ch04eval.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 損失関数とトレーニング誤差・テスト誤差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "par = np.linspace(-3,3,50)   # パラメータの範囲\n",
    "te_err = (1+par**2)/2          # テスト誤差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/B4CiAHY5zNvr6Q4yM/na4F++TI4a5dk/X8/AK4qrTClWwvTD/1rgRSYlkSNH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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109480668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# テスト誤差をプロット\n",
    "for i in range(10):\n",
    "    z = np.random.normal(size=20)                 # データ生成\n",
    "    trerr = np.mean(np.subtract.outer(z,par)**2/2, axis=0)   # トレーニング誤差\n",
    "    plt.plot(par,trerr,'b--',linewidth=2)                # トレーニング誤差をプロット\n",
    "\n",
    "plt.xlabel(\"par\")\n",
    "plt.ylabel(\"training/test errors\")\n",
    "plt.plot(par, te_err,'r-',linewidth=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# テスト誤差の推定：交差検証法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "n, K = 100, 10                                # 設定：データ数100, 10重CV.\n",
    "# データ生成 \n",
    "x = np.random.uniform(-2,2,n)    # 区間[-2,2]上の一様分布\n",
    "y = np.sin(2*np.pi*x)/x + np.random.normal(scale=0.5,size=n)\n",
    "# データをグループ分け \n",
    "cv_idx = np.tile(np.arange(K), int(np.ceil(n/K)))[:n]    \n",
    "maxdepths = np.arange(2,10)      # 決定木の深さの候補\n",
    "cverr = np.array([])\n",
    "for mp in maxdepths:\n",
    "    cverr_lambda = np.array([])\n",
    "    for k in range(K):  \n",
    "        tr_idx = (cv_idx!=k) \n",
    "        te_idx = (cv_idx==k) \n",
    "        cvx = x[tr_idx]; cvy = y[tr_idx]   # CVのためデータを分割\n",
    "        dtreg = DecisionTreeRegressor(max_depth=mp)\n",
    "        dtreg.fit(np.array([cvx]).T, cvy)               # 決定木で推定\n",
    "        ypred = dtreg.predict(np.array([x[te_idx]]).T)  # 予測\n",
    "        # CV誤差の計算\n",
    "        cl = np.append(cverr_lambda, np.mean((y[te_idx]-ypred)**2/2))\n",
    "    cverr = np.append(cverr, np.mean(cl))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7VeDxwAeS3J5k1zFOJ2mEOYX29JGqVYf5R9bMzEwtLS0NuwxJOiUWFxfZsWMHBw8eZMuW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\nahkKkqSWoSBJav1/arzRMrFdUUcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1094a1cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(maxdepths, cverr,c='k')  # cv誤差のプロット\n",
    "plt.xlabel(\"max depth\"); plt.ylabel('cv error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ROC曲線とAUC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 100     # データ数 100\n",
    "xp = np.random.normal(loc=1,size=n*2).reshape(n,2) # 信号アリ\n",
    "xn = np.random.normal(size=n*2).reshape(n,2)       # 信号ナシ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.77059999999999995"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F1 のAUC\n",
    "np.mean(np.subtract.outer(xp[:,0],xn[:,0]) >= 0)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83830000000000005"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F2 のAUC\n",
    "np.mean(np.subtract.outer(np.sum(xp,1),np.sum(xn,1)) >= 0)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 10000  # データ数 10000\n",
    "xp = np.random.normal(loc=1,size=n*2).reshape(n,2) # 信号アリ\n",
    "xn = np.random.normal(size=n*2).reshape(n,2)       # 信号ナシ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75658190000000003"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F1 のAUC\n",
    "np.mean(np.subtract.outer(xp[:,0],xn[:,0]) >= 0)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83909597999999996"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F2 のAUC\n",
    "np.mean(np.subtract.outer(np.sum(xp,1),np.sum(xn,1)) >= 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sp\n",
    "from scipy import integrate    # integrateを使う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76024810812092736"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F1のAUC\n",
    "def fpr(c):\n",
    "    return(1-sp.stats.norm.cdf(c))\n",
    "def tpr(c):\n",
    "    return(1-sp.stats.norm.cdf(c,loc=1))\n",
    "c = np.arange(-10, 10, 0.01)\n",
    "sp.integrate.cumtrapz(tpr(c)[::-1],fpr(c)[::-1])[-1]  # F1のAUCの計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.84134373785894323"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F2のAUC\n",
    "def fpr(c):\n",
    "    return(1-sp.stats.norm.cdf(c,scale=np.sqrt(2))) \n",
    "def tpr(c):\n",
    "    return(1-sp.stats.norm.cdf(c,loc=2,scale=np.sqrt(2)))\n",
    "sp.integrate.cumtrapz(tpr(c)[::-1],fpr(c)[::-1])[-1]  # F2のAUCの計算"
   ]
  },
  {
   "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
}