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PRML 7~7.1.1 + 付録E
5501 酒井⼀徳
5/2/18
1/51
今⽇の内容 2/51
7 疎な解を持つカーネルマシン
7.1 最⼤マージン分類器 + 付録E
7.1.1 重なりのあるクラス分布
疎な解を持つカーネルマシン
3/51
疎な解 4/51
疎な解(sparse solution): 訓練データの⼀部だけに対して計算し,求まる解
前章では…
例えばガウス過程などは訓練データ全ての対についてカーネル関数の計算が必要だった.
学習時,もしくは予測時に⾮常に時間がかかる可能性がある
SVMの特徴 5/51
Ø 訓練データを特徴空間において分類する
Ø 正例と負例の境界にあるもの(サポートベクトル)だけを予測に使⽤する
Ø サポートベクトルとの距離(Margin)が最⼤となる分類境界を求める
Ø モデルパラメータが凸最適化問題の解として求まる
Ø 確率的出⼒は⼀切ない
最⼤マージン分類器
6/51
解の⾮⼀意性と汎化誤差最⼩ 7/51
⼀般に線形分離可能なデータに対し,その解は多数存在し得る.
実際に予測する際の誤差(汎化誤差)を最⼩にする解が望ましい
マージン(margin)の
概念を導⼊
マージン最⼤化を⾏う動機 8/51
Ø なぜサポートベクトルに対してのみマージンを最⼤化すれば良いのだろう?
<latexit sha1_base64="IU4Xct/1tETRxwBHTx0CkY55fKc=">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</latexit>
s.t.
共通のパラメータ を持つガウスカーネルを⽤いたParzen推定法で各クラスごとの⼊⼒ベクトル の
分布を推定する.今クラスラベル について,
<latexit sha1_base64="1NqoqRxR8H33L7bAIM8HfgObyTU=">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</latexit>
<latexit sha1_base64="FnQ4L+9JWi3Obcq8iaMuiTEE7OQ=">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</latexit>
<latexit sha1_base64="JYSkfl3YrnGuUk+hCBYKJsaVyGY=">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</latexit>
であり,Nはデータの数である.ここでクラスの事前分布が求まるのであれば,
ベイズの定理 から決定境界は求まる.<latexit sha1_base64="1Cr7KcIyIoJIrdj0+SpG+1aFRC8=">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</latexit>
<latexit sha1_base64="EaFN+U+vZgD528adCqgleTTuteQ=">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</latexit>
<latexit sha1_base64="oEcQIIIWC0eXXJU4m8V8zTEDDiM=">AAACs3ichVHNStxQFP5MW2u16rTdFLoRhykuZDgRS6VQELrpSvzpqDDqkGTujMH8kdxMscEX6Au00JVCF+JjdOMLdOEjlC4tuOmiX+4EpLXgCbn33O+c7/y6SeBnWuRixLpz997o/bEH4xMPJ6ema48eb2Zxnnqq5cVBnG67TqYCP1It7etAbSepckI3UFvuwZvSvjVQaebH0Tt9mKjd0OlHfs/3HE1ob+X1TpaHHV2sdPTRfKdWl6YYmbmp2JVSRyWrce0cO+gihoccIRQiaOoBHGT82rAhSIjtoiCWUvONXeEI42iQndNP0cchfsCzz1e7QiO+y6iZ4XvME/BPyZ1BQ77LqVzKuZzJD/nNaP+PVZgYZTWHvN0hVyWd6Y9PN65uZYW8NfavWbdUrdHDkqnWZ/WJQco+vGGEwYdPlxuv1hvFczmRn+zgWC7kG3uIBr+8r2tq/YupKDUchfem59BUEXHOBW0ZM3Rp6xHLOQ/NyAUz7WNQzpQrtP9d2E1lc6FpS9NeW6wvL1XLHMMzzGKOG3uJZbzFKlrMnuIzjnFivbDalmt1h67WSMV5gr/ECv8AW1ecwA==</latexit>
<latexit sha1_base64="iDxq0aRwN6zWA5ziV/Zf369ErWw=">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</latexit>
マージン最⼤化を⾏う動機 9/51
クラス事前分布を無情報であるときに,誤分類が少ない事後分布の選択はモデルの選択と等価である.
その分類境界は2クラス分類の時,
<latexit sha1_base64="61QRp9jX+pZkJ/+7XuKhJYDwW58=">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</latexit>
で与えられる.よって,
<latexit sha1_base64="vIXfHrgOW+AbDGwsD8Ui+Z2omBM=">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</latexit>
の極限を考えると,
<latexit sha1_base64="nzh0DN2/aZT5FR8Vc2t9+feBT30=">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</latexit>
マージン最⼤化を⾏う動機 10/51
サポートベクトル以外のデータ点の影響が少なくなる.
分散⼩ 分散⼤
マージン最⼤化の定式化 11/51
<latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">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</latexit>
上記の線形モデルと⽤いて2値分類を解くことを考える.
訓練データは,
<latexit sha1_base64="Y7CxNnLYoyEru1acQx7KgNMbUXc=">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</latexit>
<latexit sha1_base64="IWLUhbyJlGGSxLXFb1ca4cNd2sY=">AAACxnichVFLS9xQFP5MX9Y+HO2m4KKDwxQL43BSBMWV4MZV8dFRwUhIMnf0YnITkpsRGwQ33fgHuuiqhS7EbfsLuvEPdOFPKF1acNOFJ3cC0lrwhNx77nfOd55+EspME50PWXfu3rv/YPjhyKPHT56O1sbG17M4TwPRCeIwTjd9LxOhVKKjpQ7FZpIKL/JDseHvLZb2jb5IMxmrt/ogEduRt6NkTwaeZsitvdCu3XLCbqyzlnbfTGlXOVLVnWLabtnO4Su31qA2GanfVOxKaaCS5bh2BgddxAiQI4KAgmY9hIeMvy3YICSMbaNgLGVNGrvAIUbQZHbOfoJ9PMb3+Nzh11aFKn6XUTPDDzhPyH/K3Dqa9INO6ILO6JR+0h+O9v9YhYlRVnPAtz/gisQdPX6+dnkrK+JbY/eadUvVGj3MmWolV58YpOwjGETov/twsTa/2ixe0mf6xR18onP6zj2o/u/gy4pY/WgqSg1HYN/0HJkqFM+5YFvGGbps6zGW8zw0Ry440y765Ux5hfa/C7uprL9u29S2V2YaC3PVMocxgUlM8cZmsYAlLKPD2d/jFF/xzVqylJVb+wNXa6jiPMNfYh1dAS3YopY=</latexit>
⼊⼒データ
対応する⽬的値
今,訓練データは特徴空間で線形分離可能とするため,
正しく線形分離できるデータについて以下が成⽴するとする.
<latexit sha1_base64="y4DI9sq2hEHDMRfvZjaQRuN1sZU=">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</latexit>
<latexit sha1_base64="5cJGC9qdoazs+hN+QOJR2ZSeYrM=">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</latexit>
<latexit sha1_base64="wHtWBjWZMXeGB/4jbiME2jqetDA=">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</latexit>
<latexit sha1_base64="ZGohuiAD0khcuR5S9unpk/FO0fo=">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</latexit>
<latexit sha1_base64="X4ADg7Tb2vS56XVLP56X23/ARmU=">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</latexit>
<latexit sha1_base64="+rCTpEXfm9Kusy7Y6SJ8W/q+gvA=">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</latexit>
マージン最⼤化の定式化 12/51
<latexit sha1_base64="19BiG9BS8YIZN4Nc9DUG1RcfaTA=">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</latexit>
超平⾯ から点 までの距離は で与えられる.<latexit sha1_base64="7exF2UQ3pUWvMTvqagSd+6YP3X0=">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</latexit>
<latexit sha1_base64="y+6FzjHIUYmrt/EIYcnUHJSGgdk=">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</latexit>
<latexit sha1_base64="FIqdfY3fmRdUnp7/I/TWxESGSfQ=">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</latexit><latexit sha1_base64="NCZWL6uomMddIRuzhfLvtfeWGO4=">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</latexit>
から分類境界から点 までの距離は次のようになる.<latexit sha1_base64="7exF2UQ3pUWvMTvqagSd+6YP3X0=">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</latexit>
マージンとは訓練データと(正しく分類する)分類境界との
最短距離である.
そのマージンを最⼤にするパラメータは以下の最適化問題によって得られる.
<latexit sha1_base64="aCjrpmBZ9brT08o7LKD9p8JGktI=">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</latexit>
<latexit sha1_base64="xkbP1YRi32CbLD3OPxKbg3SHRCw=">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</latexit>
マージン最⼤化の定式化 13/51
パラメータ を同じ値だけ定数倍しても前述の⽬的関数の値に影響がない,
よって適当な定数をかけることで分類境界に最も近い点(サポートベクトル)について,
<latexit sha1_base64="+6Z/dC2aygk7B1mamOQR6ClXBFU=">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</latexit>
<latexit sha1_base64="2FA/xsC370jZl7vLb/r3b7xHE0M=">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</latexit>
とできる.この時マージン最適化の問題は,
制約式の等号が成⽴する場合,この制約は有効であるという.
この問題は⼆次計画法の⼀例である.
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit>
<latexit sha1_base64="mHO0tisKOzYkoK0vLtaTBsamToY=">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</latexit>
ラグランジュ乗数(上巻付録E)
14/51
ラグランジュ乗数と問題例 15/51
ラグランジュ乗数(Lagrange multiplier) (未定乗数とも)
複数の変数に1つ以上の制約条件が課されたときに,(ラグランジュ)関数の停留点を求めるため
⽤いられる.
例えば以下の問題において,
<latexit sha1_base64="y0OWFQ2YsZo8NMQZlGZoT4wItxQ=">AAAC33ichVFNa9RAGH6a+lFbtau9CL0sLisVSnhTBBdBKPTisR9uW+iWMMnObkPz1WSybhv2XOhBvIkIhRY8iD9DD73ozUN/gvRYwYsH38wGRSt0Qmaeed553k8n9r1UEZ2OGKNXrl67PnZjfOLmrduTlTt3V9MoS1zZdCM/StYdkUrfC2VTecqX63EiReD4cs3ZXijsaz2ZpF4UPle7sdwMRDf0Op4rFFN2pdEKRN/O+7Y127fnBnlnpoQPB7OtnUy0q6mpzOoQdn8bn5JdqZFJelUvAqsENZRrMaqcoIU2IrjIEEAihGLsQyDlbwMWCDFzm8iZSxh52i4xwDjqrM74neQ3gvlt3rt82yjZkO+F11TrXY7j85+wtoo6faX3dE4n9IG+0U/29n9fufZRZLPLpzPUytiePLi38uNSVcCnwtYf1SVZK3TQ0Nl6nH2smaIOd+iht/f6fOXJcj1/QMd0xhUc0Sl95BrC3nf33ZJcfqszSrRG4oWuOdBZhNznnG0pR2izrcNcxv1Q7DnnSFvoFT3lEVr/DuwiWJ0zLTKtpUe1+UY5zDFM4z5meGKPMY9nWESTox/iEz7jiyGMfeOl8Wr41BgpNVP4axlvfgGVuaui</latexit>
制約条件から のような表現を⾒つけ,最⼤化問題を1変数に変えるアプローチが
考え得るだろう.しかし,
• いつも解析的に陽に表現できるとは限らない.
• 元の問題の対称性を活かせておらず,エレガントじゃない.
<latexit sha1_base64="AwVZcTFCxVXl1b7pGSm5x8X1Wic=">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</latexit>
より⼿軽で,エレガントな⼿法を
ラグランジュ乗数法の幾何学的解釈 16/51
<latexit sha1_base64="0I1CpTOStX4lslEMDkI8g20hQ3U=">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</latexit>
<latexit sha1_base64="K/Ex/k4aXvYG0w3h3EEGbDsPTDM=">AAACxnichVHNatRQFP4a/2qtdtSN0IXBYUQQhhMRLIJQcNNlf5x2YGYYbjJ3pqE3NyG5mVKD4KabvoALVy24kG7rE7jpC7joI4jLCm5ceHInIHaEnpB7z/3O+c6vn6gwM0RnM86Vq9eu35i9OXdr/vadhdrde5tZnKeBbAWxitO2LzKpQi1bJjRKtpNUishXcsvfeV3at8YyzcJYvzF7iexFYqTDYRgIw1C/9rCrha+EO3Sful3FvIFwK2jkvnKpX6tTk6y404pXKXVUshrXTtHFADEC5IggoWFYVxDI+OvAAyFhrIeCsZS10Nol3mEODWbn7CfZRzC+w+eIX50K1fwuo2aWH3AexX/KXBcN+kaf6ZxO6Zi+02+O9v9YhY1RVrPHtz/hyqS/cPBg49elrIhvg+2/rEuqNhhiyVYbcvWJRco+gkmE8dsP5xsv1xvFYzqiH9zBIZ3RV+5Bj38Gn9bk+kdbUWo5Eru258hWoXnOBdsyzjBg25CxnOdhOHLBmbYxLmfKK/QuLmxa2XzW9KjprT2vLy9Vy5zFIh7hCW/sBZaxglW0OPs+jnGCL86Ko53c2Z24OjMV5z7+Eef9H8xhof0=</latexit>
<latexit sha1_base64="IS08Iw6oxBL/6aTo3OL6c107TPg=">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</latexit>
<latexit sha1_base64="HhA34vPJNVOKCXwlGE73xfUnT84=">AAAC/XichVE7axRRFP4yPhJjNKs2gs3ishIQljMiGFIFbSws8nCzC5sQZmbvJkPm5czd1ThE+/gDLKwUUohiayNY2KS1sEipncQugk1Av7kZ8BEhZ7j3njnnfOc7DzcJ/EyL7AxZx46fODk8cmr09NiZs+OVc+cXsrifeqrpxUGctl0nU4Efqab2daDaSaqc0A1Uy127VfhbA5Vmfhzd1euJWgqdlcjv+Z6jaYorV7EIDYUHvHPpyiPZlJvyRD7KV/ks+/IeG4wI4CCEiy7fRUSMv4cqhOdP9J1OuzUhrZ9j2Fiu1KQhRqqHFbtUaihlJq5sM1UXMTz0SaVIoqkXxBm/DmzSJbQtIactpeYbv2KBo6gT3WecYoxD+xrvFf51SmtkGlDUC7xHnoAnJbaKunySl7In2/KKTe8z2/9z5SZHUc26GYbBqmR5fPPi/I8jUSFfjdXfqCOq1uhh0lTrs/rEWIo+vIMMg4dP9+an5ur5FXkhu+zguezIB/YQDb57W7Nq7pmpKDUYhfum59BUEXHOOX0ZGbr09Wjrcx6amXMyrWJQzJQrtP9d2GFl4VrDloY9e702PVkucwSXcBkT3NgNTOM2ZtAk+zt8wS6+WY+tLeu19eYg1BoqMRfwl1hvfwFV07EA</latexit>
<latexit sha1_base64="fIUcDWsm13eCBtz1vjWtmvHoxcQ=">AAADXXichVI9aBRBFH57azSe8bLGQkGL4HFBm+OtBBKsQmwED8nf5SJJOHb35i5L9o/duYvJmsJSY29hpWAhNpb2IgSsLVJZWYSUEWwE/Xb2IMYEMsvOzH7zvm++997akecmknlPK+jnBs5fGLxYvDR0uTRsXBlZTMJu7Ii6E3phvGRbifDcQNSlKz2xFMXC8m1PNOz1+9l5oyfixA2DBbkZiVXf6gRu23UsCSg0lmmMVkiSoCeYU67ZxtZXfsw7zS/Pn3GNp3nnT4m2aRRRK5iLKt4ji3yyqYX1X3aIyKPvjsL2+SPeQ/7EPx41RES3qQZWh2LMAVYBVZ+60JTkUoTVBRbTnWNaKa8tPOWIX+Z+mkaZq6zG6MmN2d+UqT9mQmMXYi0KycFVPkQDiDoqkQTPMpnEuFzSKqXAYmUmOxewUaQK2F3ECcRYwNdVCgK8HA1UQQT2Gd/BPR7eWBWuwt/4PQqwyx9QiN9QO10rVRqZm01VXMUVUXP4xfX5X2eyfKyS1o5YZ7iW1KZJ5daF+0ghWR5OrtDbenU4f2+uko7xWz5ABm94jz8jh6D303k3K+ZeK0ex4gjaUDn7ykWAOqc4S3BDC2dtYHl7t4FH8NjLaooWmv837ORm8W7V5Ko5O16emuw3c5Bu0C38RiZN0BQ9oBmqk6Pd1Ka1h1qt8F0f0If0Uh5a0Pqcq3Rs6Nf+AtrPxD8=</latexit>
ラグランジュ関数 17/51
ここで以下で定義されるラグランジュ関数(Lagrangian)
<latexit sha1_base64="ipyTG2ytrlYoBuxdZ5D5E59khW0=">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</latexit>
を導⼊することで,停留条件と制約式は以下で表現できる.
<latexit sha1_base64="vUy6v9ZjXbpgqkil7FqgRiuqehk=">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</latexit>
勾配が直交する理由 18/51
<latexit sha1_base64="pUwwmZk2qDjFUWmhlCICMOWNLX4=">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</latexit>
<latexit sha1_base64="GVZtggVWs+HUIwbN0zWfXDbNrjU=">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</latexit>
<latexit sha1_base64="svcmHW1B88nDdgYRswH8VflLFas=">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</latexit>
<latexit sha1_base64="vv+jhL5B5pupiajF0hRhfP8K3bk=">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</latexit>
<latexit sha1_base64="hEHwiPLsnKboMs/cZJyixlHiHeA=">AAADm3iclVJRSxRRFP7GsbLNcrWXIAJp2UiK5UyIShBIvkRE6NqqpCIz491t2Jm5w8zdLR0GfDT7AT70VNBD9At67sU/0IM/IXo06CWoM9fBshXE+3DnnO/e7zvfmXOdyPcSRbRv9Jn9585fGLhYujR4+cpQeXhkIZGd2BUNV/oyXnLsRPheKBrKU75YimJhB44vFp32TH6+2BVx4snwmdqIxGpgt0Kv6bm2YkiWN7ECBYFXvKe/R6LPyBhxIOFjHSnjGe72IHf+QRJsICiylHGBiDGPM4lQqx3pk6xPZP27ztMStekhvaGQWnyjhds9Fcbw4ET8LJXHjvU2SNvkUpPx0lq5QjXSa7Q3sIqggmLNyvIeS62zrIsOlxQsrzj2YXPBBMuwQFxcYZWN2Ig58vS5yMuhyuwO38sN2oy3eW9xtlygIee5aqL5rm5IskqGUVTpK32kA9qjT/SNfrHayVqp1kiOformimhtaOfa/M9TWQF/FV78ZZ3iWqGJKe3WY/eRRvI+3EOF7ubuwfz9ejW9Re/pO3fwjvbpC/cQdn+4H+ZE/a12FGuOwEvdc6BdhHrUK1y3yZHg3WZ1n/UzxiP22C1GaP0/sN5g4V7Nopo1N16ZniqGOYDruMkPy8IkpvEIs2jANZ4bW8ZrY8e8Yc6Yj80nh1f7jIJzFceW2fgDC3XNTg==</latexit>
<latexit sha1_base64="9iIo+2+0Ane+Z1Gqc4Ag4jEfgXc=">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</latexit>
<latexit sha1_base64="XLaln6xwK57Vqajjz9kwe6Jf8yc=">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</latexit>
不等式制約の解のパターン 19/51
制約が という不等式制約で与えられた際の の最⼤化問題を考える.<latexit sha1_base64="ENItnW9vHRgEyVRVa5mqzjmJxR0=">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</latexit> <latexit sha1_base64="bxNYtVZMQbl9uON0SRXNrPJ81kU=">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</latexit>
このとき解は次の⼆通りに分類できる.
① の領域にある場合…無効制約
制約領域にあるならば単に を満たせば良いだけ.<latexit sha1_base64="fODTl+e5/jZCNcjSBc9eIjrogMc=">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</latexit>
② の上にある場合…有効制約<latexit sha1_base64="lgbpIPvWGq6KsrQYG56qRzsvMqk=">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</latexit>
<latexit sha1_base64="3iz0avfv0A90oGTU4os2xBVXye8=">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</latexit>
は制約領域の外を向く必要がある.何故なら制約領域の⽅向を向いているならば,
制約領域内で停留点を取りうるためである.つまりある が存在し,<latexit sha1_base64="rfMIzLh40SyqLe3jzk8cQ3rZNO4=">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</latexit>
<latexit sha1_base64="umHzBGh5O/C7CEUG94KRg5vRlvs=">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</latexit>
が成⽴する必要がある.
<latexit sha1_base64="NWPxfy90HR21xt7KqBx/MPm9MoE=">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</latexit>
Karush-Kuhn-Tucker条件 20/51
<latexit sha1_base64="62k71GNDxcgO7ZXs3XMpcnDQa7I=">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</latexit>
前述から,上記の問題は以下の条件の元でのラグランジュ関数の停留点を求める問題になる.
<latexit sha1_base64="ipyTG2ytrlYoBuxdZ5D5E59khW0=">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</latexit>
<latexit sha1_base64="JqGYEisYztqd/92jTY+jgKreY/8=">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</latexit>
<latexit sha1_base64="vpVgyaap2arqrOao6eRDQ7sxlaI=">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</latexit>
のどちらかが成り⽴つという意味.
解が制約内部か制約⾯上かどちらかで
あるという意味でもある.
<latexit sha1_base64="wHshlPt/KudAt6Ob3+YJb8Wnsb4=">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</latexit>
<latexit sha1_base64="TyVJJoJC/cTFYnsdsX1/pTAb/ok=">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</latexit>
<latexit sha1_base64="P8q+WIhqV3xhl1g1yu1Gw5jwc00=">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</latexit>
KKT条件
最⼤化ではなく最⼩化であればラグランジュ関数を以下に変更し最⼩化すれば良い.
<latexit sha1_base64="cIiX077P6742ER0oxGfrjSzwsnE=">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</latexit>
複数条件への拡張 21/51
例として以下の複数の制約の下での最⼤化問題を考える.
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="ajHnUYG9ba51BtU4aBEahLCW9Ws=">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</latexit>
この場合,複数のラグランジュ乗数 および を導⼊し
以下のラグランジュ関数を最適化すれば良い.
<latexit sha1_base64="6kyqVsaqGV87+HhlBfiRf0HNm/4=">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</latexit>
<latexit sha1_base64="+A9dnRuMmJiYfI+w1EJ3oBspX7s=">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</latexit>
<latexit sha1_base64="6mAbhoJc7hAEEMd0sk++TVvy7qM=">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</latexit>
このときのKKT条件は以下である.
<latexit sha1_base64="G1YzK4u0ZM7T2OC7keFtJdnRAZc=">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</latexit>
<latexit sha1_base64="OKCCO+da7Z9XFpGz5nXHvmQQrzg=">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</latexit>
<latexit sha1_base64="2tkXvP060heH3iXKRINcJfg2zlU=">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</latexit>
再訪:最⼤マージン分類器
22/51
ラグランジュ乗数の導⼊ 23/51
<latexit sha1_base64="SHy946PDuuhogphSTaBlqHhhefE=">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</latexit>
<latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">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</latexit>
<latexit sha1_base64="RdlqAdGJhJ+mQoXNjGfc46Ftr9M=">AAACwHichVHNStxQFP6Mrf/VUTeWbgaHKV0NJ1KoCILoxlXxb1RQG5J4ZyaY3MTkZkTD4N4XcNGVgotSaB+iG1/AhY9QurTQjQtP7gSkteAJuffc75zv/DqR7yWK6LbH6H3xsq9/YHBoeOTV6FhpfGIzCdPYFXU39MN427ET4XtS1JWnfLEdxcIOHF9sOQdLuX2rLeLEC+WGOo7EXmA3pdfwXFsxZJVe0/xukgZWJufNzqfsYyezLVlWluxYpQrVSEv5qWIWSgWFrISla+xiHyFcpAggIKFY92Ej4W8HJggRY3vIGItZ87RdoIMhVJmdsp9gH5vxAz6b/NopUMnvPGqi+S7n8fmPmVtGlW7oC93RNX2ln3TP0f4fK9Mx8mqO+Xa6XBFZY2dT63+eZQV8K7QeWc9UrdDArK7W4+ojjeR9uN0I7ZPzu/W5tWr2li7pF3dwQbf0g3uQ7d/u1apY+6wrijVH4Ej3HOgqJM85Y1vCGfbZ1mAs5Xkojpxxphba+Ux5hea/C3uqbM7UTKqZq+8rC7PFMgfwBtN4xxv7gAUsYwV1zn6KK3zDd2PRaBmhcdh1NXoKziT+EuPkATl4oYc=</latexit>
<latexit sha1_base64="ieM1ukI341e4FGbiyIP5BLenlwg=">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</latexit>
ラグランジュ乗数 を導⼊することで,
次のラグランジュ関数を得る.
が得られる.これらの式をラグランジュ関数に代⼊することで,
ラグランジュ関数の双対表現が得られる.
<latexit sha1_base64="UNAoSyFoFp2UwwLLKbCwl03t440=">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</latexit>
<latexit sha1_base64="qLqWrVV+rXNDhRNnWX6cJhM38As=">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</latexit>
<latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit>
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit>
マージン最⼤化の双対問題 24/51
<latexit sha1_base64="pTvQBdpFvQ9xr+Iv8ZBaJE/G3aU=">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</latexit>
<latexit sha1_base64="ZBLi2ROZWoTc8LSHCZgolK5gJ+c=">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</latexit>
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="j5DA8Sdh+96unRMKfiThmXGio6s=">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</latexit>
<latexit sha1_base64="hbTGfTqroQ3ISgZg39nQqb2Z69Q=">AAADAHichVE7axRRFP4yvmJ8ZKONYBNc1mRBljMSSAgIARvLvDaJZOMyM3s3e9l5MXN3k/UyjaV/wMJKQVAsxNbGwiZ/wCI/wEKEpIhgY+GZu6OiUXKHufe73znfedzjxr5MFdH+iHXq9Jmz50bPj124eOnyeGniyloa9RJP1L3Ij5IN10mFL0NRV1L5YiNOhBO4vlh3u3dz+3pfJKmMwlU1iMVW4GyHsi09RzHVLN3vTjfcyG/p3ezWTzBVnb9jcDoI+NCNuCOzX27VB7qhxK7Sq1n2f6+parNUphqZNXkc2AUoo1iLUWkPDbQQwUMPAQRCKMY+HKT8bcIGIWZuC5q5hJE0doEMY6iwusd+gn0c5ru8b/Nts2BDvudRU6P3OI/Pf8LaSVToI72iI9qj1/SZvnO0f8fSJkZezYBPd6gVcXP88bWVbyeqAj4VOr9VJ1St0MacqVZy9bFh8j68YYT+wydHK/PLFX2TntMX7uAZ7dMH7iHsf/VeLInlp6aixGgEdkzPgaki5HfWbEs5Q4ttbeZ6/B6KI2vO1EE/f1Meof33wI6Dtds1m2r20kx5Ya4Y5iiu4wameWKzWMA9LKLO2d/jEw5waD2yXlpvrLdDV2uk0FzFH8t69wMi072h</latexit>
<latexit sha1_base64="m74Qq4cQz59B0Nh5yLxkYDmKwgA=">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</latexit>
この問題は再び⼆次計画法になっていることに注意する.
解く⽅法は後述(7.1.1節)
意味があったのか 25/51
<latexit sha1_base64="9QHeHRFNsbNSL+Z+ODN4CIoEdf4=">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</latexit>
<latexit sha1_base64="klyyKEyWXSP2RZrpUxjsk+Zi3lw=">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</latexit>
<latexit sha1_base64="jIieM9WlOuytMGbEpoS+atui3KY=">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</latexit>
※上に有界: bounded above
pdfでは “bounded below”となっていた
主問題 双対問題
<latexit sha1_base64="m74Qq4cQz59B0Nh5yLxkYDmKwgA=">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</latexit>
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit>
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit>
<latexit sha1_base64="Gx19UD4tnGWaE9zbERBVhieYmQ8=">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</latexit>
<latexit sha1_base64="7PF78odKi2Q4hlWrBrTqDakAKaw=">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</latexit>
<latexit sha1_base64="ZBLi2ROZWoTc8LSHCZgolK5gJ+c=">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</latexit>
サポートベクトル 26/51
KKT条件から以下が⾔える.
<latexit sha1_base64="PGQOPIVMggpS9KEqohVv60lVchs=">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</latexit>
<latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit>
<latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit>
<latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit>
ここで,全てのデータ点について あるいは が成⽴する.<latexit sha1_base64="gbXceMzZaBzFcz9lALG60wSu14Q=">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</latexit>
<latexit sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit>
<latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">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</latexit>
<latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">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</latexit>
<latexit sha1_base64="gbXceMzZaBzFcz9lALG60wSu14Q=">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</latexit>
となるデータ点は右記から予測に影響を及ぼさない.
となるデータ点はサポートベクトルと呼ばれ,マージンの縁に存在する.<latexit sha1_base64="bvpNjktwuYdbOUOEDcIwHW86H5E=">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</latexit>
サポートベクトルは が成⽴するデータ点でもある.<latexit sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit>
分類規則 27/51
<latexit sha1_base64="KDzDlUK19VErDrbvj89BJKgVqE8=">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</latexit>
学習したモデルを⽤いてデータを分類するには,求まったパラメータ
とカーネル関数で表される以下の関数の符号で判断できる.<latexit sha1_base64="CHB3UpVNl9cAk2rbZ3G7ZjwTYs8=">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</latexit>
<latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">AAAC5HichVFLaxRBEP4yURPXRzbxIngJLisRYakRISEQCHjxmNcmgUxcZmZ7sk3mxUzvJmszf0C8iXgQBBUP4s/wEq+Kh/wE8RjBiwdrekdEI6SH6ar+qr56emkoc0V0PGaNnzt/YWLyYu3S5StXp+rTM5t50s980faTMMm2PTcXoYxFW0kViu00E27khWLL279f2rcGIstlEm+oYSp2I3cvloH0XcVQp740nHO8QB8Wt5dKeVA81I4Sh0pvFIXjJWE3H0YstJP2ZPHb9Y4jlfaKVq1Tb1CLzJk9rdiV0kB1VpL6ERx0kcBHHxEEYijWQ7jI+duBDULK2C40Yxlr0tgFCtTQZHaf/QT7uIzv873Hr50KjfldRs0N3+c8If8Zc2fRpC/0jk7oiN7TV/rJ0f4fS5sYZTVDlt6IK9LO1OPr6z/OZEUsFXp/WGdUrRBgwVQrufrUIGUf/ijC4NHzk/XFtaa+Ra/pG3fwio7pA/cQD777b1fF2gtTUWY4Agem58hUEfOcNdtyztBlW8BYn+ehOLLmTD0MypnyCu1/F3Za2bzbsqllr95rLC9Uy5zEDdzEHG9sHst4gBW0OfsbfMQnfLYC64n11Ho2crXGKs41/HWsl78AsYexZw==</latexit>
<latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">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</latexit>
<latexit sha1_base64="z/G9/wL3OoATCsbuVarxUoKs1MQ=">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</latexit>
<latexit sha1_base64="tvqTrESbrPQz8JVmZqsA3cbaU9Y=">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</latexit>
バイアスパラメータ の導出については任意の
サポートベクトル について
が成⽴することから右記の式を⽤いた.
<latexit sha1_base64="Jo+MNvrZjL+JC+LarzYMvMJzA9U=">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</latexit>
<latexit sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit>
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<latexit sha1_base64="x5vudz69FojtLwTZ42w85sL2Xz8=">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</latexit>
<latexit sha1_base64="V7tt5fOzqpQgZ3pTWTkYMSEQXIc=">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</latexit>
はサポートベクトルの総数である.
正則化パラメータが である限り,解は⼀意に収束する.
ハードマージンSVM 28/51
<latexit sha1_base64="Ty12gyLvrAI+hfNh0DUCxwLVlyc=">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</latexit>
<latexit sha1_base64="ooFsvnugNNSni5dUOZdvTgJgigA=">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</latexit>
<latexit sha1_base64="28WcI7u/YPpcCrwk3RELIM2HVNg=">AAADHHichVHNahRBEK4Z/+JGzaoXwcvgsmH3svQGweApIILH/LhJIB2Wmdma3Sa9PZOengm7w76AL+BBEBQ8iI+hh4B4VAg+gXiM4MWDNb0DohFSw3RX19ffV1VdQSJFahg7cdwLFy9dvrJwtbZ47fqNpfrNW9tpnOkQe2EsY70b+ClKobBnhJG4m2j0x4HEneDgUYnv5KhTEaunZpLg/tgfKhGJ0DcU6tezx30uVGQmRWvannE8zETOJUaGFx4PcChU4WvtT2aFlLOaR8a8Za815UM8TKWvjMfaHucWmQuVcGxGqI9Eim0COKpBJeJxLYYj0+nXG6zDrHlnnW7lNKCy9bh+DBwGEEMIGYwBQYEhX4IPKX170AUGCcX2oaCYJk9YHGEGNWgSO6N7SHd8ih/QOqTTXhVVdC5VU8sPKY+kXxPXgyb7zN6yU3bM3rFv7Bep/V+rsBplNRPagzkXk/7SsztbP89ljWk3MPrDOqdqAxGs2moFVZ/YSNlHOFfIp89Ptx5uNotl9pp9pw5esRP2nnpQ+Y/wzQZuvrAVactBOLI9j20Vit65ICylDAPCIopl9B6GlAvKNIK8fFMaYfffgZ11tlc6XdbpbtxvrK1Ww1yAu3APWjSxB7AGT2AdepT9q+M4NWfRfel+cD+6n+ZXXafi3Ia/zP3yGwL0wIo=</latexit>
SVMの最⼤マージン学習は次の誤差関数の最⼩化に等しい.
誤分類に対して無限のペナルティを与えている.
のちのソフトマージンと⽐較してハードマージンと呼ばれる.
⾮線形SVMの適⽤例 29/51
ガウスカーネルを⽤いたSVMによる
2クラス分類.
分類境界(濃い太線)の位置はサポート
ベクトルの位置のみに依存する.
特徴空間においては線形分離可能なデータ
を⽤いた.
重なりのあるクラス分布
30/51
完全分類と汎化性能 31/51
クラスの条件付き確率分布が重なっている場合も考えうる.
訓練データに対して完全分離する解が必ず汎化性能に⻑けるとは限らない.
⼀部の訓練データに対して誤分類も許すSVMを構築したい.
ハードマージンSVMは誤分類するデータに無限⼤のペナルティを与えているも
同義なので,距離に応じたペナルティに変更しよう
スラック変数 32/51
ただし,今回はスラック変数をペナルティとして導⼊するため以下のように定義される.
<latexit sha1_base64="sSowAwIyS4v19mYheE9pW0TGAXE=">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</latexit>
不等式における両辺の差,余裕を表す変数.スラック変数を⽤いて不等式制約 を
等式制約 と⾮負条件 で表現できる.
<latexit sha1_base64="6L2tinVZ3qcAcrp95FN4fhlmfZ0=">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</latexit>
<latexit sha1_base64="xDvihjQlSRZ/gWU03Wadz6R8xDo=">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</latexit>
<latexit sha1_base64="A65xoQHKrAQFA6ERRU+MHMVIB6s=">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</latexit>
<latexit sha1_base64="d47BeaiCSggIHygDa7YsMBSVGZU=">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</latexit>
<latexit sha1_base64="Pa+yoLqzaGHp4KEvG5Egu6Soe/M=">AAACqXichVG7SsRQED3G93vVRrARlxVBXCYiKIIg2Fi66uriA0niXTdsXiR3VzT4Axa2ClYKFuJn2PgDFn6CWCrYWDi5GxAf4ITcO/fMnHmagWNHkuipSWtuaW1r7+js6u7p7evPDAxuRH4ttETR8h0/LJlGJBzbE0VpS0eUglAYrumITbO6lNg36yKMbN9bl0eB2HWNA88u25YhFbQwpe9lspQnJaO/FT1Vskhlxc88YAf78GGhBhcCHiTrDgxE/G1DByFgbBcxYyFrtrILnKALOWbX2E+wj8F4lc8Dfm2nqMfvJGqk+BbncfgPmTuKHD3SLb3SA93RM31wtL9jxSpGUs0R32aDK4K9/tPhtfd/WS7fEpUv1j9VS5Qxp6q1ufpAIUkfViNC/fj8dW1+NReP0zW9cAdX9ET33INXf7NuCmL1UlUUKo7AoerZVVV4POeYbRFn2GdbmbEaz0Ny5JgzVVBPZsor1H8u7LeyMZ3XKa8XZrKLc+kyOzCCMUzwxmaxiGWsoMjZKzjDOS60Sa2glbSthqvWlHKG8E006xMdxpgX</latexit>
<latexit sha1_base64="BqoVllRfLgucV5ke+9m6ADtsqjc=">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</latexit>
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E
PRML 7-7.1.1 + appendix E

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PRML 7-7.1.1 + appendix E

  • 1. PRML 7~7.1.1 + 付録E 5501 酒井⼀徳 5/2/18 1/51
  • 2. 今⽇の内容 2/51 7 疎な解を持つカーネルマシン 7.1 最⼤マージン分類器 + 付録E 7.1.1 重なりのあるクラス分布
  • 4. 疎な解 4/51 疎な解(sparse solution): 訓練データの⼀部だけに対して計算し,求まる解 前章では… 例えばガウス過程などは訓練データ全ての対についてカーネル関数の計算が必要だった. 学習時,もしくは予測時に⾮常に時間がかかる可能性がある
  • 5. SVMの特徴 5/51 Ø 訓練データを特徴空間において分類する Ø 正例と負例の境界にあるもの(サポートベクトル)だけを予測に使⽤する Ø サポートベクトルとの距離(Margin)が最⼤となる分類境界を求める Ø モデルパラメータが凸最適化問題の解として求まる Ø 確率的出⼒は⼀切ない
  • 8. マージン最⼤化を⾏う動機 8/51 Ø なぜサポートベクトルに対してのみマージンを最⼤化すれば良いのだろう? <latexit sha1_base64="IU4Xct/1tETRxwBHTx0CkY55fKc=">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</latexit> s.t. 共通のパラメータ を持つガウスカーネルを⽤いたParzen推定法で各クラスごとの⼊⼒ベクトル の 分布を推定する.今クラスラベル について, <latexit 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sha1_base64="JYSkfl3YrnGuUk+hCBYKJsaVyGY=">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</latexit> であり,Nはデータの数である.ここでクラスの事前分布が求まるのであれば, ベイズの定理 から決定境界は求まる.<latexit 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sha1_base64="oEcQIIIWC0eXXJU4m8V8zTEDDiM=">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</latexit> <latexit sha1_base64="iDxq0aRwN6zWA5ziV/Zf369ErWw=">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</latexit>
  • 9. マージン最⼤化を⾏う動機 9/51 クラス事前分布を無情報であるときに,誤分類が少ない事後分布の選択はモデルの選択と等価である. その分類境界は2クラス分類の時, <latexit sha1_base64="61QRp9jX+pZkJ/+7XuKhJYDwW58=">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</latexit> で与えられる.よって, <latexit sha1_base64="vIXfHrgOW+AbDGwsD8Ui+Z2omBM=">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</latexit> の極限を考えると, <latexit sha1_base64="nzh0DN2/aZT5FR8Vc2t9+feBT30=">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</latexit>
  • 11. マージン最⼤化の定式化 11/51 <latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">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</latexit> 上記の線形モデルと⽤いて2値分類を解くことを考える. 訓練データは, <latexit sha1_base64="Y7CxNnLYoyEru1acQx7KgNMbUXc=">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</latexit> <latexit sha1_base64="IWLUhbyJlGGSxLXFb1ca4cNd2sY=">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</latexit> ⼊⼒データ 対応する⽬的値 今,訓練データは特徴空間で線形分離可能とするため, 正しく線形分離できるデータについて以下が成⽴するとする. <latexit sha1_base64="y4DI9sq2hEHDMRfvZjaQRuN1sZU=">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</latexit> <latexit sha1_base64="5cJGC9qdoazs+hN+QOJR2ZSeYrM=">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</latexit> <latexit sha1_base64="wHtWBjWZMXeGB/4jbiME2jqetDA=">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</latexit> <latexit sha1_base64="ZGohuiAD0khcuR5S9unpk/FO0fo=">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</latexit> <latexit sha1_base64="X4ADg7Tb2vS56XVLP56X23/ARmU=">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</latexit> <latexit sha1_base64="+rCTpEXfm9Kusy7Y6SJ8W/q+gvA=">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</latexit>
  • 12. マージン最⼤化の定式化 12/51 <latexit sha1_base64="19BiG9BS8YIZN4Nc9DUG1RcfaTA=">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</latexit> 超平⾯ から点 までの距離は で与えられる.<latexit sha1_base64="7exF2UQ3pUWvMTvqagSd+6YP3X0=">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</latexit> <latexit sha1_base64="y+6FzjHIUYmrt/EIYcnUHJSGgdk=">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</latexit> <latexit sha1_base64="FIqdfY3fmRdUnp7/I/TWxESGSfQ=">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</latexit><latexit sha1_base64="NCZWL6uomMddIRuzhfLvtfeWGO4=">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</latexit> から分類境界から点 までの距離は次のようになる.<latexit sha1_base64="7exF2UQ3pUWvMTvqagSd+6YP3X0=">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</latexit> マージンとは訓練データと(正しく分類する)分類境界との 最短距離である. そのマージンを最⼤にするパラメータは以下の最適化問題によって得られる. <latexit sha1_base64="aCjrpmBZ9brT08o7LKD9p8JGktI=">AAADNnichVE7b9RAEB6bVwiPHNAgpYk4DiUCndYIiYgqEg1lXpdEuj0s27d3t4q9ttbryx2b/QM0lBRUIFEg/gA9Tf4ARRo6hKI0SAHRUDDec4QgSFnLnvH3zTePnTCLea4I2XfcM2fPnb8wdXH60uUrV2dq165v5GkhI9aK0jiVW2GQs5gL1lJcxWwrkyxIwphthtuPS35zyGTOU7GuxhnrJEFf8B6PAoWQX3tBC9FFnilNwzTu6h1zLzSaBrJPk2BkaMx6imrak0GkPSR2j8PorqEJF76wIW3li/lj6qmmio2UXjfGQvk4QaNpNuCmChoZXyzcDReo5P2B6kwMNU2/VidNYs/cScernDpUZzmt7QGFLqQQQQEJMBCg0I8hgByfNnhAIEOsAxoxiR63PAMD09BAdYFxDGMCxLfx28e/doUK/C+z5lYfYZ0YX4naOWiQT+QdOSJ75D05IL8w2/9zaZuj7GaMNpxoWebPPL+59vNUVYJWweCP6pSuFfRg0XbLsfvMIuUc0STD8NnLo7VHqw19h7whhzjBa7JPPuIMYvg9ervCVl/ZjqTVMNixMye2C4H3rJHLsUIXuR5iBd6HwswaKw1gWN4prtD7d2EnnY37TY80vZUH9aXFaplTMAu3YB439hCW4AksQwur/3BmndtOw/3gfna/uF8noa5TaW7AX8f99hs4n9PN</latexit> <latexit sha1_base64="xkbP1YRi32CbLD3OPxKbg3SHRCw=">AAADJXichVFNa9RAGH4Tv+r60a31IHgpLisrwjIpQosgFLx47Ne2haaGJDvZHTqZhMnstut0/AH+AQ+eFETEn+GlF28q9OTFi3is4MWDb2ajVSt0Qmbeed55nvcryjkrFCEHjnvq9Jmz5ybO1y5cvHR5sj51Za3IBjKmnTjjmdyIwoJyJmhHMcXpRi5pmEacrkfb90v/+pDKgmViVY1yupWGPcESFocKoaD+2E9kGGsViFHLjzLe1bsmELeM9jlNlL83xnaML1mvj3dz7zeh9cv3UPuK7iq9aoyFilGKh/bzPjN/it6OSt0jyT3TDuoN0iZ2zRw3vMpoQLUWs/o++NCFDGIYQAoUBCi0OYRQ4LcJHhDIEdsCjZhEi1k/BQM1aCJ7gO8ovgkR38a9h7fNChV4L1ULy48xDsdfIncGmuQDeU0OyT55Q76QH6j2fy1tNcpsRnhGYy7Ng8kn11a+n8hK8VTQP2KdkLWCBOZttgyzzy1S1hGPFYaPnh6u3F1u6pvkBfmKFTwnB+Qt1iCG3+KXS3T5mc1IWg6FHVtzarMQ2GeNvgIjdNGXIDbAfihU1hipD8OypzhC79+BHTfWZtseaXtLdxoL89UwJ+A63IAWTmwOFuABLEIHo392as60c9V95b5z37sfx09dp+JMw1/L/fQTPi7MOg==</latexit>
  • 13. マージン最⼤化の定式化 13/51 パラメータ を同じ値だけ定数倍しても前述の⽬的関数の値に影響がない, よって適当な定数をかけることで分類境界に最も近い点(サポートベクトル)について, <latexit sha1_base64="+6Z/dC2aygk7B1mamOQR6ClXBFU=">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</latexit> <latexit sha1_base64="2FA/xsC370jZl7vLb/r3b7xHE0M=">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</latexit> とできる.この時マージン最適化の問題は, 制約式の等号が成⽴する場合,この制約は有効であるという. この問題は⼆次計画法の⼀例である. <latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit> <latexit sha1_base64="mHO0tisKOzYkoK0vLtaTBsamToY=">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</latexit>
  • 15. ラグランジュ乗数と問題例 15/51 ラグランジュ乗数(Lagrange multiplier) (未定乗数とも) 複数の変数に1つ以上の制約条件が課されたときに,(ラグランジュ)関数の停留点を求めるため ⽤いられる. 例えば以下の問題において, <latexit sha1_base64="y0OWFQ2YsZo8NMQZlGZoT4wItxQ=">AAAC33ichVFNa9RAGH6a+lFbtau9CL0sLisVSnhTBBdBKPTisR9uW+iWMMnObkPz1WSybhv2XOhBvIkIhRY8iD9DD73ozUN/gvRYwYsH38wGRSt0Qmaeed553k8n9r1UEZ2OGKNXrl67PnZjfOLmrduTlTt3V9MoS1zZdCM/StYdkUrfC2VTecqX63EiReD4cs3ZXijsaz2ZpF4UPle7sdwMRDf0Op4rFFN2pdEKRN/O+7Y127fnBnlnpoQPB7OtnUy0q6mpzOoQdn8bn5JdqZFJelUvAqsENZRrMaqcoIU2IrjIEEAihGLsQyDlbwMWCDFzm8iZSxh52i4xwDjqrM74neQ3gvlt3rt82yjZkO+F11TrXY7j85+wtoo6faX3dE4n9IG+0U/29n9fufZRZLPLpzPUytiePLi38uNSVcCnwtYf1SVZK3TQ0Nl6nH2smaIOd+iht/f6fOXJcj1/QMd0xhUc0Sl95BrC3nf33ZJcfqszSrRG4oWuOdBZhNznnG0pR2izrcNcxv1Q7DnnSFvoFT3lEVr/DuwiWJ0zLTKtpUe1+UY5zDFM4z5meGKPMY9nWESTox/iEz7jiyGMfeOl8Wr41BgpNVP4axlvfgGVuaui</latexit> 制約条件から のような表現を⾒つけ,最⼤化問題を1変数に変えるアプローチが 考え得るだろう.しかし, • いつも解析的に陽に表現できるとは限らない. • 元の問題の対称性を活かせておらず,エレガントじゃない. <latexit sha1_base64="AwVZcTFCxVXl1b7pGSm5x8X1Wic=">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</latexit> より⼿軽で,エレガントな⼿法を
  • 16. ラグランジュ乗数法の幾何学的解釈 16/51 <latexit sha1_base64="0I1CpTOStX4lslEMDkI8g20hQ3U=">AAADZ3ichVJNTxNRFL3T8QMQaYXEkLgBmxKaaHPHmEBITEhgwcIFBVswQOrM+NqOnZk3mZlWsZnEtezcsHCliQvjz3DDH3DBTyDuxMSNCZ55nUShJrzFe/ede895584dK3CdKGY+1nL6lavXro+Mjt0YvzmRL9yarEeyG9qiZktXhtuWGQnX8UUtdmJXbAehMD3LFVtWZyXNb/VEGDnSfxLvB2LPM1u+03RsMwYkC89olXYpJkGvsPc7s9UV9p+OioAS4BZJcuk59ZFN6BHN42yQQfeQS3EJToRbiq5S+V8lfvdG5zU+4PbZuNKaoRb4FzXLUOVzvDZL4PPQu4+XysPumj8OLVS94IOzCUoahSJXWK2Z4cDIgiJla10WjiCZWrepSx6kfUjbsGSilYh28ChTAGwPFk0KETkqL2BrjEpgd1EnUGMC72Bv4baToT7uqWqk+LZqVkIlwQco8Tf+zKd8xF/4hH9D7f9afaWRutnHaQ24Imjk305v/rqU5eGMqf2XdYnrmJq0qNw6cB8oJO3DHij0Xh+ebi5tlPpz/JG/o4MPfMxf0YPf+2l/qoqN98pRqDiCXqqePeXCV2PexbtNRAK7CXUX+gnwAB576TfFCI2LAxsO6g8qBleM6sPi8mI2zBG6Q3fxqxi0QMu0RutUI1ub0x5rNa2eO9Hz+m19elCa0zLOFJ1b+uwfmgTBOg==</latexit> <latexit sha1_base64="K/Ex/k4aXvYG0w3h3EEGbDsPTDM=">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</latexit> <latexit sha1_base64="IS08Iw6oxBL/6aTo3OL6c107TPg=">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</latexit> <latexit sha1_base64="HhA34vPJNVOKCXwlGE73xfUnT84=">AAAC/XichVE7axRRFP4yPhJjNKs2gs3ishIQljMiGFIFbSws8nCzC5sQZmbvJkPm5czd1ThE+/gDLKwUUohiayNY2KS1sEipncQugk1Av7kZ8BEhZ7j3njnnfOc7DzcJ/EyL7AxZx46fODk8cmr09NiZs+OVc+cXsrifeqrpxUGctl0nU4Efqab2daDaSaqc0A1Uy127VfhbA5Vmfhzd1euJWgqdlcjv+Z6jaYorV7EIDYUHvHPpyiPZlJvyRD7KV/ks+/IeG4wI4CCEiy7fRUSMv4cqhOdP9J1OuzUhrZ9j2Fiu1KQhRqqHFbtUaihlJq5sM1UXMTz0SaVIoqkXxBm/DmzSJbQtIactpeYbv2KBo6gT3WecYoxD+xrvFf51SmtkGlDUC7xHnoAnJbaKunySl7In2/KKTe8z2/9z5SZHUc26GYbBqmR5fPPi/I8jUSFfjdXfqCOq1uhh0lTrs/rEWIo+vIMMg4dP9+an5ur5FXkhu+zguezIB/YQDb57W7Nq7pmpKDUYhfum59BUEXHOOX0ZGbr09Wjrcx6amXMyrWJQzJQrtP9d2GFl4VrDloY9e702PVkucwSXcBkT3NgNTOM2ZtAk+zt8wS6+WY+tLeu19eYg1BoqMRfwl1hvfwFV07EA</latexit> <latexit sha1_base64="fIUcDWsm13eCBtz1vjWtmvHoxcQ=">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</latexit>
  • 17. ラグランジュ関数 17/51 ここで以下で定義されるラグランジュ関数(Lagrangian) <latexit sha1_base64="ipyTG2ytrlYoBuxdZ5D5E59khW0=">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</latexit> を導⼊することで,停留条件と制約式は以下で表現できる. <latexit sha1_base64="vUy6v9ZjXbpgqkil7FqgRiuqehk=">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</latexit>
  • 18. 勾配が直交する理由 18/51 <latexit sha1_base64="pUwwmZk2qDjFUWmhlCICMOWNLX4=">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</latexit> <latexit 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sha1_base64="hEHwiPLsnKboMs/cZJyixlHiHeA=">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</latexit> <latexit sha1_base64="9iIo+2+0Ane+Z1Gqc4Ag4jEfgXc=">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</latexit> <latexit sha1_base64="XLaln6xwK57Vqajjz9kwe6Jf8yc=">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</latexit>
  • 19. 不等式制約の解のパターン 19/51 制約が という不等式制約で与えられた際の の最⼤化問題を考える.<latexit sha1_base64="ENItnW9vHRgEyVRVa5mqzjmJxR0=">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</latexit> <latexit sha1_base64="bxNYtVZMQbl9uON0SRXNrPJ81kU=">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</latexit> このとき解は次の⼆通りに分類できる. ① の領域にある場合…無効制約 制約領域にあるならば単に を満たせば良いだけ.<latexit sha1_base64="fODTl+e5/jZCNcjSBc9eIjrogMc=">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</latexit> ② の上にある場合…有効制約<latexit sha1_base64="lgbpIPvWGq6KsrQYG56qRzsvMqk=">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</latexit> <latexit sha1_base64="3iz0avfv0A90oGTU4os2xBVXye8=">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</latexit> は制約領域の外を向く必要がある.何故なら制約領域の⽅向を向いているならば, 制約領域内で停留点を取りうるためである.つまりある が存在し,<latexit sha1_base64="rfMIzLh40SyqLe3jzk8cQ3rZNO4=">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</latexit> <latexit sha1_base64="umHzBGh5O/C7CEUG94KRg5vRlvs=">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</latexit> が成⽴する必要がある. <latexit sha1_base64="NWPxfy90HR21xt7KqBx/MPm9MoE=">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</latexit>
  • 20. Karush-Kuhn-Tucker条件 20/51 <latexit sha1_base64="62k71GNDxcgO7ZXs3XMpcnDQa7I=">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</latexit> 前述から,上記の問題は以下の条件の元でのラグランジュ関数の停留点を求める問題になる. <latexit sha1_base64="ipyTG2ytrlYoBuxdZ5D5E59khW0=">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</latexit> <latexit sha1_base64="JqGYEisYztqd/92jTY+jgKreY/8=">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</latexit> <latexit sha1_base64="vpVgyaap2arqrOao6eRDQ7sxlaI=">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</latexit> のどちらかが成り⽴つという意味. 解が制約内部か制約⾯上かどちらかで あるという意味でもある. <latexit sha1_base64="wHshlPt/KudAt6Ob3+YJb8Wnsb4=">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</latexit> <latexit sha1_base64="TyVJJoJC/cTFYnsdsX1/pTAb/ok=">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</latexit> <latexit sha1_base64="P8q+WIhqV3xhl1g1yu1Gw5jwc00=">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</latexit> KKT条件 最⼤化ではなく最⼩化であればラグランジュ関数を以下に変更し最⼩化すれば良い. <latexit sha1_base64="cIiX077P6742ER0oxGfrjSzwsnE=">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</latexit>
  • 21. 複数条件への拡張 21/51 例として以下の複数の制約の下での最⼤化問題を考える. <latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="ajHnUYG9ba51BtU4aBEahLCW9Ws=">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</latexit> この場合,複数のラグランジュ乗数 および を導⼊し 以下のラグランジュ関数を最適化すれば良い. <latexit sha1_base64="6kyqVsaqGV87+HhlBfiRf0HNm/4=">AAACsnichVHLThRBFD00KogPRtiYsCFOxria3DYkElckblzycIDITCbdPTXQUv2gu2YMdvgBf4CFGyBhYfwMN/wACz6BsMTEjQtP13RiFBNup6tunXvPffqpDnMjcjHmjN+5e29i8v7Ug4ePHk/Xnsys58kgC1QrSHSSbfpernQYq5YJjVabaaa8yNdqw999U9o3hirLwyR+Z/ZT1Ym87Tjsh4FnCHXaRVvTued1P7QPurW6NMXK/E3FrZQ6KllOamdoo4cEAQaIoBDDUNfwkPPbggtBSqyDglhGLbR2hQNMoUH2gH6KPh7xXZ7bfG1VaMx3GTW3/IB5NP+M3Hk05Fy+yrWcyTe5lF+M9v9YhY1RVrPP2x9xVdqd/vx07eetrIi3wc4f1i1VG/SxaKsNWX1qkbKPYBRh+Onweu31aqN4LidyxQ6O5UK+s4d4+CM4XVGrX2xFmeUofLQ9R7aKmHMuaMuZoUdbn9iA8zCMXDDTDoblTLlC99+F3VTWXzZdaborC/WlxWqZk5jDM7zgxl5hCW+xjBaz7+EQRzh2Fpz3jucEI1dnrOLM4i9x9G/uqJyY</latexit> <latexit sha1_base64="+A9dnRuMmJiYfI+w1EJ3oBspX7s=">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</latexit> <latexit sha1_base64="6mAbhoJc7hAEEMd0sk++TVvy7qM=">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</latexit> このときのKKT条件は以下である. <latexit sha1_base64="G1YzK4u0ZM7T2OC7keFtJdnRAZc=">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</latexit> <latexit sha1_base64="OKCCO+da7Z9XFpGz5nXHvmQQrzg=">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</latexit> <latexit sha1_base64="2tkXvP060heH3iXKRINcJfg2zlU=">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</latexit>
  • 23. ラグランジュ乗数の導⼊ 23/51 <latexit sha1_base64="SHy946PDuuhogphSTaBlqHhhefE=">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</latexit> <latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">AAAC43ichVFNa9RAGH4aP1rrR9f2InhZXFbqZZkUwVIsFHrxJP1w20K3hiQ72x2aTEJmsu065A/oTQQP4sGCB/FneNmrgof+BPFYwYsH38wGRCv0DZN553nf5/0M0kgozdjJhHPh4qXLk1NXpq9eu35jpnZzdksleRbydphESbYT+IpHQvK2FjriO2nG/TiI+HZwsFratwc8UyKRT/Qw5Xuxvy9FT4S+JsirPewESdQ1h8VyR+WxZ+SyWzx9bHxP1jUda1XDmC7TSfuiKObHhKPCk/e8WoO1mJX6WcWtlAYqWUtqI3TQRYIQOWJwSGjSI/hQ9O3CBUNK2B4MYRlpwto5CkyjSeyc/Dj5+IQf0H+fXrsVKuldRlWWH1KeiE5G3Dqa7Cv7wE7ZiH1k39gvivb/WMbGKKsZ0h2MuTz1Zp7f2vx5LiumW6P/h3VO1Ro9LNpqBVWfWqTsIxxHGDx7fbq5tNE0d9kx+04dvGMn7BP1IAc/wvfrfOONrSizHI5D23Nsq5A0Z0M2RRm6ZOsRltM8NEU2lKmPQTlTWqH778LOKlsLLZe13PX7jZXFaplTuI07mKeNPcAKHmENbcp+jBE+44vDnRfOS+fV2NWZqDhz+Euct78BiIWw/A==</latexit> <latexit sha1_base64="RdlqAdGJhJ+mQoXNjGfc46Ftr9M=">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</latexit> <latexit sha1_base64="ieM1ukI341e4FGbiyIP5BLenlwg=">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</latexit> ラグランジュ乗数 を導⼊することで, 次のラグランジュ関数を得る. が得られる.これらの式をラグランジュ関数に代⼊することで, ラグランジュ関数の双対表現が得られる. <latexit sha1_base64="UNAoSyFoFp2UwwLLKbCwl03t440=">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</latexit> <latexit sha1_base64="qLqWrVV+rXNDhRNnWX6cJhM38As=">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</latexit> <latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit> <latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit>
  • 24. マージン最⼤化の双対問題 24/51 <latexit sha1_base64="pTvQBdpFvQ9xr+Iv8ZBaJE/G3aU=">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</latexit> <latexit sha1_base64="ZBLi2ROZWoTc8LSHCZgolK5gJ+c=">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</latexit> <latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="j5DA8Sdh+96unRMKfiThmXGio6s=">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</latexit> <latexit sha1_base64="hbTGfTqroQ3ISgZg39nQqb2Z69Q=">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</latexit> <latexit sha1_base64="m74Qq4cQz59B0Nh5yLxkYDmKwgA=">AAAC7HichVFLa9RQFP4aX7U+OupGcBMcRlwMw0kRLEKhIIKr0ofTFpoaksydaWhyk8m9Galh/oBrwUVxoaAg/RluunXhovoLxGUFNy48uRMQrdATcu+53znfeQZZHClNdDRlnTl77vyF6Yszly5fuTrbuHZ9XaVFHopumMZpvhn4SsSRFF0d6VhsZrnwkyAWG8Huw8q+MRK5ilL5RO9lYjvxBzLqR6GvGfIaj3xPugMxVLEvtU1tdzgs/J4tF5y2G/dSrdpLbbsGXVUkXsmm8dNyaVwy09aeHC9Qx2s0qUNG7JOKUytN1LKcNg7hoocUIQokEJDQrMfwofjbggNCxtg2SsZy1iJjFxhjBi1mF+wn2MdnfJfPAb+2alTyu4qqDD/kPDH/OXNttOgzfaBjOqQD+ka/ONr/Y5UmRlXNHt/BhCsyb/bFzbWfp7ISvjV2/rBOqVqjj3lTbcTVZwap+ggnEUbPXx2vPVhtlXfoLX3nDt7QEX3kHuToR/huRazum4pywxF4ZnpOTBWS51yyTXGGHtv6jBU8D82RS860g1E1U16h8+/CTirrcx2HOs7KvebifL3MadzCbdzljd3HIh5jGV3OfoBP+IKvlrReWvvW64mrNVVzbuAvsd7/BqrSslI=</latexit> この問題は再び⼆次計画法になっていることに注意する. 解く⽅法は後述(7.1.1節)
  • 25. 意味があったのか 25/51 <latexit sha1_base64="9QHeHRFNsbNSL+Z+ODN4CIoEdf4=">AAAC5XichVI9axRRFD07fm0SNas2goXRZUWb5Y4KBm0CNjaaTeImkRjDzOzbzbDzxXysxsEfYNAmiBYWomgh/gybYKspUluJZQQbC8+8HRCNkDfMe/ed+84999737Mhzk1Rku2Ls23/g4KHqyOjY4SNHx2vHjs8nYRY7qu2EXhgv2laiPDdQ7dRNPbUYxcrybU8t2P3rhX9hoOLEDYPb6Vqkln2rF7hd17FSQmHtNG7iLlIoPOCct8YkuDOiItlwKtK59aR/Zr2aXfO2ZOPxV5mWvoR4hGmcJ+seLuHCSq0uTdFjYrdhlkYd5WiFtU3KdRDCQQafsgFlHXiwkPBbgglBRGwZObGYlqv9isKjaJCd8ZziGYt4n3OPu6USDbgvoiaa71DH4x+TO4GGbMl72ZFN+SDf5Bej/T9WrmMU2axxtYdcFa2Mr5+c+7kny+eaYvUPa4+sU3QxqbN1mX2kkaIOZxhh8PDFztzV2UZ+Tt7Id1bwWrblI2sIBj+cdzNq9qXOKNYchfu6Zl9nEbDPOX0JFTr0dYll7EfKyDmVVjEoesorNP+9sN3G/MWmKU1z5nJ9arK8zCpO4SyfgokrmMINtNCm+lt8wmd8MXrGU+OZ8Xx41KiUnBP4axivfgNBsaoM</latexit> <latexit sha1_base64="klyyKEyWXSP2RZrpUxjsk+Zi3lw=">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</latexit> <latexit sha1_base64="jIieM9WlOuytMGbEpoS+atui3KY=">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</latexit> ※上に有界: bounded above pdfでは “bounded below”となっていた 主問題 双対問題 <latexit 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sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="8HLGpfVFSjoTExKiDJZHGthAoeI=">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</latexit> <latexit sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">AAACqXichVG7SsRQED3G93vVRrARlxVBCBMRFCvBxtJVVxcfSBLvumHzIrm7osEfsLBVsFKwED/Dxh+w8BPEUsHGwsndgPgAJ+TeuWfmzNMKXSeWRE8tWmtbe0dnV3dPb1//wGBuaHgjDuqRLUp24AZR2TJj4Tq+KElHuqIcRsL0LFdsWrWl1L7ZEFHsBP66PArFrmce+E7FsU2ZQrEu9b1cnnRSMv5bMTIlj0xWgtwDdrCPADbq8CDgQ7LuwkTM3zYMEELGdpEwFrHmKLvACXpQYHad/QT7mIzX+Dzg13aG+vxOo8aKb3Mel/+IueMo0CPd0is90B090wdH+ztWomKk1RzxbTW5ItwbPB1de/+X5fEtUf1i/VO1RAXzqlqHqw8VkvZhNyM0js9f1xZWC8kkXdMLd3BFT3TPPfiNN/umKFYvVUWR4ggcqp49VYXPc07YFnOGfbZVGKvzPCRHTjhTFY10prxC4+fCfisbM7pBulGczS/OZ8vswhgmMMUbm8MilrGCEmev4gznuNCmtaJW1raarlpLxhnBN9HsT5NUmEs=</latexit> <latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit> <latexit sha1_base64="Gx19UD4tnGWaE9zbERBVhieYmQ8=">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</latexit> <latexit sha1_base64="7PF78odKi2Q4hlWrBrTqDakAKaw=">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</latexit> <latexit sha1_base64="ZBLi2ROZWoTc8LSHCZgolK5gJ+c=">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</latexit>
  • 26. サポートベクトル 26/51 KKT条件から以下が⾔える. <latexit sha1_base64="PGQOPIVMggpS9KEqohVv60lVchs=">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</latexit> <latexit 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sha1_base64="4XNgddZRCjBQWtCC3mQMZlSv6j8=">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</latexit> <latexit sha1_base64="/0iKGVAWcdTKyKt/710rEdYkU1M=">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</latexit> ここで,全てのデータ点について あるいは が成⽴する.<latexit 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sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit> <latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">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</latexit> <latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">AAAC43ichVFNa9RAGH4aP1rrR9f2InhZXFbqZZkUwVIsFHrxJP1w20K3hiQ72x2aTEJmsu065A/oTQQP4sGCB/FneNmrgof+BPFYwYsH38wGRCv0DZN553nf5/0M0kgozdjJhHPh4qXLk1NXpq9eu35jpnZzdksleRbydphESbYT+IpHQvK2FjriO2nG/TiI+HZwsFratwc8UyKRT/Qw5Xuxvy9FT4S+JsirPewESdQ1h8VyR+WxZ+SyWzx9bHxP1jUda1XDmC7TSfuiKObHhKPCk/e8WoO1mJX6WcWtlAYqWUtqI3TQRYIQOWJwSGjSI/hQ9O3CBUNK2B4MYRlpwto5CkyjSeyc/Dj5+IQf0H+fXrsVKuldRlWWH1KeiE5G3Dqa7Cv7wE7ZiH1k39gvivb/WMbGKKsZ0h2MuTz1Zp7f2vx5LiumW6P/h3VO1Ro9LNpqBVWfWqTsIxxHGDx7fbq5tNE0d9kx+04dvGMn7BP1IAc/wvfrfOONrSizHI5D23Nsq5A0Z0M2RRm6ZOsRltM8NEU2lKmPQTlTWqH778LOKlsLLZe13PX7jZXFaplTuI07mKeNPcAKHmENbcp+jBE+44vDnRfOS+fV2NWZqDhz+Euct78BiIWw/A==</latexit> <latexit sha1_base64="gbXceMzZaBzFcz9lALG60wSu14Q=">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</latexit> となるデータ点は右記から予測に影響を及ぼさない. となるデータ点はサポートベクトルと呼ばれ,マージンの縁に存在する.<latexit sha1_base64="bvpNjktwuYdbOUOEDcIwHW86H5E=">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</latexit> サポートベクトルは が成⽴するデータ点でもある.<latexit sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit>
  • 27. 分類規則 27/51 <latexit sha1_base64="KDzDlUK19VErDrbvj89BJKgVqE8=">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</latexit> 学習したモデルを⽤いてデータを分類するには,求まったパラメータ とカーネル関数で表される以下の関数の符号で判断できる.<latexit sha1_base64="CHB3UpVNl9cAk2rbZ3G7ZjwTYs8=">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</latexit> <latexit sha1_base64="bL2t88VsAMbiaGya1481gey/IsA=">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</latexit> <latexit sha1_base64="r0kdg8jTfzf7sZzJ50SuECiuw8k=">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</latexit> <latexit sha1_base64="z/G9/wL3OoATCsbuVarxUoKs1MQ=">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</latexit> <latexit sha1_base64="tvqTrESbrPQz8JVmZqsA3cbaU9Y=">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</latexit> バイアスパラメータ の導出については任意の サポートベクトル について が成⽴することから右記の式を⽤いた. <latexit 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sha1_base64="di1zqbWIQW3MXOrauAKRRm4A0Ac=">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</latexit> <latexit sha1_base64="XXB1SXbP32yngcxyQEYeMSuzMxo=">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</latexit> <latexit sha1_base64="x5vudz69FojtLwTZ42w85sL2Xz8=">AAAC9HichVFPa9RAFH+NVmutdrUXwcvisrJFWSZFsAiFgpdehLbrtoWmhEl2dnfYmUlIJmnrkC/gF/BgLyo9iODFj+ClX8DDXvUkHit48eDLbFC0Ql+YzJvfe7/3N4gFTzUh4ynnwsXpS5dnrsxenbt2fb524+ZWGmVJyLphJKJkJ6ApE1yxruZasJ04YVQGgm0Ho8elfTtnScoj9VQfxmxP0oHifR5SjZBfe6J95QnW1y0vzaRvpMdV3ZNUD0MqTKcoDPVlXeMZtbwgEj1zUPjq/m9VLt4LCi/hg6FeXHH9WoO0iZX6WcWtlAZUsh7VTsCDHkQQQgYSGCjQqAugkOK3Cy4QiBHbA4NYghq3dgYFzEIT2Rn6MfShiI/wP8DXboUqfJdRU8sPMY/AkyC3Dk3yibwlp+SEvCNfyU+M9v9YxsYoqznEO5hwWezPP7/V+XEuS+KtYfiHdU7VGvqwbKvlWH1skbKPcBIhf/bitPNos2nuktfkG3bwiozJR+xB5d/D4w22+dJWlFgOg33bs7RVKJyzQVuKGXpo6yOW4Tw0RjaYaQh5OVNcofvvws4qW0ttl7TdjQeN1eVqmTNwG+5ACzf2EFZhDdahi9k/wBg+wxcnd46cN87xxNWZqjgL8Jc4738B1Ka3ag==</latexit> <latexit sha1_base64="V7tt5fOzqpQgZ3pTWTkYMSEQXIc=">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</latexit> はサポートベクトルの総数である.
  • 28. 正則化パラメータが である限り,解は⼀意に収束する. ハードマージンSVM 28/51 <latexit sha1_base64="Ty12gyLvrAI+hfNh0DUCxwLVlyc=">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</latexit> <latexit sha1_base64="ooFsvnugNNSni5dUOZdvTgJgigA=">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</latexit> <latexit sha1_base64="28WcI7u/YPpcCrwk3RELIM2HVNg=">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</latexit> SVMの最⼤マージン学習は次の誤差関数の最⼩化に等しい. 誤分類に対して無限のペナルティを与えている. のちのソフトマージンと⽐較してハードマージンと呼ばれる.
  • 32. スラック変数 32/51 ただし,今回はスラック変数をペナルティとして導⼊するため以下のように定義される. <latexit sha1_base64="sSowAwIyS4v19mYheE9pW0TGAXE=">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</latexit> 不等式における両辺の差,余裕を表す変数.スラック変数を⽤いて不等式制約 を 等式制約 と⾮負条件 で表現できる. <latexit sha1_base64="6L2tinVZ3qcAcrp95FN4fhlmfZ0=">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</latexit> <latexit sha1_base64="xDvihjQlSRZ/gWU03Wadz6R8xDo=">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</latexit> <latexit sha1_base64="A65xoQHKrAQFA6ERRU+MHMVIB6s=">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</latexit> <latexit sha1_base64="d47BeaiCSggIHygDa7YsMBSVGZU=">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</latexit> <latexit sha1_base64="Pa+yoLqzaGHp4KEvG5Egu6Soe/M=">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</latexit> <latexit sha1_base64="BqoVllRfLgucV5ke+9m6ADtsqjc=">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</latexit>