3e\u4f8b\u8bf4\u660e\uff1a<\/strong><\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u51b3\u7b56\u6811\u7b97\u6cd5\uff1a<\/strong> \u5f53\u4f7f\u7528\u51b3\u7b56\u6811\u4f5c\u4e3a\u5f31\u5b66\u4e60\u7b97\u6cd5\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u91cd\u65b0\u91c7\u6837\u65b9\u6cd5\u3002\u6839\u636e\u5206\u5e03 p\u1d57 \u5bf9\u539f\u59cb\u8bad\u7ec3\u6837\u672c\u8fdb\u884c\u91cd\u65b0\u91c7\u6837\uff0c\u7136\u540e\u4f7f\u7528\u65b0\u7684\u8bad\u7ec3\u96c6\u6784\u5efa\u51b3\u7b56\u6811\u3002<\/li>\n    <li><strong>\u652f\u6301\u5411\u91cf\u673a\u7b97\u6cd5\uff1a<\/strong> \u5f53\u4f7f\u7528\u652f\u6301\u5411\u91cf\u673a\u4f5c\u4e3a\u5f31\u5b66\u4e60\u7b97\u6cd5\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7\u4fee\u6539\u76ee\u6807\u51fd\u6570\u6765\u4f7f\u7528\u6837\u672c\u6743\u91cd\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u53ef\u4ee5\u5c06\u6bcf\u4e2a\u6837\u672c\u7684\u635f\u5931\u4e58\u4ee5\u5176\u5bf9\u5e94\u7684\u6743\u91cd p\u1d57\u1d62\uff0c\u7136\u540e\u4f7f\u7528\u4fee\u6539\u540e\u7684\u76ee\u6807\u51fd\u6570\u6765\u8bad\u7ec3\u652f\u6301\u5411\u91cf\u673a\u3002<br><\/li>\n<\/ul>\n\n\n<p><strong>\u603b\u7ed3:<\/strong><\/p>\n\n\n<p>\u5f31\u5b66\u4e60\u7b97\u6cd5\u4f7f\u7528\u5206\u5e03 p\u1d57 \u7684\u76ee\u7684\u662f\uff0c\u8ba9\u7b97\u6cd5\u66f4\u52a0\u5173\u6ce8\u6743\u91cd\u8f83\u9ad8\u7684\u6837\u672c\uff0c\u4ece\u800c\u5728\u4e0b\u4e00\u8f6e\u8fed\u4ee3\u4e2d\u5b66\u4e60\u5230\u66f4\u6709\u6548\u7684\u5f31\u5047\u8bbe\u3002\u5177\u4f53\u4f7f\u7528\u65b9\u5f0f\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u5f31\u5b66\u4e60\u7b97\u6cd5\uff0c\u53ef\u4ee5\u91c7\u7528\u91cd\u65b0\u91c7\u6837\u65b9\u6cd5\u6216\u4fee\u6539\u76ee\u6807\u51fd\u6570\u7684\u65b9\u6cd5\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\"> \\(\\epsilon_t \\)\u4e0e \\(\\omega_{t+1}\\) \u4e4b\u95f4\u7684\u5173\u7cfb<\/h3>\n\n\n<p>\u5728 AdaBoost.M1 \u7b97\u6cd5\u4e2d\uff0c\u03b5\u209c (epsilon_t) \u4ee3\u8868\u7b2c t \u8f6e\u5f31\u5b66\u4e60\u5668 h\u209c \u7684\u5206\u7c7b\u8bef\u5dee\uff0c\u800c w\u1d57\u207a\u00b9 (omega_{t+1}) \u4ee3\u8868\u7b2c t+1 \u8f6e\u8fed\u4ee3\u7684\u6837\u672c\u6743\u91cd\u5411\u91cf\u3002 \u8fd9\u4e24\u8005\u4e4b\u95f4\u5b58\u5728\u7740\u5bc6\u5207\u7684\u8054\u7cfb\uff0c \u03b5\u209c  \u76f4\u63a5\u5f71\u54cd w\u1d57\u207a\u00b9 \u7684\u66f4\u65b0\u3002<\/p>\n\n\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u4ed6\u4eec\u7684\u5173\u7cfb\u4f53\u73b0\u5728\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u03b5\u209c \u51b3\u5b9a \u03b2\u209c\uff0c\u8fdb\u800c\u5f71\u54cd w\u1d57\u207a\u00b9\uff1a<\/strong><br><ul>\n            <li>\u66f4\u65b0\u53c2\u6570 \u03b2\u209c \u7531  \u03b2\u209c = \u03b5\u209c \/ (1 &#8211; \u03b5\u209c) \u8ba1\u7b97\u5f97\u5230\uff0c\u03b5\u209c \u8d8a\u5927\uff0c \u03b2\u209c \u4e5f\u8d8a\u5927\u3002<\/li>\n            <li>\u6837\u672c\u6743\u91cd\u66f4\u65b0\u516c\u5f0f\u4e3a w\u1d57\u207a\u00b9\u1d62 = w\u1d57\u1d62 \u03b2\u209c ^(1-[h\u209c(x\u1d62) \u2260 y\u1d62]) \u3002 \u03b2\u209c \u8d8a\u5927\uff0c\u5206\u7c7b\u6b63\u786e\u7684\u6837\u672c\u6743\u91cd\u964d\u4f4e\u8d8a\u591a\uff0c\u800c\u5206\u7c7b\u9519\u8bef\u7684\u6837\u672c\u6743\u91cd\u4fdd\u6301\u4e0d\u53d8\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u03b5\u209c \u8d8a\u5927\uff0cw\u1d57\u207a\u00b9 \u4e2d\u96be\u4ee5\u5206\u7c7b\u6837\u672c\u7684\u6743\u91cd\u5360\u6bd4\u8d8a\u9ad8\uff1a<\/strong><br><ul>\n            <li>\u5f53 \u03b5\u209c \u8f83\u5927\u65f6\uff0c\u8bf4\u660e\u5f53\u524d\u5f31\u5b66\u4e60\u5668 h\u209c \u6027\u80fd\u8f83\u5dee\uff0c\u5f88\u591a\u6837\u672c\u90fd\u88ab\u5206\u7c7b\u9519\u8bef\u3002 <\/li>\n            <li>\u6b64\u65f6 \u03b2\u209c \u4e5f\u4f1a\u8f83\u5927\uff0c\u5bfc\u81f4\u5206\u7c7b\u6b63\u786e\u7684\u6837\u672c\u6743\u91cd\u88ab\u5927\u5e45\u964d\u4f4e\uff0c\u800c\u5206\u7c7b\u9519\u8bef\u7684\u6837\u672c\u6743\u91cd\u4fdd\u6301\u4e0d\u53d8\u3002<\/li>\n            <li>\u6700\u7ec8\u7ed3\u679c\u662f\uff0c w\u1d57\u207a\u00b9 \u4e2d\u90a3\u4e9b\u96be\u4ee5\u5206\u7c7b\u7684\u6837\u672c\u7684\u6743\u91cd\u5360\u6bd4\u4f1a\u663e\u8457\u63d0\u9ad8\uff0c\u4f7f\u5f97\u4ed6\u4eec\u5728\u4e0b\u4e00\u8f6e\u8fed\u4ee3\u4e2d\u5f97\u5230\u66f4\u591a\u5173\u6ce8\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u03b5\u209c  \u5f15\u5bfc\u540e\u7eed\u5f31\u5b66\u4e60\u5668\u5173\u6ce8\u96be\u4ee5\u5206\u7c7b\u7684\u6837\u672c\uff1a<\/strong> <br><ul>\n            <li>AdaBoost.M1 \u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff0c\u6bcf\u4e00\u8f6e\u8fed\u4ee3\u90fd\u91cd\u70b9\u5173\u6ce8\u90a3\u4e9b\u88ab\u5148\u524d\u5f31\u5b66\u4e60\u5668\u5206\u7c7b\u9519\u8bef\u7684\u6837\u672c\u3002<\/li>\n            <li>\u03b5\u209c  \u53cd\u6620\u4e86\u5f53\u524d\u5f31\u5b66\u4e60\u5668\u7684\u5206\u7c7b\u6027\u80fd\uff0c\u901a\u8fc7 \u03b2\u209c  \u5f71\u54cd\u6837\u672c\u6743\u91cd  w\u1d57\u207a\u00b9\uff0c\u8fdb\u800c\u5f15\u5bfc\u540e\u7eed\u5f31\u5b66\u4e60\u5668\u66f4\u52a0\u5173\u6ce8\u90a3\u4e9b\u96be\u4ee5\u5206\u7c7b\u7684\u6837\u672c\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ol>\n\n\n<p><strong>\u603b\u7ed3:<\/strong><\/p>\n\n\n<p>\u03b5\u209c \u548c w\u1d57\u207a\u00b9 \u4e4b\u95f4\u7684\u5173\u7cfb\u662f AdaBoost.M1 \u7b97\u6cd5\u7684\u6838\u5fc3\u673a\u5236\u3002 <strong>\u03b5\u209c  \u8d8a\u5927\uff0c\u8bf4\u660e\u5f53\u524d\u5f31\u5b66\u4e60\u5668\u6027\u80fd\u8d8a\u5dee\uff0c\u7b97\u6cd5\u4f1a\u901a\u8fc7\u589e\u5927 \u03b2\u209c  \u6765\u5927\u5e45\u964d\u4f4e\u5206\u7c7b\u6b63\u786e\u6837\u672c\u7684\u6743\u91cd\uff0c\u4ece\u800c\u4f7f\u5f97 w\u1d57\u207a\u00b9 \u4e2d\u96be\u4ee5\u5206\u7c7b\u6837\u672c\u7684\u6743\u91cd\u5360\u6bd4\u66f4\u9ad8\u3002<\/strong>  \u8fd9\u5c31\u8feb\u4f7f\u540e\u7eed\u5f31\u5b66\u4e60\u5668\u66f4\u52a0\u5173\u6ce8\u8fd9\u4e9b\u96be\u4ee5\u5206\u7c7b\u7684\u6837\u672c\uff0c\u6700\u7ec8\u63d0\u9ad8\u6574\u4e2a\u6a21\u578b\u7684\u5206\u7c7b\u7cbe\u5ea6\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5bf9\u8f93\u51fa\u7ed3\u679c\u7684\u89e3\u91ca<\/h3>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"688\" height=\"124\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.41.00@2x.png\" class=\"wp-image-325\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.41.00@2x.png 688w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.41.00@2x-300x54.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.41.00@2x-624x112.png 624w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/figure><\/div>\n\n\n<p>\u8fd9\u4e2a\u516c\u5f0f\u5b9a\u4e49\u4e86 AdaBoost.M1 \u7b97\u6cd5\u7684\u6700\u7ec8\u5047\u8bbe h\ua730(x)\uff0c\u5b83\u662f\u4e00\u4e2a\u6574\u5408\u4e86\u6240\u6709\u5f31\u5047\u8bbe\u7684\u5f3a\u5206\u7c7b\u5668\u3002<\/p>\n\n\n<p>\u5177\u4f53\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>h_f(x):<\/strong>  \u4ee3\u8868\u6700\u7ec8\u5047\u8bbe h\ua730 \u5bf9\u65b0\u6837\u672c x \u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u4e5f\u5c31\u662f\u6700\u7ec8\u9884\u6d4b\u7684\u6807\u7b7e\u3002<\/li>\n    <li><strong>arg max\u1d67\u2208Y :<\/strong>  \u4ee3\u8868\u53d6\u4f7f\u5f97\u540e\u9762\u8868\u8fbe\u5f0f\u6700\u5927\u5316\u7684\u6807\u7b7e y\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6700\u7ec8\u9884\u6d4b\u7684\u6807\u7b7e\u662f\u6240\u6709\u6807\u7b7e\u4e2d\uff0c\u5f97\u5206\u6700\u9ad8\u7684\u90a3\u4e2a\u6807\u7b7e\u3002<\/li>\n    <li><strong>\u03a3\u209c (log 1\/\u03b2\u209c) [h\u209c(x) = y]\uff1a<\/strong> \u8fd9\u662f\u6bcf\u4e2a\u6807\u7b7e y \u7684\u5f97\u5206\u8ba1\u7b97\u516c\u5f0f\uff0c\u5b83\u7d2f\u52a0\u4e86\u6240\u6709\u5f31\u5047\u8bbe\u5bf9\u8be5\u6807\u7b7e\u7684\u652f\u6301\u7a0b\u5ea6\u3002<br><ul>\n            <li><strong>\u03a3\u209c\uff1a<\/strong> \u4ee3\u8868\u5bf9\u6240\u6709 T \u4e2a\u5f31\u5b66\u4e60\u5668\u8fdb\u884c\u6c42\u548c\u3002<\/li>\n            <li><strong>log 1\/\u03b2\u209c\uff1a<\/strong>  \u4ee3\u8868\u7b2c t \u4e2a\u5f31\u5b66\u4e60\u5668 h\u209c \u7684\u6743\u91cd\uff0c\u8be5\u6743\u91cd\u7531\u66f4\u65b0\u53c2\u6570 \u03b2\u209c \u51b3\u5b9a\u3002 \u03b2\u209c \u8d8a\u5c0f\uff0c\u8bf4\u660e\u5f31\u5b66\u4e60\u5668 h\u209c \u7684\u8bef\u5dee\u8d8a\u5c0f\uff0c\u5176\u6743\u91cd\u5c31\u8d8a\u5927\u3002<\/li>\n            <li><strong>[h\u209c(x) = y]\uff1a<\/strong>  \u8fd9\u662f\u4e00\u4e2a\u6307\u793a\u51fd\u6570\uff0c\u5f53\u5f31\u5b66\u4e60\u5668 h\u209c \u5c06\u6837\u672c x \u9884\u6d4b\u4e3a\u6807\u7b7e y \u65f6\u4e3a 1\uff0c\u5426\u5219\u4e3a 0\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ul>\n\n\n<p>\u56e0\u6b64\uff0c\u8fd9\u4e2a\u516c\u5f0f\u7684\u542b\u4e49\u662f\uff1a<\/p>\n\n\n<p>\u5bf9\u4e8e\u65b0\u6837\u672c x\uff0c\u6700\u7ec8\u5047\u8bbe h\ua730 \u4f1a\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u6807\u7b7e y\uff0c\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u6807\u7b7e y \u7684\u5f97\u5206\u3002\u6bcf\u4e2a\u6807\u7b7e y \u7684\u5f97\u5206\u662f\u6240\u6709\u5c06\u6837\u672c x \u9884\u6d4b\u4e3a\u6807\u7b7e y \u7684\u5f31\u5b66\u4e60\u5668\u7684\u6743\u91cd\u4e4b\u548c\u3002\u6700\u7ec8\u9884\u6d4b\u7684\u6807\u7b7e\u662f\u5f97\u5206\u6700\u9ad8\u7684\u90a3\u4e2a\u6807\u7b7e\u3002<\/p>\n\n\n<p><strong>\u7b80\u5355\u6765\u8bf4\uff0cAdaBoost.M1 \u7b97\u6cd5\u7684\u6700\u7ec8\u5047\u8bbe h\ua730 \u662f\u5bf9\u6240\u6709\u5f31\u5047\u8bbe\u7684\u52a0\u6743\u6295\u7968\uff0c\u6bcf\u4e2a\u5f31\u5047\u8bbe\u7684\u6295\u7968\u6743\u91cd\u7531\u5176\u5206\u7c7b\u8bef\u5dee\u51b3\u5b9a\u3002<\/strong>  \u5206\u7c7b\u8bef\u5dee\u8d8a\u5c0f\u7684\u5f31\u5047\u8bbe\u62e5\u6709\u66f4\u5927\u7684\u6295\u7968\u6743\u91cd\uff0c\u4ece\u800c\u5bf9\u6700\u7ec8\u9884\u6d4b\u7ed3\u679c\u7684\u5f71\u54cd\u4e5f\u8d8a\u5927\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">3. AdaBoost.M2\u7b97\u6cd5<\/h2>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"1424\" height=\"1452\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x.png\" class=\"wp-image-324\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x.png 1424w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x-294x300.png 294w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x-1004x1024.png 1004w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x-768x783.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-18.55.17@2x-624x636.png 624w\" sizes=\"auto, (max-width: 1424px) 100vw, 1424px\" \/><\/figure><\/div>\n\n\n<p>AdaBoost.M2 \u7b97\u6cd5\u662f AdaBoost \u7b97\u6cd5\u7684\u53e6\u4e00\u4e2a\u591a\u7c7b\u522b\u5206\u7c7b\u6269\u5c55\u7248\u672c\uff0c\u5b83\u5728\u5f31\u5b66\u4e60\u5668\u548c boosting \u7b97\u6cd5\u4e4b\u95f4\u91c7\u7528\u4e86\u66f4\u590d\u6742\u7684\u901a\u4fe1\u673a\u5236\uff0c\u4e3a\u5f31\u5b66\u4e60\u5668\u63d0\u4f9b\u4e86\u66f4\u5927\u7684\u7075\u6d3b\u6027\u3002<\/p>\n\n\n<p><strong>\u7b97\u6cd5\u89e3\u91ca\uff1a<\/strong><\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u8f93\u5165\uff1a<\/strong><br><ul>\n            <li> N \u4e2a\u5e26\u6807\u7b7e\u7684\u6837\u672c ((x\u2081, y\u2081), &#8230;, (x\u2099, y\u2099))\uff0c\u5176\u4e2d\u6807\u7b7e y\u1d62 \u2208 Y = {1, &#8230;, k}\u3002<\/li>\n            <li> \u6837\u672c\u5206\u5e03 D\u3002<\/li>\n            <li> \u5f31\u5b66\u4e60\u7b97\u6cd5 WeakLearn\u3002<\/li>\n            <li> \u8fed\u4ee3\u6b21\u6570 T\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u521d\u59cb\u5316\uff1a<\/strong> \u4e3a\u6bcf\u4e2a\u6837\u672c x\u1d62 \u548c\u6bcf\u4e2a\u4e0d\u7b49\u4e8e\u771f\u5b9e\u6807\u7b7e y\u1d62 \u7684\u6807\u7b7e y\uff0c\u521d\u59cb\u5316\u4e00\u4e2a\u6743\u91cd \\(w_{i, y}^1=D(i) \/(k-1)\\)\u3002\u8fd9\u8868\u793a\u6bcf\u4e2a\u6837\u672c\u5728\u521d\u59cb\u65f6\uff0c\u5bf9\u6bcf\u4e2a\u9519\u8bef\u6807\u7b7e\u7684\u6743\u91cd\u90fd\u76f8\u7b49\u3002<br><\/li>\n    <li><strong>\u8fed\u4ee3\uff1a<\/strong> \u7b97\u6cd5\u8fdb\u884c T \u8f6e\u8fed\u4ee3\uff0c\u6bcf\u8f6e\u8fed\u4ee3\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<br><br>a. <strong>\u8ba1\u7b97\u6837\u672c\u6743\u91cd\u548c\u6807\u7b7e\u6743\u91cd\u51fd\u6570\uff1a<\/strong><\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684\u6743\u91cd\\(W_i^t=\\sum_{y \\neq y_i} w_{i, y}^t\\) \u3002<\/li>\n    <li>\u8ba1\u7b97\u6807\u7b7e\u6743\u91cd\u51fd\u6570 \\(q_t(i, y)=\\frac{w_{i, y}^t}{W_i^t}\\)\u3002 \u8fd9\u8868\u793a\u5728\u6837\u672c x\u1d62 \u4e0a\uff0c\u533a\u5206\u771f\u5b9e\u6807\u7b7e y\u1d62 \u548c\u9519\u8bef\u6807\u7b7e y \u7684\u91cd\u8981\u6027\u3002<\/li>\n    <li>\u8ba1\u7b97\u6837\u672c\u5206\u5e03 \\(D_t(i)=\\frac{W_i^t}{\\sum_{i=1}^N W_i^t}\\)\u3002<br><br>b. <strong>\u8c03\u7528\u5f31\u5b66\u4e60\u5668\uff1a<\/strong> \u4f7f\u7528\u5206\u5e03 D\u1d57 \u548c\u6807\u7b7e\u6743\u91cd\u51fd\u6570 q\u1d57 \u8c03\u7528 WeakLearn\uff0c\u5f97\u5230\u4e00\u4e2a\u5f31\u5047\u8bbe h\u209c: X \u00d7 Y \u2192 [0, 1]\u3002 <\/li>\n    <li>\u4e0e AdaBoost.M1 \u4e0d\u540c\uff0c\u8fd9\u91cc\u7684\u5f31\u5047\u8bbe\u8f93\u51fa\u4e00\u4e2a\u4ecb\u4e8e 0 \u5230 1 \u4e4b\u95f4\u7684\u503c\uff0c\u8868\u793a\u5bf9\u6bcf\u4e2a\u6807\u7b7e\u7684\u7f6e\u4fe1\u5ea6\u3002<br><br>c. <strong>\u8ba1\u7b97\u4f2a\u635f\u5931\uff1a<\/strong> \u8ba1\u7b97\u5f31\u5047\u8bbe h\u209c \u7684\u4f2a\u635f\u5931 \u03b5\u209c = (1\/2) \u03a3\u1d62 D\u1d57(i) (1 &#8211; h\u209c(x\u1d62, y\u1d62) + \u03a3\u1d67\u2260y\u1d62 q\u1d57(i, y) h\u209c(x\u1d62, y))\u3002<br><\/li>\n    <li>\u4f2a\u635f\u5931\u8861\u91cf\u4e86\u5f31\u5047\u8bbe\u5728\u533a\u5206\u771f\u5b9e\u6807\u7b7e\u548c\u5176\u4ed6\u6807\u7b7e\u65b9\u9762\u7684\u80fd\u529b\u3002<br><br>d. <strong>\u8ba1\u7b97\u66f4\u65b0\u53c2\u6570\uff1a<\/strong> \u6839\u636e\u4f2a\u635f\u5931 \u03b5\u209c \u8ba1\u7b97\u66f4\u65b0\u53c2\u6570 \u03b2\u209c = \u03b5\u209c \/ (1 &#8211; \u03b5\u209c)\u3002<br><br>e. <strong>\u66f4\u65b0\u6743\u91cd\u5411\u91cf\uff1a<\/strong> \u4f7f\u7528\u66f4\u65b0\u53c2\u6570 \u03b2\u209c \u66f4\u65b0\u6837\u672c\u6743\u91cd\u5411\u91cf w\u1d57\u207a\u00b9\u1d62,\u1d67 = w\u1d57\u1d62,\u1d67 \u03b2\u209c^(1\/2)(1+h\u209c(x\u1d62,y\u1d62)-h\u209c(x\u1d62,y))\uff0cy \u2260 y\u1d62\u3002<\/li>\n    <li>\u66f4\u65b0\u89c4\u5219\u4e0e AdaBoost.M1 \u7c7b\u4f3c\uff0c\u4f46\u8003\u8651\u4e86\u5f31\u5047\u8bbe\u5bf9\u6bcf\u4e2a\u6807\u7b7e\u7684\u7f6e\u4fe1\u5ea6\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li><strong>\u8f93\u51fa\uff1a<\/strong> \u8fed\u4ee3\u7ed3\u675f\u540e\uff0c\u7b97\u6cd5\u8f93\u51fa\u6700\u7ec8\u5047\u8bbe h\ua730(x) = arg max\u1d67\u2208Y \u03a3\u209c (log 1\/\u03b2\u209c) h\u209c(x, y)\u3002<br><ul>\n            <li>\u6700\u7ec8\u5047\u8bbe\u4e5f\u662f\u5bf9\u6240\u6709\u5f31\u5047\u8bbe\u7684\u52a0\u6743\u6295\u7968\uff0c\u4f46\u6295\u7968\u6743\u91cd\u8003\u8651\u4e86\u5f31\u5047\u8bbe\u5bf9\u6bcf\u4e2a\u6807\u7b7e\u7684\u7f6e\u4fe1\u5ea6\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ol>\n\n\n<p><strong>\u603b\u7ed3\uff1a<\/strong><\/p>\n\n\n<p>AdaBoost.M2 \u7b97\u6cd5\u901a\u8fc7\u5f15\u5165\u6807\u7b7e\u6743\u91cd\u51fd\u6570\u548c\u4f2a\u635f\u5931\uff0c\u4f7f\u5f97\u5f31\u5b66\u4e60\u5668\u80fd\u591f\u66f4\u7075\u6d3b\u5730\u8fdb\u884c\u9884\u6d4b\uff0c\u5373\u4f7f\u5728\u67d0\u4e9b\u6837\u672c\u4e0a\u65e0\u6cd5\u51c6\u786e\u9884\u6d4b\u771f\u5b9e\u6807\u7b7e\uff0c\u4e5f\u80fd\u901a\u8fc7\u533a\u5206\u5176\u4ed6\u6807\u7b7e\u6765\u63d0\u4f9b\u6709\u7528\u4fe1\u606f\uff0c\u6700\u7ec8\u63d0\u9ad8\u6574\u4e2a\u6a21\u578b\u7684\u5206\u7c7b\u7cbe\u5ea6\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">AdaBoost.M2\u7b97\u6cd5\u7684\u6743\u91cd\u7c7b\u578b\u5176\u53ca\u7528\u6cd5<\/h3>\n\n\n<h3 class=\"wp-block-heading\">AdaBoost.M2\u7b97\u6cd5\u4e2d\u7684\u6743\u91cd\u7c7b\u578b\u53ca\u7528\u6cd5<\/h3>\n\n\n<p>\u5728AdaBoost.M2\u7b97\u6cd5\u4e2d\uff0c\u6d89\u53ca\u7684\u6743\u91cd\u7c7b\u578b\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u6837\u672c\u6743\u91cd \\(w_{i,j}^t\\)<\/strong>:<br><ul>\n            <li><strong>\u7c7b\u578b<\/strong>\uff1a\u521d\u59cb\u6743\u91cd\u548c\u66f4\u65b0\u6743\u91cd<\/li>\n            <li><strong>\u521d\u59cb\u5316<\/strong>\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u6837\u672c \\(i\\) \u548c\u7c7b\u522b \\(y \\neq y_i\\)\uff0c\u521d\u59cb\u5316\u6743\u91cd\u4e3a \\(w_{i,j}^t = \\frac{D(i)}{k-1}\\)\uff0c\u5176\u4e2d \\(k\\) \u662f\u7c7b\u522b\u6570\uff0c\\(D(i)\\) \u662f\u6837\u672c \\(i\\) \u7684\u521d\u59cb\u6743\u91cd\u3002<\/li>\n            <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u5728\u6bcf\u6b21\u8fed\u4ee3\u7ed3\u675f\u540e\uff0c\u6743\u91cd \\(w_{i,j}^t\\) \u4f1a\u6839\u636e\u4ee5\u4e0b\u516c\u5f0f\u8fdb\u884c\u66f4\u65b0\uff1a<br>\n                <p class=\"has-text-align-center\">\\(\\displaystyle w_{i,j}^{t+1} = w_{i,j}^t \\beta_t^{\\frac{1}{2}(1 + h_t(x_i, y_i) &#8211; h_t(x_i, y))}\\)<\/p>\n                \n                \u5176\u4e2d\uff0c\\(\\beta_t = \\frac{\\epsilon_t}{1 &#8211; \\epsilon_t}\\)\u3002<\/li>\n            <li><strong>\u4f5c\u7528<\/strong>\uff1a\u521d\u59cb\u5316\u65f6\u8868\u793a\u6bcf\u4e2a\u6837\u672c\u7684\u521d\u59cb\u91cd\u8981\u6027\uff0c\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u8868\u73b0\u8c03\u6574\u6837\u672c\u7684\u6743\u91cd\uff0c\u4f7f\u5f97\u9519\u8bef\u5206\u7c7b\u7684\u6837\u672c\u5728\u540e\u7eed\u8fed\u4ee3\u4e2d\u5f97\u5230\u66f4\u5927\u7684\u5173\u6ce8\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u5f52\u4e00\u5316\u6743\u91cd \\(W_i^t\\)<\/strong>:<br><ul>\n            <li><strong>\u7c7b\u578b<\/strong>\uff1a\u5f52\u4e00\u5316\u6743\u91cd<\/li>\n            <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u8ba1\u7b97\u5f53\u524d\u8fed\u4ee3\u7684\u5f52\u4e00\u5316\u6743\u91cd \\(W_i^t\\)\uff1a<br>\n                <p class=\"has-text-align-center\">\\(\\displaystyle W_i^t = \\sum_{y \\neq y_i} w_{i,y}^t\\)<\/p>\n                <\/li>\n            <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5c06\u5f53\u524d\u8fed\u4ee3\u7684\u6743\u91cd \\(w_{i,y}^t\\) \u5f52\u4e00\u5316\u4e3a\u6982\u7387\u5206\u5e03\uff0c\u4ee5\u4fbf\u63d0\u4f9b\u7ed9\u5f31\u5b66\u4e60\u5668 WeakLearn\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u7c7b\u522b\u6743\u91cd \\(q_t(i, y)\\)<\/strong>:<br><ul>\n            <li><strong>\u7c7b\u578b<\/strong>\uff1a\u8ba1\u7b97\u8f85\u52a9\u6743\u91cd<\/li>\n            <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u7c7b\u522b\u6743\u91cd \\(q_t(i, y)\\) \u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<br>\n                <p class=\"has-text-align-center\">\\(\\displaystyle q_t(i, y) = \\frac{w_{i,y}^t}{W_i^t}\\)<\/p>\n                \n                \u5176\u4e2d \\(y \\neq y_i\\)\u3002<\/li>\n            <li><strong>\u4f5c\u7528<\/strong>\uff1a\u7528\u4e8e\u8ba1\u7b97 \\(h_t\\) \u7684\u4f2a\u635f\u5931 \\(\\epsilon_t\\)\uff0c\u8868\u793a\u6837\u672c \\(i\\) \u88ab\u9519\u8bef\u5206\u7c7b\u4e3a\u7c7b\u522b \\(y\\) \u7684\u6743\u91cd\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u4f2a\u635f\u5931 \\(\\epsilon_t\\)<\/strong>:<br><ul>\n            <li><strong>\u7c7b\u578b<\/strong>\uff1a\u8ba1\u7b97\u8f85\u52a9\u6743\u91cd<\/li>\n            <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u4f2a\u635f\u5931 \\(\\epsilon_t\\) \u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<br>\n                <p class=\"has-text-align-center\">\\(\\displaystyle \\epsilon_t = \\frac{1}{2} \\sum_{i=1}^N D_t(i) \\left(1 &#8211; h_t(x_i, y_i) + \\sum_{y \\neq y_i} q_t(i, y) h_t(x_i, y)\\right)\\)<\/p>\n                <\/li>\n            <li><strong>\u4f5c\u7528<\/strong>\uff1a\u8861\u91cf\u5f31\u5b66\u4e60\u5668\u5728\u5f53\u524d\u8fed\u4ee3\u4e2d\u7684\u9519\u8bef\u7387\uff0c\u6307\u5bfc\u4e0b\u4e00\u6b65\u7684\u6743\u91cd\u66f4\u65b0\u3002<br><\/li>\n        <\/ul><\/li>\n    <li><strong>\u5206\u5e03 \\(D_t(i)\\)<\/strong>:<br><ul>\n            <li><strong>\u7c7b\u578b<\/strong>\uff1a\u5206\u5e03\u6743\u91cd<\/li>\n            <li><strong>\u8ba1\u7b97\u516c\u5f0f<\/strong>\uff1a\u5206\u5e03 \\(D_t(i)\\) \u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<br>\n                <p class=\"has-text-align-center\">\\(\\displaystyle D_t(i) = \\frac{W_i^t}{\\sum_{i=1}^N W_i^t}\\)<\/p>\n                <\/li>\n            <li><strong>\u4f5c\u7528<\/strong>\uff1a\u7528\u4e8e\u8868\u793a\u5f53\u524d\u8fed\u4ee3\u4e2d\u6bcf\u4e2a\u6837\u672c\u7684\u5206\u5e03\u6743\u91cd\uff0c\u6307\u5bfc\u5f31\u5b66\u4e60\u5668\u7684\u8bad\u7ec3\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ol>\n\n\n<p>\u901a\u8fc7\u4ee5\u4e0a\u51e0\u79cd\u6743\u91cd\u7684\u76f8\u4e92\u4f5c\u7528\uff0cAdaBoost.M2\u7b97\u6cd5\u80fd\u591f\u9010\u6b65\u63d0\u5347\u6574\u4f53\u5206\u7c7b\u5668\u7684\u6027\u80fd\uff0c\u6bcf\u6b21\u8fed\u4ee3\u4e2d\uff0c\u6837\u672c\u7684\u6743\u91cd\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u8868\u73b0\u8fdb\u884c\u8c03\u6574\uff0c\u4f7f\u5f97\u96be\u5206\u7c7b\u7684\u6837\u672c\u5f97\u5230\u66f4\u591a\u7684\u5173\u6ce8\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u635f\u5931\u51fd\u6570\u7684\u89e3\u91ca<\/h3>\n\n\n<p>\u635f\u5931\u51fd\u6570\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \\epsilon_t = \\frac{1}{2} \\sum_{i=1}^{N} D_t(i) \\left( 1 &#8211; h_t(x_i, y_i) + \\sum_{y \\neq y_i} q_t(i, y) h_t(x_i, y) \\right)\\)<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle \\epsilon_t\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u7b2c \\(t\\) \u8f6e\u5f31\u5206\u7c7b\u5668 \\(h_t\\) \u7684\u52a0\u6743\u8bef\u5dee\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u8fd9\u4e2a\u503c\u8d8a\u5c0f\uff0c\u8868\u793a\u5f53\u524d\u5f31\u5206\u7c7b\u5668 \\(h_t\\) \u5728\u5f53\u524d\u6743\u91cd\u5206\u5e03 \\(D_t\\) \u4e0b\u8868\u73b0\u8d8a\u597d\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle \\frac{1}{2}\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u7f29\u653e\u56e0\u5b50\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u5c06\u6574\u4e2a\u516c\u5f0f\u7684\u503c\u7f29\u5c0f\u5230\u5408\u7406\u7684\u8303\u56f4\uff0c\u901a\u5e38\u57280\u52301\u4e4b\u95f4\uff0c\u65b9\u4fbf\u540e\u7eed\u8ba1\u7b97\u548c\u6bd4\u8f83\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle \\sum_{i=1}^{N}\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5bf9\u6240\u6709\u8bad\u7ec3\u6837\u672c\u6c42\u548c\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u7d2f\u79ef\u6bcf\u4e2a\u6837\u672c\u7684\u52a0\u6743\u8bef\u5dee\uff0c\u5f97\u5230\u6574\u4f53\u7684\u52a0\u6743\u8bef\u5dee\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle D_t(i)\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u7b2c \\(t\\) \u8f6e\u4e2d\u7b2c \\(i\\) \u4e2a\u8bad\u7ec3\u6837\u672c\u7684\u6743\u91cd\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u53cd\u6620\u4e86\u5f53\u524d\u8f6e\u6b21\u4e2d\u6bcf\u4e2a\u6837\u672c\u7684\u91cd\u8981\u6027\u3002\u6743\u91cd\u8d8a\u5927\u7684\u6837\u672c\u5bf9\u603b\u8bef\u5dee\u7684\u5f71\u54cd\u8d8a\u5927\uff0c\u7b97\u6cd5\u4f1a\u66f4\u5173\u6ce8\u8fd9\u4e9b\u6837\u672c\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle 1 &#8211; h_t(x_i, y_i)\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5982\u679c\u5f31\u5206\u7c7b\u5668 \\(h_t\\) \u5bf9\u7b2c \\(i\\) \u4e2a\u6837\u672c\u5206\u7c7b\u6b63\u786e\uff0c\u8fd9\u4e00\u9879\u4e3a0\uff1b\u5982\u679c\u5206\u7c7b\u9519\u8bef\uff0c\u8fd9\u4e00\u9879\u4e3a1\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u8861\u91cf\u5206\u7c7b\u5668\u5728\u6b63\u786e\u5206\u7c7b\u65f6\u7684\u8868\u73b0\u3002\u5982\u679c\u5206\u7c7b\u6b63\u786e\uff0c\u5219\u4e0d\u589e\u52a0\u8bef\u5dee\uff1b\u5982\u679c\u5206\u7c7b\u9519\u8bef\uff0c\u5219\u589e\u52a0\u8bef\u5dee\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle \\sum_{y \\neq y_i} q_t(i, y) h_t(x_i, y)\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5bf9\u6240\u6709\u975e\u771f\u5b9e\u6807\u7b7e \\(y \\neq y_i\\) \u7684\u8bef\u5dee\u8fdb\u884c\u52a0\u6743\u6c42\u548c\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u8861\u91cf\u5206\u7c7b\u5668\u5728\u9519\u8bef\u5206\u7c7b\u65f6\u7684\u7f6e\u4fe1\u5ea6\u3002\u5982\u679c\u5206\u7c7b\u5668\u8ba4\u4e3a\u9519\u8bef\u6807\u7b7e \\(y\\) \u662f\u6b63\u786e\u7684\uff0c\u5e76\u4e14\u7f6e\u4fe1\u5ea6\u9ad8\uff0c\u5219\u8fd9\u4e00\u9879\u4f1a\u589e\u52a0\u603b\u8bef\u5dee\u3002\\(q_t(i, y)\\) \u662f\u6807\u7b7e \\(y\\) \u7684\u6743\u91cd\uff0c\u8868\u793a\u4e0d\u540c\u9519\u8bef\u6807\u7b7e\u7684\u91cd\u8981\u6027\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"7\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle q_t(i, y)\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u6807\u7b7e\u6743\u91cd\u5206\u5e03\uff0c\u9488\u5bf9\u7b2c \\(i\\) \u4e2a\u6837\u672c\u5bf9\u6240\u6709\u975e\u771f\u5b9e\u6807\u7b7e \\(y \\neq y_i\\) \u7684\u6743\u91cd\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u5f3a\u8c03\u5728\u533a\u5206\u771f\u5b9e\u6807\u7b7e\u548c\u4e0d\u540c\u9519\u8bef\u6807\u7b7e\u65f6\u7684\u96be\u5ea6\u3002\u5982\u679c\u67d0\u4e2a\u9519\u8bef\u6807\u7b7e\u5bb9\u6613\u88ab\u6df7\u6dc6\uff0c\u8be5\u6807\u7b7e\u7684\u6743\u91cd\u4f1a\u66f4\u9ad8\uff0c\u4ece\u800c\u5728\u8ba1\u7b97\u8bef\u5dee\u65f6\u66f4\u7a81\u51fa\u5176\u5f71\u54cd\u3002<br><\/li>\n<\/ul>\n\n\n<ol class=\"wp-block-list\" start=\"8\">\n    <li>\n        <p class=\"has-text-align-center\">\\(\\displaystyle h_t(x_i, y)\\)<\/p>\n        <\/li>\n<\/ol>\n\n\n<ul class=\"wp-block-list\">\n    <li><strong>\u4f5c\u7528<\/strong>\uff1a\u5f31\u5206\u7c7b\u5668 \\(h_t\\) \u5bf9\u6837\u672c \\(x_i\\) \u9884\u6d4b\u6807\u7b7e \\(y\\) \u7684\u8f93\u51fa\u3002<\/li>\n    <li><strong>\u610f\u4e49<\/strong>\uff1a\u5982\u679c\u5206\u7c7b\u5668\u8ba4\u4e3a\u6807\u7b7e \\(y\\) \u662f\u6b63\u786e\u7684\uff0c\u8f93\u51fa\u8f83\u9ad8\uff1b\u5426\u5219\u8f93\u51fa\u8f83\u4f4e\u3002\u8fd9\u4e00\u9879\u5728\u8ba1\u7b97\u9519\u8bef\u6807\u7b7e\u7684\u7f6e\u4fe1\u5ea6\u65f6\u8d77\u4f5c\u7528\u3002<br><\/li>\n<\/ul>\n\n\n<p>\u901a\u8fc7\u4ee5\u4e0a\u6bcf\u4e00\u9879\u7684\u89e3\u91ca\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u516c\u5f0f\u6574\u4f53\u4e0a\u662f\u5982\u4f55\u7efc\u5408\u8003\u8651\u5206\u7c7b\u5668\u5728\u6b63\u786e\u5206\u7c7b\u548c\u9519\u8bef\u5206\u7c7b\u65f6\u7684\u8868\u73b0\uff0c\u901a\u8fc7\u6837\u672c\u6743\u91cd \\(D_t(i)\\) \u548c\u6807\u7b7e\u6743\u91cd \\(q_t(i, y)\\) \u52a8\u6001\u8c03\u6574\u5206\u7c7b\u5668\u7684\u5173\u6ce8\u70b9\uff0c\u4ece\u800c\u5728\u6bcf\u4e00\u8f6e\u8fed\u4ee3\u4e2d\u9010\u6b65\u4f18\u5316\u5206\u7c7b\u5668\u7684\u6574\u4f53\u6027\u80fd\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u8f93\u51fa\u51fd\u6570\u7684\u89e3\u91ca<\/h3>\n\n\n<p>\u5728AdaBoost.M2\u7b97\u6cd5\u4e2d\uff0c\u6700\u7ec8\u8f93\u51fa\u7684\u5206\u7c7b\u5668\u662f\u901a\u8fc7\u7efc\u5408\u6240\u6709\u5f31\u5206\u7c7b\u5668\u7684\u8f93\u51fa\u5f97\u5230\u7684\u3002\u5177\u4f53\u5f62\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle h_f(x) = \\arg \\max_{y \\in Y} \\sum_{t=1}^T \\left( \\log \\frac{1}{\\beta_t} \\right) h_t(x, y)\\)<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\\(h_f(x)\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<p>\u8fd9\u662f\u6700\u7ec8\u7684\u7ec4\u5408\u5206\u7c7b\u5668\uff0c\u7528\u4e8e\u5bf9\u8f93\u5165 \\(x\\) \u8fdb\u884c\u5206\u7c7b\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li><strong>\\(\\arg \\max_{y \\in Y}\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<p>\u8868\u793a\u5728\u6240\u6709\u7c7b\u522b \\(y \\in Y\\) \u4e2d\u627e\u5230\u4f7f\u5f97\u540e\u9762\u8868\u8fbe\u5f0f\u6700\u5927\u7684\u7c7b\u522b\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6700\u7ec8\u7684\u5206\u7c7b\u7ed3\u679c\u662f\u4f7f\u5f97\u540e\u9762\u52a0\u6743\u548c\u6700\u5927\u7684\u7c7b\u522b\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li><strong>\\(\\sum_{t=1}^T\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<p>\u8868\u793a\u5bf9\u6240\u6709 \\(T\\) \u4e2a\u5f31\u5206\u7c7b\u5668\u7684\u52a0\u6743\u548c\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li><strong>\\(\\left( \\log \\frac{1}{\\beta_t} \\right)\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<p>\u8fd9\u662f\u5bf9\u6bcf\u4e2a\u5f31\u5206\u7c7b\u5668\u7684\u6743\u91cd\uff0c\\(\\beta_t = \\frac{\\epsilon_t}{1 &#8211; \\epsilon_t}\\)\uff0c\u5176\u4e2d \\(\\epsilon_t\\) \u662f\u7b2c \\(t\\) \u4e2a\u5f31\u5206\u7c7b\u5668\u7684\u4f2a\u635f\u5931\u3002\u901a\u8fc7\u53d6\u5bf9\u6570\u5e76\u53d6\u5012\u6570\uff0c\u589e\u52a0\u4e86\u5f31\u5206\u7c7b\u5668\u5728\u6700\u7ec8\u5206\u7c7b\u5668\u4e2d\u7684\u6743\u91cd\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n    <li><strong>\\(h_t(x, y)\\)<\/strong>:<\/li>\n<\/ol>\n\n\n<p>\u8fd9\u662f\u7b2c \\(t\\) \u4e2a\u5f31\u5206\u7c7b\u5668\u5728\u8f93\u5165 \\(x\\) \u4e0a\u5bf9\u7c7b\u522b \\(y\\) \u7684\u9884\u6d4b\uff0c\\(h_t : X \\times Y \\rightarrow [0,1]\\)\u3002\u8868\u793a\u8f93\u5165 \\(x\\) \u88ab\u5206\u7c7b\u4e3a \\(y\\) \u7684\u6982\u7387\u3002<\/p>\n\n\n<p>\u603b\u7ed3\uff1a<\/p>\n\n\n<p>\u6700\u7ec8\u7684\u8f93\u51fa\u5206\u7c7b\u5668 \\(h_f(x)\\) \u901a\u8fc7\u52a0\u6743\u6c42\u548c\u6240\u6709\u5f31\u5206\u7c7b\u5668 \\(h_t\\) \u5bf9\u8f93\u5165 \\(x\\) \u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u5e76\u9009\u62e9\u4f7f\u52a0\u6743\u548c\u6700\u5927\u7684\u7c7b\u522b\u4f5c\u4e3a\u6700\u7ec8\u7684\u5206\u7c7b\u7ed3\u679c\u3002\u6743\u91cd \\(\\left( \\log \\frac{1}{\\beta_t} \\right)\\) \u53cd\u6620\u4e86\u6bcf\u4e2a\u5f31\u5206\u7c7b\u5668\u7684\u51c6\u786e\u6027\uff0c\u51c6\u786e\u6027\u8d8a\u9ad8\u7684\u5f31\u5206\u7c7b\u5668\u5728\u6700\u7ec8\u7ed3\u679c\u4e2d\u5360\u7684\u6bd4\u91cd\u8d8a\u5927\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0cAdaBoost.M2 \u80fd\u591f\u6709\u6548\u5730\u63d0\u5347\u5206\u7c7b\u6027\u80fd\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u6743\u91cd\u66f4\u65b0\u5f0f\u7684\u89e3\u91ca<\/h3>\n\n\n<p>\u8fd9\u4e2a\u6743\u91cd\u66f4\u65b0\u516c\u5f0f\u5728Adaboost.M2\u7b97\u6cd5\u4e2d\u7528\u4e8e\u66f4\u65b0\u6bcf\u4e00\u8f6e\u8fed\u4ee3\u540e\u7684\u6837\u672c\u6743\u91cd\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle w_{i,y}^{t+1} = w_{i,y}^t \\beta_t^{(1\/2)(1 + h_t(x_i, y_i) &#8211; h_t(x_i, y))} \\)<\/p>\n\n\n<p>\u516c\u5f0f\u4e2d\u6bcf\u4e00\u9879\u7684\u4f5c\u7528\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li>\\( w_{i,y}^{t+1} \\)\uff1a<\/li>\n<\/ol>\n\n\n<p><strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u7b2c (t+1) \u8f6e\u4e2d\u6837\u672c\\(x_i\\) \u7684\u6807\u7b7e y \u7684\u6743\u91cd\u3002<\/p>\n\n\n<p> <strong>\u610f\u4e49<\/strong>\uff1a\u8fd9\u662f\u6211\u4eec\u66f4\u65b0\u540e\u7684\u6743\u91cd\uff0c\u7528\u4e8e\u4e0b\u4e00\u8f6e\u8fed\u4ee3\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li>\\(w_{i,y}^t\\)\uff1a<\/li>\n<\/ol>\n\n\n<p><strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u7b2c (t) \u8f6e\u4e2d\u6837\u672c\\(x_i\\)\u7684\u6807\u7b7e y\u7684\u6743\u91cd\u3002<\/p>\n\n\n<p><strong>\u610f\u4e49<\/strong>\uff1a\u8fd9\u662f\u5f53\u524d\u8f6e\u6b21\u7684\u6743\u91cd\uff0c\u65b0\u7684\u6743\u91cd\u662f\u57fa\u4e8e\u5f53\u524d\u6743\u91cd\u8fdb\u884c\u8c03\u6574\u7684\u57fa\u7840\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li>\\(\\beta_t\\)\uff1a<\/li>\n<\/ol>\n\n\n<p><strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u7528\u4e8e\u8c03\u6574\u6743\u91cd\u7684\u7cfb\u6570\uff0c\u901a\u5e38\u57fa\u4e8e\u5f53\u524d\u8f6e\u6b21\u5f31\u5206\u7c7b\u5668\u7684\u8bef\u5dee\\(\\epsilon_t\\)\u8ba1\u7b97\u5f97\u51fa\u3002<\/p>\n\n\n<p><strong>\u610f\u4e49<\/strong>\uff1a\u5b83\u51b3\u5b9a\u4e86\u6743\u91cd\u8c03\u6574\u7684\u5e45\u5ea6\u3002\u901a\u5e38\uff0c\\(\\beta_t\\)\u7684\u503c\u662f \\(\\beta_t = \\frac{\\epsilon_t}{1 &#8211; \\epsilon_t}\\)\u3002\u5206\u7c7b\u5668\u8868\u73b0\u8d8a\u597d\uff08\u8bef\u5dee\u8d8a\u5c0f\uff09\uff0c\\(\\beta_t\\)\u8d8a\u5c0f\uff0c\u53cd\u4e4b\uff0c\u5206\u7c7b\u5668\u8868\u73b0\u8d8a\u5dee\uff0c\\(\\beta_t\\)\u8d8a\u5927\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li>\\((1\/2)(1 + h_t(x_i, y_i) &#8211; h_t(x_i, y)) \\)\uff1a<\/li>\n<\/ol>\n\n\n<p><strong>\u4f5c\u7528<\/strong>\uff1a\u8c03\u6574\u6743\u91cd\u7684\u56e0\u5b50\uff0c\u6839\u636e\u5206\u7c7b\u5668\u5728\u771f\u5b9e\u6807\u7b7e\u548c\u9519\u8bef\u6807\u7b7e\u4e0a\u7684\u8f93\u51fa\u8fdb\u884c\u8c03\u6574\u3002<\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li>\\(h_t(x_i, y_i)\\)\u662f\u5f31\u5206\u7c7b\u5668\u5bf9\u6837\u672c\\(x_i\\)\u7684\u771f\u5b9e\u6807\u7b7e\\(y_i\\)\u7684\u8f93\u51fa\u53ef\u80fd\u6027\u3002<br><ul>\n            <li>\\(h_t(x_i, y)\\)\u662f\u5f31\u5206\u7c7b\u5668\u5bf9\u6837\u672c \\(x_i\\)\u7684\u6807\u7b7e y\u7684\u8f93\u51fa\u53ef\u80fd\u6027\u3002<\/li>\n        <\/ul><\/li>\n<\/ul>\n\n\n<p><strong>\u610f\u4e49<\/strong>\uff1a<\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u5982\u679c\\(y = y_i\\)\uff0c\u5219 \\(h_t(x_i, y_i) &#8211; h_t(x_i, y_i) = 0\\)\uff0c\u6240\u4ee5\u8c03\u6574\u56e0\u5b50\u4e3a\\((1\/2)(1 + 0) = 1\/2\\)\uff0c\u8868\u793a\u6743\u91cd\u7f29\u5c0f\u4e00\u534a\u3002<br><ul>\n            <li>\u5982\u679c\\(y \\neq y_i\\)\uff0c\u5219\\(h_t(x_i, y_i) &#8211; h_t(x_i, y)\\) \u53cd\u6620\u4e86\u5206\u7c7b\u5668\u533a\u5206\u771f\u5b9e\u6807\u7b7e\u548c\u9519\u8bef\u6807\u7b7e\u7684\u80fd\u529b\uff1a<\/li>\n            <li>\u82e5\\(h_t(x_i, y_i)\\)\u8f83\u5927\u800c \\(h_t(x_i, y)\\)\u8f83\u5c0f\uff0c\u5219\\(1 + h_t(x_i, y_i) &#8211; h_t(x_i, y)\\) \u63a5\u8fd12\uff0c\u8c03\u6574\u56e0\u5b50\u8f83\u5927\uff0c\u6743\u91cd\u53d8\u5316\u663e\u8457\u3002<\/li>\n            <li>\u53cd\u4e4b\uff0c\u82e5\u5206\u7c7b\u5668\u5728\u9519\u8bef\u6807\u7b7e\u4e0a\u7684\u8f93\u51fa\u8f83\u5927\uff0c\u5219\u8c03\u6574\u56e0\u5b50\u8f83\u5c0f\uff0c\u6743\u91cd\u53d8\u5316\u8f83\u5c0f\u3002<br><\/li>\n        <\/ul><\/li>\n<\/ul>\n\n\n<p>\u603b\u4f53\u89e3\u91ca\uff1a<\/p>\n\n\n<p>\u8be5\u516c\u5f0f\u63cf\u8ff0\u4e86\u5982\u4f55\u5728\u6bcf\u4e00\u8f6e\u8fed\u4ee3\u4e2d\u6839\u636e\u5f31\u5206\u7c7b\u5668\u7684\u8f93\u51fa\u548c\u5f53\u524d\u6837\u672c\u6743\u91cd\u6765\u66f4\u65b0\u6837\u672c\u7684\u6807\u7b7e\u6743\u91cd\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u901a\u8fc7\u7f29\u653e\u56e0\u5b50 (beta_t) \u6765\u8c03\u6574\u6743\u91cd\uff0c\u540c\u65f6\u8003\u8651\u4e86\u5206\u7c7b\u5668\u5728\u771f\u5b9e\u6807\u7b7e\u548c\u9519\u8bef\u6807\u7b7e\u4e0a\u7684\u8f93\u51fa\u53ef\u80fd\u6027\uff0c\u786e\u4fdd\u5206\u7c7b\u5668\u5728\u4e0b\u4e00\u8f6e\u4e2d\u66f4\u5173\u6ce8\u90a3\u4e9b\u5f53\u524d\u5206\u7c7b\u9519\u8bef\u7684\u6837\u672c\uff0c\u4ece\u800c\u9010\u6b65\u63d0\u9ad8\u6574\u4f53\u5206\u7c7b\u6027\u80fd\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3<\/h3>\n\n\n<p>AdaBoost.M2\u7b97\u6cd5\u53ef\u9002\u7528\u4e8e\u591a\u5206\u7c7b\u95ee\u9898\uff0c\u5b83\u5e76\u4e0d\u76f4\u63a5\u8f93\u51fa\u6240\u5c5e\u7684\u7c7b\u522b\u7684\u6807\u7b7e\uff0c\u800c\u662f\u8f93\u51fa\u4e00\u4e2a\u5728[0, 1]\u8303\u56f4\u4e4b\u5185\u7684\u6570\u503c\uff0c\u4ee5\u6b64\u6765\u8868\u793a\u6b64\u6837\u672c\u4e3a\u67d0\u4e00\u7c7b\u522b\u7684\u53ef\u80fd\u6027\uff0c\u6b64\u6570\u503c\u8d8a\u5927\uff0c\u5219\u5c5e\u4e8e\u8be5\u7c7b\u522b\u7684\u53ef\u80fd\u6027\u8d8a\u5927\u3002\u8fd9\u4e2a\u53ef\u80fd\u6027\u6570\u503c\u662f\u6bcf\u4e2aweakLearner\u7684\u8f93\u51fa\uff0c\u5728\u5c06\u6240\u6709\u7684weakLearner\u7684\u8f93\u51fa\u7efc\u5408\u8d77\u6765\u65f6\uff0c\u5e76\u4e0d\u662f\u7b80\u5355\u7684\u7efc\u5408\uff0c\u800c\u662f\u4f7f\u7528\u4e86\u8f93\u51fa\u51fd\u6570\u3002\u5728\u8f93\u51fa\u51fd\u6570\u4e2d\u4f7f\u7528\u4e86\u4e00\u4e2a\u6743\u91cd\\(\\beta_t = \\frac{\\epsilon_t}{1 &#8211; \\epsilon_t}\\)\uff0c\u5176\u4e2d\\(\\epsilon_t\\)\u4e3a\u635f\u5931\u51fd\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\\(\\epsilon_t\\)\u8d8a\u5927\uff0c\\(\\beta_t\r\n\\)\u4e5f\u5c31\u8d8a\u5927\u3002\u5728\u8ba1\u7b97\\(\\epsilon_t\\)\u65f6\uff0c\u7528\u5230\u4e86\u7c7b\u522b\u6743\u91cd\\(q_t(i,y)\\)\u548c\u6837\u672c\u6743\u91cd\\(D_t(i)\\)\uff0c\u8fd9\u4e24\u4e2a\u6743\u91cd\u53c8\u4f1a\u7528\u5230\u6837\u672c\u4e0e\u7c7b\u522b\u7684\u8054\u5408\u6743\u91cd\\(w^t_{i,y}\\)\uff0c\\(w^t_{i,y}\\)\u53c8\u4f1a\u5728\u6bcf\u4e00\u6b21\u8fed\u4ee3\u65f6\u8fdb\u884c\u66f4\u65b0\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">4. AdaBoost.R \u7b97\u6cd5<\/h2>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"1476\" height=\"1712\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x.png\" class=\"wp-image-322\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x.png 1476w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x-259x300.png 259w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x-883x1024.png 883w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x-768x891.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x-1324x1536.png 1324w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.35.15@2x-624x724.png 624w\" sizes=\"auto, (max-width: 1476px) 100vw, 1476px\" \/><\/figure><\/div>\n\n\n<p>AdaBoost.R \u7b97\u6cd5\u662f AdaBoost \u7b97\u6cd5\u7684\u4e00\u79cd\u6269\u5c55\uff0c\u7528\u4e8e\u89e3\u51b3\u56de\u5f52\u95ee\u9898\uff0c\u5176\u6807\u7b7e\u7a7a\u95f4\u4e3a \\(Y = [0,1]\\)\u3002 \u8be5\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u56de\u5f52\u95ee\u9898\u8f6c\u5316\u4e3a\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\uff0c\u5e76\u5229\u7528 AdaBoost \u7b97\u6cd5\u6765\u63d0\u5347\u5f31\u56de\u5f52\u7b97\u6cd5\u7684\u6027\u80fd\u3002<\/p>\n\n\n<p>\u7b97\u6cd5\u89e3\u91ca\uff1a<\/p>\n\n\n<p>\u8f93\u5165\uff1a<\/p>\n\n\n<p>\\(N\\) \u4e2a\u5e26\u6807\u7b7e\u7684\u6837\u672c \\(((x_1, y_1), &#8230;, (x_N, y_N))\\)\uff0c\u5176\u4e2d\u6807\u7b7e \\(y_i \\in Y = [0, 1]\\)\u3002<\/p>\n\n\n<p>\u6837\u672c\u5206\u5e03 \\(D\\)\u3002<\/p>\n\n\n<p>\u5f31\u5b66\u4e60\u7b97\u6cd5 WeakLearn\u3002<\/p>\n\n\n<p>\u8fed\u4ee3\u6b21\u6570 \\(T\\)\u3002<\/p>\n\n\n<p>\u521d\u59cb\u5316\uff1a \u4e3a\u6bcf\u4e2a\u6837\u672c \\(x_i\\) \u548c\u6bcf\u4e2a\u6807\u7b7e\u503c \\(y \\in Y\\)\uff0c\u521d\u59cb\u5316\u6743\u91cd\u4e3a\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\nw_{i,y}^1 = \\frac{D(i)|y-y_i|}{Z}\r\n\\)<\/p>\n\n\n<p>\u5176\u4e2d \\(Z\\) \u662f\u4e00\u4e2a\u5f52\u4e00\u5316\u5e38\u6570\uff0c\u7528\u4e8e\u786e\u4fdd\u6743\u91cd\u4e4b\u548c\u4e3a 1\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\nZ = \\sum_{i=1}^N D(i) \\int_0^1 |y &#8211; y_i| dy.\r\n\\)<\/p>\n\n\n<p>\u8fed\u4ee3\uff1a \u7b97\u6cd5\u8fdb\u884c \\(T\\) \u8f6e\u8fed\u4ee3\uff0c\u6bcf\u8f6e\u8fed\u4ee3\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n\n\n<p>a. \u8ba1\u7b97\u5bc6\u5ea6\u51fd\u6570: \u6839\u636e\u5f53\u524d\u6743\u91cd \\(w^t\\) \u8ba1\u7b97\u5bc6\u5ea6\u51fd\u6570 \\(p^t\\)\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\np^t = \\frac{w^t}{\\sum_{i=1}^N \\int_0^1 w_{i,y}^t dy}\r\n\\)<\/p>\n\n\n<p>b. \u8c03\u7528\u5f31\u5b66\u4e60\u5668: \u4f7f\u7528\u5bc6\u5ea6\u51fd\u6570 \\(p^t\\) \u8c03\u7528 WeakLearn\uff0c\u5f97\u5230\u4e00\u4e2a\u5f31\u5047\u8bbe \\(h_t: X \\to Y\\)\u3002<\/p>\n\n\n<p>c. \u8ba1\u7b97\u635f\u5931: \u8ba1\u7b97\u5f31\u5047\u8bbe \\(h_t\\) \u7684\u635f\u5931 \\(\\epsilon_t\\)\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\n\\epsilon_t = \\sum_{i=1}^N \\left| \\int_{y_i}^{h_t(x_i)} p_{i,y}^t dy \\right|\r\n\\)<\/p>\n\n\n<p>\u5982\u679c \\(\\epsilon_t > 1\/2\\)\uff0c\u5219\u8bbe\u7f6e \\(T = t-1\\) \u5e76\u505c\u6b62\u8fed\u4ee3\u3002<\/p>\n\n\n<p>d. \u8ba1\u7b97\u66f4\u65b0\u53c2\u6570: \u6839\u636e\u635f\u5931 \\(\\epsilon_t\\) \u8ba1\u7b97\u66f4\u65b0\u53c2\u6570 \\(\\beta_t = \\epsilon_t \/ (1 &#8211; \\epsilon_t)\\)\u3002<\/p>\n\n\n<p>e. \u66f4\u65b0\u6743\u91cd\u5411\u91cf: \u4f7f\u7528\u66f4\u65b0\u53c2\u6570 \\(\\beta_t\\) \u66f4\u65b0\u6743\u91cd\u5411\u91cf\uff1a<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"836\" height=\"122\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.27@2x.png\" class=\"wp-image-321\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.27@2x.png 836w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.27@2x-300x44.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.27@2x-768x112.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.27@2x-624x91.png 624w\" sizes=\"auto, (max-width: 836px) 100vw, 836px\" \/><\/figure><\/div>\n\n\n<p>\u8f93\u51fa\uff1a \u8fed\u4ee3\u7ed3\u675f\u540e\uff0c\u7b97\u6cd5\u8f93\u51fa\u6700\u7ec8\u5047\u8bbe\uff1a<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"844\" height=\"106\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.51@2x.png\" class=\"wp-image-318\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.51@2x.png 844w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.51@2x-300x38.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.51@2x-768x96.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-01-at-19.58.51@2x-624x78.png 624w\" sizes=\"auto, (max-width: 844px) 100vw, 844px\" \/><\/figure><\/div>\n\n\n<p>\u89e3\u91ca\uff1a<\/p>\n\n\n<p>AdaBoost.R \u7b97\u6cd5\u5c06\u6bcf\u4e2a\u6837\u672c\u548c\u6bcf\u4e2a\u53ef\u80fd\u7684\u6807\u7b7e\u503c\u7ec4\u5408\u6210\u4e00\u4e2a\u65b0\u7684\u6837\u672c\uff0c\u5e76\u901a\u8fc7\u6743\u91cd\u51fd\u6570\u5c06\u56de\u5f52\u95ee\u9898\u8f6c\u5316\u4e3a\u4e8c\u5143\u5206\u7c7b\u95ee\u9898\u3002 \u7b97\u6cd5\u8fed\u4ee3\u5730\u8bad\u7ec3\u5f31\u5b66\u4e60\u5668\uff0c\u5e76\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u6027\u80fd\u8c03\u6574\u6837\u672c\u6743\u91cd\uff0c\u4f7f\u5f97\u96be\u4ee5\u9884\u6d4b\u7684\u6837\u672c\u5f97\u5230\u66f4\u591a\u5173\u6ce8\u3002\u6700\u7ec8\u5047\u8bbe\u662f\u6240\u6709\u5f31\u5047\u8bbe\u7684\u52a0\u6743\u4e2d\u4f4d\u6570\uff0c\u5176\u4e2d\u6743\u91cd\u7531\u6bcf\u4e2a\u5f31\u5047\u8bbe\u7684\u635f\u5931\u51b3\u5b9a\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">y \u662f\u8fde\u7eed\u7684\uff0c\u90a3\u4e48\\(w_{i, y}\\)\u4f1a\u6709\u65e0\u7a77\u591a\u4e2a\uff1f<\/h3>\n\n\n<p>\u5728 AdaBoost.R \u4e2d\uff0c\u56e0\u4e3a \\(y\\) \u662f\u8fde\u7eed\u7684\uff0c\u6240\u4ee5 \\(w_{i, y}\\) \u786e\u5b9e\u4f1a\u6709\u65e0\u7a77\u591a\u4e2a\u3002<\/p>\n\n\n<p>\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\\(w_{i, y}\\) \u662f\u4e00\u4e2a\u5173\u4e8e \\(y\\) \u7684\u51fd\u6570\uff0c\u5b83\u7684\u503c\u8868\u793a\u5b9e\u4f8b \\(i\\) \u5728 \\(y\\) \u5904\u88ab\u5f31\u5b66\u4e60\u5668\u9009\u4e2d\u7684\u6982\u7387\uff0c\u5b83\u88ab\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\nw_{i, y}^1=\\frac{D(i)\\left|y-y_i\\right|}{Z}\r\n\\)<\/p>\n\n\n<p>\u5176\u4e2d\uff0c\\(D(i)\\) \u662f\u5b9e\u4f8b \\(i\\) \u5728\u8bad\u7ec3\u96c6\u4e2d\u7684\u6743\u91cd\uff0c\\(Z\\) \u662f\u4e00\u4e2a\u5f52\u4e00\u5316\u5e38\u6570\uff0c\u4f7f\u5f97\u6240\u6709 \\(w_{i, y}\\) \u7684\u79ef\u5206\u7b49\u4e8e 1\u3002<\/p>\n\n\n<p>\u7531\u4e8e \\(y\\) \u662f\u8fde\u7eed\u7684\uff0c\u6240\u4ee5 \\(w_{i, y}\\) \u7684\u503c\u5728 \\(y\\) \u4e0a\u662f\u8fde\u7eed\u53d8\u5316\u7684\uff0c\u800c\u4e0d\u662f\u79bb\u6563\u7684\u3002 \u4e3a\u4e86\u5728\u5b9e\u8df5\u4e2d\u4f7f\u7528 AdaBoost.R\uff0c\u901a\u5e38\u4f1a\u5c06 \\(y\\) \u8fdb\u884c\u79bb\u6563\u5316\uff0c\u4f8b\u5982\u5c06 \\(y\\) \u5212\u5206\u6210 \\(k\\) \u4e2a\u7b49\u95f4\u9694\u7684\u5b50\u533a\u95f4\u3002 \u8fd9\u6837\u4e00\u6765\uff0c\\(w_{i, y}\\) \u5c31\u53d8\u6210\u4e86 \\(k\\) \u4e2a\u79bb\u6563\u7684\u6743\u91cd\uff0c\u6bcf\u4e2a\u6743\u91cd\u8868\u793a\u5b9e\u4f8b \\(i\\) \u5c5e\u4e8e\u76f8\u5e94\u5b50\u533a\u95f4\u7684\u6982\u7387\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u4e0b\u9762\u516c\u5f0f\u4e2d\u7684\\(\\mathbf{w}\\)\u662f\u4ec0\u4e48<\/h3>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"988\" height=\"224\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.21.46@2x.png\" class=\"wp-image-323\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.21.46@2x.png 988w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.21.46@2x-300x68.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.21.46@2x-768x174.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.21.46@2x-624x141.png 624w\" sizes=\"auto, (max-width: 988px) 100vw, 988px\" \/><\/figure><\/div>\n\n\n<p>\u8fd9\u4e2a\u5f0f\u5b50\u4e2d \\(\\mathbf{w}^t\\) \u7684\u8868\u793a\u65b9\u6cd5\u53ef\u80fd\u9020\u6210\u4e86\u4e00\u4e9b\u56f0\u60d1\u3002\u5b9e\u9645\u4e0a\uff0c\u5728\u8fd9\u4e2a\u7b97\u6cd5\u4e2d\uff0c\u5e76\u6ca1\u6709\u4e00\u4e2a\u76f4\u63a5\u53eb\u505a \\(\\mathbf{w}^t\\) \u7684\u5411\u91cf\u3002\u66f4\u786e\u5207\u5730\u8bf4\uff0c\u5728\u6bcf\u4e00\u8f6e \\(t\\)\uff0c\u7b97\u6cd5\u7ef4\u62a4\u7684\u662f\u4e00\u4e2a \u6743\u91cd\u51fd\u6570 \\(w^t_{i,y}\\)\uff0c\u5b83\u5b9a\u4e49\u5728\u6bcf\u4e2a\u5b9e\u4f8b \\(i\\) \u548c\u6bcf\u4e2a\u53ef\u80fd\u7684\u6807\u7b7e\u503c \\(y \\in [0,1]\\) \u4e0a\u3002<\/p>\n\n\n<p>\u56e0\u6b64\uff0c\u4e0e\u5176\u8bf4 \\(\\mathbf{w}^t\\) \u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u4e0d\u5982\u8bf4\u5b83\u4ee3\u8868\u4e86\u6240\u6709 \\(w^t_{i,y}\\) \u7684\u96c6\u5408\u3002<\/p>\n\n\n<p>\u5728\u60a8\u5f15\u7528\u7684\u6b65\u9aa4 1 \u4e2d\uff0c\u7b97\u6cd5\u8ba1\u7b97\u7684\u662f\u4e00\u4e2a \u6982\u7387\u5bc6\u5ea6\u51fd\u6570 \\(\\mathbf{p}^t\\)\uff0c\u5b83\u4e5f\u662f\u5b9a\u4e49\u5728\u6bcf\u4e2a\u5b9e\u4f8b \\(i\\) \u548c\u6bcf\u4e2a\u53ef\u80fd\u7684\u6807\u7b7e\u503c \\(y \\in [0,1]\\) \u4e0a\u3002\u8fd9\u4e2a\u5bc6\u5ea6\u51fd\u6570\u662f\u901a\u8fc7\u5bf9 \\(w^t_{i,y}\\) \u8fdb\u884c\u5f52\u4e00\u5316\u5f97\u5230\u7684\uff0c\u4e5f\u5c31\u662f\u9664\u4ee5\u6240\u6709 \\(w^t_{i,y}\\) \u7684\u79ef\u5206\uff1a<\/p>\n\n\n<p class=\"has-text-align-center\">\\(\\displaystyle \r\n\\mathbf{p}^t=\\frac{\\mathbf{w}^t}{\\sum_{i=1}^N \\int_0^1 w_{i, y}^t d y} .\r\n\\)<\/p>\n\n\n<p>\u6240\u4ee5\uff0c\u8fd9\u91cc\u7684 \\(\\mathbf{w}^t\\) \u5b9e\u9645\u4e0a\u4ee3\u8868\u4e86\u6240\u6709 \\(w^t_{i,y}\\) \u7684\u96c6\u5408\uff0c\u800c\u4e0d\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u5411\u91cf\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5982\u4f55\u89e3\u91ca\u8f93\u51fa\u51fd\u6570<\/h3>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"832\" height=\"124\" src=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.49.57@2x.png\" class=\"wp-image-320\" srcset=\"https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.49.57@2x.png 832w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.49.57@2x-300x45.png 300w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.49.57@2x-768x114.png 768w, https:\/\/www.xuzhe.tj.cn\/wp-content\/uploads\/2024\/08\/CleanShot-2024-08-02-at-11.49.57@2x-624x93.png 624w\" sizes=\"auto, (max-width: 832px) 100vw, 832px\" \/><\/figure><\/div>\n\n\n<p>\u6b64\u51fd\u6570\u662f AdaBoost.R \u7b97\u6cd5\u4e2d\u6700\u7ec8\u7684\u9884\u6d4b\u51fd\u6570 \\(h_f(x)\\)\uff0c\u5b83\u7528\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u5373\u9884\u6d4b\u4e00\u4e2a\u8fde\u7eed\u7684\u6807\u7b7e\u503c\u3002<\/p>\n\n\n<p>\u8ba9\u6211\u4eec\u9010\u6b65\u89e3\u91ca\u8fd9\u4e2a\u51fd\u6570\u7684\u542b\u4e49\uff1a<\/p>\n\n\n<p>\u5f31\u5b66\u4e60\u5668\u9884\u6d4b: \\(h_t(x)\\) \u4ee3\u8868\u7b2c \\(t\\) \u4e2a\u5f31\u5b66\u4e60\u5668\u5728\u8f93\u5165 \\(x\\) \u4e0a\u7684\u9884\u6d4b\u503c\u3002<\/p>\n\n\n<p>\u6743\u91cd: \\(\\log(1\/\\beta_t)\\) \u4ee3\u8868\u7b2c \\(t\\) \u4e2a\u5f31\u5b66\u4e60\u5668\u7684\u6743\u91cd\u3002\u6ce8\u610f\u5230 \\(\\beta_t = \\epsilon_t \/ (1 &#8211; \\epsilon_t)\\)\uff0c\u5176\u4e2d \\(\\epsilon_t\\) \u662f\u7b2c \\(t\\) \u4e2a\u5f31\u5b66\u4e60\u5668\u7684\u8bef\u5dee\u3002\u56e0\u6b64\uff0c\u5f31\u5b66\u4e60\u5668\u7684\u8bef\u5dee\u8d8a\u5c0f\uff0c\u5b83\u7684\u6743\u91cd\u5c31\u8d8a\u5927\u3002<\/p>\n\n\n<p>\u7d2f\u79ef\u6743\u91cd: \\(\\sum_{t: h_t(x) \\leq y} \\log \\left(1 \/ \\beta_t\\right)\\) \u4ee3\u8868\u6240\u6709\u9884\u6d4b\u503c\u5c0f\u4e8e\u7b49\u4e8e \\(y\\) \u7684\u5f31\u5b66\u4e60\u5668\u7684\u6743\u91cd\u4e4b\u548c\u3002<\/p>\n\n\n<p>\u4e2d\u4f4d\u6570: \\(\\frac{1}{2} \\sum_t \\log \\left(1 \/ \\beta_t\\right)\\) \u4ee3\u8868\u6240\u6709\u5f31\u5b66\u4e60\u5668\u6743\u91cd\u4e4b\u548c\u7684\u4e00\u534a\u3002<\/p>\n\n\n<p>\u6700\u7ec8\u9884\u6d4b:   \u8fd9\u4e2a\u8f93\u51fa\u51fd\u6570\u7684\u610f\u601d\u662f\uff0c\u627e\u5230\u6700\u5c0f\u7684 \\(y\\) \u503c\uff0c\u4f7f\u5f97\u6240\u6709\u9884\u6d4b\u503c\u5c0f\u4e8e\u7b49\u4e8e \\(y\\) \u7684\u5f31\u5b66\u4e60\u5668\u7684\u6743\u91cd\u4e4b\u548c\u81f3\u5c11\u4e3a\u6240\u6709\u5f31\u5b66\u4e60\u5668\u6743\u91cd\u4e4b\u548c\u7684\u4e00\u534a\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c<strong>\\(h_f(x)\\) \u662f\u6240\u6709\u5f31\u5b66\u4e60\u5668\u9884\u6d4b\u503c\u7684\u4e00\u4e2a\u52a0\u6743\u4e2d\u4f4d\u6570\u3002<\/strong><\/p>\n\n\n<p>\u76f4\u89c2\u89e3\u91ca:<\/p>\n\n\n<p>AdaBoost.R \u7684\u6700\u7ec8\u9884\u6d4b\u51fd\u6570 \\(h_f(x)\\) \u901a\u8fc7\u5bf9\u6240\u6709\u5f31\u5b66\u4e60\u5668\u7684\u9884\u6d4b\u503c\u8fdb\u884c\u52a0\u6743\u6295\u7968\u6765\u5f97\u5230\u6700\u7ec8\u7684\u9884\u6d4b\u503c\u3002 \u6bcf\u4e2a\u5f31\u5b66\u4e60\u5668\u7684\u6295\u7968\u6743\u91cd\u7531\u5176\u51c6\u786e\u6027\u51b3\u5b9a\uff1a\u8bef\u5dee\u8d8a\u5c0f\u7684\u5f31\u5b66\u4e60\u5668\u6743\u91cd\u8d8a\u5927\u3002 \\(h_f(x)\\) \u5bfb\u627e\u4e00\u4e2a\u9884\u6d4b\u503c\uff0c\u4f7f\u5f97\u6743\u91cd\u66f4\u5927\u7684\u5f31\u5b66\u4e60\u5668 &#8220;\u652f\u6301&#8221; \u8fd9\u4e2a\u9884\u6d4b\u503c\u3002<\/p>\n\n\n<p>\u4f8b\u5b50:<\/p>\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6709\u4e09\u4e2a\u5f31\u5b66\u4e60\u5668\uff0c\u5b83\u4eec\u7684\u9884\u6d4b\u503c\u5206\u522b\u662f \\(h_1(x) = 0.2\\), \\(h_2(x) = 0.6\\), \\(h_3(x) = 0.8\\)\uff0c\u5bf9\u5e94\u7684\u6743\u91cd\u5206\u522b\u662f \\(\\log(1\/\\beta_1) = 1\\), \\(\\log(1\/\\beta_2) = 2\\), \\(\\log(1\/\\beta_3) = 3\\)\u3002 \u90a3\u4e48\u6240\u6709\u5f31\u5b66\u4e60\u5668\u6743\u91cd\u4e4b\u548c\u7684\u4e00\u534a\u662f \\((1 + 2 + 3)\/2 = 3\\)\u3002 \u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5f53 \\(y = 0.6\\) \u65f6\uff0c\u6240\u6709\u9884\u6d4b\u503c\u5c0f\u4e8e\u7b49\u4e8e \\(y\\) \u7684\u5f31\u5b66\u4e60\u5668\u7684\u6743\u91cd\u4e4b\u548c\u4e3a \\(1 + 2 = 3\\)\uff0c\u6b63\u597d\u7b49\u4e8e\u6240\u6709\u5f31\u5b66\u4e60\u5668\u6743\u91cd\u4e4b\u548c\u7684\u4e00\u534a\u3002 \u56e0\u6b64\uff0c\u6700\u7ec8\u9884\u6d4b\u503c \\(h_f(x) = 0.6\\)\u3002<\/p>\n\n\n<p>\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/www.jianguoyun.com\/p\/Da9MdtYQhs2mCRiAn9IFIAA <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u82f1\u6587\u9898\u76ee\uff1aA decision-theoretic gene&#8230;<\/p>\n","protected":false},"author":1,"featured_media":511,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[27,23],"class_list":["post-326","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-26","tag-ensemble-learning","tag-machine-learning"],"_links":{"self":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/326","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=326"}],"version-history":[{"count":9,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/326\/revisions"}],"predecessor-version":[{"id":512,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/posts\/326\/revisions\/512"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media\/511"}],"wp:attachment":[{"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/media?parent=326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/categories?post=326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.xuzhe.tj.cn\/index.php\/wp-json\/wp\/v2\/tags?post=326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}