{"id":1150,"date":"2023-07-27T12:12:52","date_gmt":"2023-07-27T12:12:52","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%81%8f%e5%b7%ae%e6%96%b9%e5%b7%ae%e6%8a%98%e8%a1%b7\/"},"modified":"2023-07-27T12:12:52","modified_gmt":"2023-07-27T12:12:52","slug":"%e5%81%8f%e5%b7%ae%e6%96%b9%e5%b7%ae%e6%8a%98%e8%a1%b7","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%81%8f%e5%b7%ae%e6%96%b9%e5%b7%ae%e6%8a%98%e8%a1%b7\/","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u504f\u5dee-\u65b9\u5dee\u6743\u8861\u662f\u4ec0\u4e48\uff1f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u8bc4\u4f30\u6a21\u578b\u5728\u6570\u636e\u96c6\u4e0a\u7684\u6027\u80fd\uff0c\u6211\u4eec\u9700\u8981\u6d4b\u91cf\u6a21\u578b\u7684\u9884\u6d4b\u4e0e\u89c2\u5bdf\u5230\u7684\u6570\u636e\u7684\u5339\u914d\u7a0b\u5ea6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5bf9\u4e8e<a href=\"https:\/\/statorials.org\/cn\/\u56de\u5f52\u4e0e\u5206\u7c7b\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u56de\u5f52\u6a21\u578b<\/a>\uff0c\u6700\u5e38\u7528\u7684\u6307\u6807\u662f\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\uff0c\u5176\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = (1\/n)*\u03a3(y <sub>i<\/sub> \u2013 f(x <sub>i<\/sub> )) <sup>2<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n\uff1a<\/strong>\u89c2\u5bdf\u603b\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>y <sub>i<\/sub> \uff1a<\/strong><sup>\u7b2c i \u4e2a<\/sup>\u89c2\u6d4b\u503c\u7684\u54cd\u5e94\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>f( <sub>xi<\/sub> ):<\/strong>\u7b2c i<sup>\u4e2a<\/sup>\u89c2\u6d4b\u503c\u7684\u9884\u6d4b\u54cd\u5e94\u503c<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6a21\u578b\u9884\u6d4b\u4e0e\u89c2\u6d4b\u503c\u8d8a\u63a5\u8fd1\uff0cMSE \u5c31\u8d8a\u4f4e\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u800c\uff0c\u6211\u4eec\u53ea\u5173\u5fc3<strong>MSE \u6d4b\u8bd5<\/strong>\u2014\u2014\u5f53\u6211\u4eec\u7684\u6a21\u578b\u5e94\u7528\u4e8e\u770b\u4e0d\u89c1\u7684\u6570\u636e\u65f6\u7684 MSE\u3002\u8fd9\u662f\u56e0\u4e3a\u6211\u4eec\u53ea\u5173\u5fc3\u6a21\u578b\u5728\u672a\u77e5\u6570\u636e\u4e0a\u7684\u8868\u73b0\uff0c\u800c\u4e0d\u662f\u5728\u73b0\u6709\u6570\u636e\u4e0a\u7684\u8868\u73b0\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5982\u679c\u9884\u6d4b\u80a1\u7968\u4ef7\u683c\u7684\u6a21\u578b\u5728\u5386\u53f2\u6570\u636e\u4e0a\u7684 MSE \u8f83\u4f4e\uff0c\u90a3\u4e5f\u6ca1\u5173\u7cfb\uff0c\u4f46\u6211\u4eec<em>\u786e\u5b9e<\/em>\u5e0c\u671b\u80fd\u591f\u4f7f\u7528\u8be5\u6a21\u578b\u6765\u51c6\u786e\u9884\u6d4b\u672a\u6765\u6570\u636e\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e8b\u5b9e\u8bc1\u660e\uff0cMSE\u6d4b\u8bd5\u4ecd\u7136\u53ef\u4ee5\u5206\u4e3a\u4e24\u90e8\u5206\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(1) \u65b9\u5dee\uff1a<\/strong>\u6307\u7684\u662f\u5982\u679c\u6211\u4eec\u4f7f\u7528\u4e0d\u540c\u7684\u8bad\u7ec3\u96c6\u6765\u4f30\u8ba1\u51fd\u6570<em>f \u7684<\/em>\u53d8\u5316\u91cf\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(2)\u504f\u5dee\uff1a<\/strong>\u6307\u7528\u7b80\u5355\u5f97\u591a\u7684\u6a21\u578b\u6765\u5904\u7406\u53ef\u80fd\u6781\u5176\u590d\u6742\u7684\u5b9e\u9645\u95ee\u9898\u800c\u5f15\u5165\u7684\u8bef\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7528\u6570\u5b66\u672f\u8bed\u5199\u6210\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE \u68c0\u9a8c = Var( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> )) + [\u504f\u5dee( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> ))] <sup>2<\/sup> + Var(\u03b5)<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE \u68c0\u9a8c = \u65b9\u5dee + \u504f\u5dee<sup>2<\/sup> + \u4e0d\u53ef\u7ea6\u8bef\u5dee<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b2c\u4e09\u9879\u662f\u4e0d\u53ef\u7ea6\u8bef\u5dee\uff0c\u662f\u4efb\u4f55\u6a21\u578b\u90fd\u65e0\u6cd5\u7ea6\u7b80\u7684\u8bef\u5dee\uff0c\u56e0\u4e3a\u89e3\u91ca\u53d8\u91cf\u96c6\u4e0e<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u54cd\u5e94\u53d8\u91cf<\/a>\u4e4b\u95f4\u7684\u5173\u7cfb\u4e2d\u59cb\u7ec8\u5b58\u5728<em>\u566a\u58f0<\/em>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5177\u6709<strong>\u9ad8\u504f\u5dee\u7684<\/strong>\u6a21\u578b\u5f80\u5f80\u5177\u6709<strong>\u4f4e\u65b9\u5dee<\/strong>\u3002\u4f8b\u5982\uff0c\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5f80\u5f80\u5177\u6709\u9ad8\u504f\u5dee\uff08\u5047\u8bbe\u89e3\u91ca\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u7b80\u5355\u7684\u7ebf\u6027\u5173\u7cfb\uff09\u548c\u4f4e\u65b9\u5dee\uff08\u6a21\u578b\u4f30\u8ba1\u503c\u5728\u6837\u672c\u4e4b\u95f4\u4e0d\u4f1a\u6709\u592a\u5927\u53d8\u5316\uff09\u3002\u53e6\u4e00\u4e2a\uff09\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u800c\uff0c<strong>\u4f4e\u504f\u5dee<\/strong>\u7684\u6a21\u578b\u5f80\u5f80\u5177\u6709<strong>\u9ad8\u65b9\u5dee<\/strong>\u3002\u4f8b\u5982\uff0c\u590d\u6742\u7684\u975e\u7ebf\u6027\u6a21\u578b\u5f80\u5f80\u5177\u6709\u4f4e\u504f\u5dee\uff08\u4e0d\u5047\u8bbe\u89e3\u91ca\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u67d0\u79cd\u5173\u7cfb\uff09\u548c\u9ad8\u65b9\u5dee\uff08\u6a21\u578b\u4f30\u8ba1\u503c\u4ece\u4e00\u4e2a\u5b66\u4e60\u6837\u672c\u5230\u53e6\u4e00\u4e2a\u5b66\u4e60\u6837\u672c\u53ef\u80fd\u4f1a\u53d1\u751f\u663e\u7740\u53d8\u5316\uff09\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u504f\u5dee\u4e0e\u65b9\u5dee\u7684\u6743\u8861<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\"><strong>\u504f\u5dee-\u65b9\u5dee\u6743\u8861<\/strong>\u662f\u6307\u5f53\u6211\u4eec\u9009\u62e9\u51cf\u5c11\u504f\u5dee\uff08\u901a\u5e38\u4f1a\u589e\u52a0\u504f\u5dee\uff09\u6216\u51cf\u5c11\u65b9\u5dee\uff08\u901a\u5e38\u4f1a\u589e\u52a0\u504f\u5dee\uff09\u65f6\u53d1\u751f\u7684\u6743\u8861\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0b\u56fe\u63d0\u4f9b\u4e86\u4e00\u79cd\u53ef\u89c6\u5316\u8fd9\u79cd\u6743\u8861\u7684\u65b9\u6cd5\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11515 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/biais_variance1.png\" alt=\"\u504f\u5dee-\u65b9\u5dee\u6743\u8861\" width=\"551\" height=\"400\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u603b\u8bef\u5dee\u968f\u7740\u6a21\u578b\u590d\u6742\u6027\u7684\u589e\u52a0\u800c\u51cf\u5c11\uff0c\u4f46\u4ec5\u9650\u4e8e\u67d0\u4e00\u70b9\u3002\u8d85\u8fc7\u67d0\u4e2a\u70b9\u540e\uff0c\u65b9\u5dee\u5f00\u59cb\u589e\u52a0\uff0c\u603b\u8bef\u5dee\u4e5f\u5f00\u59cb\u589e\u52a0\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u5b9e\u8df5\u4e2d\uff0c\u6211\u4eec\u53ea\u5173\u5fc3\u6700\u5c0f\u5316\u6a21\u578b\u7684\u603b\u8bef\u5dee\uff0c\u800c\u4e0d\u4e00\u5b9a\u6700\u5c0f\u5316\u65b9\u5dee\u6216\u504f\u5dee\u3002<\/span><span style=\"color: #000000;\">\u4e8b\u5b9e\u8bc1\u660e\uff0c\u6700\u5c0f\u5316\u603b\u8bef\u5dee\u7684\u65b9\u6cd5\u662f\u5728\u65b9\u5dee\u548c\u504f\u5dee\u4e4b\u95f4\u627e\u5230\u9002\u5f53\u7684\u5e73\u8861\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u60f3\u8981\u4e00\u4e2a\u8db3\u591f\u590d\u6742\u7684\u6a21\u578b\u6765\u6355\u83b7\u89e3\u91ca\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u7684\u771f\u5b9e\u5173\u7cfb\uff0c\u4f46\u53c8\u4e0d\u4f1a\u592a\u590d\u6742\u800c\u65e0\u6cd5\u68c0\u6d4b\u5b9e\u9645\u4e0d\u5b58\u5728\u7684\u6a21\u5f0f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u6a21\u578b\u8fc7\u4e8e\u590d\u6742\u65f6\uff0c\u5c31\u4f1a<a href=\"https:\/\/statorials.org\/cn\/\u673a\u5668\u5b66\u4e60\u8fc7\u5ea6\u62df\u5408\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>\u8fc7\u5ea6\u62df\u5408<\/strong><\/a>\u6570\u636e\u3002\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\u662f\u56e0\u4e3a\u5f88\u96be\u5728\u8bad\u7ec3\u6570\u636e\u4e2d\u627e\u5230\u7eaf\u7cb9\u7531\u5076\u7136\u5f15\u8d77\u7684\u6a21\u5f0f\u3002\u8fd9\u79cd\u7c7b\u578b\u7684\u6a21\u578b\u53ef\u80fd\u5728\u4e0d\u53ef\u89c1\u6570\u636e\u4e0a\u8868\u73b0\u4e0d\u4f73\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f46\u5f53\u6a21\u578b\u592a\u7b80\u5355\u65f6\uff0c\u5b83<strong>\u5c31\u4f1a\u4f4e\u4f30<\/strong>\u6570\u636e\u3002\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\u662f\u56e0\u4e3a\u5047\u8bbe\u89e3\u91ca\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u7684\u771f\u5b9e\u5173\u7cfb\u6bd4\u5b9e\u9645\u60c5\u51b5\u66f4\u7b80\u5355\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u9009\u62e9\u6700\u4f73\u6a21\u578b\u7684\u65b9\u6cd5\u662f\u5728\u504f\u5dee\u548c\u65b9\u5dee\u4e4b\u95f4\u627e\u5230\u5e73\u8861\uff0c\u4ee5\u6700\u5c0f\u5316\u5728\u672a\u6765\u672a\u89c1\u8fc7\u7684\u6570\u636e\u4e0a\u6d4b\u8bd5\u6a21\u578b\u7684\u8bef\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5728\u5b9e\u8df5\u4e2d\uff0c\u6700\u5c0f\u5316\u6d4b\u8bd5 MSE \u7684\u6700\u5e38\u89c1\u65b9\u6cd5\u662f\u4f7f\u7528<a href=\"https:\/\/statorials.org\/cn\/k\u6298\u4ea4\u53c9\u9a8c\u8bc1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u4ea4\u53c9\u9a8c\u8bc1<\/a>\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e3a\u4e86\u8bc4\u4f30\u6a21\u578b\u5728\u6570\u636e\u96c6\u4e0a\u7684\u6027\u80fd\uff0c\u6211\u4eec\u9700\u8981\u6d4b\u91cf\u6a21\u578b\u7684\u9884\u6d4b\u4e0e\u89c2\u5bdf\u5230\u7684\u6570\u636e\u7684\u5339\u914d\u7a0b\u5ea6\u3002 \u5bf9\u4e8e\u56de\u5f52\u6a21\u578b\uff0c\u6700\u5e38\u7528\u7684\u6307\u6807\u662f\u5747 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1150","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u504f\u5dee-\u65b9\u5dee\u6743\u8861\u662f\u4ec0\u4e48\uff1f<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u89e3\u91ca\u4e86\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u504f\u5dee-\u65b9\u5dee\u6743\u8861\uff0c\u5305\u62ec\u793a\u4f8b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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