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基底関数回帰の概要について

 基底関数回帰の概要について

kichinosukey

August 22, 2018
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  1. ྑ͋͘ΔઢܗճؼϞσϧ ↟࿥ᧄؔ਺͞ၞḄᙚ΀ᦉᷯ ↟%ᮈᡯ΀᱅ᵪኈ ↟XġᬍΑfX΁᨜ᵡ y(x, w) = w0 + w1x1

    + ... + wDxD <latexit sha1_base64="w5wnl2NMa0DjdVLqGEbLnVcauoo=">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</latexit> <latexit sha1_base64="w5wnl2NMa0DjdVLqGEbLnVcauoo=">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</latexit> <latexit sha1_base64="w5wnl2NMa0DjdVLqGEbLnVcauoo=">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</latexit> <latexit sha1_base64="w5wnl2NMa0DjdVLqGEbLnVcauoo=">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</latexit>
  2. ઢܗجఈؔ਺Ϟσϧ ↟ϧόϰ΁ᤎ᷀ͺͼΝ ↟ǫKΤ࿥ᧄؔ਺ ↟ϧόϰ΀ᶡḿΤแΓΝᐙᐠ y(x, w) = M 1 X

    j=0 Wj j(x) = WT (x) <latexit sha1_base64="ZiOcmhEw8yT3RiaDgb/INUH9i74=">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</latexit> <latexit sha1_base64="ZiOcmhEw8yT3RiaDgb/INUH9i74=">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</latexit> <latexit sha1_base64="ZiOcmhEw8yT3RiaDgb/INUH9i74=">AAACvXichVFNaxRBEH0ZNcZVk1UvgpfBJSGCWWpEUIRg0IsXIV+bXcgmw8ykk+3NfDHTu3Ed5g/4Bzx4UpAQ/A+55OIf8JC7FwnJJQEvHlIzO5AvYqrp7qpX71VXd9uhK2NFtDugXbt+Y/Dm0K3S7Tt3h0fK9+4vxEEnckTNCdwgathWLFzpi5qSyhWNMBKWZ7uibq+/zfL1rohiGfjzqheKJc9a8+WqdCzFkFlu9MabnqVakZd8eKpvpE/0Sb0Zd7zl5P2EkZpJe5JSvW62m2FLmu0Tbp9YRPXl+TQjnE6b5QpVKTf9omMUTgWFTQflTTSxggAOOvAg4EOx78JCzGMRBgghY0tIGIvYk3leIEWJtR1mCWZYjK7zusbRYoH6HGc141zt8Ckuz4iVOkbpF23RIf2kH/SH/l1aK8lrZL30eLf7WhGaI58ezv29UuXxrtA6Uf23Z4VVvMx7ldx7mCPZLZy+vvvx8+Hcq9nRZIy+0R73/5V2aYdv4HePnO8zYvYLSvwBxvnnvugsPKsaVDVmnlem3hRfMYRHeIxxfu8XmMI7TKPG527jN/ZxoL3WhOZqfp+qDRSaBzhj2sYx/UasSQ==</latexit> <latexit sha1_base64="ZiOcmhEw8yT3RiaDgb/INUH9i74=">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</latexit>
  3. جఈؔ਺ ↟ၞḄᙚ ↟αΫμΧϸ ↟μεϧΩώfϚ⑲ϯέͼͻďઆ኏ͩͼ͖Đ j(x) = xj <latexit sha1_base64="TWSgByiapwoRLk+govjFQcrNb3w=">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</latexit> <latexit

    sha1_base64="TWSgByiapwoRLk+govjFQcrNb3w=">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</latexit> <latexit sha1_base64="TWSgByiapwoRLk+govjFQcrNb3w=">AAACfXichVHLSiNBFD1px1d8Rd0IboIhoiDhtgiKIIhuXPqKCkZDd1ua0n7RXQlq0A/wB1y4UhQZhvEn3PgDLvwEcakwmwG96TQMo6i3qKpTp+65darK9G0ZKqKHhNbwo7GpuaU12dbe0dmV6u5ZCb1yYIm85dlesGYaobClK/JKKlus+YEwHNMWq+bebG1/tSKCUHrusjrwxYZj7LhyW1qGYqqY6is4hioFTrXgl2Rxd2h/+Cg9ld7f3C2mMpSjKNIfgR6DDOKY91LXKGALHiyU4UDAhWJsw0DIbR06CD5zG6gyFzCS0b7AEZKsLXOW4AyD2T0ed3i1HrMur2s1w0ht8Sk294CVaWTpnn7SM93RL3qkv5/WqkY1al4OeDbrWuEXu076lv58q3J4Vij9U33pWWEbE5FXyd79iKndwqrrK4enz0uTi9nqIF3QE/s/pwe65Ru4lRfrakEsniHJH6C/f+6PYGU0p1NOXxjLTM/EX9GCfgxgiN97HNOYwzzyfO4xLvEbN4lXLauNaLl6qpaINb34L7TxN+qpk2A=</latexit> <latexit sha1_base64="TWSgByiapwoRLk+govjFQcrNb3w=">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</latexit> j(x) = exp (x µj )2 2s2 <latexit sha1_base64="+jBTgP4EQe8NVoXn1wUPjIYLPp8=">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</latexit> <latexit sha1_base64="+jBTgP4EQe8NVoXn1wUPjIYLPp8=">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</latexit> <latexit sha1_base64="+jBTgP4EQe8NVoXn1wUPjIYLPp8=">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</latexit> <latexit sha1_base64="+jBTgP4EQe8NVoXn1wUPjIYLPp8=">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</latexit>