ch13gaussprocess.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np               \n",
    "import matplotlib.pyplot as plt  \n",
    "import sklearn.gaussian_process as gp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ベイズ推定とガウス過程モデル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# カーネル関数 k(x,x') を定義\n",
    "def GPk(xv,zv,sd=1):\n",
    "    return(np.outer(xv,zv) + sd**2 * np.equal.outer(xv,zv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n, sd =30, 0.5;  # 設定\n",
    "theta = 1           # 回帰係数\n",
    "# データ生成\n",
    "X = np.random.normal(scale=3,size=n)\n",
    "Yob = np.dot(X,theta) + np.random.normal(scale=sd,size=n)\n",
    "newx = np.linspace(X.min(),X.max(),100) # 予測点 \n",
    "# カーネル関数の計算\n",
    "Kob  = GPk(X,X,sd=sd)\n",
    "kx   = GPk(newx,X,sd=sd)\n",
    "knewx = GPk(newx,newx,sd=sd)\n",
    "# ガウス過程による回帰関数の予測\n",
    "GPf = np.dot(kx, np.linalg.solve(Kob,Yob))\n",
    "GPv =  np.maximum(np.diag(knewx- np.dot(kx, np.linalg.solve(Kob,kx.T))),0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fm5sbe/fuBaBChQpMnz6djh07Gp0bDwgIwNXVFSsrK+rXry+nFwnx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\nhd055zLM/wCxz/igAafDiQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a186cc320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# プロット\n",
    "plt.xlim(X.min(),X.max())\n",
    "plt.scatter(X,Yob)                   # データ点\n",
    "plt.plot(newx, GPf, 'k-', lw=2)  # 推定した回帰関数\n",
    "# 信頼区間\n",
    "plt.plot(newx, GPf+np.sqrt(GPv), 'k--', lw=1)\n",
    "plt.plot(newx, GPf-np.sqrt(GPv), 'k--', lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ガウス過程モデルによる回帰分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SK0YQ8sCqVavo3r07s2bNIjk52eRc0OOvAK8QATR6ZzVvP1rfuDU/p4Rbls53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\nbqvFnh+Sk5O5desWFSpUICMjgxMnThgt8cqVK+P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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1777c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# トレーニングデータの生成\n",
    "n, sd = 100, 1    # 設定\n",
    "theta = 1            #  回帰係数\n",
    "X = np.random.normal(scale=3, size=n).reshape(n,-1)\n",
    "Yob = np.dot(X,theta) + np.random.normal(scale=sd,size=n).reshape(n,-1)\n",
    "# カーネル関数の定義：ガウスカーネル + ホワイトカーネル\n",
    "kk = gp.kernels.RBF() + gp.kernels.WhiteKernel()\n",
    "gpm = gp.GaussianProcessRegressor(kernel=kk)\n",
    "gpm.fit(X, Yob)                                # データへのフィッティング\n",
    "newx = np.linspace(-7,7,100).reshape(100,-1)   # 予測点\n",
    "GPf, GPv = gpm.predict(newx, return_cov=True)  # 予測値と分散共分散行列\n",
    "GPsd = np.sqrt(np.diag(GPv))                   # 予測値の標準偏差\n",
    "# プロット\n",
    "plt.xlim(-7,7)\n",
    "plt.scatter(X,Yob)\n",
    "plt.plot(newx, GPf,'k-', lw=2)\n",
    "plt.plot(newx, GPf+GPsd,'k--', lw=1)\n",
    "plt.plot(newx, GPf-GPsd,'k--', lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ガウス過程モデルによる判別分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wJ4ICQIqgAJAiKACkCAoAKYICQIqgAJAiKACkfg1Z/WNQ7mW07QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a186f0a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from common import mlbench as ml                      # code_mlbench.spirals を使う\n",
    "X, y = ml.spirals(200,cycles=1.2,sd=0.16)           # データ生成\n",
    "kk = gp.kernels.RBF()+gp.kernels.WhiteKernel()  # カーネル設定\n",
    "gpm = gp.GaussianProcessClassifier(kernel=kk)\n",
    "gpm.fit(X,y)                              # データ・フィッティング\n",
    "m = 100; newx = np.linspace(-1.2,1.2,m)   # 予測点生成\n",
    "newdat = np.array([(y, x) for x in newx for y in newx])\n",
    "GPpred = gpm.predict(newdat)              # 予測ラベル\n",
    "# プロット\n",
    "ext=(-1.2,1.2,-1.2,1.2)\n",
    "plt.imshow(GPpred.reshape(m,-1)[::-1],cmap='gray',extent=ext)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ベイズ最適化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No: 1 started. Evaluating function at provided point.\n",
      "Iteration No: 1 ended. Evaluation done at provided point.\n",
      "Time taken: 0.0092\n",
      "Function value obtained: 0.3700\n",
      "Current minimum: 0.3700\n",
      "Iteration No: 2 started. Evaluating function at random point.\n",
      "Iteration No: 2 ended. Evaluation done at random point.\n",
      "Time taken: 0.0101\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 3 started. Evaluating function at random point.\n",
      "Iteration No: 3 ended. Evaluation done at random point.\n",
      "Time taken: 0.0117\n",
      "Function value obtained: 0.5900\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 4 started. Evaluating function at random point.\n",
      "Iteration No: 4 ended. Evaluation done at random point.\n",
      "Time taken: 0.0108\n",
      "Function value obtained: 0.4450\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 5 started. Evaluating function at random point.\n",
      "Iteration No: 5 ended. Evaluation done at random point.\n",
      "Time taken: 0.0164\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 6 started. Evaluating function at random point.\n",
      "Iteration No: 6 ended. Evaluation done at random point.\n",
      "Time taken: 0.0130\n",
      "Function value obtained: 0.7150\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 7 started. Evaluating function at random point.\n",
      "Iteration No: 7 ended. Evaluation done at random point.\n",
      "Time taken: 0.0125\n",
      "Function value obtained: 0.4150\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 8 started. Evaluating function at random point.\n",
      "Iteration No: 8 ended. Evaluation done at random point.\n",
      "Time taken: 0.0116\n",
      "Function value obtained: 0.2750\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 9 started. Evaluating function at random point.\n",
      "Iteration No: 9 ended. Evaluation done at random point.\n",
      "Time taken: 0.0122\n",
      "Function value obtained: 0.4300\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 10 started. Evaluating function at random point.\n",
      "Iteration No: 10 ended. Evaluation done at random point.\n",
      "Time taken: 0.0111\n",
      "Function value obtained: 0.3800\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 11 started. Evaluating function at random point.\n",
      "Iteration No: 11 ended. Evaluation done at random point.\n",
      "Time taken: 0.2356\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 12 started. Searching for the next optimal point.\n",
      "Iteration No: 12 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4383\n",
      "Function value obtained: 0.2950\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 13 started. Searching for the next optimal point.\n",
      "Iteration No: 13 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2795\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 14 started. Searching for the next optimal point.\n",
      "Iteration No: 14 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3670\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 15 started. Searching for the next optimal point.\n",
      "Iteration No: 15 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2258\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 16 started. Searching for the next optimal point.\n",
      "Iteration No: 16 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2954\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 17 started. Searching for the next optimal point.\n",
      "Iteration No: 17 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2792\n",
      "Function value obtained: 0.2250\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 18 started. Searching for the next optimal point.\n",
      "Iteration No: 18 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3825\n",
      "Function value obtained: 0.3450\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 19 started. Searching for the next optimal point.\n",
      "Iteration No: 19 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3521\n",
      "Function value obtained: 0.2100\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 20 started. Searching for the next optimal point.\n",
      "Iteration No: 20 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2281\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 21 started. Searching for the next optimal point.\n",
      "Iteration No: 21 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2651\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 22 started. Searching for the next optimal point.\n",
      "Iteration No: 22 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3587\n",
      "Function value obtained: 0.3950\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 23 started. Searching for the next optimal point.\n",
      "Iteration No: 23 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2110\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 24 started. Searching for the next optimal point.\n",
      "Iteration No: 24 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3135\n",
      "Function value obtained: 0.4900\n",
      "Current minimum: 0.1950\n",
      "Iteration No: 25 started. Searching for the next optimal point.\n",
      "Iteration No: 25 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2656\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 26 started. Searching for the next optimal point.\n",
      "Iteration No: 26 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2811\n",
      "Function value obtained: 0.3550\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 27 started. Searching for the next optimal point.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kanamori/.pyenv/versions/anaconda3-5.0.1/lib/python3.6/site-packages/skopt/optimizer/optimizer.py:399: UserWarning: The objective has been evaluated at this point before.\n",
      "  warnings.warn(\"The objective has been evaluated \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No: 27 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3346\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 28 started. Searching for the next optimal point.\n",
      "Iteration No: 28 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4996\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 29 started. Searching for the next optimal point.\n",
      "Iteration No: 29 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3963\n",
      "Function value obtained: 0.2150\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 30 started. Searching for the next optimal point.\n",
      "Iteration No: 30 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.9189\n",
      "Function value obtained: 0.3200\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 31 started. Searching for the next optimal point.\n",
      "Iteration No: 31 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3763\n",
      "Function value obtained: 0.3300\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 32 started. Searching for the next optimal point.\n",
      "Iteration No: 32 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3369\n",
      "Function value obtained: 0.2900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 33 started. Searching for the next optimal point.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kanamori/.pyenv/versions/anaconda3-5.0.1/lib/python3.6/site-packages/skopt/optimizer/optimizer.py:399: UserWarning: The objective has been evaluated at this point before.\n",
      "  warnings.warn(\"The objective has been evaluated \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No: 33 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4883\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 34 started. Searching for the next optimal point.\n",
      "Iteration No: 34 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3587\n",
      "Function value obtained: 0.1900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 35 started. Searching for the next optimal point.\n",
      "Iteration No: 35 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.2872\n",
      "Function value obtained: 0.1850\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 36 started. Searching for the next optimal point.\n",
      "Iteration No: 36 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3832\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 37 started. Searching for the next optimal point.\n",
      "Iteration No: 37 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3988\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 38 started. Searching for the next optimal point.\n",
      "Iteration No: 38 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3529\n",
      "Function value obtained: 0.5600\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 39 started. Searching for the next optimal point.\n",
      "Iteration No: 39 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3797\n",
      "Function value obtained: 0.3000\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 40 started. Searching for the next optimal point.\n",
      "Iteration No: 40 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3284\n",
      "Function value obtained: 0.4900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 41 started. Searching for the next optimal point.\n",
      "Iteration No: 41 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4038\n",
      "Function value obtained: 0.2950\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 42 started. Searching for the next optimal point.\n",
      "Iteration No: 42 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.3368\n",
      "Function value obtained: 0.6800\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 43 started. Searching for the next optimal point.\n",
      "Iteration No: 43 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5150\n",
      "Function value obtained: 0.3350\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 44 started. Searching for the next optimal point.\n",
      "Iteration No: 44 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4383\n",
      "Function value obtained: 0.2900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 45 started. Searching for the next optimal point.\n",
      "Iteration No: 45 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4534\n",
      "Function value obtained: 0.1900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 46 started. Searching for the next optimal point.\n",
      "Iteration No: 46 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4351\n",
      "Function value obtained: 0.7050\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 47 started. Searching for the next optimal point.\n",
      "Iteration No: 47 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4647\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 48 started. Searching for the next optimal point.\n",
      "Iteration No: 48 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4115\n",
      "Function value obtained: 0.2150\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 49 started. Searching for the next optimal point.\n",
      "Iteration No: 49 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4501\n",
      "Function value obtained: 0.1850\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 50 started. Searching for the next optimal point.\n",
      "Iteration No: 50 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4381\n",
      "Function value obtained: 0.4750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 51 started. Searching for the next optimal point.\n",
      "Iteration No: 51 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4205\n",
      "Function value obtained: 0.1900\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 52 started. Searching for the next optimal point.\n",
      "Iteration No: 52 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4783\n",
      "Function value obtained: 0.2050\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 53 started. Searching for the next optimal point.\n",
      "Iteration No: 53 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4262\n",
      "Function value obtained: 0.2750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 54 started. Searching for the next optimal point.\n",
      "Iteration No: 54 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.7363\n",
      "Function value obtained: 0.3500\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 55 started. Searching for the next optimal point.\n",
      "Iteration No: 55 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5259\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 56 started. Searching for the next optimal point.\n",
      "Iteration No: 56 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4493\n",
      "Function value obtained: 0.3500\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 57 started. Searching for the next optimal point.\n",
      "Iteration No: 57 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6177\n",
      "Function value obtained: 0.7400\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 58 started. Searching for the next optimal point.\n",
      "Iteration No: 58 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4775\n",
      "Function value obtained: 0.2850\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 59 started. Searching for the next optimal point.\n",
      "Iteration No: 59 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5409\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 60 started. Searching for the next optimal point.\n",
      "Iteration No: 60 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4672\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 61 started. Searching for the next optimal point.\n",
      "Iteration No: 61 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4612\n",
      "Function value obtained: 0.4200\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 62 started. Searching for the next optimal point.\n",
      "Iteration No: 62 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5108\n",
      "Function value obtained: 0.2850\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 63 started. Searching for the next optimal point.\n",
      "Iteration No: 63 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4715\n",
      "Function value obtained: 0.4800\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 64 started. Searching for the next optimal point.\n",
      "Iteration No: 64 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4798\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 65 started. Searching for the next optimal point.\n",
      "Iteration No: 65 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6286\n",
      "Function value obtained: 0.3050\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 66 started. Searching for the next optimal point.\n",
      "Iteration No: 66 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5271\n",
      "Function value obtained: 0.3200\n",
      "Current minimum: 0.1750\n",
      "Iteration No: 67 started. Searching for the next optimal point.\n",
      "Iteration No: 67 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4442\n",
      "Function value obtained: 0.1700\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 68 started. Searching for the next optimal point.\n",
      "Iteration No: 68 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5202\n",
      "Function value obtained: 0.4900\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 69 started. Searching for the next optimal point.\n",
      "Iteration No: 69 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4969\n",
      "Function value obtained: 0.4150\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 70 started. Searching for the next optimal point.\n",
      "Iteration No: 70 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5069\n",
      "Function value obtained: 0.4650\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 71 started. Searching for the next optimal point.\n",
      "Iteration No: 71 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4903\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 72 started. Searching for the next optimal point.\n",
      "Iteration No: 72 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5100\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 73 started. Searching for the next optimal point.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration No: 73 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4807\n",
      "Function value obtained: 0.1850\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 74 started. Searching for the next optimal point.\n",
      "Iteration No: 74 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4736\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 75 started. Searching for the next optimal point.\n",
      "Iteration No: 75 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4822\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 76 started. Searching for the next optimal point.\n",
      "Iteration No: 76 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4977\n",
      "Function value obtained: 0.1700\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 77 started. Searching for the next optimal point.\n",
      "Iteration No: 77 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4384\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 78 started. Searching for the next optimal point.\n",
      "Iteration No: 78 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4507\n",
      "Function value obtained: 0.1950\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 79 started. Searching for the next optimal point.\n",
      "Iteration No: 79 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4707\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 80 started. Searching for the next optimal point.\n",
      "Iteration No: 80 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4456\n",
      "Function value obtained: 0.3200\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 81 started. Searching for the next optimal point.\n",
      "Iteration No: 81 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4928\n",
      "Function value obtained: 0.3550\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 82 started. Searching for the next optimal point.\n",
      "Iteration No: 82 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.4941\n",
      "Function value obtained: 0.2600\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 83 started. Searching for the next optimal point.\n",
      "Iteration No: 83 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5744\n",
      "Function value obtained: 0.1800\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 84 started. Searching for the next optimal point.\n",
      "Iteration No: 84 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.5268\n",
      "Function value obtained: 0.1850\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 85 started. Searching for the next optimal point.\n",
      "Iteration No: 85 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.7754\n",
      "Function value obtained: 0.1800\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 86 started. Searching for the next optimal point.\n",
      "Iteration No: 86 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6055\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 87 started. Searching for the next optimal point.\n",
      "Iteration No: 87 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6730\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 88 started. Searching for the next optimal point.\n",
      "Iteration No: 88 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6797\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 89 started. Searching for the next optimal point.\n",
      "Iteration No: 89 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.6715\n",
      "Function value obtained: 0.7500\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 90 started. Searching for the next optimal point.\n",
      "Iteration No: 90 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.7356\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 91 started. Searching for the next optimal point.\n",
      "Iteration No: 91 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.7519\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 92 started. Searching for the next optimal point.\n",
      "Iteration No: 92 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.7734\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 93 started. Searching for the next optimal point.\n",
      "Iteration No: 93 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.8289\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 94 started. Searching for the next optimal point.\n",
      "Iteration No: 94 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.8586\n",
      "Function value obtained: 0.3850\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 95 started. Searching for the next optimal point.\n",
      "Iteration No: 95 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.9989\n",
      "Function value obtained: 0.4750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 96 started. Searching for the next optimal point.\n",
      "Iteration No: 96 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.8586\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 97 started. Searching for the next optimal point.\n",
      "Iteration No: 97 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.9083\n",
      "Function value obtained: 0.2000\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 98 started. Searching for the next optimal point.\n",
      "Iteration No: 98 ended. Search finished for the next optimal point.\n",
      "Time taken: 0.9850\n",
      "Function value obtained: 0.3200\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 99 started. Searching for the next optimal point.\n",
      "Iteration No: 99 ended. Search finished for the next optimal point.\n",
      "Time taken: 1.0569\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n",
      "Iteration No: 100 started. Searching for the next optimal point.\n",
      "Iteration No: 100 ended. Search finished for the next optimal point.\n",
      "Time taken: 1.1547\n",
      "Function value obtained: 0.1750\n",
      "Current minimum: 0.1700\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import cross_validate\n",
    "from skopt import gp_minimize\n",
    "from scipy.spatial import distance           # distanceの計算\n",
    "\n",
    "X,y = ml.spirals(200,cycles=1,sd=0.1,label=[0,1]) # データ生成\n",
    "\n",
    "# 目的関数を定義\n",
    "def svmcv(par):\n",
    "    logC, logsig = par\n",
    "    sv = SVC(kernel=\"rbf\", gamma=10**logsig, C=10**logC)\n",
    "    cv = cross_validate(sv,X,y,scoring='accuracy',cv=5)\n",
    "    return(1-np.mean(cv['test_score']))\n",
    "\n",
    "# カーネル幅の範囲をデータから決める\n",
    "from scipy.spatial import distance               # distanceの計算\n",
    "cg = np.log10(1/np.percentile(distance.pdist(X),[1,99])**2)\n",
    "space = [(-5.,5.), (cg[1],cg[0])]\n",
    "\n",
    "x0 = [0., np.mean(cg)]\n",
    "op = gp_minimize(svmcv,space,x0=x0,acq_func=\"EI\",n_calls=100,verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(664.31885020300763, 41.988299803418066)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optC,optsig = 10**np.array(op.x)\n",
    "optC,optsig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aYD+SdV2arrUlmfvLLRUzs+3V8pzKCxGxICKeiohVhVeV544Gnsnsd6Zp5ZwF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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a186ea390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skopt.plots import plot_convergence\n",
    "plot_convergence(op)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}