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PRML 10.5-10.6
9/14/2018
酒井 ⼀徳
⽬次 2/56
Ø 10.5 局所的変分推論法
Ø 10.6 変分ロジスティック回帰
Ø 10.6.1 変分事後分布
Ø 10.6.2 変分パラメータの最適化
Ø 10.6.3 超パラメータの推論
10.5 局所的変分推論法
モチベーション 4/56
Ø すべての変数における事後分布を直接近似。
これまで
Ø 各変数や変数群における関数の近似。
Ø 全体の計算可能な近似を得る。
ここから
凸関数 5/56
<latexit sha1_base64="9C98peB2xLfL2FeLOcnOmUwdDYE=">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</latexit>
<latexit sha1_base64="OFUbOVVJlChoGW4jxtUJId6CKQM=">AAAC3HichVE7axRRGD0ZX3moWbUR0gwuKxFx+SYICWIRsLHMw00CMS4zk7vJkHkxc3fNOthZKbaxkBQKFuLPSKFFUqbITxDLCDYWnrk74COod7hzzz3fPd/TS8Mg1yJHQ9ap02fOnhseGR07f+HieO3S5aU86Wa+avlJmGQrnpurMIhVSwc6VCtpptzIC9Wyt3WvtC/3VJYHSfxA91O1FrkbcdAJfFeTatemO/akre1t+yZPx75FfMPuc98lKm3bxL/aSo72dq0uTTHLPgmcCtRRrbmk9hEPsY4EPrqIoBBDE4dwkfNbhQNBSm4NBbmMKDB2hacYpbbLV4ovXLJb/G/wtlqxMe+lz9yofUYJuTMqbTTkUN7LsXySD/JZvv/VV2F8lLn0eXoDrUrb48+vLn77ryriqbH5U0VF4x9Za3QwY7INmH1qmLIOf+Ch9+TV8eKdhUZxXd7KF1bwRo5kjzXEva/+u3m18NpklBmNwmNTc2SyiNnlgracEdZp65Drsh+angtG2kSv7CgH6Pw5rpNgaarpSNOZv12fnalGOYwJXMMk5zWNWdzHHFqMvos97OPAemQ9s15YLwdPraFKcwW/LWvnB26tpC4=</latexit>
広義:
狭義:
※wikiより
(等号成⽴は )
はパラメータ を持つ⼀次関数
凸関数の接線は下界 6/56
<latexit sha1_base64="2XAIiyCU1NQoQUqB59AT005TsyM=">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</latexit>
<latexit sha1_base64="Rt8nnLvi7SbeMI4vtWC6B7S+pWQ=">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</latexit>
における接線は、
<latexit sha1_base64="S57dKv3EOwl2m1CE3oZlEoZTCG8=">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</latexit>
<latexit sha1_base64="SZSq+TGCEflOiSpowPztIXxnwgk=">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</latexit>
<latexit sha1_base64="Rt8nnLvi7SbeMI4vtWC6B7S+pWQ=">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</latexit>
<latexit sha1_base64="CUOz4p3oZ51Cp2DuvlGEOETiy+o=">AAACp3ichVFLSxtRFP4cbX3VJtWN4EYaImYTzoiglC4EN+6Mj8SAisxMbsyQeTFzE00H/4ALtxG6quBC/Bku9A+48CdIlwpuuuiZm4FSRT3D3Hvud853nmbg2JEkuuvT+gc+fBwcGh4Z/TT2OZP9Ml6J/FZoibLlO35YNY1IOLYnytKWjqgGoTBc0xFbZnM5sW+1RRjZvrcpO4HYdY19z67bliETqDN7WNjL5qhISqZfKnqq5JBKyc9eYwc1+LDQggsBD5J1BwYi/rahgxAwtouYsZA1W9kFjjDC3BZ7CfYwGG3yuc+v7RT1+J3EjBTb4iwO/yEzp5GnW7qgB7qhS7qnP6/GilWMpJYO32aPK4K9zPHkxtO7LJdvicY/FjPyb1QtUceiqtbm6gOFJH1YvQjtH92HjW/r+XiGzug3d/CL7uiKe/Daj9b5mlj/qSoKFUfgQPXsqio8nnLMtogz1NhWZ6zF85AcOeZMDbSTifIC9efreqlU5oo6FfW1+dzS93SVQ5jCV8zyvhawhBWUUObsDZygi1OtoK1qFa3ac9X6Us4E/hPN+AvcZ5ge</latexit> <latexit sha1_base64="ShLK0uIOXzmGXX9dHw1ZMjdUqiQ=">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</latexit>
( の変更)=(接線の変更) を意味し、
凸関数の下界による近似 7/56
<latexit sha1_base64="DUGMXH/QO09Jintxsy2cBdDrj1g=">AAACu3ichVHNTtRQFP6oiogKoybGxM3EyRhcMDk1JhijySRuWPLjAAlDJm05A1f6R3tbGasv4Au4cAWJCwJvwQJegAWPYFxi4saFp3eaGCXqaXrvud853/l1Y1+lmuhsxLp0+cro1bFr49dv3JyYrN26vZRGWeJxx4v8KFlxnZR9FXJHK+3zSpywE7g+L7tbL0v7cs5JqqLwlR7EvBY4G6HqK8/RAvVqd7usnXqXtzOV16d5J56a7u6oR71ag1pkpH5RsSulgUrmotoxulhHBA8ZAjBCaNF9OEjlW4UNQizYGgrBEtGUsTPeY1y4mXixeDiCbsm5Ia/VCg3lXcZMDduTLL78iTDraNIp7dM5ndABfaEff41VmBhlLQO53SGX497kh3uL3//LCuTW2PzFEkbzH1Vr9PHUVKuk+tggZR/eMEL+9uP54rOFZvGQ9uirdLBLZ3QkPYT5N+/zPC98MhUlhsN4Y3oOTBWhTLkQWyoZ1sXWFyyTeWiJXEimTeTlRGWB9p/ruqgsPW7Z1LLnnzTaz6tVjuE+HmBK9jWDNmYxh45kf4c9HODQemF51mvLH7paIxXnDn4TK/sJlcafUg==</latexit>
とすると接線は、
<latexit sha1_base64="KoGuoEgkIZxQctHdNJSNNeZ1BUw=">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</latexit>
<latexit sha1_base64="e8sx5JLcmkulywdPDdmp6zcFTQE=">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</latexit>
<latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit>
<latexit sha1_base64="qLnOF0HvLjDz9gnn81OZSiMzswY=">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</latexit>
であるので、
⼀次関数で近似に成功。
ただし、変分パラメータ の最適化が必要。<latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit>
xは固定
凸双対性(凸共役性) 8/56
Ø ルジャンドル変換
関数の変数変換⼿法。
凸関数を接線で表現できることに基づく(らしい)。
<latexit sha1_base64="+Lf3EE5tCBHWJ0cMwMl/bJS2d3s=">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</latexit>
Ø 再度変換
<latexit sha1_base64="val2wi8uc8H5+A2kySCXNHxnhWo=">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</latexit>
凸関数の時、 <latexit sha1_base64="p2jX1w7rhiZKcaPFNQxhhkbYE/k=">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</latexit>
凸な関数
凸双対性(凸共役性) 9/56
<latexit sha1_base64="urMAGuHwdsLWjSP3bI1/t/IvwXE=">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</latexit>
<latexit sha1_base64="V44FKJx7AsnXG5hdegTFBvob+dQ=">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</latexit>
接線
を固定
<latexit sha1_base64="QigStEQS1nbpaCOxUqiyWk0RXng=">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</latexit>
<latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit>
凹関数
切⽚ <latexit sha1_base64="kZYJdecMeXUdA9R50TaOm85lsT4=">AAACqnichVHNShtRFP4ytWrT1qR1U+gmNEQslHBGBMVVoBtXokmTWJIgM5ObOGT+mLlJiUNfwJ2rQl0puCh9jC7aF+gijyBdWujGhWduBkRFe4a599zvnO/8moFjR5JoktEezTyenZt/kn367PlCLv/iZSPyh6El6pbv+OGuaUTCsT1Rl7Z0xG4QCsM1HdE0B+8Te3Mkwsj2vQ9yHIiOa/Q9u2dbhmSo2V9uC2m83csXqUxKCncVPVWKSGXbz/9EG134sDCECwEPknUHBiL+WtBBCBjrIGYsZM1WdoHPyDJ3yF6CPQxGB3z2+dVKUY/fScxIsS3O4vAfMrOAEv2mb3RBv+g7ndPlvbFiFSOpZcy3OeWKYC93+Kr2778sl2+J/WsWM0oPVC3Rw7qq1ubqA4UkfVjTCKODLxe1jWopXqJT+sMdnNCEfnAP3uivdbYjqseqolBxBD6pnl1VhcdTjtkWcYYu23qMDXkekiPHnGkfo2SivED99rruKo2Vsk5lfWe1WNlKVzmP13iDZd7XGirYxDbqqrcjfMWx9k6rah+11tRVy6ScRdwQrXsFst2ZWg==</latexit>
凸双対性(凸共役性) 10/56
<latexit sha1_base64="JLvqXGCoF2qJ5FVzMKYWvcRG7aA=">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</latexit>
<latexit sha1_base64="QU4hgV4ofArtMy2vMNm2wPBrMXY=">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</latexit>
を固定
凹関数
Ø の共役関数 を求める。
凸双対性(凸共役性)の具体例 11/56
<latexit sha1_base64="A6aAvMq5s2cVr1P2hEWZiaeYfgE=">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</latexit>
微分し、0とおくことで、
<latexit sha1_base64="bg9OUKGCz5rUCRZvCqsZa08e4i0=">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</latexit>
<latexit sha1_base64="gjySLL2vs1Od9+fNdPVePMmMyX8=">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</latexit>
よって共役関数は、
<latexit sha1_base64="+Lf3EE5tCBHWJ0cMwMl/bJS2d3s=">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</latexit>
<latexit sha1_base64="KbNCqoC3CFIEWaPWkWeRrbP2gM4=">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</latexit>
凸双対性(凸共役性)の具体例 12/56
Ø さらにその共役関数 を求める。
<latexit sha1_base64="val2wi8uc8H5+A2kySCXNHxnhWo=">AAACz3ichVHPSxRhGH6cyl+lbnUJugwtG+uCyzsSFEEgdOkUrrYqOLrMjN/o4Pxi5tt1bdjwqqduHToleIjuXQs61D/QwT8hOhp48dA73w6IivoN833P97zf8/60Y99LJdHhgHbj5q3BoeGR0dt3xsYnSnfvLaRRO3FE04n8KFmyrVT4Xiia0pO+WIoTYQW2LxbtzZe5fbEjktSLwjdyOxYrgbUeeq7nWJKpVqnmrma1Wq/anXxhBla3ZQpp6WbW1RWY0t3VWjWHk2avVSpTndTSLwKjAGUUazYq/YSJNURw0EYAgRCSsQ8LKX/LMECImVtBxlzCyFN2gR5GWdvmV4JfWMxu8r7Ot+WCDfme+0yV2uEoPv8JK3VU6Dd9piP6RV/oD51c6itTPvJctvm0+1oRtyb2HswfX6sK+JTYOFWxonJF1hIunqlsPc4+Vkxeh9P30Hn74Wj++Vwle0z79Jcr+ESH9INrCDv/nIOGmPuoMkqURmBL1RyoLELucsa2lCOssc1lrs39kOw540gb6OQd5QEa58d1ESxM1w2qG40n5ZnXxSiH8RCPUOV5PcUMXmEWTY7+Hl/xDd+1hralvdN2+k+1gUJzH2eWtvsfsU6miA==</latexit>
<latexit sha1_base64="TDyv0fiKxCNeNhFE+J6lKXCv250=">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</latexit>
微分し、0とおくことで、
<latexit sha1_base64="lLwYkzEinUZhe2HEn/ZQMs7r6VU=">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</latexit>
Ø 代⼊して元の関数が得られる。
<latexit sha1_base64="43PB+1JFTBi1xr2VMMXjnpDJC3g=">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</latexit>
凸関数と凹関数 13/56
<latexit sha1_base64="zjOkaDzbNOrX78AdrgGQFKkP9dg=">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</latexit>
<latexit sha1_base64="b/wQSdvnHYjiJWJIrvAr2XGrDyU=">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</latexit>
Ø 凸関数なら次式で下界が、
Ø 凹関数なら次式で上界が得られる。
Ø 凸でも凹でもない関数は?
ロジスティックシグモイド関数の共役関数 14/56
<latexit sha1_base64="74wxtiGn5YoZ8MZcnGlVXXfGKBg=">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</latexit>
Ø 凸でも凹でもないが、対数を取ると凹になる。
<latexit sha1_base64="ZMpjiiM6JDJHDE1yQ+egQgUZX6Y=">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</latexit>
<latexit sha1_base64="VuWh4aw50XFhchnUyg4pBCjJnVk=">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</latexit>
<latexit sha1_base64="u7uRQ/BtNIsomfCUn7VfjRQkgZw=">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</latexit>
Ø 可逆な変換で凸か凹にする。
ロジスティックシグモイド関数の共役関数 15/56
<latexit sha1_base64="XerOIyeWDNRnOpCpGwCXlTO887g=">AAAC6XichVE7b9NQFP5qXqU8GtoFicUiCkqGRMcVEgipUqUyMKE+SFupriLbvUmvYl9b9k2aYvUPsDGBYALEAPwMBhhZGMI/QIxFYmHg+MYIQQVcy/ec+53znaefhDLTROMp68TJU6fPTJ+dOXf+wsXZyqW5jSwepIFoB3EYp1u+l4lQKtHWUodiK0mFF/mh2PT7y4V9cyjSTMbqnj5IxE7k9ZTsysDTDHUqt3t1V2ivsehGUnVGtpsXT3tkN+1ufdRwDxebBnBDZWTTrjsGaTDyU+1UqtQic+zjilMqVZRnJa68g4tdxAgwQAQBBc16CA8Zf9twQEgY20HOWMqaNHaBQ8wwd8Begj08Rvt89/i1XaKK30XMzLADzhLynzLTRo0+0is6ovf0hj7T97/Gyk2MopYDlv6EK5LO7IPL69/+y4pYauz9YjGj9o+qNbq4aaqVXH1ikKKPYBJheP/R0fqttVp+jZ7TF+7gGY3pLfeghl+Dl6ti7ampKDUcgX3Tc2SqUDzlnG0ZZ9hlW5exAc9Dc+ScM+1hWEyUF+j8ua7jysZCy6GWs3q9unS3XOU0ruAq6ryvG1jCHaygzdlf4wPG+GT1rYfWY+vJxNWaKjnz+O1YL34A3rWvVA==</latexit>
⼆値エントロピー関数
シグモイド関数の上界 16/56
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<latexit sha1_base64="PeFsI3XEhSRRAROy8o4OYdqkIec=">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</latexit>
シグモイド関数の下界 17/56
Ø ガウス分布の関数形で下から抑えることもできる。
第⼆項に着⽬し、
<latexit sha1_base64="KRjXMoKW98Xn1SugNtD/eOdeFgE=">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</latexit>
について上記式は凸関数である。<latexit sha1_base64="Ri5Ac3BlTHNNPmYm8OUYpsx5b7Q=">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</latexit>
<latexit sha1_base64="Qq/s4lPLRiDEzf1XdvOropU1MZw=">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</latexit>
<latexit sha1_base64="tjrV1L8dINvgPV0bIW9YNv1V1DI=">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</latexit>
<latexit sha1_base64="nmJGcUfSNgOHmBJLiRz8iJ7jN8s=">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</latexit>
<latexit sha1_base64="xTieu3DeF0PgJrifQw09SFq/fN0=">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</latexit>
シグモイド関数の下界 18/56
共役関数:
<latexit sha1_base64="k48GeoXSEoUFQPKodexvHagt5c4=">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</latexit>
<latexit sha1_base64="TAaOQfzTlaTYwpOGcchauA4YChs=">AAAC1nichVFLaxRBEP4yPhLjIxu9CF6Cy0pEWGpCQBGEgBdPkoebLGTC0jPp2W0yL3p6N4nDeBPBk7ccPCl4EH+DJ8H4BzzkJ4jHCF48WNM7IBrUGqa7+qv66ulnkcoN0dGEc+r0mbOTU+emz1+4eGmmMXt5PU+HOpCdII1S3fVFLiOVyI5RJpLdTEsR+5Hc8HfuV/aNkdS5SpNHZj+TW7HoJypUgTAM9Rou3fOkEbe8UIugcMtica/0jEgGXiRDMz+G98piofS06g/MzXav0aQ2WZk7qbi10kQty2njEB62kSLAEDEkEhjWIwjk/G3CBSFjbAsFY5o1Ze0SJaaZO2QvyR6C0R0++/zarNGE31XM3LIDzhLxr5k5hxZ9prd0TJ/oHX2hH3+NVdgYVS37fPtjrsx6M8+vrn3/Lyvm22Dwi8WM1j+qNghxx1aruPrMIlUfwTjC6PHB8drd1VZxg17TV+7gFR3RB+4hGX0L3qzI1Ze2Im05Eru259hWkfCUC7blnGGbbSFjQ56H4cgFZxpgVE2UF+j+ua6TyvpC26W2u7LYXHpYr3IK13Ad87yv21jCAyyjw9kP8B4fceh0nSfOU+fZ2NWZqDlX8Js4L34CuHerbQ==</latexit>
変数 の凹関数<latexit sha1_base64="/Iy9HCtO8+r4iBZ9KRQ1lphmnsw=">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</latexit>
停留点の条件は
上記を満たす傾き の接線の接点の値 を とし以下を定義する。<latexit sha1_base64="QU4hgV4ofArtMy2vMNm2wPBrMXY=">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</latexit>
<latexit sha1_base64="lLo2QWxiuplwRfdeurknXoUEzzo=">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</latexit>
<latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit>
<latexit sha1_base64="RFDa8VTQyg6T4EqVg/PzllMb73M=">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</latexit>
<latexit sha1_base64="Ri5Ac3BlTHNNPmYm8OUYpsx5b7Q=">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</latexit>
<latexit sha1_base64="i+O+40JjvfQcfICXXwb9LEXzCLs=">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</latexit>
<latexit sha1_base64="seJd2bGCSpCTc7QBBwAkdO5RmgY=">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</latexit>
シグモイド関数の下界 19/56
<latexit sha1_base64="D/Ae+V7Q3lSpjqqd7O3P9dMsllk=">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</latexit>
Ø よって共役関数は、
<latexit sha1_base64="/PeAmxVC3Sxc8/vP9sWOwfLzdo0=">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</latexit>
Ø さらにその共役関数は、
<latexit sha1_base64="xzXG4i5JhpB7wYaRdFonM398vZo=">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</latexit>
Ø 上記から次が⾔える。
シグモイド関数の下界 20/56
<latexit sha1_base64="BdFR/kuo06b8uEzA2NBJJl7gmyE=">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</latexit>
利⽤法 21/56
Ø 例えば、次の計算をしたい。
<latexit sha1_base64="BsrCOlULvLUfPiPtdeU2t4p97Z4=">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</latexit>
<latexit sha1_base64="TOHusnu9V8vRVUMjPRbvHscduqw=">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</latexit>
<latexit sha1_base64="XQ3zACNF9B6i3eVpyLm3rvW6/cA=">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</latexit>
ガウス確率密度
Ø が成り⽴っていれば、
Ø を最⼤化することでより良い の近似が得られる。<latexit sha1_base64="k6YAghwPw02QfdG7jZaVdHLROqU=">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</latexit>
<latexit sha1_base64="oLHLOE+LM1OXMzkXaVxtjqRdjZ8=">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</latexit>
利⽤法 22/56
Ø 最適化した時の下界は⼀般に正確でない。
Ø 選んだξはあるaに依存するため。
10.6 変分ロジスティック回帰
変分近似とラプラス近似 24/56
Ø 局所的変分法をベイズロジスティック回帰で試そう。
Ø ラプラス近似同様に事後分布をガウス分布で近似する。
Ø ラプラス近似より⾼い精度。
Ø (データが相対的に少ない時?)
Ø モデルエビデンスの厳密な下界として与えられる明確な⽬的関数を
最適化する。
10.6.1 変分事後分布
ベイズロジスティック回帰 26/56
<latexit sha1_base64="NTHRShrf8QBjGCd8EO3bMqbuLGs=">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</latexit>
Ø 周辺尤度
Ø 前節から
<latexit sha1_base64="auBGISuM2E0lrp8PNg5C3ut19VM=">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</latexit>
<latexit sha1_base64="+fak5d0Hxfskxj51ODUZx6TZZEM=">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</latexit>
尤度の下界 27/56
Ø 前節から
<latexit sha1_base64="BdFR/kuo06b8uEzA2NBJJl7gmyE=">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</latexit>
再掲
<latexit sha1_base64="KRxItl9qc7qESpOsqWNK3U54S40=">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</latexit>
Ø 観測値ごとに変分パラメータを⽤意する。
同時分布の下界 28/56
<latexit sha1_base64="pn/4oYN8oh9lK07eCoW2QCMzQLY=">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</latexit>
<latexit sha1_base64="clRvhZ6HKAe66BFzcy0qmc7Vo4I=">AAAEinicpVHLbtNAFL0xBkopNIUNEpsRUapUgBlHSLyEVAkWSEhVX2krxSHyY2KP6hf2JG1q5Qf4ARasQGKB+AwW8AMsumeDWBaJDQuux24KLZRFJ4rnzLlzzr13rhX7PBWU7laUU+rpM2cnzk2en7pwcbo6c2ktjfqJzVp25EfJhmWmzOchawkufLYRJ8wMLJ+tW5uP8vj6gCUpj8JVMYxZJzDdkPe4bQqkujOVL4bPekIzLObyMDN97obMGRGPNIgRmMKzeiQjW2REbhBjm5M58pDMImPESeSQLqIQGR3jzxAv4G6k3A1MIm0bUlPcwkjCXU/MEYNtx8TIDvnneskkAaJVZFBhRb6TDgPcZE6PI7lvJ8bo5jjbyRyv/7XcW6SZnwzsO0+Eb+sc314Zyrf2SUsqTDtS2Cxa/S3lPjtOjZCFzsEYi4DWrdaoRuUiR4FeghqUazGqfgQDHIjAhj4EwCAEgdgHE1L8tUEHCjFyHciQSxBxGWcwgknU9vEWwxsmspv4dfHULtkQz7lnKtU2ZvHxn6CSQJ1+pu/oHv1E39Ov9Oc/vTLpkdcyxN0qtCzuTr+4svLjv6oAdwHegQoV9WOqFtCDu7JajtXHksn7sAuHwc7LvZX7y/Vslr6h37CD13SXfsAewsF3++0SW34lK0qkhsGW7DmQVYT4yhnGUszgYKyHXB/fQ6Bzhpk8GOQvigPUD4/rKFhrajrV9KXbtfmFcpQTcBWuQQPndQfm4QksQgts5anyXNlRMnVKbar31AfFVaVSai7DH0t9/AtYxTLP</latexit>
<latexit sha1_base64="pYtNZg2paon8StH4xBwbnoJgSFY=">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</latexit>
正規化されていない
Ø 事後分布は不等式の左辺を正規化する必要がある。
Ø 事前分布 を代⼊。
Ø wに関して整理。
同時分布の下界 29/56
<latexit sha1_base64="KJPnbIWxmnwfaZAP/gmhXjAMmAI=">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</latexit>
<latexit sha1_base64="w1Yj6XHxfvMKMrXFKDR3a3TTcao=">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</latexit>
<latexit sha1_base64="fPq3ubv6IWiGkjtDOB7TqGf9DNo=">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</latexit>
<latexit sha1_base64="OTHT0BWFqlyj14TmEiNGsmyQgXI=">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</latexit>
<latexit sha1_base64="lFtmVVgv30BVasQmy54awBDZmmo=">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</latexit>
変分事後分布 30/56
Ø wの2次と1次の項にそれぞれ着⽬。
Ø 事後分布の変分近似は、以下のガウス分布。
<latexit sha1_base64="LIazSVhfl6dDlvF7MdNWCnNvaG4=">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</latexit>
<latexit sha1_base64="RlZGYDbyt7ZCQf/kWtThYWfolZQ=">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</latexit>
<latexit sha1_base64="ViaPDGaKb9JaVzXSHgGdnDjDfUo=">AAADC3ichVE7axRRFP4yPhLjI6s2gs3FZSUBWe6IoAhCwCZVSLJuEkjCMjO5kx0yr8zc3RDH/AEhtYWVgoVY2omdiBa2FvkJYmcEC1P4zd0B1wT1DnPvOd8533m6aRjkWsr9EevEyVOnR8fOjJ89d/7CRO3ipcU86WWeantJmGTLrpOrMIhVWwc6VMtpppzIDdWSu3m/tC/1VZYHSfxA76RqLXI24sAPPEcT6tT8LTEpViNHd11fFGJb7IopcW+AeE5IaJbQUZdHQ3pEvVP53RjCW0P4VKdWl01pjjgu2JVQR3XmktoHrGIdCTz0EEEhhqYcwkHObwU2JFJiayiIZZQCY1fYxTi5PXopejhEN3lvUFup0Jh6GTM3bI9ZQv4ZmQIN+Vm+lAfyo3wlv8jDv8YqTIyylh2+7oCr0s7E4yutH/9lRXw1ur9ZZDT+UbWGjzum2oDVpwYp+/AGEfoPnxy07i40iuvyufzKDp7JffmOPcT9796LebXw1FSUGY7Ctuk5MlXEnHJBW84M67T5xHqch2bkgpm66JcT5QLto+s6LizebNqyac/fqk/PVqscw1VcwyT3dRvTmMEc2sz+Cd/wE4fWnvXaemO9HbhaIxXnMv441vtf7Ei51w==</latexit>
ただし、
ラプラス近似と変分近似 31/56
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<latexit sha1_base64="+eUiHNS+mqu4nHPxFHfjRI07lg0=">AAADGXichVHNahRBEK4Zo0nWn6zmInhpXFYSkKUmBBRBSPDixbDJZpNAEpaZSW92yPw507shmewL+AIeclLwID5FyCHBq3hI3kA8RvDiwW96B9QNag3TXfVVffXT5cS+lyrmM8O8MnL12ujYeOn6jZu3Jsq376ykUTdxZdON/ChZc+xU+l4om8pTvlyLE2kHji9XnZ1nuX+1J5PUi8JltRfLzcDeDr2259oKUKusXoopsRHYquO0RSZ2RV9Mi6cDxLV9QAuAhkMOhuwWbo0kAbQX83VgffHwt6hGEZVnm26VK1xjLeKyYhVKhQqpR+UT2qAtisilLgUkKSQF3SebUnzrZBFTDGyTMmAJNE/7JfWpBG4XURIRNtAdnNuw1gs0hJ3nTDXbRRUffwKmoCp/5vd8waf8gb/wj7/mynSOvJc93M6AK+PWxKu7je//ZQW4FXV+scCo/qNrRW16rLv10H2skXwOd5Cht//6ovFkqZo94Lf8FRO84TM+xgxh75v7blEuHeqOEs2RtKtnDnQXIV45gy9FhS342sC6eA+FzBkqdaiXvygWaA2v67KyMlOzuGYtzlbmFopVjtE9uk9T2NcjmqPnVKcmqp8bZIwbJfPQPDJPzY+DUNMoOJP0h5iffgJYwbw9</latexit>
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<latexit sha1_base64="LIazSVhfl6dDlvF7MdNWCnNvaG4=">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</latexit>
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<latexit sha1_base64="g5hV1WO8BRkRcOMI6jDwKR+ekYw=">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</latexit>
ラプラス近似 変分近似
10.6.2 変分パラメータの最適化
変分パラメータの最適化 33/56
Ø 周辺尤度の最⼤化で変分パラメータの決定を⾏う。
<latexit sha1_base64="EbiGLqo3150yogEcP/2ij48L5O8=">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</latexit>
Ø 決定⽅法は⼆通り。
1. wを潜在変数とみなしてEMアルゴリズム。
2. wに対する積分を解析的に計算し、直接最⼤化。
変分パラメータの最適化(EMアルゴリズム) 34/56
Ø Eステップ
Ø Mステップ
変分パラメータに初期値を与え、事後分布を計算。
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<latexit sha1_base64="qTAIIDoZxOf/chfgH2Z2mM2J40U=">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</latexit>
Mステップの導出は次⾴
<latexit sha1_base64="dlNbpx4vI4Cch2999gRmw2MAnhc=">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</latexit>
Mステップの導出 35/56
<latexit sha1_base64="nAH8H/iBJ/UQzVdxVzNvNxLgvjo=">AAADt3ichVHNitNQFD6Z+DPWn2l1I7i5WFpakHIjgjOCMCCCK5nO2JmB3lqS9Ka5TP6a3KStoS/gC7gQBAVR8TFc6Au4mEcQlyO4ceFJGhg7dfSG5Jx83/nOzz1G4IhIUnqorKhnzp47v3qhdPHS5Str5crV3ciPQ5N3TN/xw31Dj7gjPN6RQjp8Pwi57hoO3zMOHmT8XsLDSPjeEzkNeM/Vh56whKlLhPoVpdImzOGWbBBm+M4gmrpoSErYRJAZufVX9GnmST6RaJFFZEZYKIa2bJJSnfFRLBLCXF3ahoEhD5HuYhWP2KRR4Bbi41MLNEmwFNkkPcJYqX6fCU+S0TGfjjOSOf4QMXsRX0ifYvITuefaJhn8AfTLVdqi+SHLjlY4VSjOll/+DAwG4IMJMbjAwQOJvgM6RPh0QQMKAWI9SBEL0RM5z2EGJdTGGMUxQkf0AL9D/OsWqIf/Wc4oV5tYxcE3RCWBGv1KP9Aj+oV+pN/or1NzpXmOrJcpWmOu5UF/7fn1nZ//VbloJdjHKlTU/tG1BAvW824Fdh/kSDaHOc+QPHtxtHNvu5bW6Rv6HSd4TQ/pJ5zBS36Yb9t8+2XeUZhrOIzzmd28Cw9vOUUuwgoD5CzEYrwPiZlTrGRDkt0oLlA7ua5lZ/d2S6MtrX2nuvm4WOUq3ICb0MB93YVNeARb0AFTmSivlHfKe3VD7auWas9DV5RCcw0Wjjr6DRwE8Tg=</latexit>
Ø 変分パラメータのみに着⽬。
Ø 次式の期待完全データ対数尤度の最⼤化。
<latexit sha1_base64="mOlpuwuwP70InmKqMZj8oFCU0Ck=">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</latexit>
Mステップの導出 36/56
<latexit sha1_base64="Wjq9SmREfZOm+3vI+JIkgj1yyqo=">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</latexit>
Ø よって停留条件は、
<latexit sha1_base64="pYuKEdQWwA/S54Iq01Dzm3QDebg=">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</latexit>
Mステップの導出 37/56
<latexit sha1_base64="tNfEyMsrCmb48i8vAqbpjGV6bTs=">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</latexit>
の範囲で なので(らしいので)。
Mステップの導出 38/56
<latexit sha1_base64="9j7iqVUU5GmMcdap/y2zPyhutYc=">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</latexit>
<latexit sha1_base64="vj4gVcf2qtrYp0KyD5uShtKEbUU=">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</latexit>
<latexit sha1_base64="u4c41hRcLRwjjR8kmdYuxYMQfzo=">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</latexit>
<latexit sha1_base64="RRO/+syrrmDGgwrD/C7ETeFV+NI=">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</latexit>
Mステップの導出 39/56
<latexit sha1_base64="RkXfS6adws2Y/NEprDkjbGUXA/s=">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</latexit>
<latexit sha1_base64="nsCdJYvXSPrJqzQYgZa+RDH36Es=">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</latexit>
なので、
<latexit sha1_base64="2wrOnUDb+2ggKVGZg9ISLgKyK8E=">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</latexit>
Ø よって更新式は
EMアルゴリズム再掲 40/56
Ø Eステップ
Ø Mステップ
変分パラメータに初期値を与え、事後分布を計算。
<latexit sha1_base64="ztCNKfptK8V/LmsaZikT5EUxlvs=">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</latexit>
<latexit sha1_base64="qTAIIDoZxOf/chfgH2Z2mM2J40U=">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</latexit>
<latexit sha1_base64="dlNbpx4vI4Cch2999gRmw2MAnhc=">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</latexit>
変分パラメータの最適化(直接計算) 41/56
Ø 解析的に計算をする。
<latexit sha1_base64="29G1w0vb81zT+aX55MUa0Tc1pgA=">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</latexit>
<latexit sha1_base64="eUjU7iUOCywaK1G8W3W/fqM7Eb4=">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</latexit>
<latexit sha1_base64="pGZGcpbiP7KW1GYx5s/LIhWuNMA=">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</latexit>
変分パラメータの最適化(直接計算) 42/56
<latexit sha1_base64="pGZGcpbiP7KW1GYx5s/LIhWuNMA=">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</latexit>
を変分パラメータについて微分。
<latexit sha1_base64="wpY5xvHIBD26CbwkRWBWiKKGtSA=">AAADUXichVHLahRBFL3d4yMmasa4Edw0GUbiwqFaBIMgJLpxJXlNEkjHobpTPVOkX1TXjMYmP5AfyMKVggvRv3Che8kinxBcRhDBhadrGjQZo9V01b3n3nOffhbJXDN2aNm1c+cvXBy7ND5x+crVyfq1qdU87atAtIM0StW6z3MRyUS0tdSRWM+U4LEfiTV/+3FpXxsIlcs0WdE7mdiMeTeRoQy4BtSpf/BCxQOncLyMKy155Oz+qbyA6kUi1DOOF3Pd80NY5wE+w3vHcUuzkt2evu08hH6mz+kkJx1HU/49TqfeYC1mjjMquJXQoOospPVP5NEWpRRQn2ISlJCGHBGnHN8GucQoA7ZJBTAFSRq7oF0aB7cPLwEPDnQbdxfaRoUm0MuYuWEHyBLhV2A61GQH7B07Zp/Ze3bEfp4ZqzAxylp28PpDrsg6k3s3lr//lxXj1dT7zQKj+Y+qNYU0a6qVqD4zSNlHMIwweLl/vPxgqVncYm/YV3Twmh2yj+ghGXwL3i6KpVemImU4gp6bnmNTRYIpF7DlyLAFWwisj3loRC6QqUeDcqJYoHt6XaPC6t2Wy1ru4r3G3NNqlWN0k6ZpBvu6T3P0hBaoTYE1Zc1a89Yj+4v9o0Y1e+hqWxXnOp04tYlfWsXNTg==</latexit>
<latexit sha1_base64="N26PLkkMymPvo5oRwid9oc3HeTY=">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</latexit>
<latexit sha1_base64="2cxSTgfaglPQw7rj2exLhRUfldY=">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</latexit>
<latexit sha1_base64="E68yQUgcmWZG+h6Oj9/0ORlJ9gQ=">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</latexit>
⼀項⽬について、
<latexit sha1_base64="lC2d+qFtZQ0Tixcx2uhKXNbmLQc=">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</latexit>
変分パラメータの最適化(直接計算) 43/56
⼆項⽬について、
<latexit sha1_base64="WG5RcEGNcWj7NaAhAO0PtGZNcMc=">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</latexit>
<latexit sha1_base64="v21CAA0ElvGN5sa0a5hKKbYheIw=">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</latexit>
三項⽬について、
<latexit sha1_base64="uNGszaGZidF8u1u9exhyt5iwMqM=">AAADk3iclVFNa9VAFL1p/Kj1o6+KILgZfDypiI9JESqKUNSFG6Vfry00NUzyJu8NnUzCZN7TNryVrvwDLlwpuBB/hgv9Ay76E0RwU8GNC28mUavFihOSuTnnnjP3zg0zKXJD6Y4z5h46fOTo+LGJ4ydOnppsTJ1eydOBjngnSmWq10KWcykU7xhhJF/LNGdJKPlquHm75FeHXOciVctmK+MbCespEYuIGYSCxmc/1iwq/IxpI5gc/YyI/0gEauRLHptpXyri56KXMFIBJUsCUhBFRsTXotc3l8gVYs0Q9RAtyEzJ7cm7jGKsrHugyV7sQWVSUzd/qEvYz7RIeKn7L6ug0aRtahfZH3h10IR6zaeNd+BDF1KIYAAJcFBgMJbAIMdnHTygkCG2AQViGiNheQ4jmEDtALM4ZjBEN/Hbw7/1GlX4X3rmVh3hKRJfjUoCLfqBvqa79D19Qz/Sb3/1KqxHWcsW7mGl5Vkw+fTc0td/qhLcDfR/qVDROqBqAzFcs9UKrD6zSNlHVDkMt5/tLl1fbBUX6Uv6CTt4QXfoW+xBDb9Erxb44nNbkbYaDg9tz4mtQuEtF8jleEIXuRixAd6HQecCT+rDsLxRHKD357j2ByszbY+2vYWrzbn79SjH4TxcgGmc1yzMwV2Yhw5EzrKz7Tx2nrhn3RvuLfdOlTrm1Joz8Nty730HSbXlgA==</latexit>
変分パラメータの最適化(直接計算) 44/56
<latexit sha1_base64="9o3GmLPX44o5vnqi/eclSsPTJjw=">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</latexit>
<latexit sha1_base64="6TK7HxMutL9rpUQgsJFcCTjZZI0=">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</latexit>
Ø 整理して、
予測分布と分離境界 45/56
10.6.3 超パラメータの推論
よりbayesianに 47/56
Ø ここまでは事前分布の超パラメータは既知の定数。
超パラメータもデータから決定しよう‼
Ø 事前分布に次の等⽅ガウス分布を仮定する。
<latexit sha1_base64="XUQytaIJRAonVtNofVeS+XPnYTU=">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</latexit>
Ø 共役超事前分布はガンマ分布。
<latexit sha1_base64="mxkhMYexzNIrskUaDqYQ8YwWdJM=">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</latexit>
周辺尤度 48/56
<latexit sha1_base64="DvlxvY/jPpqiPK1BX2a3V6n9s80=">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</latexit>
<latexit sha1_base64="BbkFih2soHrnlTk2OPf3teldP+w=">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</latexit>
<latexit sha1_base64="pYtNZg2paon8StH4xBwbnoJgSFY=">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</latexit>
sigmoid gauss gamma
Ø 解析的に計算不可。
Ø 局所的変分法と⼤域的変分法でなんとかしよう。
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6
PRML 10.5-10.6

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PRML 10.5-10.6

  • 2. ⽬次 2/56 Ø 10.5 局所的変分推論法 Ø 10.6 変分ロジスティック回帰 Ø 10.6.1 変分事後分布 Ø 10.6.2 変分パラメータの最適化 Ø 10.6.3 超パラメータの推論
  • 4. モチベーション 4/56 Ø すべての変数における事後分布を直接近似。 これまで Ø 各変数や変数群における関数の近似。 Ø 全体の計算可能な近似を得る。 ここから
  • 5. 凸関数 5/56 <latexit sha1_base64="9C98peB2xLfL2FeLOcnOmUwdDYE=">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</latexit> <latexit sha1_base64="OFUbOVVJlChoGW4jxtUJId6CKQM=">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</latexit> 広義: 狭義: ※wikiより
  • 6. (等号成⽴は ) はパラメータ を持つ⼀次関数 凸関数の接線は下界 6/56 <latexit sha1_base64="2XAIiyCU1NQoQUqB59AT005TsyM=">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</latexit> <latexit sha1_base64="Rt8nnLvi7SbeMI4vtWC6B7S+pWQ=">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</latexit> における接線は、 <latexit sha1_base64="S57dKv3EOwl2m1CE3oZlEoZTCG8=">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</latexit> <latexit sha1_base64="SZSq+TGCEflOiSpowPztIXxnwgk=">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</latexit> <latexit sha1_base64="Rt8nnLvi7SbeMI4vtWC6B7S+pWQ=">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</latexit> <latexit sha1_base64="CUOz4p3oZ51Cp2DuvlGEOETiy+o=">AAACp3ichVFLSxtRFP4cbX3VJtWN4EYaImYTzoiglC4EN+6Mj8SAisxMbsyQeTFzE00H/4ALtxG6quBC/Bku9A+48CdIlwpuuuiZm4FSRT3D3Hvud853nmbg2JEkuuvT+gc+fBwcGh4Z/TT2OZP9Ml6J/FZoibLlO35YNY1IOLYnytKWjqgGoTBc0xFbZnM5sW+1RRjZvrcpO4HYdY19z67bliETqDN7WNjL5qhISqZfKnqq5JBKyc9eYwc1+LDQggsBD5J1BwYi/rahgxAwtouYsZA1W9kFjjDC3BZ7CfYwGG3yuc+v7RT1+J3EjBTb4iwO/yEzp5GnW7qgB7qhS7qnP6/GilWMpJYO32aPK4K9zPHkxtO7LJdvicY/FjPyb1QtUceiqtbm6gOFJH1YvQjtH92HjW/r+XiGzug3d/CL7uiKe/Daj9b5mlj/qSoKFUfgQPXsqio8nnLMtogz1NhWZ6zF85AcOeZMDbSTifIC9efreqlU5oo6FfW1+dzS93SVQ5jCV8zyvhawhBWUUObsDZygi1OtoK1qFa3ac9X6Us4E/hPN+AvcZ5ge</latexit> <latexit sha1_base64="ShLK0uIOXzmGXX9dHw1ZMjdUqiQ=">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</latexit>
  • 7. ( の変更)=(接線の変更) を意味し、 凸関数の下界による近似 7/56 <latexit sha1_base64="DUGMXH/QO09Jintxsy2cBdDrj1g=">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</latexit> とすると接線は、 <latexit sha1_base64="KoGuoEgkIZxQctHdNJSNNeZ1BUw=">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</latexit> <latexit sha1_base64="e8sx5JLcmkulywdPDdmp6zcFTQE=">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</latexit> <latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit> <latexit sha1_base64="qLnOF0HvLjDz9gnn81OZSiMzswY=">AAACvnichVHNStxQFP6M2lpb62g3FTehw8gIMpwUweJqoJuuij8dFRwZknijwZsfkzvTGUPpvi/QRVctuChC+xAu7Au48BHEpUI3XfTkTkBUbE/Ived+53zn14mlnyqiswFjcGj4wcORR6OPn4w9HS9NTK6lUTtxRcONZJRsOHYqpB+KhvKVFBtxIuzAkWLd2Xud29c7Ikn9KHynerHYCuyd0Pd811YMtUpTvWp3zmwKZc+aTSn2U2mHyvSq3dlWqUw10mLeVaxCKaOQpah0gia2EcFFGwEEQijWJWyk/G3CAiFmbAsZYwlrvrYLfMAoc9vsJdjDZnSPzx1+bRZoyO88ZqrZLmeR/CfMNFGhU/pOl/SLjuic/twbK9Mx8lp6fDt9rohb45+er/7+LyvgW2H3msWMyj+qVvDwSlfrc/WxRvI+3H6EzsHny9XFlUo2Q9/ogjv4Smd0zD2EnSv3cFmsfNEVJZoj8F73HOgqQp5yxraUM2yzzWOszfNQHDnjTLvo5BPlBVq313VXWXtZs6hmLc+X62+LVY5gGi9Q5X0toI43WEKDs3/EIX7gp1E3PCMwor6rMVBwnuGGGN2/0hGgRA==</latexit> であるので、 ⼀次関数で近似に成功。 ただし、変分パラメータ の最適化が必要。<latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit> xは固定
  • 8. 凸双対性(凸共役性) 8/56 Ø ルジャンドル変換 関数の変数変換⼿法。 凸関数を接線で表現できることに基づく(らしい)。 <latexit sha1_base64="+Lf3EE5tCBHWJ0cMwMl/bJS2d3s=">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</latexit> Ø 再度変換 <latexit sha1_base64="val2wi8uc8H5+A2kySCXNHxnhWo=">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</latexit> 凸関数の時、 <latexit sha1_base64="p2jX1w7rhiZKcaPFNQxhhkbYE/k=">AAACq3ichVHNShtRFP6capumtUa7KXQjDSkiGM6IUCkIgW66KtGYGPxlZryjg/PHzM2UdMgLdNlNF+lGoYvSx+iivoCLPELpMoVuXHjmZkBU1DPMved+53zn1wxdJ5ZEgzHtwfjEw0eFx8UnTyefTZWmZ1px0Iks0bQCN4japhEL1/FFUzrSFe0wEoZnumLDPHqX2TcSEcVO4K/Lbih2POPAd2zHMiRDbXs3nZ/vrdh7pTJVScnsTUXPlTJyqQel39jGPgJY6MCDgA/JugsDMX9b0EEIGdtByljEmqPsAj0UmdthL8EeBqNHfB7waytHfX5nMWPFtjiLy3/EzFlU6Ix+0JBO6Sf9ofNbY6UqRlZLl29zxBXh3tTnF43/97I8viUOL1nMqNxRtYSNZVWtw9WHCsn6sEYRkk9fh423a5X0NZ3QX+7gmAb0i3vwk3/W91Wx1lcVRYoj8FH17KkqfJ5yyraYM+yzzWasw/OQHDnlTIdIsonyAvXr67qptBarOlX11aVy7UO+ygJe4hXmeF9vUMN71NFUe/qCPr5pC1pD29S2R67aWM55jiuiiQu+gJnJ</latexit>
  • 9. 凸な関数 凸双対性(凸共役性) 9/56 <latexit sha1_base64="urMAGuHwdsLWjSP3bI1/t/IvwXE=">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</latexit> <latexit sha1_base64="V44FKJx7AsnXG5hdegTFBvob+dQ=">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</latexit> 接線 を固定 <latexit sha1_base64="QigStEQS1nbpaCOxUqiyWk0RXng=">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</latexit> <latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit> 凹関数 切⽚ <latexit sha1_base64="kZYJdecMeXUdA9R50TaOm85lsT4=">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</latexit>
  • 10. 凸双対性(凸共役性) 10/56 <latexit sha1_base64="JLvqXGCoF2qJ5FVzMKYWvcRG7aA=">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</latexit> <latexit sha1_base64="QU4hgV4ofArtMy2vMNm2wPBrMXY=">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</latexit> を固定 凹関数
  • 11. Ø の共役関数 を求める。 凸双対性(凸共役性)の具体例 11/56 <latexit sha1_base64="A6aAvMq5s2cVr1P2hEWZiaeYfgE=">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</latexit> 微分し、0とおくことで、 <latexit sha1_base64="bg9OUKGCz5rUCRZvCqsZa08e4i0=">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</latexit> <latexit sha1_base64="gjySLL2vs1Od9+fNdPVePMmMyX8=">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</latexit> よって共役関数は、 <latexit sha1_base64="+Lf3EE5tCBHWJ0cMwMl/bJS2d3s=">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</latexit> <latexit sha1_base64="KbNCqoC3CFIEWaPWkWeRrbP2gM4=">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</latexit>
  • 12. 凸双対性(凸共役性)の具体例 12/56 Ø さらにその共役関数 を求める。 <latexit sha1_base64="val2wi8uc8H5+A2kySCXNHxnhWo=">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</latexit> <latexit sha1_base64="TDyv0fiKxCNeNhFE+J6lKXCv250=">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</latexit> 微分し、0とおくことで、 <latexit sha1_base64="lLwYkzEinUZhe2HEn/ZQMs7r6VU=">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</latexit> Ø 代⼊して元の関数が得られる。 <latexit sha1_base64="43PB+1JFTBi1xr2VMMXjnpDJC3g=">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</latexit>
  • 13. 凸関数と凹関数 13/56 <latexit sha1_base64="zjOkaDzbNOrX78AdrgGQFKkP9dg=">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</latexit> <latexit sha1_base64="b/wQSdvnHYjiJWJIrvAr2XGrDyU=">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</latexit> Ø 凸関数なら次式で下界が、 Ø 凹関数なら次式で上界が得られる。 Ø 凸でも凹でもない関数は?
  • 14. ロジスティックシグモイド関数の共役関数 14/56 <latexit sha1_base64="74wxtiGn5YoZ8MZcnGlVXXfGKBg=">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</latexit> Ø 凸でも凹でもないが、対数を取ると凹になる。 <latexit sha1_base64="ZMpjiiM6JDJHDE1yQ+egQgUZX6Y=">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</latexit> <latexit sha1_base64="VuWh4aw50XFhchnUyg4pBCjJnVk=">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</latexit> <latexit sha1_base64="u7uRQ/BtNIsomfCUn7VfjRQkgZw=">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</latexit> Ø 可逆な変換で凸か凹にする。
  • 16. シグモイド関数の上界 16/56 <latexit sha1_base64="oHaEoGfHCcIxfi1+gW5QF5PrVmg=">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</latexit> <latexit sha1_base64="Pe7ZGgSMkldnVSjRai8IqHu8T08=">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</latexit>
  • 17. <latexit sha1_base64="PeFsI3XEhSRRAROy8o4OYdqkIec=">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</latexit> シグモイド関数の下界 17/56 Ø ガウス分布の関数形で下から抑えることもできる。 第⼆項に着⽬し、 <latexit sha1_base64="KRjXMoKW98Xn1SugNtD/eOdeFgE=">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</latexit> について上記式は凸関数である。<latexit sha1_base64="Ri5Ac3BlTHNNPmYm8OUYpsx5b7Q=">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</latexit> <latexit sha1_base64="Qq/s4lPLRiDEzf1XdvOropU1MZw=">AAAC2XichVG9axRBFP9lTTTGaM7YCDbB4+RSeMweAUUIBGysJF+XBG7DsTuZvRsy+8Hs3Jm4XGEnaS0ErRQsxH8iYGG0t8ifIJYRbCx8O7cQYlBn2Xlvfu/93meQKpkZxo7HnAvjExcvTV6eujJ99dpM5frsRpb0NRctnqhEbwV+JpSMRctIo8RWqoUfBUpsBrsPC/vmQOhMJvG62U/FduR3YxlK7huCOpWFsL43v3jXU7GnRGjqTY8nWW+ke6H2eb43zJtDT8tuz8yXolOpsgazZ+684pZKFeVZTiqf4GEHCTj6iCAQw5Cu4COjrw0XDClh28gJ06RJaxcYYoq4ffIS5OETukt3l17tEo3pXcTMLJtTFkW/JuYcauwre89O2BH7wL6xX3+NldsYRS37JIMRV6SdmYObaz//y4pIGvROWcSo/aNqgxD3bbWSqk8tUvTBRxEGT1+erD1YreV32Fv2nTp4w47ZR+ohHvzg71bE6mtbkbYcgSe258hWEdOUc7JllGGHbCFhfZqHocg5ZephUEyUFuj+ua7zykaz4bKGu7JQXXpcrnISt3AbddrXPSzhEZbRouyvcIjP+OK0nWfOc+dg5OqMlZwbOHOcF78B44asPw==</latexit> <latexit sha1_base64="tjrV1L8dINvgPV0bIW9YNv1V1DI=">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</latexit> <latexit sha1_base64="nmJGcUfSNgOHmBJLiRz8iJ7jN8s=">AAACsXichVHLThRBFD20Lx4Ko25M3EycjMEFk9toonFF4oaFC14DGAaxu6lhOtOvdNeMYocf8AckcQWJC8NnsJAfcMEnEJaQuHHh6ZpODBD1drrq1rn33KebBH6mRY6HrGvXb9y8NTwyOnb7zvhE5e695SzupZ5qenEQp6uuk6nAj1RT+zpQq0mqnNAN1IrbfVXYV/oqzfw4WtLbiVoPna3Ib/ueowm9nWoFUXWy5cVZp/rhyUalJg0xUr2q2KVSQylzceU7WthEDA89hFCIoKkHcJDxW4MNQUJsHTmxlJpv7Ao7GCW3Ry9FD4dol+cWX2slGvFdxMwM22OWgH9KZhV1+SHf5EyO5EBO5NdfY+UmRlHLNm93wFXJxsSnB4s//8sKeWt0/rDIqP+jao02XphqfVafGKTowxtE6H/8fLb4cqGeP5Z9OWUHe3Ish+wh6p97X+fVwhdTUWo4Cu9Nz6GpIuKUc9oyZtikrU2sx3loRs6ZqYN+MVEu0L68rqvK8nTDloY9/6w287pc5TAe4hEmua/nmMEs5tBk9hS72MO+9dR6Y72z3IGrNVRy7uOCWN3fp8ebxQ==</latexit> <latexit sha1_base64="xTieu3DeF0PgJrifQw09SFq/fN0=">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</latexit>
  • 18. シグモイド関数の下界 18/56 共役関数: <latexit sha1_base64="k48GeoXSEoUFQPKodexvHagt5c4=">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</latexit> <latexit sha1_base64="TAaOQfzTlaTYwpOGcchauA4YChs=">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</latexit> 変数 の凹関数<latexit sha1_base64="/Iy9HCtO8+r4iBZ9KRQ1lphmnsw=">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</latexit> 停留点の条件は 上記を満たす傾き の接線の接点の値 を とし以下を定義する。<latexit sha1_base64="QU4hgV4ofArtMy2vMNm2wPBrMXY=">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</latexit> <latexit sha1_base64="lLo2QWxiuplwRfdeurknXoUEzzo=">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</latexit> <latexit sha1_base64="XVj0lrm+BjzxuE85C26PUXYT/Oc=">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</latexit> <latexit sha1_base64="RFDa8VTQyg6T4EqVg/PzllMb73M=">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</latexit> <latexit sha1_base64="Ri5Ac3BlTHNNPmYm8OUYpsx5b7Q=">AAACpnichVFNTxNRFD2MiggCRTcmbohNDavmDiHBsGrixhUBaikJX84Mr2XS+crMa7VO/AMkbGXhShMXxp/hQv+AC36CcYmJGxeeeZ2EAFHuZN6779x77qebBH6mRU7HrBs3b43fnrgzOXV3ema2MndvM4v7qadaXhzE6ZbrZCrwI9XSvg7UVpIqJ3QD1XZ7Twt7e6DSzI+j53qYqN3Q6UZ+x/ccTaj5am9xv1KVuhiZv6rYpVJFKWtx5St2cIAYHvoIoRBBUw/gIOO3DRuChNgucmIpNd/YFd5gktw+vRQ9HKI9nl2+tks04ruImRm2xywB/5TMedTku3ySM/kmn+WH/PlnrNzEKGoZ8nZHXJXszx49aP6+lhXy1jg8Z5FR+0/VGh08MdX6rD4xSNGHN4oweH1y1lzZqOWP5YP8ZAfv5VS+sIdo8Mv7uK423pmKUsNReGl6Dk0VEaec05YxwwFtHWJ9zkMzcs5MhxgUE+UC7cvruqpsLtZtqdvrS9XGarnKCTzEIyxwX8to4BnW0GL2Lo7xFifWgrVqtaz2yNUaKzn3cUGsF38BOMiX7A==</latexit> <latexit sha1_base64="i+O+40JjvfQcfICXXwb9LEXzCLs=">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</latexit> <latexit sha1_base64="seJd2bGCSpCTc7QBBwAkdO5RmgY=">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</latexit>
  • 19. シグモイド関数の下界 19/56 <latexit sha1_base64="D/Ae+V7Q3lSpjqqd7O3P9dMsllk=">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</latexit> Ø よって共役関数は、 <latexit sha1_base64="/PeAmxVC3Sxc8/vP9sWOwfLzdo0=">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</latexit> Ø さらにその共役関数は、 <latexit sha1_base64="xzXG4i5JhpB7wYaRdFonM398vZo=">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</latexit> Ø 上記から次が⾔える。
  • 21. 利⽤法 21/56 Ø 例えば、次の計算をしたい。 <latexit sha1_base64="BsrCOlULvLUfPiPtdeU2t4p97Z4=">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</latexit> <latexit sha1_base64="TOHusnu9V8vRVUMjPRbvHscduqw=">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</latexit> <latexit sha1_base64="XQ3zACNF9B6i3eVpyLm3rvW6/cA=">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</latexit> ガウス確率密度 Ø が成り⽴っていれば、 Ø を最⼤化することでより良い の近似が得られる。<latexit sha1_base64="k6YAghwPw02QfdG7jZaVdHLROqU=">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</latexit> <latexit sha1_base64="oLHLOE+LM1OXMzkXaVxtjqRdjZ8=">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</latexit>
  • 24. 変分近似とラプラス近似 24/56 Ø 局所的変分法をベイズロジスティック回帰で試そう。 Ø ラプラス近似同様に事後分布をガウス分布で近似する。 Ø ラプラス近似より⾼い精度。 Ø (データが相対的に少ない時?) Ø モデルエビデンスの厳密な下界として与えられる明確な⽬的関数を 最適化する。
  • 26. ベイズロジスティック回帰 26/56 <latexit sha1_base64="NTHRShrf8QBjGCd8EO3bMqbuLGs=">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</latexit> Ø 周辺尤度 Ø 前節から <latexit sha1_base64="auBGISuM2E0lrp8PNg5C3ut19VM=">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</latexit> <latexit sha1_base64="+fak5d0Hxfskxj51ODUZx6TZZEM=">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</latexit>
  • 27. 尤度の下界 27/56 Ø 前節から <latexit sha1_base64="BdFR/kuo06b8uEzA2NBJJl7gmyE=">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</latexit> 再掲 <latexit sha1_base64="KRxItl9qc7qESpOsqWNK3U54S40=">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</latexit> Ø 観測値ごとに変分パラメータを⽤意する。
  • 28. 同時分布の下界 28/56 <latexit sha1_base64="pn/4oYN8oh9lK07eCoW2QCMzQLY=">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</latexit> <latexit sha1_base64="clRvhZ6HKAe66BFzcy0qmc7Vo4I=">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</latexit> <latexit sha1_base64="pYtNZg2paon8StH4xBwbnoJgSFY=">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</latexit> 正規化されていない Ø 事後分布は不等式の左辺を正規化する必要がある。
  • 29. Ø 事前分布 を代⼊。 Ø wに関して整理。 同時分布の下界 29/56 <latexit sha1_base64="KJPnbIWxmnwfaZAP/gmhXjAMmAI=">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</latexit> <latexit sha1_base64="w1Yj6XHxfvMKMrXFKDR3a3TTcao=">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</latexit> <latexit sha1_base64="fPq3ubv6IWiGkjtDOB7TqGf9DNo=">AAAD8HicjVFLaxRBEK7J+IjxkY1eBC+Ny0pEXHuCkCAIAS/iIeS1SSATl5nZ3t0m82Kmd5N12D/gH1DwIBE8qCd/gwf9AyK56VE8RvDiwW96R1dNYuxlp6q/qq/q6yo39mWqON81Rsxjx0+cHD01dvrM2XPjpYnzK2nUSTxR8yI/StZcJxW+DEVNSeWLtTgRTuD6YtXdvJPHV7siSWUULqteLDYCpxXKpvQcBag+Ydy7xuy0E7A6y1jIbjOL9dl9+HOwti+ays6YHTiq7TaBbhVRjSQBvGUgyHQjv5H2Apg8GrclwEHJoswkU7+A6+hyg00xO5GttrqKu+1DcsP5mWpvyyG7SPoPEQV5qCXLlfwm5NDIgeUObDxA7T7D3JTYVoC9KExVlfXrpTKvcn3YfscqnDIVZz4qvSWbGhSRRx0KSFBICr5PDqX4rZNFnGJgG5QBS+BJHRfUpzFwO8gSyHCAbuLbwm29QEPc85qpZnvo4uOfgMmowt/zF3yPv+Ov+Gf+/dBama6Ra+nBugOuiOvjDy8ufTuSFcAqag9ZYFT+oVpRk2a0Wgn1sUbyd3iDCt0Hj/aWbi1Wsiv8Gf+CF+zwXf4Gbwi7X73nC2LxiVaUaI6gLf3mQKsIMeUMsRQdGog1gXUwD4XKGTq1qZtPFAu0/l7XfmdlqmrxqrVwszw7V6xylC7RZZrEvqZplu7SPNXIM14bH4yPxiczMR+bT82dQeqIUXAu0B/HfPkDPBsGSA==</latexit> <latexit sha1_base64="OTHT0BWFqlyj14TmEiNGsmyQgXI=">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</latexit> <latexit sha1_base64="lFtmVVgv30BVasQmy54awBDZmmo=">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</latexit>
  • 30. 変分事後分布 30/56 Ø wの2次と1次の項にそれぞれ着⽬。 Ø 事後分布の変分近似は、以下のガウス分布。 <latexit sha1_base64="LIazSVhfl6dDlvF7MdNWCnNvaG4=">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</latexit> <latexit sha1_base64="RlZGYDbyt7ZCQf/kWtThYWfolZQ=">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</latexit> <latexit sha1_base64="ViaPDGaKb9JaVzXSHgGdnDjDfUo=">AAADC3ichVE7axRRFP4yPhLjI6s2gs3FZSUBWe6IoAhCwCZVSLJuEkjCMjO5kx0yr8zc3RDH/AEhtYWVgoVY2omdiBa2FvkJYmcEC1P4zd0B1wT1DnPvOd8533m6aRjkWsr9EevEyVOnR8fOjJ89d/7CRO3ipcU86WWeantJmGTLrpOrMIhVWwc6VMtpppzIDdWSu3m/tC/1VZYHSfxA76RqLXI24sAPPEcT6tT8LTEpViNHd11fFGJb7IopcW+AeE5IaJbQUZdHQ3pEvVP53RjCW0P4VKdWl01pjjgu2JVQR3XmktoHrGIdCTz0EEEhhqYcwkHObwU2JFJiayiIZZQCY1fYxTi5PXopejhEN3lvUFup0Jh6GTM3bI9ZQv4ZmQIN+Vm+lAfyo3wlv8jDv8YqTIyylh2+7oCr0s7E4yutH/9lRXw1ur9ZZDT+UbWGjzum2oDVpwYp+/AGEfoPnxy07i40iuvyufzKDp7JffmOPcT9796LebXw1FSUGY7Ctuk5MlXEnHJBW84M67T5xHqch2bkgpm66JcT5QLto+s6LizebNqyac/fqk/PVqscw1VcwyT3dRvTmMEc2sz+Cd/wE4fWnvXaemO9HbhaIxXnMv441vtf7Ei51w==</latexit> ただし、
  • 31. ラプラス近似と変分近似 31/56 <latexit sha1_base64="aIoONOQCyR0CV59pEA/k2/nepb0=">AAADBXichVHLahRBFL1pXzE+MupGcFM4jMTNUC2CISAE3LiSvCYJpOPY3VM9XaRfVNVMGJtZC/6AC1cKLkTciVsXgvoDLvIJorv42LjwdE2LaFCr6bq3zqlzH3WDIpHacL435Rw6fOTosenjMydOnjo92zhzdl3nAxWKTpgnudoMfC0SmYmOkSYRm4USfhokYiPYuVHxG0OhtMyzNTMqxHbq9zMZydA3gLqNOyPWZSXL2JhdZ56W/dRnXiIiM8e81DdxEIHdBXsb1iIqhbcGZMy8IE96epTCVGwRS4A/w3lK9mNzudto8ja3ix103NppUr2W8sZb8qhHOYU0oJQEZWTgJ+STxrdFLnEqgG1TCUzBk5YXNKYZaAe4JXDDB7qDvY/TVo1mOFcxtVWHyJLgV1AyavH3/Cnf5+/4M/6Bf/9rrNLGqGoZwQYTrSi6s/fPr377ryqFNRT/UkHR+kfVhiKat9VKVF9YpOojnEQY3n2wv7qw0iov8cf8Izp4xPf4a/SQDT+HT5bFykNbkbIaQbu259RWkeGVS3AaGXrgImADvIdB5BKZYhpWL4oBun+O66CzfqXt8ra7fLW5eKse5TRdoIs0h3ldo0W6SUvUQfY39Im+0FfnnvPceeG8nFx1pmrNOfptOa9+AKmMuoI=</latexit> <latexit sha1_base64="+eUiHNS+mqu4nHPxFHfjRI07lg0=">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</latexit> <latexit sha1_base64="izyZ0d9yB83LdAnmAQ9OFCOKOdQ=">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</latexit> <latexit sha1_base64="LIazSVhfl6dDlvF7MdNWCnNvaG4=">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</latexit> <latexit sha1_base64="RlZGYDbyt7ZCQf/kWtThYWfolZQ=">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</latexit> <latexit sha1_base64="ViaPDGaKb9JaVzXSHgGdnDjDfUo=">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</latexit> <latexit sha1_base64="g5hV1WO8BRkRcOMI6jDwKR+ekYw=">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</latexit> ラプラス近似 変分近似
  • 33. 変分パラメータの最適化 33/56 Ø 周辺尤度の最⼤化で変分パラメータの決定を⾏う。 <latexit sha1_base64="EbiGLqo3150yogEcP/2ij48L5O8=">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</latexit> Ø 決定⽅法は⼆通り。 1. wを潜在変数とみなしてEMアルゴリズム。 2. wに対する積分を解析的に計算し、直接最⼤化。
  • 34. 変分パラメータの最適化(EMアルゴリズム) 34/56 Ø Eステップ Ø Mステップ 変分パラメータに初期値を与え、事後分布を計算。 <latexit sha1_base64="ztCNKfptK8V/LmsaZikT5EUxlvs=">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</latexit> <latexit sha1_base64="qTAIIDoZxOf/chfgH2Z2mM2J40U=">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</latexit> Mステップの導出は次⾴ <latexit sha1_base64="dlNbpx4vI4Cch2999gRmw2MAnhc=">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</latexit>
  • 35. Mステップの導出 35/56 <latexit sha1_base64="nAH8H/iBJ/UQzVdxVzNvNxLgvjo=">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</latexit> Ø 変分パラメータのみに着⽬。 Ø 次式の期待完全データ対数尤度の最⼤化。 <latexit sha1_base64="mOlpuwuwP70InmKqMZj8oFCU0Ck=">AAAET3ichVFPaxNBFH/ZRG3jn6b1IngZDAkVNc4GqSIUAyJ4Kk3btIVsDLubSTJ0/7E7SRuXfAG/gAdPCh6KH8ODXj146EcQjxV6EfHNZJsaU+OE7Hvv997vvd+bsQKHR4LSo5SWzly4eGluPnv5ytVrC7nFpe3I74U2q9m+44e7lhkxh3usJrhw2G4QMtO1HLZj7T2V+Z0+CyPue1tiELCGa3Y83ua2KRBqLqYOq8RwWFssE8PynVY0cNGQmBgHnAzJ3XPRF9IT7ECgxSwiQ2KEvNMVt0m2uEqMqOeSJiY9skr0hLAmi+QkA8mOh0W845rj4dh4xDhrdW8CvU/KEnFwt9ZM2vQ6sRF0+XBcqOS7puiGLnpbI/kytiyMn53qrCdgG8H9cclpdG4TpaAxY/TkSrJH+U/lyhoIGNninfEV274XCTJs5vK0RNUh046eOHlIzrqf+wQGtMAHG3rgAgMPBPoOmBDhrw46UAgQa0CMWIgeV3kGQ8git4dVDCtMRPfw28GonqAexrJnpNg2TnHwHyKTQIF+pYf0mH6mH+g3+vOfvWLVQ2oZoLVGXBY0F17d2Dz5L8tFK6B7xkJGYYZqAW14pNRyVB8oRO5hjzr0X74+3ny8UYiL9B39jhu8pUf0I+7g9X/Y76ts441SFCoOg321s6tUeHjLMeYinNDCXBuxHt6HwM4xTupCX94oPqD+93NNO9vlkk5LevVBvrKWPOUc3IRbsIzv9RAq8BzWoQa2ltNWtCdaJf0lfZL+lUlKtVTiXIeJk5n/DULIItA=</latexit>
  • 36. Mステップの導出 36/56 <latexit sha1_base64="Wjq9SmREfZOm+3vI+JIkgj1yyqo=">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</latexit> Ø よって停留条件は、 <latexit sha1_base64="pYuKEdQWwA/S54Iq01Dzm3QDebg=">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</latexit>
  • 38. の範囲で なので(らしいので)。 Mステップの導出 38/56 <latexit sha1_base64="9j7iqVUU5GmMcdap/y2zPyhutYc=">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</latexit> <latexit sha1_base64="vj4gVcf2qtrYp0KyD5uShtKEbUU=">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</latexit> <latexit sha1_base64="u4c41hRcLRwjjR8kmdYuxYMQfzo=">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</latexit> <latexit sha1_base64="RRO/+syrrmDGgwrD/C7ETeFV+NI=">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</latexit>
  • 39. Mステップの導出 39/56 <latexit sha1_base64="RkXfS6adws2Y/NEprDkjbGUXA/s=">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</latexit> <latexit sha1_base64="nsCdJYvXSPrJqzQYgZa+RDH36Es=">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</latexit> なので、 <latexit sha1_base64="2wrOnUDb+2ggKVGZg9ISLgKyK8E=">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</latexit> Ø よって更新式は
  • 40. EMアルゴリズム再掲 40/56 Ø Eステップ Ø Mステップ 変分パラメータに初期値を与え、事後分布を計算。 <latexit sha1_base64="ztCNKfptK8V/LmsaZikT5EUxlvs=">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</latexit> <latexit sha1_base64="qTAIIDoZxOf/chfgH2Z2mM2J40U=">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</latexit> <latexit sha1_base64="dlNbpx4vI4Cch2999gRmw2MAnhc=">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</latexit>
  • 41. 変分パラメータの最適化(直接計算) 41/56 Ø 解析的に計算をする。 <latexit sha1_base64="29G1w0vb81zT+aX55MUa0Tc1pgA=">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</latexit> <latexit sha1_base64="eUjU7iUOCywaK1G8W3W/fqM7Eb4=">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</latexit> <latexit sha1_base64="pGZGcpbiP7KW1GYx5s/LIhWuNMA=">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</latexit>
  • 42. 変分パラメータの最適化(直接計算) 42/56 <latexit sha1_base64="pGZGcpbiP7KW1GYx5s/LIhWuNMA=">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</latexit> を変分パラメータについて微分。 <latexit sha1_base64="wpY5xvHIBD26CbwkRWBWiKKGtSA=">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</latexit> <latexit sha1_base64="N26PLkkMymPvo5oRwid9oc3HeTY=">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</latexit> <latexit sha1_base64="2cxSTgfaglPQw7rj2exLhRUfldY=">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</latexit> <latexit sha1_base64="E68yQUgcmWZG+h6Oj9/0ORlJ9gQ=">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</latexit> ⼀項⽬について、 <latexit sha1_base64="lC2d+qFtZQ0Tixcx2uhKXNbmLQc=">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</latexit>
  • 43. 変分パラメータの最適化(直接計算) 43/56 ⼆項⽬について、 <latexit sha1_base64="WG5RcEGNcWj7NaAhAO0PtGZNcMc=">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</latexit> <latexit sha1_base64="v21CAA0ElvGN5sa0a5hKKbYheIw=">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</latexit> 三項⽬について、 <latexit sha1_base64="uNGszaGZidF8u1u9exhyt5iwMqM=">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</latexit>
  • 44. 変分パラメータの最適化(直接計算) 44/56 <latexit sha1_base64="9o3GmLPX44o5vnqi/eclSsPTJjw=">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</latexit> <latexit sha1_base64="6TK7HxMutL9rpUQgsJFcCTjZZI0=">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</latexit> Ø 整理して、
  • 47. よりbayesianに 47/56 Ø ここまでは事前分布の超パラメータは既知の定数。 超パラメータもデータから決定しよう‼ Ø 事前分布に次の等⽅ガウス分布を仮定する。 <latexit sha1_base64="XUQytaIJRAonVtNofVeS+XPnYTU=">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</latexit> Ø 共役超事前分布はガンマ分布。 <latexit sha1_base64="mxkhMYexzNIrskUaDqYQ8YwWdJM=">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</latexit>
  • 48. 周辺尤度 48/56 <latexit sha1_base64="DvlxvY/jPpqiPK1BX2a3V6n9s80=">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</latexit> <latexit sha1_base64="BbkFih2soHrnlTk2OPf3teldP+w=">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</latexit> <latexit sha1_base64="pYtNZg2paon8StH4xBwbnoJgSFY=">AAACr3ichVHLThRRED00KAOoDLoxcUOcjGE1qSYkEFYkblwRXsOQMIDdTQ1zQ7/SfWdg7PADfoAuXCgmLoif4UJ+wAWfYFxCwoYF1Xc6MULA6vS9dU/Vqacb+yrVRGcD1uDQg4fDpZHRsUePn4yXJ56up1En8bjuRX6UbLhOyr4Kua6V9nkjTtgJXJ8b7v7r3N7ocpKqKFzTvZi3AmcvVC3lOVqgZlPzoc4O2pzw0U65QjUyMnlbsQulgkKWovJPNLGLCB46CMAIoUX34SCVbxM2CLFgW8gES0RTxs44wqhwO+LF4uEIui/nnrw2CzSUdx4zNWxPsvjyJ8KcRJV+0Qmd0yl9p990dWeszMTIa+nJ7fa5HO+Mv3++evlfViC3RvsvSxjVe6rWaGHOVKuk+tggeR9eP0L33cfz1fmVavaKvtIf6eCYzuiH9BB2L7xvy7zyyVSUGA7jwPQcmCpCmXImtlQy7IqtJVhH5qElciaZ2ujmE5UF2jfXdVtZn67ZVLOXZyoLi8UqS3iBl5iSfc1iAW+whLpkj/EBn/HFsq2GtW297btaAwXnGf4RS10DCm2ccg==</latexit> sigmoid gauss gamma Ø 解析的に計算不可。 Ø 局所的変分法と⼤域的変分法でなんとかしよう。