{"id":9725,"date":"2026-09-24T15:46:49","date_gmt":"2026-09-24T06:46:49","guid":{"rendered":"https:\/\/since2020.jp\/media\/?p=9725"},"modified":"2026-09-24T16:07:11","modified_gmt":"2026-09-24T07:07:11","slug":"meta-learner","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/meta-learner\/","title":{"rendered":"\u30e1\u30bf\u5b66\u7fd2\u5668\uff1aT-Learner\u3068X-Learner"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u30e1\u30bf\u5b66\u7fd2\u5668\u3068\u306f<\/h2>\n\n\n\n<p>A\/B\u30c6\u30b9\u30c8\u3084\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u65bd\u7b56\u306e\u5206\u6790\u3067\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u65bd\u7b56\u5168\u4f53\u306e\u5e73\u5747\u52b9\u679c\u3067\u3042\u308b\u5e73\u5747\u51e6\u7f6e\u52b9\u679c\uff08Average Treatment Effect, ATE\uff09\u304c\u5831\u544a\u3055\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u5b9f\u52d9\u3067\u306f\u3001\u300c\u3053\u306e\u65bd\u7b56\u306f\u8ab0\u306b\u52b9\u679c\u304c\u3042\u308a\u3001\u8ab0\u306b\u306f\u52b9\u679c\u304c\u306a\u3044\u306e\u304b\u300d\u3068\u3044\u3046\u52b9\u679c\u306e\u500b\u4eba\u5dee\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u500b\u4eba\u5dee\u306f\u3001\u6761\u4ef6\u4ed8\u304d\u5e73\u5747\u51e6\u7f6e\u52b9\u679c\uff08Conditional Average Treatment Effect, CATE\uff09\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c4<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>\ud835\udd3c<\/mi><mspace width=\"-0.1667em\" style=\"margin-left:-0.1667em\"><\/mspace><mrow><mo fence=\"true\" form=\"prefix\">[<\/mo><mi>Y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>Y<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo fence=\"true\" form=\"postfix\">]<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\tau(x)\n=\n\\mathbb{E}\\!\\left[Y(1)-Y(0)\\mid X=x\\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u5404\u8a18\u53f7\u306f\u6b21\u306e\u610f\u5473\u3092\u6301\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$Y(1)$\uff1a\u51e6\u7f6e\u3092\u53d7\u3051\u305f\u5834\u5408\u306e\u6f5c\u5728\u7684\u7d50\u679c<\/li>\n\n\n\n<li>$Y(0)$\uff1a\u51e6\u7f6e\u3092\u53d7\u3051\u306a\u304b\u3063\u305f\u5834\u5408\u306e\u6f5c\u5728\u7684\u7d50\u679c<\/li>\n\n\n\n<li>$X$\uff1a\u500b\u4f53\u306e\u5c5e\u6027\u3084\u7279\u5fb4\u91cf<\/li>\n\n\n\n<li>$\\tau(x)$\uff1a\u7279\u5fb4\u91cf\u304c $x$ \u3067\u3042\u308b\u500b\u4f53\u306e\u5e73\u5747\u7684\u306a\u51e6\u7f6e\u52b9\u679c<\/li>\n<\/ul>\n\n\n\n<p>\u305f\u3060\u3057\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001\u5404\u500b\u4f53\u306b\u3064\u3044\u3066 $Y(1)$ \u3068 $Y(0)$ \u306e\u3069\u3061\u3089\u304b\u4e00\u65b9\u3057\u304b\u89b3\u6e2c\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u30e1\u30bf\u5b66\u7fd2\u5668\uff08meta-learner\uff09\u306f\u3001\u3053\u306e\u63a8\u5b9a\u554f\u984c\u3092\u3001\u56de\u5e30\u6728\u30fb\u52fe\u914d\u30d6\u30fc\u30b9\u30c6\u30a3\u30f3\u30b0\u30fb\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306a\u3069\u306e\u4efb\u610f\u306e\u6a5f\u68b0\u5b66\u7fd2\u30e2\u30c7\u30eb\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u89e3\u304f\u305f\u3081\u306e\u67a0\u7d44\u307f\u3067\u3059\u3002\u4ee3\u8868\u7684\u306a\u624b\u6cd5\u306b\u306fS-Learner\u3001T-Learner\u3001X-Learner\u3001R-Learner\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u57fa\u672c\u7684\u306aT-Learner\u3068\u3001\u305d\u306e\u5f31\u70b9\u3092\u88dc\u3046X-Learner\u3092\u6271\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\uff1a\u30af\u30fc\u30dd\u30f3\u914d\u5e03\u554f\u984c<\/h3>\n\n\n\n<p>\u3042\u308bEC\u30b5\u30a4\u30c8\u304c\u3001\u4e00\u90e8\u306e\u9867\u5ba2\u306b\u3060\u3051\u5272\u5f15\u30af\u30fc\u30dd\u30f3\u3092\u914d\u5e03\u3057\u305f\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u51e6\u7f6e\u7fa4\uff1a\u30af\u30fc\u30dd\u30f3\u3092\u914d\u5e03\u3057\u305f\u9867\u5ba2\uff08$W=1$\uff09<\/li>\n\n\n\n<li>\u5bfe\u7167\u7fa4\uff1a\u30af\u30fc\u30dd\u30f3\u3092\u914d\u5e03\u3057\u306a\u304b\u3063\u305f\u9867\u5ba2\uff08$W=0$\uff09<\/li>\n\n\n\n<li>\u7d50\u679c\uff1a\u8cfc\u5165\u984d $Y$<\/li>\n\n\n\n<li>\u9867\u5ba2\u5c5e\u6027\uff1a$X$<\/li>\n<\/ul>\n\n\n\n<p>\u77e5\u308a\u305f\u3044\u306e\u306f\u3001\u30af\u30fc\u30dd\u30f3\u306b\u3088\u308b\u8cfc\u5165\u984d\u306e\u5e73\u5747\u7684\u306a\u5897\u52a0\u984d\u3060\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u300c\u4f11\u7720\u9867\u5ba2\u306b\u306f\u52b9\u679c\u304c\u5927\u304d\u3044\u304c\u3001\u5e38\u9023\u9867\u5ba2\u306b\u306f\u52b9\u679c\u304c\u5c0f\u3055\u3044\u300d\u3068\u3044\u3063\u305f\u3001\u9867\u5ba2\u5c5e\u6027 $X$ \u306b\u5fdc\u3058\u305f\u52b9\u679c $\\tau(x)$ \u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">T-Learner\u306e\u4ed5\u7d44\u307f<\/h2>\n\n\n\n<p>T-Learner\uff08Two-model learner\uff09\u306f\u3001\u6700\u3082\u76f4\u611f\u7684\u306a\u30e1\u30bf\u5b66\u7fd2\u5668\u3067\u3059\u3002\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30c7\u30fc\u30bf\u3092\u5206\u3051\u3001\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u72ec\u7acb\u3057\u305f\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30c3\u30d71\uff1a\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3059\u308b<\/h3>\n\n\n\n<p>\u51e6\u7f6e\u7fa4\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u3001\u51e6\u7f6e\u7fa4\u306e\u30c7\u30fc\u30bf\u3060\u3051\u3067\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>\ud835\udd3c<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>Y<\/mi><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>W<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\mu}_1(x)\n=\n\\mathbb{E}[Y\\mid W=1,X=x]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u540c\u69d8\u306b\u3001\u5bfe\u7167\u7fa4\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u3001\u5bfe\u7167\u7fa4\u306e\u30c7\u30fc\u30bf\u3060\u3051\u3067\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>0<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>\ud835\udd3c<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>Y<\/mi><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>W<\/mi><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\mu}_0(x)\n=\n\\mathbb{E}[Y\\mid W=0,X=x]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30c3\u30d72\uff1a2\u3064\u306e\u4e88\u6e2c\u5024\u306e\u5dee\u3092\u53d6\u308b<\/h3>\n\n\n\n<p>CATE\u306f\u30012\u3064\u306e\u30e2\u30c7\u30eb\u306b\u3088\u308b\u4e88\u6e2c\u5024\u306e\u5dee\u3068\u3057\u3066\u63a8\u5b9a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03c4<\/mi><mo stretchy=\"true\" class=\"tml-crooked-4\">^<\/mo><\/mover><mi>T<\/mi><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>0<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\tau}_{T}(x)\n=\n\\widehat{\\mu}_1(x)-\\widehat{\\mu}_0(x)\n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u3042\u308b\u9867\u5ba2\u5c5e\u6027 $x$ \u306b\u3064\u3044\u3066\u3001\u30af\u30fc\u30dd\u30f3\u3092\u914d\u5e03\u3057\u305f\u5834\u5408\u306e\u4e88\u6e2c\u8cfc\u5165\u984d\u304c3,000\u5186\u3001\u914d\u5e03\u3057\u306a\u304b\u3063\u305f\u5834\u5408\u304c2,600\u5186\u3067\u3042\u308c\u3070\u3001\u30af\u30fc\u30dd\u30f3\u52b9\u679c\u306f400\u5186\u3068\u63a8\u5b9a\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"623\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig1_t_learner-1024x623.png\" alt=\"\" class=\"wp-image-9729\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig1_t_learner-1024x623.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig1_t_learner-300x183.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig1_t_learner-768x468.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig1_t_learner.png 1360w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\"><em>\u56f31\uff1a\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u3067\u72ec\u7acb\u3057\u305f\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3057\u3001\u4e88\u6e2c\u5024\u306e\u5dee\u304b\u3089CATE\u3092\u63a8\u5b9a\u3059\u308b\u3002<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">T-Learner\u306e\u5f31\u70b9<\/h2>\n\n\n\n<p>T-Learner\u306f\u5358\u7d14\u3067\u7406\u89e3\u3057\u3084\u3059\u3044\u4e00\u65b9\u3001\u4e3b\u306b2\u3064\u306e\u5f31\u70b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30c7\u30fc\u30bf\u6570\u306e\u504f\u308a\u306b\u5f31\u3044<\/h3>\n\n\n\n<p>\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30c7\u30fc\u30bf\u6570\u304c\u5927\u304d\u304f\u7570\u306a\u308b\u5834\u5408\u3001\u5c11\u6570\u6d3e\u5074\u306e\u30e2\u30c7\u30eb\u306f\u5b66\u7fd2\u30c7\u30fc\u30bf\u304c\u4e0d\u8db3\u3057\u3001\u4e88\u6e2c\u7cbe\u5ea6\u304c\u4f4e\u4e0b\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u30af\u30fc\u30dd\u30f3\u3092\u914d\u5e03\u3057\u305f\u9867\u5ba2\u304c\u5168\u4f53\u306e5%\u3057\u304b\u3044\u306a\u3044\u5834\u5408\u3001\u51e6\u7f6e\u7fa4\u306e\u30e2\u30c7\u30eb $\\widehat{\\mu}_1(x)$ \u306f\u5341\u5206\u306a\u30d1\u30bf\u30fc\u30f3\u3092\u5b66\u7fd2\u3067\u304d\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u72b6\u6cc1\u3067\u306f\u3001\u6b63\u5247\u5316\u306e\u5f71\u97ff\u306b\u3088\u3063\u3066\u7fa4\u9593\u306e\u5dee\u304c\u904e\u5ea6\u306b\u7e2e\u5c0f\u3055\u308c\u308b\u6b63\u5247\u5316\u30d0\u30a4\u30a2\u30b9\u3082\u554f\u984c\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7fa4\u3092\u307e\u305f\u3044\u3060\u60c5\u5831\u5171\u6709\u304c\u3067\u304d\u306a\u3044<\/h3>\n\n\n\n<p>$\\widehat{\\mu}_1(x)$ \u3068 $\\widehat{\\mu}_0(x)$ \u306f\u72ec\u7acb\u306b\u5b66\u7fd2\u3055\u308c\u308b\u305f\u3081\u3001\u4e00\u65b9\u306e\u30e2\u30c7\u30eb\u304c\u5b66\u7fd2\u3057\u305f\u300c\u7279\u5fb4\u91cf $X$ \u3068\u7d50\u679c $Y$ \u306e\u95a2\u4fc2\u300d\u3092\u3001\u3082\u3046\u4e00\u65b9\u306e\u30e2\u30c7\u30eb\u304c\u76f4\u63a5\u6d3b\u7528\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u7279\u306b\u89b3\u5bdf\u30c7\u30fc\u30bf\uff08\u975e\u30e9\u30f3\u30c0\u30e0\u5316\u30c7\u30fc\u30bf\uff09\u3067\u306f\u3001\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30b5\u30a4\u30ba\u3084\u5c5e\u6027\u5206\u5e03\u304c\u504f\u308b\u3053\u3068\u304c\u591a\u3044\u305f\u3081\u3001\u3053\u306e\u5f31\u70b9\u3092\u7121\u8996\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">X-Learner\u306e\u4ed5\u7d44\u307f<\/h2>\n\n\n\n<p>X-Learner\u306fT-Learner\u3092\u62e1\u5f35\u3057\u305f\u624b\u6cd5\u3067\u3001\u7279\u306b\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30c7\u30fc\u30bf\u6570\u304c\u504f\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u6709\u52b9\u3067\u3059\u3002\u51e6\u7406\u306f4\u3064\u306e\u30b9\u30c6\u30fc\u30b8\u306b\u5206\u304b\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30fc\u30b81\uff1a\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3059\u308b<\/h3>\n\n\n\n<p>T-Learner\u3068\u540c\u69d8\u306b\u3001\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>\ud835\udd3c<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>Y<\/mi><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>W<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\mu}_1(x)\n=\n\\mathbb{E}[Y\\mid W=1,X=x]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>0<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>\ud835\udd3c<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>Y<\/mi><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>W<\/mi><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\mu}_0(x)\n=\n\\mathbb{E}[Y\\mid W=0,X=x]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30fc\u30b82\uff1a\u7591\u4f3c\u7684\u306a\u51e6\u7f6e\u52b9\u679c\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n\n\n\n<p>\u5404\u500b\u4f53\u306b\u3064\u3044\u3066\u3001\u53cd\u5b9f\u4eee\u60f3\u306e\u4e88\u6e2c\u5024\u3092\u4f7f\u3063\u3066\u7591\u4f3c\u52b9\u679c\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u51e6\u7f6e\u7fa4\u306e\u500b\u4f53 $i$ \u3067\u306f\u3001\u5b9f\u969b\u306e\u7d50\u679c\u304b\u3089\u300c\u51e6\u7f6e\u3092\u53d7\u3051\u306a\u304b\u3063\u305f\u5834\u5408\u300d\u306e\u4e88\u6e2c\u5024\u3092\u5f15\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msubsup><mi>D<\/mi><mi>i<\/mi><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msubsup><mo>=<\/mo><msub><mi>Y<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>0<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><msub><mi>W<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">D_i^{(1)}\n=\nY_i-\\widehat{\\mu}_0(X_i),\n\\qquad W_i=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u5bfe\u7167\u7fa4\u306e\u500b\u4f53 $i$ \u3067\u306f\u3001\u300c\u51e6\u7f6e\u3092\u53d7\u3051\u305f\u5834\u5408\u300d\u306e\u4e88\u6e2c\u5024\u304b\u3089\u5b9f\u969b\u306e\u7d50\u679c\u3092\u5f15\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msubsup><mi>D<\/mi><mi>i<\/mi><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mn>0<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msubsup><mo>=<\/mo><msub><mover><mi>\u03bc<\/mi><mo stretchy=\"true\" class=\"tml-crooked-3\">^<\/mo><\/mover><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><msub><mi>Y<\/mi><mi>i<\/mi><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><msub><mi>W<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">D_i^{(0)}\n=\n\\widehat{\\mu}_1(X_i)-Y_i,\n\\qquad W_i=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u9867\u5ba2<\/th><th>\u7fa4\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000<\/th><th>\u5b9f\u6e2c\u8cfc\u5165\u984d $Y$<\/th><th>\u53cd\u5b9f\u4eee\u60f3\u306e\u4e88\u6e2c\u5024<\/th><th>\u7591\u4f3c\u52b9\u679c $D$<\/th><\/tr><\/thead><tbody><tr><td>\u9867\u5ba2A<\/td><td>\u51e6\u7f6e\u7fa4<br>\uff08$W=1$\uff09<\/td><td>120<\/td><td>$\\widehat{\\mu}_0(X_A)=80$<\/td><td>$D_A^{(1)}=120<br>-80=40$<\/td><\/tr><tr><td>\u9867\u5ba2B<\/td><td>\u5bfe\u7167\u7fa4<br>\uff08$W=0$\uff09<\/td><td>50<\/td><td>$\\widehat{\\mu}_1(X_B)=70$<\/td><td>$D_B^{(0)}=70<br>-50=20$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30fc\u30b83\uff1a\u7591\u4f3c\u52b9\u679c\u3092\u4e88\u6e2c\u3059\u308b\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3059\u308b<\/h3>\n\n\n\n<p>\u51e6\u7f6e\u7fa4\u306e\u7591\u4f3c\u52b9\u679c $D^{(1)}$ \u3092\u76ee\u7684\u5909\u6570\u3068\u3057\u3066\u3001\u52b9\u679c\u30e2\u30c7\u30eb $\\widehat{\\tau}_1(x)$ \u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\widehat{\\tau}_1(x)<br>\\approx<br>\\mathbb{E}[D^{(1)}\\mid X=x,W=1]<br>$$<\/p>\n\n\n\n<p>\u540c\u69d8\u306b\u3001\u5bfe\u7167\u7fa4\u306e\u7591\u4f3c\u52b9\u679c $D^{(0)}$ \u3092\u76ee\u7684\u5909\u6570\u3068\u3057\u3066\u3001\u52b9\u679c\u30e2\u30c7\u30eb $\\widehat{\\tau}_0(x)$ \u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\widehat{\\tau}_0(x)<br>\\approx<br>\\mathbb{E}[D^{(0)}\\mid X=x,W=0]<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b9\u30c6\u30fc\u30b84\uff1a2\u3064\u306e\u52b9\u679c\u30e2\u30c7\u30eb\u3092\u7d71\u5408\u3059\u308b<\/h3>\n\n\n\n<p>\u50be\u5411\u30b9\u30b3\u30a2 $g(x)$ \u3092\u3001\u305d\u306e\u500b\u4f53\u304c\u51e6\u7f6e\u7fa4\u306b\u5c5e\u3059\u308b\u78ba\u7387\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>g<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mover><mi>P<\/mi><mo stretchy=\"true\">^<\/mo><\/mover><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>W<\/mi><mo>=<\/mo><mn>1<\/mn><mo lspace=\"0.22em\" rspace=\"0.22em\" stretchy=\"false\">|<\/mo><mi>X<\/mi><mo>=<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">g(x)\n=\n\\widehat{P}(W=1\\mid X=x)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u6700\u7d42\u7684\u306aCATE\u63a8\u5b9a\u5024\u306f\u30012\u3064\u306e\u52b9\u679c\u30e2\u30c7\u30eb\u3092\u50be\u5411\u30b9\u30b3\u30a2\u3067\u91cd\u307f\u4ed8\u3051\u3057\u3066\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mover><mi>\u03c4<\/mi><mo stretchy=\"true\" class=\"tml-crooked-4\">^<\/mo><\/mover><mi>X<\/mi><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>g<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msub><mover><mi>\u03c4<\/mi><mo stretchy=\"true\" class=\"tml-crooked-4\">^<\/mo><\/mover><mn>0<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>g<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><msub><mover><mi>\u03c4<\/mi><mo stretchy=\"true\" class=\"tml-crooked-4\">^<\/mo><\/mover><mn>1<\/mn><\/msub><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\widehat{\\tau}_{X}(x)\n=\ng(x)\\widehat{\\tau}_0(x)\n+\\left(1-g(x)\\right)\\widehat{\\tau}_1(x)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>\u3053\u306e\u91cd\u307f\u4ed8\u3051\u3067\u306f\u3001\u51e6\u7f6e\u7fa4\u304c\u5c11\u306a\u3044\u9818\u57df\u3001\u3059\u306a\u308f\u3061 $g(x)$ \u304c\u5c0f\u3055\u3044\u9818\u57df\u3067 $\\widehat{\\tau}_1(x)$ \u306e\u91cd\u307f\u304c\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5bfe\u7167\u7fa4\u306e\u8c4a\u5bcc\u306a\u30c7\u30fc\u30bf\u304b\u3089 $\\widehat{\\mu}_0(x)$ \u3092\u7cbe\u5ea6\u3088\u304f\u63a8\u5b9a\u3067\u304d\u3001\u305d\u306e\u4e88\u6e2c\u3092\u4f7f\u3063\u3066\u51e6\u7f6e\u7fa4\u306e\u7591\u4f3c\u52b9\u679c $D^{(1)}$ \u3092\u69cb\u6210\u3067\u304d\u308b\u305f\u3081\u3067\u3059\u3002\u53cd\u5bfe\u306b\u3001$g(x)$ \u304c\u5927\u304d\u3044\u9818\u57df\u3067\u306f\u3001\u51e6\u7f6e\u7fa4\u304b\u3089\u7cbe\u5ea6\u3088\u304f\u63a8\u5b9a\u3057\u305f $\\widehat{\\mu}_1(x)$ \u3092\u4f7f\u3046 $\\widehat{\\tau}_0(x)$ \u304c\u91cd\u8996\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"623\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig2_x_learner-1024x623.png\" alt=\"\" class=\"wp-image-9733\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig2_x_learner-1024x623.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig2_x_learner-300x183.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig2_x_learner-768x468.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/09\/fig2_x_learner.png 1360w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\"><em>\u56f32\uff1a\u50be\u5411\u30b9\u30b3\u30a2 $g(x)$ \u3092\u4f7f\u3044\u3001\u51e6\u7f6e\u7fa4\u5074\u3068\u5bfe\u7167\u7fa4\u5074\u306e\u52b9\u679c\u63a8\u5b9a\u3092\u7d71\u5408\u3059\u308b\u3002<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">T-Learner\u3068X-Learner\u306e\u6bd4\u8f03<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6bd4\u8f03\u9805\u76ee<\/th><th>T-Learner<\/th><th>X-Learner<\/th><\/tr><\/thead><tbody><tr><td>\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9<\/td><td>2\u3064\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u306e\u5dee\u3092\u53d6\u308b<\/td><td>\u7591\u4f3c\u52b9\u679c\u3092\u5b66\u7fd2\u3057\u3001\u91cd\u307f\u4ed8\u3051\u3057\u3066\u7d71\u5408\u3059\u308b<\/td><\/tr><tr><td>\u5b66\u7fd2\u3059\u308b\u30e2\u30c7\u30eb<\/td><td>\u7d50\u679c\u30e2\u30c7\u30eb2\u500b<\/td><td>\u7d50\u679c\u30e2\u30c7\u30eb2\u500b\uff0b\u52b9\u679c\u30e2\u30c7\u30eb2\u500b\uff0b\u50be\u5411\u30b9\u30b3\u30a2\u30e2\u30c7\u30eb<\/td><\/tr><tr><td>\u7fa4\u306e\u30b5\u30a4\u30ba\u304c\u5747\u8861\u3057\u3066\u3044\u308b\u5834\u5408<\/td><td>\u5341\u5206\u306b\u6a5f\u80fd\u3057\u3084\u3059\u3044<\/td><td>T-Learner\u3068\u540c\u7a0b\u5ea6\u306e\u5834\u5408\u304c\u591a\u3044<\/td><\/tr><tr><td>\u7fa4\u306e\u30b5\u30a4\u30ba\u304c\u504f\u3063\u3066\u3044\u308b\u5834\u5408<\/td><td>\u5c11\u6570\u6d3e\u5074\u306e\u7cbe\u5ea6\u304c\u4f4e\u4e0b\u3057\u3084\u3059\u3044<\/td><td>\u591a\u6570\u6d3e\u5074\u306e\u60c5\u5831\u3092\u6d3b\u7528\u3057\u3084\u3059\u3044<\/td><\/tr><tr><td>\u5b9f\u88c5\u30fb\u89e3\u91c8<\/td><td>\u30b7\u30f3\u30d7\u30eb<\/td><td>\u3084\u3084\u8907\u96d1<\/td><\/tr><tr><td>\u8a08\u7b97\u30b3\u30b9\u30c8<\/td><td>\u6bd4\u8f03\u7684\u5c0f\u3055\u3044<\/td><td>\u6bd4\u8f03\u7684\u5927\u304d\u3044<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f7f\u3044\u5206\u3051\u306e\u76ee\u5b89<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>T-Learner\u304c\u5411\u3044\u3066\u3044\u308b\u5834\u5408\uff1a\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30b5\u30a4\u30ba\u304c\u8fd1\u304f\u3001\u307e\u305a\u5358\u7d14\u306a\u57fa\u6e96\u30e2\u30c7\u30eb\u3092\u4f5c\u308a\u305f\u3044<\/li>\n\n\n\n<li>X-Learner\u304c\u5411\u3044\u3066\u3044\u308b\u5834\u5408\uff1a\u7fa4\u306e\u30b5\u30a4\u30ba\u304c\u5927\u304d\u304f\u504f\u3063\u3066\u304a\u308a\u3001\u591a\u6570\u6d3e\u5074\u306e\u60c5\u5831\u3092\u6d3b\u7528\u3057\u305f\u3044<\/li>\n<\/ul>\n\n\n\n<p>X-Learner\u304c\u5e38\u306bT-Learner\u3088\u308a\u9ad8\u7cbe\u5ea6\u306b\u306a\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u6700\u7d42\u7684\u306b\u306f\u3001\u4ea4\u5dee\u691c\u8a3c\u3084\u65bd\u7b56\u8a55\u4fa1\u306b\u9069\u3057\u305f\u6307\u6a19\u3092\u4f7f\u3063\u3066\u6bd4\u8f03\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>T-Learner\u306f\u3001\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306b\u3064\u3044\u3066\u5225\u3005\u306e\u7d50\u679c\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3057\u3001\u305d\u306e\u4e88\u6e2c\u5024\u306e\u5dee\u304b\u3089CATE\u3092\u63a8\u5b9a\u3059\u308b\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u30e1\u30bf\u5b66\u7fd2\u5668\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001X-Learner\u306f\u3001\u53cd\u5b9f\u4eee\u60f3\u306e\u4e88\u6e2c\u5024\u304b\u3089\u7591\u4f3c\u52b9\u679c\u3092\u4f5c\u308a\u3001\u305d\u308c\u3092\u518d\u5ea6\u30e2\u30c7\u30eb\u5316\u3057\u305f\u3046\u3048\u3067\u3001\u50be\u5411\u30b9\u30b3\u30a2\u3092\u4f7f\u3063\u3066\u7d71\u5408\u3057\u307e\u3059\u3002\u624b\u9806\u306f\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u51e6\u7f6e\u7fa4\u3068\u5bfe\u7167\u7fa4\u306e\u30c7\u30fc\u30bf\u6570\u304c\u504f\u3063\u3066\u3044\u308b\u72b6\u6cc1\u3067\u6709\u5229\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u8981\u70b9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>T-Learner\u306f\u5b9f\u88c5\u3057\u3084\u3059\u304f\u3001\u6bd4\u8f03\u306e\u57fa\u6e96\u3068\u3057\u3066\u4f7f\u3044\u3084\u3059\u3044<\/li>\n\n\n\n<li>X-Learner\u306f\u7591\u4f3c\u52b9\u679c\u3092\u4ecb\u3057\u3066\u3001\u7fa4\u9593\u306e\u60c5\u5831\u3092\u6d3b\u7528\u3059\u308b<\/li>\n\n\n\n<li>\u30c7\u30fc\u30bf\u306e\u504f\u308a\u304c\u5927\u304d\u3044\u5834\u5408\u306f\u3001X-Learner\u3092\u6bd4\u8f03\u5019\u88dc\u306b\u3059\u308b<\/li>\n\n\n\n<li>\u3069\u3061\u3089\u306e\u624b\u6cd5\u3067\u3082\u3001\u5185\u90e8\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u76ee\u7684\u306b\u5fdc\u3058\u3066\u9078\u629e\u3067\u304d\u308b<\/li>\n<\/ol>\n\n\n\n<p>\u5b9f\u52d9\u3067\u306f\u3001\u307e\u305aT-Learner\u3092\u30d9\u30fc\u30b9\u30e9\u30a4\u30f3\u3068\u3057\u3066\u69cb\u7bc9\u3057\u3001\u7fa4\u306e\u504f\u308a\u3084\u63a8\u5b9a\u7cbe\u5ea6\u3092\u78ba\u8a8d\u3057\u305f\u3046\u3048\u3067\u3001X-Learner\u3068\u6bd4\u8f03\u3059\u308b\u9032\u3081\u65b9\u304c\u73fe\u5b9f\u7684\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30e1\u30bf\u5b66\u7fd2\u5668\u3068\u306f 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