{"id":1147,"date":"2023-07-27T12:12:52","date_gmt":"2023-07-27T12:12:52","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%83%8f%e3%82%99%e3%82%a4%e3%82%a2%e3%82%b9%e5%88%86%e6%95%a3%e3%81%ae%e5%a6%a5%e5%8d%94\/"},"modified":"2023-07-27T12:12:52","modified_gmt":"2023-07-27T12:12:52","slug":"%e3%83%8f%e3%82%99%e3%82%a4%e3%82%a2%e3%82%b9%e5%88%86%e6%95%a3%e3%81%ae%e5%a6%a5%e5%8d%94","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%83%8f%e3%82%99%e3%82%a4%e3%82%a2%e3%82%b9%e5%88%86%e6%95%a3%e3%81%ae%e5%a6%a5%e5%8d%94\/","title":{"rendered":"\u6a5f\u68b0\u5b66\u7fd2\u306b\u304a\u3051\u308b\u30d0\u30a4\u30a2\u30b9\u3068\u5206\u6563\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3068\u306f\u4f55\u3067\u3059\u304b?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u5bfe\u3059\u308b\u30e2\u30c7\u30eb\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u8a55\u4fa1\u3059\u308b\u306b\u306f\u3001\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u304c\u89b3\u5bdf\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3068\u3069\u306e\u7a0b\u5ea6\u4e00\u81f4\u3059\u308b\u304b\u3092\u6e2c\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u56de\u5e30\u3068\u5206\u985e\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u56de\u5e30\u30e2\u30c7\u30eb<\/a>\u306e\u5834\u5408\u3001\u6700\u3082\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u6307\u6a19\u306f\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee (MSE) \u3067\u3001\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/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\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong>\u89b3\u6e2c\u5024\u306e\u7dcf\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>y <sub>i<\/sub> :<\/strong> <sup>i \u756a\u76ee<\/sup>\u306e\u89b3\u6e2c\u5024\u306e\u5fdc\u7b54\u5024<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>f( <sub>xi<\/sub> ):<\/strong> i<sup>\u756a\u76ee<\/sup>\u306e\u89b3\u6e2c\u5024\u306e\u4e88\u6e2c\u5fdc\u7b54\u5024<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u304c\u89b3\u6e2c\u5024\u306b\u8fd1\u3065\u304f\u307b\u3069\u3001MSE \u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3060\u3057\u3001\u79c1\u305f\u3061\u304c\u6c17\u306b\u3059\u308b\u306e\u306f<strong>MSE \u30c6\u30b9\u30c8<\/strong>\u3001\u3064\u307e\u308a\u30e2\u30c7\u30eb\u304c\u76ee\u306b\u898b\u3048\u306a\u3044\u30c7\u30fc\u30bf\u306b\u9069\u7528\u3055\u308c\u308b\u3068\u304d\u306e MSE \u3060\u3051\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u3067\u306f\u306a\u304f\u3001\u672a\u77e5\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u30e2\u30c7\u30eb\u304c\u3069\u306e\u3088\u3046\u306b\u5b9f\u884c\u3055\u308c\u308b\u304b\u306e\u307f\u3092\u8003\u616e\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3068\u3048\u3070\u3001\u682a\u4fa1\u3092\u4e88\u6e2c\u3059\u308b\u30e2\u30c7\u30eb\u306e\u5c65\u6b74\u30c7\u30fc\u30bf\u306e MSE \u304c\u4f4e\u3044\u306e\u306f\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u304c\u3001<em>\u5b9f\u969b\u306b\u306f<\/em>\u3001\u305d\u306e\u30e2\u30c7\u30eb\u3092\u4f7f\u7528\u3057\u3066\u5c06\u6765\u306e\u30c7\u30fc\u30bf\u3092\u6b63\u78ba\u306b\u4e88\u6e2c\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u305f\u3044\u3068\u8003\u3048\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE \u30c6\u30b9\u30c8\u306f\u4f9d\u7136\u3068\u3057\u3066 2 \u3064\u306e\u90e8\u5206\u306b\u5206\u5272\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(1) \u5206\u6563:<\/strong>\u5225\u306e\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0 \u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570<em>f \u3092<\/em>\u63a8\u5b9a\u3057\u305f\u5834\u5408\u306b\u5909\u5316\u3059\u308b\u91cf\u3092\u6307\u3057\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>(2) \u30d0\u30a4\u30a2\u30b9:<\/strong>\u975e\u5e38\u306b\u8907\u96d1\u306a\u5b9f\u969b\u306e\u554f\u984c\u306b\u3001\u3088\u308a\u5358\u7d14\u306a\u30e2\u30c7\u30eb\u3092\u4f7f\u7528\u3057\u3066\u30a2\u30d7\u30ed\u30fc\u30c1\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u751f\u3058\u308b\u8aa4\u5dee\u3092\u6307\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6570\u5b66\u7528\u8a9e\u3067\u66f8\u304f\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE \u30c6\u30b9\u30c8 = Var( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> )) + [\u30d0\u30a4\u30a2\u30b9( <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 \u30c6\u30b9\u30c8 = \u5206\u6563 + \u30d0\u30a4\u30a2\u30b9<sup>2<\/sup> + \u65e2\u7d04\u8aa4\u5dee<\/span><\/p>\n<p><span style=\"color: #000000;\">3 \u756a\u76ee\u306e\u9805\u3067\u3042\u308b\u65e2\u7d04\u8aa4\u5dee\u306f\u3001\u8aac\u660e\u5909\u6570\u306e\u30bb\u30c3\u30c8\u3068<a href=\"https:\/\/statorials.org\/ja\/\u5909\u6570\u306e\u8aac\u660e\u5fdc\u7b54\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5fdc\u7b54\u5909\u6570<\/a>\u306e\u9593\u306e\u95a2\u4fc2\u306b\u5e38\u306b<em>\u30ce\u30a4\u30ba\u304c<\/em>\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\u3069\u306e\u30e2\u30c7\u30eb\u3067\u3082\u524a\u6e1b\u3067\u304d\u306a\u3044\u8aa4\u5dee\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u9ad8\u3044\u30d0\u30a4\u30a2\u30b9\u3092<\/strong>\u6301\u3064\u30e2\u30c7\u30eb\u306f\u3001<strong>\u5206\u6563\u304c\u5c0f\u3055\u3044<\/strong>\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u3001\u30d0\u30a4\u30a2\u30b9\u304c\u9ad8\u304f (\u8aac\u660e\u5909\u6570\u3068\u5fdc\u7b54\u5909\u6570\u306e\u9593\u306b\u5358\u7d14\u306a\u7dda\u5f62\u95a2\u4fc2\u304c\u3042\u308b\u3068\u4eee\u5b9a)\u3001\u5206\u6563\u304c\u4f4e\u3044 (\u30e2\u30c7\u30eb\u306e\u63a8\u5b9a\u5024\u306f\u30b5\u30f3\u30d7\u30eb\u9593\u3067\u3042\u307e\u308a\u5909\u5316\u3057\u306a\u3044) \u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u3082\u3046\u4e00\u65b9\uff09\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u305f\u3060\u3057\u3001<strong>\u30d0\u30a4\u30a2\u30b9\u304c\u4f4e\u3044<\/strong>\u30e2\u30c7\u30eb\u306f<strong>\u5206\u6563\u304c\u9ad8\u304f\u306a\u308b<\/strong>\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u8907\u96d1\u306a\u975e\u7dda\u5f62\u30e2\u30c7\u30eb\u306f\u3001\u30d0\u30a4\u30a2\u30b9\u304c\u4f4e\u304f (\u8aac\u660e\u5909\u6570\u3068\u5fdc\u7b54\u5909\u6570\u306e\u9593\u306b\u7279\u5b9a\u306e\u95a2\u4fc2\u3092\u4eee\u5b9a\u3057\u306a\u3044)\u3001\u5206\u6563\u304c\u5927\u304d\u304f\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059 (\u30e2\u30c7\u30eb\u306e\u63a8\u5b9a\u5024\u306f\u3001\u5b66\u7fd2\u306e\u30b5\u30f3\u30d7\u30eb\u304b\u3089\u5225\u306e\u30b5\u30f3\u30d7\u30eb\u306b\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059)\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u30d0\u30a4\u30a2\u30b9\u3068\u5206\u6563\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\"><strong>\u30d0\u30a4\u30a2\u30b9\u3068\u5206\u6563\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306f\u3001<\/strong>\u30d0\u30a4\u30a2\u30b9\u3092\u6e1b\u3089\u3059\u3053\u3068\u3092\u9078\u629e\u3057\u305f\u5834\u5408\uff08\u4e00\u822c\u306b\u5206\u6563\u304c\u5897\u52a0\u3059\u308b\uff09\u3001\u307e\u305f\u306f\u5206\u6563\u3092\u6e1b\u5c11\u3059\u308b\u3053\u3068\u3092\u9078\u629e\u3057\u305f\u5834\u5408\uff08\u4e00\u822c\u306b\u30d0\u30a4\u30a2\u30b9\u304c\u5897\u52a0\u3059\u308b\uff09\u306b\u767a\u751f\u3059\u308b\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3092\u6307\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b0\u30e9\u30d5\u306f\u3001\u3053\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3092\u8996\u899a\u5316\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/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=\"\u30d0\u30a4\u30a2\u30b9\u3068\u5206\u6563\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\" width=\"551\" height=\"400\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u30e2\u30c7\u30eb\u306e\u8907\u96d1\u3055\u304c\u5897\u3059\u306b\u3064\u308c\u3066\u5408\u8a08\u8aa4\u5dee\u306f\u6e1b\u5c11\u3057\u307e\u3059\u304c\u3001\u305d\u308c\u306f\u3042\u308b\u6642\u70b9\u307e\u3067\u306b\u9650\u3089\u308c\u307e\u3059\u3002\u7279\u5b9a\u306e\u70b9\u3092\u8d85\u3048\u308b\u3068\u3001\u5206\u6563\u304c\u5897\u52a0\u3057\u59cb\u3081\u3001\u5408\u8a08\u8aa4\u5dee\u3082\u5897\u52a0\u3057\u59cb\u3081\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5b9f\u969b\u306b\u306f\u3001\u30e2\u30c7\u30eb\u306e\u5408\u8a08\u8aa4\u5dee\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u306e\u307f\u3092\u8003\u616e\u3057\u3001\u5fc5\u305a\u3057\u3082\u5206\u6563\u3084\u504f\u308a\u3092\u6700\u5c0f\u5316\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span><span style=\"color: #000000;\">\u5408\u8a08\u8aa4\u5dee\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u308b\u65b9\u6cd5\u306f\u3001\u5206\u6563\u3068\u504f\u308a\u306e\u9593\u306e\u9069\u5207\u306a\u30d0\u30e9\u30f3\u30b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u8aac\u660e\u5909\u6570\u3068\u5fdc\u7b54\u5909\u6570\u306e\u9593\u306e\u771f\u306e\u95a2\u4fc2\u3092\u6349\u3048\u308b\u306e\u306b\u5341\u5206\u306a\u8907\u96d1\u3055\u306e\u30e2\u30c7\u30eb\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u5b58\u5728\u3057\u306a\u3044\u30d1\u30bf\u30fc\u30f3\u3092\u691c\u51fa\u3067\u304d\u308b\u307b\u3069\u8907\u96d1\u3059\u304e\u306a\u3044\u30e2\u30c7\u30eb\u304c\u5fc5\u8981\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u30e2\u30c7\u30eb\u304c\u8907\u96d1\u3059\u304e\u308b\u3068\u3001\u30c7\u30fc\u30bf\u304c<a href=\"https:\/\/statorials.org\/ja\/\u6a5f\u68b0\u5b66\u7fd2\u306e\u904e\u5b66\u7fd2\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>\u904e\u5270\u9069\u5408\u3057\u3066\u3057\u307e\u3044<\/strong><\/a>\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0 \u30c7\u30fc\u30bf\u5185\u3067\u5358\u306b\u5076\u7136\u306b\u767a\u751f\u3057\u305f\u30d1\u30bf\u30fc\u30f3\u3092\u898b\u3064\u3051\u308b\u306e\u304c\u975e\u5e38\u306b\u96e3\u3057\u3044\u305f\u3081\u306b\u767a\u751f\u3057\u307e\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30e2\u30c7\u30eb\u306f\u3001\u975e\u8868\u793a\u306e\u30c7\u30fc\u30bf\u3067\u306f\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u4f4e\u4e0b\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3057\u304b\u3057\u3001\u30e2\u30c7\u30eb\u304c\u5358\u7d14\u3059\u304e\u308b\u3068\u3001\u30c7\u30fc\u30bf\u304c<strong>\u904e\u5c0f\u8a55\u4fa1\u3055\u308c\u3066\u3057\u307e\u3044<\/strong>\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u8aac\u660e\u5909\u6570\u3068\u5fdc\u7b54\u5909\u6570\u306e\u9593\u306e\u771f\u306e\u95a2\u4fc2\u304c\u5b9f\u969b\u3088\u308a\u3082\u5358\u7d14\u3067\u3042\u308b\u3068\u60f3\u5b9a\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u306b\u767a\u751f\u3057\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: 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