{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# scikit-learnによるサポートベクトルマシン分類(SVC)とサポートベクトル回帰(SVR)\n", "\n", "
\n", " このページのオリジナルのipynbファイル\n", "
\n", "\n", "## 前置き\n", "\n", "本講義では、説明変数$x$と目的変数$y$の関係の推定(回帰)問題を扱っている。\n", "\n", "これまでは、その関係を、\n", "\n", "$$\n", "y = \\sum_{i=1}^M w_i \\phi_i(x)\n", "$$\n", "\n", "のように、説明変数(*)の関数を$M$個用意して、その線形結合で目的変数を表すという形に持ち込むと、$M$個の重回帰と同じ形式で扱えること、それをベイズ的な考え方で扱うと、誤差分布に関する見通しが良くなることを学んだ。\n", "\n", "説明変数の関数の組$\\{\\phi_i (x)\\ | \\ i=1,\\cdots,M \\}$は、基底関数と呼ばれた。\n", "\n", "ここでは基底関数を選ばなくても、データ自体からもっともらしい推定値とその周りの分散が求められる方法を考える。\n", "\n", "ここでは、その代表的な例であるサポートベクトル回帰(SVR)を扱う。\n", "\n", "サポートベクトルの考え方はもともとは、回帰と並ぶ機械学習のもう一つの課題である「分類」(classification)の手法として考案されたものである。\n", "\n", "そこで、まずは分類の手法である「サポートベクトルマシン」(SVM)について試してみる。\n", "\n", "(*) 説明変数のことを、機械学習の分野では、特徴量(features)、目的変数のことをtargetとと呼ぶことが多い。\n", "\n", "## サポートベクトルマシン概説\n", "\n", "\n", "別のノートで説明する。[こちら](http://8tops.yamanashi.ac.jp/~toyoki/lectures/simulationMethods/svc_note.html)\n", "\n", "\n", "## skitlearnにおけるサポートベクトルマシンの利用例\n", "\n", "「Ipythonデータサイエンスクックブック」に載っている例でsvmの振る舞いを調べてみる。\n", "\n", "原文(ただし、第2版)はgithubのサイトで公開されている。\n", "\n", "\n", "第8章「機械学習」レシピ8.5 https://ipython-books.github.io/85-using-support-vector-machines-for-classification-tasks/\n", "\n", "以下の英語の部分は、この書籍の原著からの引用である。\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 訓練データ (1)\n", "2. We generate 2D points and assign a binary label according to a linear operation on the coordinates.\n", "\n", "$x + y >1$のときtrue, それ以外はfalseになる$200\\times 200$の2次元データyを作る。 [スクリプトに関するコメント](comments_python_scripts.html#numpy1)\n", "\n", "2つの説明変数$x$, $y$に対して、目的変数$z$が対応すると考える。下図では面に$(x,y)$の値を、面に垂直方向に$z$があると想像してほしい。$z$の値は今の場合はTrueあるいはFalseであり、図では濃い青と薄い青で示している。" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "# 平面上で適当に200個の点を選ぶ 座標値(x,y)の200個の組 X[200,2]\n", "X = np.random.randn(200, 2)\n", "# ターゲットt[x[i],y[i]]の値を x[i]+ y[i] > 1 のときtrue, それ以外 false => それデータとしてtrue or falseの境界をsvcで見つける\n", "# 右辺の評価式がtrueかfalseかを配列としてyに与える (ここでは200個の一次元は配列)\n", "y = X[:, 0] + X[:, 1] > 1\n", "\n", "# We display the points with their true labels.\n", "fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n", "cmap = plt.cm.Blues\n", "ax.scatter(X[:, 0], X[:, 1],\n", " s=50, c=.5 + .5 * y,\n", " edgecolors='k',\n", " lw=1, cmap=cmap,\n", " vmin=0, vmax=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## サポートベクトル識別 (1) 線形\n", "\n", "3. We now fit a linear **Support Vector Classifier** (SVC). This classifier tries to separate the two groups of points with a linear boundary (a line here, more generally a hyperplane).\n", "\n", " - 線形識別機の用意 (LinearSVC関数の利用)\n", " - データ(X,y)によりトレーニング(fit関数)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sklearn.svm as svm\n", "# We train the classifier.\n", "est = svm.LinearSVC()\n", "est.fit(X, y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "識別実行のための関数定義\n", "\n", "4. We define a function that displays the boundaries and decision function of a trained classifier.\n", "\n", " - 2次元面のメッシュ (xx, yy) を作成し、メッシュ上のすべての点について境界のどちらかを判定 (decision_function)\n", " - 返り値をZ (「高さ」)に代入\n", " - Zの値をグラデーションで表示\n", " - 境界 (Z(x,y)=0)の線を引く" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# We generate a grid in the square [-3,3 ]^2.\n", "xx, yy = np.meshgrid(np.linspace(-3, 3, 500),\n", " np.linspace(-3, 3, 500))\n", "\n", "# This function takes a SVM estimator as input.\n", "\n", "def plot_decision_function(est, title):\n", " # We evaluate the decision function on the grid.\n", " Z = est.decision_function(np.c_[xx.ravel(),\n", " yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", " cmap = plt.cm.Blues\n", "\n", " # We display the decision function on the grid.\n", " fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n", " ax.imshow(Z,\n", " extent=(xx.min(), xx.max(),\n", " yy.min(), yy.max()),\n", " aspect='auto',\n", " origin='lower',\n", " cmap=cmap)\n", "\n", " # We display the boundaries.\n", " ax.contour(xx, yy, Z, levels=[0],\n", " linewidths=2,\n", " colors='k')\n", "\n", " # We display the points with their true labels.\n", " ax.scatter(X[:, 0], X[:, 1],\n", " s=50, c=.5 + .5 * y,\n", " edgecolors='k',\n", " lw=1, cmap=cmap,\n", " vmin=0, vmax=1)\n", " ax.axhline(0, color='k', ls='--')\n", " ax.axvline(0, color='k', ls='--')\n", " ax.axis([-3, 3, -3, 3])\n", " ax.set_axis_off()\n", " ax.set_title(title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Let's take a look at the classification results with the linear SVC.\n", "\n", "識別の実行と図示" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plot_decision_function(\n", " est, \"Linearly separable, linear SVC\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The linear SVC tried to separate the points with a line and it did a pretty good job." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**[学習]**\n", "\n", "$x + y> a$ ($a$はデータが2分類できるように、$-2" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import sklearn.model_selection as ms\n", "\n", "y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0) # 第1象限と第3象限のみfalse\n", "\n", "# We train the classifier.\n", "est = ms.GridSearchCV(svm.LinearSVC(),\n", " {'C': np.logspace(-3., 3., 10)})\n", "est.fit(X, y)\n", "print(\"Score: {0:.1f}\".format(\n", " ms.cross_val_score(est, X, y).mean()))\n", "\n", "# We plot the decision function.\n", "ax = plot_decision_function(\n", " est, \"XOR, linear SVC\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "実行してみると警告がたくさん出る。\n", "\n", "これは、直線による区分は、当然だが、できないことを意味する。(収束しない!)\n", "\n", "そこでSVRが登場するのだが、基本的なロジックは\n", "\n", "1. これまでに用いてきたの同様に、線形分類で切るように、ある非線形関数(基底)により変換する。\n", "2. そのような基底を見つけるのは一般には困難であるが、それは「カーネルトリック」と呼ばれる巧妙な方法で解決できる。\n", "\n", "この部分は[別のノート](svc_note.html)で述べる。\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 非線形変換を含む識別機 (カーネル法の導入)\n", "\n", "SVMでは、カーネルを用いて分類線(境界)を計算することができる。\n", "\n", "データ${\\bf x}$ に対する非線形関数$\\{{\\bf\\phi}_1, {\\bf\\phi}_2, \\cdots, {\\bf\\phi}_M\\}$を用意し、\n", "$$\n", "y({\\bf x}) = {\\bf w}^T {\\bf \\phi}({\\bf x}) +b\n", "$$\n", "のような、目標変数と説明変数の間に非線形な関係があるとし、係数${\\bf w} = (w_1, w_2, \\cdots, w_M)^T$を学習により求める。\n", "\n", "この問題は、$k({\\bf x},{\\bf x'})= {\\bf \\phi} ({\\bf x})^T{\\bf \\phi} ({\\bf x}')$で定義されるカーネルを用いて\n", "\n", "$$\n", " y({\\bf x}) = \\sum_{n=1}^{N} a_n t_n k({\\bf x}, {\\bf x_n}) + b\n", "$$\n", "\n", "の形式に変換できることが知られている。ここで$t_n$は訓練データ${\\bf x_n}$に対する目標値であり、$a_n$は学習により求める係数である。\n", "\n", "ここからは、${\\bf \\phi}$からカーネル$k({\\bf x},{\\bf x'})$を作ったことは**忘れることにする。**\n", "\n", "つまり、、非線形関数${\\bf \\phi}$を設定するのではなく、カーネル$k({\\bf x},{\\bf x'})$自体に何らかの関数を指定することにより識別学習を行えることである。(逆に言えば関数${\\bf \\phi}$はどのようなものかわからない。)\n", "\n", "Scikit-learnのSVCでは、カーネルとしては標準的にガウシアン放射基底関数(Gaussian Radial Basis Function)が用いられている。この置き換えは**kernel trick**と呼ばれると書籍では述べている。\n", "\n", "$$\n", "k({\\bf x},{\\bf x'}) = \\exp ( -\\gamma || {\\bf x}-{\\bf x'} ||^2)\n", "$$\n", "\n", "が用いられる。パラメータ$\\gamma$の値はグリッドサーチや交差検定を使って定められる。\n", "\n", "> The $\\phi$ function does not need to be computed explicitly. This is the kernel trick; it suffices to know the kernel $k(x,x')$. The existence of a function $\\phi$ corresponding to a given kernel $k(x, x')$ is guaranteed by a mathematical theorem in functional analysis (Mercer's theorem).\n", "\n", "\n", "7. Fortunately, it is possible to use nonlinear SVCs by using **nonlinear kernels**. Kernels specify a nonlinear transformation of the points into a higher dimensional space. Transformed points in this space are assumed to be more linearly separable. By default, the **SVC** classifier in scikit-learn uses the **Radial Basis Function (RBF)** kernel:\n", "\n", "\n", "もう少し立ち入った説明は[こちら](https://8tops.yamanashi.ac.jp/~toyoki/lectures/simulationMethods/svr_note.html)\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Score: 0.945\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)\n", "\n", "# determine the hyper-parameters C and gamma, and then create the SVM machine object with the optimal parameters\n", "est = ms.GridSearchCV(\n", " svm.SVC(), {'C': np.logspace(-3., 3., 10),\n", " 'gamma': np.logspace(-3., 3., 10)})\n", "est.fit(X, y)\n", "print(\"Score: {0:.3f}\".format(\n", " ms.cross_val_score(est, X, y).mean()))\n", "\n", "plot_decision_function(\n", " est.best_estimator_, \"XOR, non-linear SVC\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time, the non-linear SVC does a pretty good job at classifying these non-linearly separable points.\n", "\n", "**[練習]**\n", "\n", "最初の訓練データを作り変えてSVCの性能を試してみよう。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 関数近似に対するサポートベクトルマシンの利用 (SVR)\n", "\n", "分類のためのSVMは、逆に、境界領域にたくさんのデータがあり、境界線より離れたところに少ないデータが存在する場合を想定すると、境界線が回帰線に対応する。そのことを積極的に使ったのがサポートベクトル(マシン)回帰(SVR)である。若干の数理的ノートは[こちら](svr_note.html)\n", "\n", "ここでは、「Ipythonデータサイエンスクックブック」に載っているサンプルを試してみる。\n", "\n", "\n", "例によって、つぎのような、sin関数にノイズを載せたデータを用いる。\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# データ作成用関数\n", "\n", "def make_data_by_sin_gaussian(x):\n", " # y=sin (x)を計算し、ガウス分布に従うノイズを加える\n", " y = np.sin(x)\n", " e = [random.gauss(0, 0.2) for i in range(len(y))]\n", " # e = np.random.randn(len(x))*0.2\n", " y += e\n", " return y\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### SVRによる推定\n", "\n", "データの範囲を越えた予測は困難だが、無難な値に収まっている。(基底関数を多項式にとったリッジ回帰などと比べてみてほしい。)\n", "\n", "[pythonスクリプトに関するコメント](comments_python_scripts.html#numpy2)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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3jovbRzD1m60cOKa7UilVXX4d9DUdYlm56yj3vptIuxYNmX13P5qEBp31HtEZaU5fG5WRrkM6HiYiTCsewhn/2UYcDu+6v6SU1zLGeNVPnz59jDusfvplkxUUYgyc+ckKCjGrn37Z6fkrdqSbjv/82lz+3BKTdiKnwvcoLPXr0j/HwhrX6PNU7X24ap9p8+hXZvbKvVaXopTXABJNBbnqt7NuUppFY3dy9Z0SHoX9eGqZYyt2HuGed9fQunkDPryvPxGNQip9DwdlvwplB4WQExhCs+wT1fo85RpjDCPfWs26/cdZ9Lc/ENe8QdUvUsrP1ctZN9VdRbl8xxHu/t8a2rZoyEelQr6y94CiAHcgpIRHsfmJGTTNPlmjOlTtFQ3hdMcmwqNzdK9ZpaoSWPUpviktPNLp1XhaeCT24l8v3Z7OfbMTaRfRkA/uvYAWjUKq+R6/X6Xbi39SZkyu8vOU+7Rq1oAJV3Xin/M28+nagwQH2Ji+aBuHMrKJCQ9j3KCODO0da3WZSnkFv72iPzB2UqWrKL9LSuXe2YmcE9mID+/rf1bIV+c9anuuco9b+7Wmb9tm/OuLLUyYs5HkjGwMkJyRzWNzNzFvfbLVJSrlFfw26PtOHMPmJ2acNcTSd+IY5q47yP3vr6VzyyZ8eO8FNG8YXOP3cOVc5R42mzB1WHey8grJKXCUeS47v5Dpi7ZZVJlS3sUvbsbOW59c7a/t76zYw5NfJjHg3BbMuiOeRiF+O3pVb7SdsMDpcQH2TLu6botRyiKV3Yz1+ZSbtz6Zx+ZuIju/EPj9aztQJuyNMbz4ww5e+H4HV3aJ5qVbepdZ8ap8V0zTUA5l5px9PDzMgmqU8j4+P3QzfdG2MyFfovzX9oJCB4/P38IL3++gX9vmbE7OpPOkhSRMW6zjuH5g/OBOBAeU/aMcFhTAuEEdLapIKe/i80F/KCO70uOncwsY/d5a3vtlHwM7RbHxYAaHMnP0pp0fGdo7lmdv7EHD4KJvaJGNQpg6rHuNZt3oqmblz3w+6Cv6eh4THkZKZg43vb6Sn7an8/TQbmxLOak37fzU0N6xrPzHH4luEkKLRsFc3aNltV+rjeqU1X49kMFd7xQtAvQEnw/6cYM6ElZurD0sKIBb+7Xm+ldXsO/oad4aFc/t/dtUefWvfFuT0CCeuq4bW1NOMmvp7mq/ThvVKavsSj/FfbMTGfrfFaw/kMHhjLPvNbmDz9+MLfl6XnrWzcBOUbz84w7Cw4L59P4BdIlpAhRd5Sc7CXW9aec/BnW1M7irnRd/2MHV3VvSNqJhla/RvWhVXTt6KpcXf9jBB6v2ExYUwNgrO3BnQjuPzQL0+St6KAr7FRMGsn3KVQzuZue9X/bRIzacLx5KOBPyUPHVv9608y//urYrwQE2Js3fXK32CBXtOat70Sp3M8bw8er9XDZjCR+s2s8t/eJYMu5Sxgxs79Gp3n4R9ABHTuVy+5ureGv5Hu4c0JYP7ruAqMahZc4Z2juWqcO6ExsehgCx4WE1vmmnvJ+9aSiPXNmBZTuOsGDT4SrP11XNqi7sSj/FiFm/MGHuJjrZm7Dwrxfz9NDuZfpreYrPD92UeG/lPn49kMHzw3sy7PxWFZ43tHesBns9MLJ/G+asO8hTXyZxSYdIGocGVXhu34ljWEPRWL3uRavczRjD/37ey9RvthISaGPqsO7cHB+HzSZ1VoNfrIwFyC90sPfIadpHN/ZAVcoXbTiQwdBXVzDqwrb869quVpej6qH0k7mM+2wDS7alM7BTFNOGdSeqSWjVL6wFv14ZWyIowKYhr8roGRfOyP5tmL1yLzec34rurZpaXZKqR5ZuT+fvn/zKyZwCnrquKyP7t0Gk7q7iS/ObMXrluzy5WOmRKzvSvGEIE+dtolC3HlR1wBjDq0t2Muqd1bRoGMKXD13EHRe2tSzkQYNeWczTi5WahgUxaUhnNh7M5INV+9zynkpV5HRuAQ9+uI5nF27jmh4xfP7gADp4wUiDBn0xXQJvjbpYrHRtzxguOi+C6Qu3kXbCMwtSlDpwLIvrX13Bws0p/PPqzrw4ohcNgr1jdFyDHl0Cb6W6WKwkIkwe2o3cQgdPL/jNbe+rVIlNBzO5/tWfST2Ry3v3XMC9F59j6VBNeRr06BJ4K9XVYqV2EQ154NJz+WLDIZbt0BWvyn1+3JrG8JkrCQm0MecvF5JwXoTVJZ1Fgx5dAm+lulysdP8l59IuoiGT5m0mp1xra6Vq4+PV+7l3diLnRjXk8wcHcF6U9ePxzrgU9CIyXERWi8haEXnOyfMPi8gaEflVRMa68lmepEvgrVOXWzCGBgUw+bpu7D2axWtLdrn9/VX98uay3UyYu4mLzovg/0ZfeNZKfG9S66AXkTbAZOAKIB5oJSI3lHo+AbgFSAD6AUNFxOlkfqvpEnhr9Z04BvvxVGzGgf14qkdXpF7UPoLresXw2pJd7E4/5bHPUf7t5R928PSC37i6e0veuCOehl6+JakrV/SDgTnGmExTtLx2JjC01PNDgHeMMXnGmDzgbeA6Fz7PY3Rj7/pl4tWdCQmqftMzpUoYY3h24Vae+247w3rH8uKIXgQHev8IuCsVtgBSSj0+DETV4PkzRGS0iCSKSGJ6ujXj4nV5VamsFdU4lPGDO7Fi51G+2HDI6nKUF6jO9GpjDE8v+I1Xl+zi1gtaM+OmngQGeH/Ig2tBn0rZ4LYXH6vu82cYY2YZY+KNMfGRkTourtyjsr+8t/ZrTc+4cCZ/lURmVr6FVSqrVWd6tTGGZxZuO9Mdd8rQbnXalMxVrgT918D1IlJym/luYH6p5+cDd4hIkIgEAKOAL1z4PKWqraq/vAE2YcrQbhw7ncezi7ZaXK2yUnWmV7+8eCev/7SL2y5ozRPXdPGqOfLVUeugN8YcBv4NLBWRVUCqMWaOiCwREbsxJpGiYF8F/AJ8WXxMKY+rzl/ebrFNuSuhHR+u3u+xvTqV96tqevWspbt4/rvt3HB+KyZf183nQh78qE2xUqU5xIaNs/9sOxBs5vcN4k/nFnD58z/RNCyILx+6iCAfGXNV7pPSLBp7RtrZx8Oj+O7rVUyav4UhPVry4ojeBHjxcE1lbYr1T7XyS9VdG9EwJJB/XduVrSkneWfFnrooTXmZiqZXf/TXaUyav4UrukTzn5t7eXXIV0WDXvmlmqyNGNTVzuWdo/nPdzs4eDyrrkpUXsLZ9OqPJr7Cq/nRXNCuOS/f0tvnv+n5dvVKVaCmayOevK5oB6p/fbGlzNz6eeuTSZi2mHYTFpAwbTHz1ifXSf2qbpWeXn10y3aed8RxbmQjZt0RT2hQgNXluUzH6JUqNmvpLv799VZev70Pg7vZmbc+mcfmbiK7VF+csKAA3VDejx04lsWw134myCbMfSABe1PvbWtQno7RK1VKRfPr70poRyd7Y/71xRZO5RYwfdG2MiEPkJ1fyPRF26woW3nYsdN5jHp7NXkFDt69u59PhXxVNOhVvVLZ/PqgABv/Htad1JM5PP/tdg5lZDt9jz4rvtZNavxMTn4h9767huSMbN4cFe93+09r0Kt6par59ee3bsat/Vrzv5/3ENEo5KzXX7vlR6YtfEU3qfEjxhgmfr6ZdfszeOHmXvRt29zqktxOg17VK9XZe2D84E40bxhCaJCN0HINq8YvnU2DAt2kxp+8vWIvc9Yd5G+Xt+eq7i2tLscjNOhVvVKd+fUlG4ofOJ7N1T1aEhsehgCx4WHEnDji9PW6SY1vWr7jCFMWJDGoazQPD2xvdTkeo0Gv6pXqzq+/tmcMF7ePYNGWVOY+MIA9065mxYSBukmNH9l75DQPfriO9lGNeX54L59qUlZTGvSqXqnu/HoRYfJ13cgrdPDUV0lnjusmNf7hVG4B981ORASf2DjEVRr0qt6p7t4DbSMa8tBl57Fg42GWbEs781rdpMa3zV13kPjJ37Ej7RSBIvWioZ0umFKqErkFhfzpxWXkFTr49m+XEBbs+6sk67N565MZ++kGChy/556/LILTBVNK1VJIYABTru/OgWPZvPD9dqvLUS566sukMiEP9WMRnAa9UlXof04LbukXxxvLdrPxYIbV5ahaSjp0gmNZeU6fq2hxnL/QoFeqGh77U2ciG4cw/rON5BU4qn6B8ipHT+Vy3+xEKppYExMeVrcF1TENeqWqoUloEFOGdmdryklm/rTL6nJUDeQXOnjgg3UcOZXL3y7vQFi5bpRhQQGMG9TRourqhn/PKVLKjS7vEs01PWN4efFOBnez+10/FH8zb30y0xdtI7l4WOb2C1rz8B/b07p5A6Yv2sahjGxiwsMYN6ijz9+IrYoGvVI18MQ1XVi+I53xczby2f0DfHrXIX/mrMX0nHXJxLdtztDesX4f7OXp0I1SNRDRKIQnrunK+v0ZvPvzXqvLURXQFtNladArVUPX9Yrhso6RTF+0jQPHdOtBb5RcwSwaf59dUxENeqVqSESYcn13AmzCY3M34W2LDuu77LxCggKcD6n5++yaimjQK1ULMeFhTLiqE8t3HuH/1hywuhxVzBjD+DkbKSg0BJfb0Ls+zK6piAa9UrV0a7/WDDi3BZO/StIhHC/x2k+7+HLDIcYN7sizN/Yo02LaH9oc1JYGvVK1ZLMJz97YAxFh7KcbcDg8M4RT0R63qqzFW1OZvmgb1/SM4S+XnMvQ3rGsmDDwTIvp+hryoEGvlEtaNWvA49d0YdWeY7y9Yo/b37+yPW7ro3nrk0mYtph2ExaQMG0x89YnA7Az7SR//ehXusY04dkbiv7xVb/T7pVKucgYw32zE1myLZ3mDYNJP5nrtoU4Kc2isWeknX08PAr78VSX3tvXOJsbHxYUwKQhnXlj2R5O5uQzf8xFxNbTG67avVIpDxIR/tA+kgKHIe1kLoai6X2Pzd105oqztqqzx219UdHc+Ce/TOLg8Sxeu71PvQ35qujKWKXcYObS3WcdK71Ap7ZL7tPCI51e0aeFR2J3rWSfU9Ec+NwCBzfHx/G3j3+tV20NaqLWV/RSZKqIrBKRX0XkNifnBIrIERFZUuon2LWSlfI+FYVQyZV9ckZ2ra70devC31U0Bz44wMYXGw7V+ve4PnBl6OZWoD3QH/gDMFFEWpY7Jw741hhzaakf5w2hlfJhFYVQgIhLS/F168LfjRvU8azOkzaBBsE2bXdQBVeCfggwyxQ5AXwG/KncOW2BKBH5RkSWicgIZ28kIqNFJFFEEtPT69/Yo/J9zkIoQITCCiY71GQpfnX3uPV3Q3vHMnVYd+xNQgEIsAlPXduNzOwCp+fX13YHzlQZ9CIysNzQyxIRWQK0AFJKnXoYiCr38ixgCUX/KAwBxolIl/KfYYyZZYyJN8bER0ZG1vJ/RSnrlIRQyQKdxiGBFBpDswZBTs+vr0vxXTW4m53oJiE0CA5gwcMXcfuFbSr8vdTf499VeTPWGLMYWFz+uIi8R9lgtwP7yr12FbCq+GGmiPwA9AGSaluwUt6qdPvbgkIHt7zxCxsPZhISaCO31K5U9XkpviuMMTw6ZyMbDmYyc2QfOtmbAEXfppxNu9Tf49+5MnQzH7gHQEQaAMOAb0qfICIJJcM1IhICXAqsd+EzlfIJgQE2XhjRm5BAG9FNQolpGqpL8V302k+7mP/rIcZe2YFBXX+fc1T+25T+Hp/NlemVc4ALRSQRMMA0Y8xhEekFTDDGjAB+A/4qIo8ABRSN6W92uWqlfEBseBjP3NCDv3ywjtF/OId//Kmz1SX5rO+Tfm9v8OBl5531fH3cTKQmah30pmhJ7SNOjv8KjCj+9TFgeK2rU8rHXdW9Jbdd0JpZS3fTp02zMleiqnq2pZzkrx+vp1tMU21vUEu6MlYpD3v8mi70bNWUsZ9sYHf6KavL8SnpJ3O55901NAgJ5I074gkLDqj6ReosGvRKeVhIYACv3t6HwADhL++vIyuvoMLmXOp32XmF3PvuGo6cyuXNO+KxNw21uiSfpUGvVB2IDQ/jpVt6sz3tJCPfXM2EORs9spLTHS2NvaEtcqHD8PDH69mYnMlLI3rTMy68zmvwJxr0StWRi9tH8sgVHVi7/zg5paZbgntWcrqjpbG3tEV+ekES3yWl8sSQLlyp9zVcplEaD08AAAx7SURBVEGvVB164NKzZ4yUcHUlZ9yMyYTl55Y5FpafS9yMyXX6Hq56e/ke3lmxl7sT2nFnQrs6+1x/pkGvVB2y2YSWFYw1u7qS0x0tja1ui7xw82EmL0hiUNdoJl6t01HdRYNeqTr26OBOhAS6f+PqtHDn7UMqOu6p96hIRTegS463nbCA+99fR5vmDXjh5t6sm/pfy+8V+AsNeqXq2NDesTxzQw8iGhV17A4OsDH5uq4uL/hxR0tjT7VFLtkdqvwN6H/O23TmeImUzBy+fHS6V9wr8Bca9EpZYGjvWBL/eQUv3NyLvEIHK3YddXlzcXe0NPZUW+SKdof6aNWBs47nFDhIePt5y+8V+BPdM1Ypi738ww6e+247dye0Y9KQzn658rPdhAXUJGl2P3MNNievcCDYjMPJK5TuGauUFxsz8DzuHNCWt1fs4dUlu6wuxyNqeqP5cJMIp8fdca+gPtKgV8piIsLjQ7owtFcM0xdt46PV+60uye2cbcwiQHCgzemN6RV3/123UHQj3RxcKS9gswnTb+pJZnY+//h8E0EBNm7s08rqstym5Ebz9EXbSM7IJkCE0CAbn94/gO2pJ51snj6YNRGNiJsxmaiMdNLCIzkwdlK93V3LVTpGr5QXyckv5L7ZiSzfeYRnhvVgeN84q0tyqx2pJxn51mpyCwr54N7+dIlpYnVJfkPH6JXyEaFBAbxxRzwXt49k/JyNfOxHwzhr9x3nxtdXUmgMH96nIV+XNOiV8jKhQQHMGtmHSzpEMmHuJt5cttvqkly2eGsqt735C80aBDH3LwPo3FJDvi5p0CvlhUKDApg5sg9XdbPz9ILfmPxVksvz7K3y4ar93Dd7Le2jGvPZXwYQ17yB1SXVOxr0Snmp0KAAXrn1fO4c0Ja3lu/hoY/Xk1NucZE3yy908Pj8zfzj801cdF4EH43uT0SjkKpfqNxOg14pL1K+F/y6qf/liWu68NhVnViw8TDDZ64s0y7AahX1rzl2Oo873lrN7JX7GP2Hc3j7zr40CtFJflbRWTdKeYmSXvCll/5nB4WcaUGwaEsKj3yygeBAG6/c0psB5zlfVFRXSvrXlG5hEBYUwN0Jbfls3UGOn85n6rDu3OBH00S9WWWzbjTolfISKc2isWeknX08PAr78VQAdqWf4s/vrWV3+ikevOw8Hv5je4IC6uaL+bz1yWXmu2flFXA8K9/puedENOSlW3rTLbZpndSmNOiV8gkOsVWrv8up3AIen7+ZueuS6RbbhP8M70X76MYerc3Z1Xtltjw5iIY6VFOndB69Uj6gur3gG4UE8vzwXrx++/kcysjh6peW8+zCrWTlFXisNmfdJysSGx6mIe9lNOiV8hI17QU/uFtLFv3tDwzp0ZJXl+xi4IyfmLvuIAWF7u/uWN1tDt2xgYpyPw16pbxEbXrBRzYO4fmbe/HZ/RcS0TiYv3+ygSv+s5RPEw+QW+C+qZgVdZ8MtAmRjUIQiq7kpw7r7vIGKsr9dIxeKT/hcBi+TUrl5cU72HLoBM0bBjOsdyw3xreiY3TjWve5dzgMz323jdeX7KawVF4EB9h49sYeGuxeQm/GKlWPGGNYtuMIH63ez3dJqRQ4DK2ahTGwUxR92jSje2xT2rZoiM3mPPhz8gvZmXaKLYcy+XnXUVbsPMKRU3mEBNoIECErv5DYM10mNeS9hQa9UvXUkVO5fJeUyg+/pbFi55EzN1QDbUJ0k1AiGgUTGGDDJnAyp4DjWXmkn8ylpNtCRKMQLjqvBQM7R3NF52jCggMq+TRlJY8EvYiEAH8GbgSSjTG3ODknGHgN6AyEAuONMd9X9r4a9Ep5Rn6hg51pp9h0MJO9R0+TkpnDkdN5FDocFDoMjUKCaN4wCHvTMDpGN6ajvTHnRjb0y60N/VFlQe/KHKgCYCswFRhVwTnjgAxjzAARiQWWiEg3Y0xuBecrpappzZRXarQxR1CAjc4tm2jnyHqo1rNujDGFxphvgcrmXQ0BZhafnwysBC6q7WcqpYqUtEuwZ6Rhw2DPSKPbk2NZM+UVq0tTXqjKoBeRgSKyxMmPvRrv3wJIKfX4MBDl5DNGi0iiiCSmp6dXv3ql6qm4GZPL9MQBCMvPJW7GZIsqUt6syqEbY8xiYHEt3z+VomA/UfzYXnys/GfMAmZB0Rh9LT9LqXojKsP5BVFFx1X95ukFU/OBewFEJBroD6zw8Gcq5feq2y5BKfBA0ItILxH5uPjhS0CsiKwCvgQe1BuxSrmupu0SVP3mctAbY5YYY0aUevxryWNjTJ4xZqQx5gJjTL+qplYqpaqnpu0Sym9oojdt6xddMKWUn6tqQxPlH7RNsVL1mM7QURr0Svk5naGjNOiV8nNWzNDRewLeRYNeKT9X1zN0dNWu99GgV8rP1WZDE1foPQHvo7NulFJuVd1NzpV76awbpVSd0VW73keDXinlVrpq1/to0Cul3Kqu7wmoqukYvVJK+QEdo1dKqXpMg14ppfycBr1SSvk5DXqllPJzGvRKKeXnNOiVUsrPadArpZSf06BXSik/p0GvlFJ+ToNeKaX8nAa9Ukr5OQ16peox3fKvfgi0ugCllDVKtvwr2Q3KnpFG0yfHsga006Sf0St6peop3fKv/tCgV6qeispIr9Fx5bs06JWqp3TLv/pDg16pekq3/Ks/an0zVkRCgD8DNwLJxphbnJwTCKQAm0sdvtIYk1fbz1VKuUffiWNYQ9FYfVRGOmnhkRwYO0lvxPqhWm8lKCIBwB+BAGCUMWaEk3PaAVOMMbdW9311K0GllKo5j2wlaIwpNMZ8C2RXclpbIEpEvhGRZSJy1j8GSimlPKvKoRsRGQg87uSpEcaYlCpengUsAaYCjYDFIrLRGJNU7jNGA6MBWrduXY2ylVJKVVeVQW+MWQwsrs2bG2NWAauKH2aKyA9AHyCp3HmzgFlQNHRTm89SSinlnEdn3YhIQslwTfHN20uB9Z78TKWUUmW5PehFpJeIfFz88DdgmIisoWgIZ5YxZnOFL1ZKKeV2tZ514ykikg7sq+XLI4AjbizH03ypXl+qFXyrXl+qFXyrXl+qFVyrt40xxulqN68LeleISGJF04u8kS/V60u1gm/V60u1gm/V60u1gufq1ZWxSinl5zTolVLKz/lb0M+yuoAa8qV6falW8K16falW8K16falW8FC9fjVGr5RS6mz+dkWvlFKqHA16pZTyc34T9CIyXERWi8haEXnO6noqIyI3isgnIrLf6lqqo/j3dmVxY7pPRKSB1TVVRETGi8jPIrJORN4WkWCra6qKiEwSkSVW11EVEXlXRH4RkSXFP9daXVNlRCRORL4QkR9F5DsROd/qmpwRkUtK/Z4uEZFdIvKCOz/DLzYHF5E2wGSgH3AC+FhEbjDGzLG2sgqlAw9Qtk+/VxKR5sB44GJjTLaITAfuBV6ytrKziUgE0BRIMMaY4hXa1wGfWltZxUQkHmhndR3VFAdcZoyprGOtN5kFPGqM2Vj85zjA6oKcMcb8RFF7GETEBvwETHfnZ/jLFf1gYI4xJtMU3V2eCQy1uKYKGWN+Msb4xGo9Y8wx4KJSf7kDqbw1tWWMMUeMMROLQ74RRaHvtf+YikgY8AIwwepaqikceE1ElorIK17+zc4OhAJ3i8hSYApw2tqqqmUU8L0xJtmdb+ovQd+Cop2sShwGoiyqxe8YY3JEJFREXgTCgLetrqkyIvIBsAf4AdhqcTmVmQ68YIxJs7qQakoEJhlj/kDRt1Jv3nOwNdAbeLe43kM4b7fuNYp35HsYeNHd7+0vQZ9K2WC3Fx9TbiAirYDPgYXGmPuNMYVW11QZY8xtQBvgQoqukLyOiAwCmhljPrO6luoyxow2xhwofvgpRUOl3ioDSDLGlHTL/Qzoa2E91XEj8LMxJsPdb+wvQf81cL2INC5+fDcw38J6/IaIhAL/A0YbY76xuJxKFXdOHQVgjMkCtlM03OCNhgCRIjJPROYB3URkttVFVUREwkRkcqmb21cB66ysqQo7gVAR6VT8+HK8v0X6n4F3PfHGfrNgSkRuA8YCecAyY8xYi0uqkoikGGPsVtdRGREZQtE9jx2lDi82xjxlUUkVKjXm3Yei+wgHgXuKQ9+ricgSY8ylVtdRGRH5K3AXkAkkA382xpy0tqqKiUgPioZBAoE04G5jTKa1VTknIlHABiDGeCCU/SbolVJKOecvQzdKKaUqoEGvlFJ+ToNeKaX8nAa9Ukr5OQ16pZTycxr0Sinl5zTolVLKz/1/YFmElYkh7JcAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import random\n", "import matplotlib.pyplot as plt\n", "from sklearn import svm\n", "\n", "x_max = 7. # 予測の範囲の上限\n", "\n", "# トレーニングデータ作成\n", "n_tr = 50\n", "x = np.linspace(0., np.pi*2., n_tr) # リスト 0から2πまでをn_tr等分した値を一次元配列\n", "y = make_data_by_sin_gaussian(x)\n", "X = x[:, np.newaxis]\n", " \n", "# 学習を行う\n", "svr = svm.SVR(kernel='rbf')\n", "svr.fit(X, y)\n", " \n", "# 回帰曲線を描く\n", "x_test = np.linspace(0, x_max, 10000)\n", "y_test = svr.predict(x_test[:, np.newaxis])\n", " \n", "#グラフにプロットする。\n", "plt.scatter(x, y)\n", "plt.plot(x_test, y_test)\n", "# サポートベクトルの表示(データポイントに赤で上書き)\n", "plt.scatter(X[svr.support_], y[svr.support_], c=\"red\") \n", "plt.show()\n", "# print(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "上の出力では、サポートベクトルであるデータを赤色で表示した。\n", "\n", "推定の計算はデータの周辺部分(サポートベクトル)について行われる。サポートベクトルがデータ全体の数に比べて少なければ(疎(スパース)であるという)、計算時間の節約になる。これがSVRの利点である。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## skitlearnのカーネルリッジ回帰\n", "\n", "内部のアルゴリズムは筆者にはわからないが、scikit-learnにはリッジ回帰のカーネル版があるようだ。\n", "\n", "これを利用すると、基底関数を選ぶのではなく、カーネルを選択する。標準はrbfカーネルである。\n", "\n", "以下は、その利用例である。\n", "\n", "なお、SVRとKernelRidgeの比較は、\n", "\n", "https://scikit-learn.org/stable/auto_examples/miscellaneous/plot_kernel_ridge_regression.html#sphx-glr-auto-examples-miscellaneous-plot-kernel-ridge-regression-py\n", "\n", "にある。\n", "\n", "(注)\n", "\n", "このページにあるように、一般にはハイパーパラメータをいろいろ試して最適な値にするために「虱潰し」に探索する(交差検定)を行うGridSearchCVがよく利用される。" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ehody3ZwVHNQ9Z5Vqlm2nbjolRDtM1C1dRVlWWU1UWAhlDqZr0hKiWTxtzGHv1c/ju3s/1XKp8dE8ddEQLn1hCdPnr+aJSYN574ft+nxEKSdsO6L3ZBXlvoMVTP7395RX1RAecvhEjbNr6KrN1pXZM4lbTuvN+yu3c+vbK7WrpVJNsO2Ivn405+oob2tBCVNeXMq2wlL+efFQKqpqWnQNd++n3HfdiT3I2byPeTlHJvT65yP6/VcKxNkGD1bJyMgwy5cvd+kz3iprXLxhDze9nkt1jeH5KRnapCwAFJVUMujeTx0eE2DjzHGtG5BSFhGRFcaYDEfHAn5E740ySmMM//ryN2YtXEeP5Fj+dekweiTH+ixm5T3xbcJJjo0k38GKWX0+olStgE/0TZVROkr0jUf/15zQnS9/zueLdbsZNyCVh84bSExkwH9bgspd4/py2zsrD1vMps9HlPqfgM9orpRROhr9//X9HwkLEf46vh9XZKZrF8oANGFIGsYY7spaQ0lFNYkxEdwzvp9L03e6qlnZWcBX3biyGYWzBVDtYyK48rhumuQD2DlDO5Nzz6n0TY2j2hiGdW3X4s/qXrTK7gI+0btS1uhsAVR+sXZEtIOo8FCevXgo1TWGG17LobzqyF/qjuhetMruAj7RTxiSxoyJA45Yqdrwz+6D5VU8s2gDIU4G7PrQzj7Sk2J45PxBrNpWxL0frG3RZ3QvWmV3AT9HDzjdjGLbvhLmfL+FN5dtYV9JJX1T2/Lb7oOUN2hzqw/t7Oe0Y1K49sQe/OvLXxme3r7ZuXZPV1Er5e9skegbKq2oJnvdbt7N3Ub2ut0AnNqvI9ec2IOhXdrpQ7cgcetpvcjZso87311N/7R4enZwXi5729jehz2kBx0AKHuxxYIpgOWbCnj1u818/tMuSiqqSW4byQUZnZk8sitpOjILSrv2l3HmE1+TFBtJ1g2ZREeEOj1XBwAq0Nl6wVS9dTuL+eqXfM4enMbvB6Uyslsioc4m5VVQ6BgXxWMXDmbKS0v52/treOi8QU7P1b1olZ3ZJtGfN6wzFw4/ivDQgH++rLzohF7J3HhyT57K3sDIbomcO6yz1SEp1epsk+ijwp3/Wa78m6+nTf54ytEs3VjA3VlrGNg5nqM7tvXatZUKBDr8VZZqjcVKYaEhPHXREGIiQ7l+bg4lFbpZiQoumujrZOXmkTkzm27TFpA5M1tXRbaS1lqs1CEuiscvHMKG/APck/WjV6+tlL/TRI8ugbdSay5WOu7oJG4aczTzcrbx9vKtXr++Uv5KEz26BN5KrvQq8oY/nnI0x/ZI5J731rB+Z7FP7qGUv9FEjy6Bt1Jrb8EYGiI8PmkwsZHhXD9XNxdXwcGjRC8iF4jIUhFZISKPODh+s4gsE5EfRORWT+7lS609qlT/05JeRd7WoW0UT04azMY9B7k7aw3+tmhQKW9zu7xSRLoC9wEjgP3AGyJyrjFmXt3xTOAiILPuI9kissgY4/qyVx/TJfDWsmKx0rE9k/jjKb147POfGdW9PRcO79Kq91eqrLKa3/IP8svuYrbsLWHbvlLOGZrGqO6JXr+XJ3X0pwPzjDFFACLyHHAFMK/u+HjgJWNMRd3xF4GzAb9L9Lqxd3C6cUxPlm0q4K/v/cjAzgn0TY2zOiRlU1XVNfy0o5gVmwtYsaWQVdsK2VJQQsM/JpNiIxnRzTf7VHuS6BOBnQ1e7wA6NDr+XaPjIx1dSESmAlMBunSxZmSlS+CDT2iI8NiFgznzya+5YW4O7990HLG6jWRQ8sWivb0Hylm0Pp/s9bv56ud8istqnwelxEUxpEsCEwancXTHWHp2iCU9Mcaniz49+b96F9CtweuUuvcaHu/QxPFDjDGzgdlQ29TMg5iUOqQlP7zJbSN5ctIQLn7+e+56dzWPXzhYdxoLMo62GJ0+fzWAy8m+rLKaz9buYn7ONr76ZQ/VNYYObSM5s38qmUcnkdG1nSXP/jxJ9B8Bn4vIg8aYYuBKIKvB8feAR0XkFaAGmAL47QNZZS+u/PCO7pHIn3/Xi0c++5lR3RO5aITO1weTpsqrW5ro8wpLeXnxRt5YtpXisipS46OYekJ3xg1IpV9qHCEWN1h0O9EbY3aIyAPAVyJSAXxtjJknIouAScaY5SLyPrAEqAbe8McHscqeXP3hvf7knizdVMDf3v+RQZ0T6NdJ5+uDhSfl1et3FvNU9i98vKZ2FvuM/ilMHtGFUd0TLU/uDXk0IWmMmQvMbfTeSQ3+/WHgYU/uoZQ7XP3hPTRf/8TX3PiaztcHE3d2GNuyt4THPv+ZrB/yiIkI46rjujHl2HS/3ftCF0wpW3JnbURSbCRPXjSETXsPcuf81VpfHyRcWbR3sLyKBz76iTGPLOKj1TuYekJ3vrnjZO48s6/fJnmwUZtipRpyd23EqO6J/OXUXjz8ae18/eSROl9vdy0przbG8Mmandz74Vp2FJVxYcZR/OW0XnSMi7IqbJdoole25MnaiOtP6smSjQX8/YMf2XewgteWbtH1FTbXVHn1ngPlTJ+/ms/W7qJvahxPTx7KsK7tWjlCz9hmz1ilvGnPgXJOeeRL9pdW0vAnJDo81OctGpT/+HztLqbNX8X+0ipuHduLKzO7Eeanu9gFxZ6xSrVUS+rrk2IjCQ8VGg+DXC27U4GpvKqaez9Yy9wlW+ibGsfcqwfTOyVwdybTRK+Ciiv19XsPVDi8Rl5hKZkzs3U6x6a2F5Zy3ZwVrNxWxNQTunPLab2IDAvsrUr9828QpXzElb0HnFXoCOgmNTa1eMMexj/1Db/mH+RflwzjzjP7BnySB030Ksi4Ul/vqOwOcDqdowLbnO83c+kLS0iMieD9GzM5vX+K1SF5jU7dqKDiyuKYhpU7jj7TkG5SE7hqagwPLlzHc1/+xsm9k3l68lBibLZYTkf0Kqi4uqPVhCFpLJ42hk0zxzVZg6+b1ASmsspqbn4jl+e+/I2LR3bh35dl2C7JgyZ6FWQ82dHquhN70MdB5YVuUhOYDpZXccVLy/hw1Q6mndGH+yf099vSSU9pHb1SLth7oJwxj3zJgfIqqmsMaVp1E3CycvN48ON17NhfBsAlI7tw/zkDLI7Kc03V0dvz15dSPpIYG8nzU2p/lsYPTOWbO07WJB9AsnLzmDZv1aEkDzAvJ8/2VVOa6JVy0fD09txyWi8+XLWDOUu2WB2OcsHMj9dRVlVz2HvBUDWliV4pN1x7Qg9O7JXMfR+sZU1ekdXhqBbYe6CcnQ1G8g3ZvWpKE71Sbgip61/fPiaCG17Lobis0uqQVBOKSiq59IWlTo/bvWpKE71SbmofE8FTk4ewbV8p07R/vd8qLqvkspeWsmH3Aa45obtL5bV2Yb+CUaVa0fD09tx6Wm8e/GQdo7q159LR6VaHpOpk5ebx4Cfr2FFUO11z9XHdmH5mX/qmxrnVvjqQaaJXykPXnNCdJRv3ct+HPzGkSzv6p8VbHVLQq6+uafjgde6SLfRPi2+y97xd6dSNUh4KCREevWAwibG18/X7db7ecg99EpzVNc5oolfKC9rHRPDURbXz9dPn6Xy91bYXBWd1jTOa6JXykoz09tw2tjcLVu/g1e82Wx1O0HqtibUNdq+ucUYTvVJeNPX47ozp04H7F6xlxeYCq8MJOl/8tIu7s1bTLzWOqLDD01swVNc4o4leKS8KCREeu2AwnRKiuW5ODrudLNBR3rdyayE3vpbLMZ3iefva0cw8d6BbzevsSJuaKeUD63bu55x/fssxneJ47Q+jiAhzf0zVkj1ug93mvQeZ+My3tIkMZf51mSS3jbQ6pFanTc2UamV9UuJ48LyBLN+8j38sWOv2der3uNWtC2tl5eaROTObbtMWkDkzm6zcPAoOVnD5S8uoNoaXrxgRlEm+OVpHr5SXOBp5X31cN57/ZiMDOydw7rDOLl+zqT1ug21U72hj92nzVpESH8WOojJe+8NIeiTHWhylf9IRvVJe4Gzk3Tc1jlHd23Pnu6vdan7myh63dufol15ZVQ2b9pbwxKTBDOva3qLI/J8meqW8wNnI+9HPfmbcgFSqqg3jn/qGUQ984dK0i7NywGAsE2zql1tZZc0RUzrqf9xO9FJrhogsEZEfRORiB+eEicgeEVnU4CvCs5CV8j/OklBeYSkPfLSO6rqih537y5g2b1WLE5Gre9zambNfbgnR4focoxmejOgnA0cDo4ATgLtEJLXROUcBnxpjTmrwVeHBPZXyS86SUKiIw+mGli7F92SPW7tx9EsvKiwEEZw+x1C1PEn044HZptZ+4B3gzEbnpAMdRORjEflaRCY5upCITBWR5SKyPD8/34OQlLKGs5F3tZPy5TwX5tgnDElj8bQxbJw5jsXTxgRlkofa78OVx6Ufet0pPoqZ5w6ksMRxb6FgfI7hTLNVNyIyBvirg0MVwM4Gr3cAHRqdUwIsAmYAsUC2iKwyxhxWb2aMmQ3Mhto6+pYGr5S/qE++jatuZi1c7zSpf7thD8f2TGrNMAPaz7uKefW7zfTsEMu8a48lvk04gNPvcTA+x3Cm2URvjMkGshu/LyL/4fDEngIc1uDDGLMEWFL3skhEvgCGAe4XFivlp5y1v21YEgi10w0JbSK4bm4O715/LN21JLBZO4vKuPzFpUSFh/LyFcMPJXmo/Wuq8fc4WJ9jOOPJ1M17wFUAItIGmAh83PAEEcmsn64RkUjgJCDXg3sqFVAczbHPPHcgb10zmtAQ4epXllPkZOpB1dpfVsnlLy2lqLSSly4fTud2bQ47rs8xmud2CwQREeBh4ETAAI8bY+aKyGBgmjFmkoi0B/4FdAOqgBeMMc83dV1tgaCCxdKNBVz8/PeM6Nael68YQXioVjs3Vl5VzeUvLmPZpgJeumI4xx+dbHVIfqupFgja60YpC72zYhu3vr2SiUPTeOT8QdSOnxRATY3hT2/+wPsrt/PoBYOYONT1lcXBpKlEry0QlLLQecM6s72wlEc/+5mUuChuP72P1SH5jZmfrOP9ldu54/Q+muQ9pIleKQs07IuTGh/F6O6JPLPoVzrGRTHl2HSrw7PcC99sZPZXv3HZ6K5ce2J3q8MJeJrolWpljZtzbS8qo+BgBf07xfH3D36kQ9tIzhjQeO1hy6/taUtjq9sif7ByO/cvWMvYYzryt98fo9NZXqCJXqlW5qw5196DFQw5KoE/vvkD7WIiGNU90aXrOuruOH3+aoAWJ2pvXMMT/123mz+/+QPDu7bniUlDCA3RJO8N+phfqVbmbMXmzqIyXpgynC7t23DVy8vI2bLPpes21dK4Na/hru9+3cu1c1bQJ7Utz1+eQVSjlcbKfZrolWplTXWkbBcTwdyrR5LUNpIpLy51qbWxN1oaW9UW+YethVz9yjK6tG/Dq1eOJC4qvPkPqRbTRK9UK2uuI2XHuChe+8Mo4qLCueSFJazbub9F1/VGS2NftkV2tDsUwDP/3cA5zyzmYEU1xWVVfPVzfpPnK9dpoleqlbVkJWdaQjSv/WEkkWEhXPL8En7ZVdzsdb3R0thXbZGdbcxyw9wVPLRwPfXLeXbuL2P6/NXcnbVaWw97kS6YUsqP/Zp/gEmzv6e6xvDqlSPonxbf5Pn+WnWTOTPbpY6doSIOO3+mJUSzeNoYj2KxK10Zq1QA27TnIBc/v4T9pZW8dMVwMtIDb8u8btMW4I1MI8DGmeO8cCX7aSrR69SNUn4uPSmGt68dTXLbSC59YSlf/xJ4ezY4m+N3loBCndTOa+th92iiVyoAdEqI5s1rRtM1sQ1XvryMeSu2WR2SSxzN/UeGhTB5VBeHzwQuGnmUbqHoRZrolQoQyW0jefOa0Yzo1p5b3l7JI5+up6bGv6ZenZkwJI0z+qccep0aF8WD5w7k/gkDHD6Ydva+th52j87RKxVgKqtruPvdNby5fCvjB6Yy67xBREf47+Kiyuoa7v9wLa98t5nT+nXkyYuG6GIoH9DulUrZSHhoCDPPHUB6UgwPLVzHL7sO8MwlQ+nhhztV5ReXc8PcHJZuKuDq47ox/cy+2tbAAjp1o1QAEhGuO6kHL18xgvwD5Zz11De8v3K71WEdZtmmAs56+htW5RXyxKTB3D2+nyZ5i2iiV4a2lc0AAAlOSURBVCqAndgrmQU3H0ef1Dhufj2XP72Ry76DFZbGVFldw6yF67jwue8IDw3hnWuP5ezBOrduJZ26USrApcZH88bUUfzzvxt4OnsD32zYy/0TjmHsMSmt3uJ3TV4R0+evZnVeEecP68zfzjqG2EhNM1bTh7FK+RFPV6Wu3b6fW99eydod+zmuZxJ3j+9Ln5Q4n8ebV1hKTEQoJZXVJMZEct/Zx7jdU1+5R1fGKhUAGveCh9racVfLCiura5jz/WYe//wXissqOXdoZ649qYfXH9Zm5eYxbd4qyqpqDr0XGiLcd/YxTB7Z1av3Us3TRK9UAHDWD8bd/i6FJRU8+cUG5i7ZTEV1DWP7pTB5ZBcyeya59VC04V8bHdpGUlhaSXmDJO9pvMozWl6pVADwdi/4hDYR/PX3/bj+5B688u0mXv1uM5/8uJOUuCjOHJDKCb2SGNktsUU1+PNztjF9/upDiX1XcbnL/x3KOprolfITnRKiHY7oPe3vkhQbyS2n9eaGk3vyxU+7mZ+zjTlLNvPi4o2EhQjdk2PonRJHp/goEtpEEBUeQlW1oaSimu2FpWzdV8J3v+5tcVMy7UfjfzTRK+Unbhvb2+Ecvbf6u0SFhzJuYCrjBqZSVlnN0o0FfP/bXtbvLCZ3yz4WFpdT0WgqJrltJJ0Soluc5LUfjX/SRK+Un6h/4OrtXvCORIWHckKvZE7olXzoPWNqR/HlVTWEhwqRYaFEhNUutXH2/CAhOpyYyDCfx6s8ow9jlVLN8lZFkPIdfRirlPJIa/61obxPE71SqkUmDEnTxB6g3O51IyKRInKziHwlIq87OSdCRF4QkW9FJEdEfud+qEoppdzhyYi+ClgHzACmODnnNqDQGHOsiKQBi0SkvzHGeRGuUqpFfLGJt7Int0f0xphqY8ynQFOrI8YDz9Wdnwd8Bxzn7j2VUrXqH47mFZZigLzCUqbPX01Wbp7VoSk/1GyiF5ExIrLIwVdKc58FEoGdDV7vADo4uMdUEVkuIsvz8wNv42OlWtushesPq4ABKK2sZtbC9RZFpPxZs1M3xphsINvN6++iNrHvr3udUvde43vMBmZDbXmlm/dSKmh4u12CsjdfbzzyHnA1gIh0BEYBi318T6Vsz1mbAW0/oBzxeqIXkcEi8kbdyyeBNBFZAnwA3KAPYpXy3G1jexPdaINtbT+gnPG4jt4YswhY1OD1D8Ckun+vAC719B5KqcO5uoBJK3SCmy6YUipAtXQBU+P2BfUVOvXXUPanm4MrZXNaoaM00Stlc1qho3TqRimb89WGJk3RZwL+RUf0Stlca1fo6Kpd/6OJXimbmzAkjRkTB5CWEI1Qu3m3L/vI6zMB/6NTN0oFgdZsMazPBPyPjuiVUl6lq3b9jyZ6pZRX6apd/6NTN0opr9JtB/2PJnqllNfptoP+RadulFLK5jTRK6WUzWmiV0opm9NEr5RSNqeJXimlbE4TvVJK2ZwmeqWUsjlN9EopZXOa6JVSyuY00SullM1poldKKZvTXjdKBTHd8i84aKJXKkjVb/lXvxtU/ZZ/gCZ7m9GpG6WClG75Fzw00SsVpHTLv+ChiV6pIKVb/gUPTfRKBSnd8i94uP0wVkQigWuA84A8Y8xFDs4JA3YCaxq8fZoxpsLd+yqlvEO3/AsenlTdVAHrgBnAFCfnHAV8aoyZ7MF9lFI+olv+BQe3p26MMdXGmE+Bpp7cpAMdRORjEflaRCa5ez+llFLuaXZELyJjgL86ODTJGLOzmY+XAIuoHfXHAtkissoYs7bRPaYCUwG6dOnSgrCVUkq1VLOJ3hiTDWS7c3FjzBJgSd3LIhH5AhgGrG103mxgNkBGRoZx515KKaUc82nVjYhk1k/X1D28PQnI9eU9lVJKHc7riV5EBovIG3UvfwImisgyaqdwZhtj1jj9sFJKKa8TY/xrpkRE8oHNbn48CdjjxXB8LZDiDaRYIbDiDaRYIbDiDaRYwbN4uxpjkh0d8LtE7wkRWW6MybA6jpYKpHgDKVYIrHgDKVYIrHgDKVbwXby6MlYppWxOE71SStmc3RL9bKsDcFEgxRtIsUJgxRtIsUJgxRtIsYKP4rXVHL1SSqkj2W1Er5RSqhFN9EopZXO2SfQicoGILBWRFSLyiNXxNEVEzhORt0Rki9WxtETd9/a7usZ0b4lIG6tjckZEbheRb0UkR0ReFJEIq2NqjojcIyKLrI6jOSLyioh8LyKL6r7OsjqmpojIUSLyvoj8V0Q+E5GhVsfkiIic2OB7ukhEfhWRx715D1tsDi4iXYH7gBHAfuANETnXGDPP2sicygeu5/A+/X5JRNoDtwPHG2NKRWQWcDXwpLWRHUlEkoB4INMYY+pWaJ8NvG1tZM6JSAbQzeo4Wugo4GRjTKDsNTgbuMMYs6ru/+PQ5j5gBWPMl9S2h0FEQoAvgVnevIddRvSnA/OMMUWm9unyc8AEi2NyyhjzpTEmIFbrGWMKgOMa/HCH0XRrassYY/YYY+6qS/Kx1CZ9v/1lKiLRwOPANKtjaaEE4FkR+UpEnvbzv+xSgCjgShH5CvgHcNDaqFpkCvC5MSbPmxe1S6JPpHYnq3o7gA4WxWI7xpgyEYkSkSeAaOBFq2NqiojMBTYCX1C7OY6/mgU8bozZbXUgLbQcuMcYcwK1f5XeY3E8TekCDAFeqYt3O47brfuNuh35bgae8Pa17ZLod3F4Yk+pe095gYh0Bt4FPjHGXGuMqbY6pqYYYy4GugKjcb77maVEZCzQzhjzjtWxtJQxZqoxZmvdy7epnSr1V4XAWmNMfbfcd4DhFsbTEucB3xpjCr19Ybsk+o+Ac0Skbd3rK4H3LIzHNkQkCngZmGqM+djicJpU1zl1CoAxpgT4mdrpBn80HkgWkSwRyQL6i8irVgfljIhEi8h9DR5unwHkWBlTMzYAUSLSp+717/D/FunXAK/44sK2WTAlIhcDtwIVwNfGmFstDqlZIrLTGJNidRxNEZHx1D7z+KXB29nGmHstCsmpBnPew6h9jrANuKou6fs1EVlkjDnJ6jiaIiJ/BK4AioA84BpjTLG1UTknIgOpnQYJA3YDVxpjiqyNyjER6QCsBDoZHyRl2yR6pZRSjtll6kYppZQTmuiVUsrmNNErpZTNaaJXSimb00SvlFI2p4leKaVsThO9UkrZ3P8D1RAv5VBn/C0AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.kernel_ridge import KernelRidge\n", "\n", "kernel_ridge = KernelRidge(kernel=\"rbf\")\n", "\n", "# 学習を行う\n", "kernel_ridge.fit(X, y)\n", " \n", "# 回帰曲線を描く\n", "x_test = np.linspace(0, x_max, 10000)\n", "y_test = kernel_ridge.predict(x_test[:, np.newaxis])\n", " \n", "#グラフにプロットする。\n", "plt.scatter(x, y)\n", "plt.plot(x_test, y_test)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考:リッジ回帰による推定\n", "\n", "比較のために、以前試したリッジ回帰(基底関数を$n$次のべき関数にしたもの:プログラム中ではdeg)を書いてみる。\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.06 -0.54 1.05 0.00\n", "-0.00 0.07 -0.35 0.37 0.48 0.00\n", "0.00 -0.00 0.00 0.04 -0.15 0.05 0.26 0.29 0.00\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import sklearn.linear_model as lm\n", "ridge = lm.Ridge()\n", "\n", "for deg in [3,5,8]:\n", " ridge.fit(np.vander(X[:,0], deg +1), y)\n", " y_ridge = ridge.predict(np.vander(x_test, deg+1))\n", " plt.plot(x_test, y_ridge,\n", " label='degree ' + str(deg))\n", " plt.legend(loc=2)\n", " # モデルの係数表示\n", " print(' '. join(['%.2f' % c for c in ridge.coef_]))\n", " plt.scatter(x, y, c='gray')\n", " plt.xlim(0, x_max)\n", " plt.title('Ridge Regression')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 偏ったデータの場合\n", "\n", "初回にサンプルとして見せたデータに立ち返ってみる。\n", "とりあえず[こちら](various_data4fitting.html)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Relevance Vector Machine\n", "\n", "PRML7章によれば、\n", "\n", "SVMは様々なところで実用的に用いられているが、得られるのは識別や回帰の結果だけであり、予測に対する事後確率は計算できない。その点を改良する方法として関連ベクトルマシン(RVM: relevance vector machine)というのが考案されている。「疎なカーネルベースのベイズ流学習手法」であるらしい。\n", "\n", "その解説がPRML7.2節に述べられている。この方法はMacrosoftが特許であったが、2019/09に期限切れになった。そのために、scikit-learnへの実装も昨年来進められているようだ。興味があればそれも使ってみてほしい。\n", "\n", "- Wikipediaの解説 https://en.wikipedia.org/wiki/Relevance_vector_machine\n", "- scikit-learnへの実装 https://sklearn-rvm.readthedocs.io/en/latest/about.html\n", "- PRMLの記述に沿って実装して見ているページ https://qiita.com/ctgk/items/ee512530618a5eeccd1a\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.11" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }