src/chapter5.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Chapter 5: Cross-Validation and Bootstrap ##"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import pandas as pd\n",
      "import numpy as np\n",
      "import scipy as sp\n",
      "import matplotlib.pyplot as plt\n",
      "from sklearn.linear_model import LinearRegression\n",
      "from sklearn.cross_validation import LeaveOneOut\n",
      "from sklearn.cross_validation import KFold\n",
      "from sklearn.cross_validation import Bootstrap\n",
      "from sklearn.metrics import mean_squared_error\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "auto_df = pd.read_csv(\"../data/Auto.csv\", na_values=\"?\")\n",
      "auto_df.dropna(inplace=True)\n",
      "auto_df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>mpg</th>\n",
        "      <th>cylinders</th>\n",
        "      <th>displacement</th>\n",
        "      <th>horsepower</th>\n",
        "      <th>weight</th>\n",
        "      <th>acceleration</th>\n",
        "      <th>year</th>\n",
        "      <th>origin</th>\n",
        "      <th>name</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 18</td>\n",
        "      <td> 8</td>\n",
        "      <td> 307</td>\n",
        "      <td> 130</td>\n",
        "      <td> 3504</td>\n",
        "      <td> 12.0</td>\n",
        "      <td> 70</td>\n",
        "      <td> 1</td>\n",
        "      <td> chevrolet chevelle malibu</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 15</td>\n",
        "      <td> 8</td>\n",
        "      <td> 350</td>\n",
        "      <td> 165</td>\n",
        "      <td> 3693</td>\n",
        "      <td> 11.5</td>\n",
        "      <td> 70</td>\n",
        "      <td> 1</td>\n",
        "      <td>         buick skylark 320</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 18</td>\n",
        "      <td> 8</td>\n",
        "      <td> 318</td>\n",
        "      <td> 150</td>\n",
        "      <td> 3436</td>\n",
        "      <td> 11.0</td>\n",
        "      <td> 70</td>\n",
        "      <td> 1</td>\n",
        "      <td>        plymouth satellite</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 16</td>\n",
        "      <td> 8</td>\n",
        "      <td> 304</td>\n",
        "      <td> 150</td>\n",
        "      <td> 3433</td>\n",
        "      <td> 12.0</td>\n",
        "      <td> 70</td>\n",
        "      <td> 1</td>\n",
        "      <td>             amc rebel sst</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 17</td>\n",
        "      <td> 8</td>\n",
        "      <td> 302</td>\n",
        "      <td> 140</td>\n",
        "      <td> 3449</td>\n",
        "      <td> 10.5</td>\n",
        "      <td> 70</td>\n",
        "      <td> 1</td>\n",
        "      <td>               ford torino</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 9 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "   mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
        "0   18          8           307         130    3504          12.0    70   \n",
        "1   15          8           350         165    3693          11.5    70   \n",
        "2   18          8           318         150    3436          11.0    70   \n",
        "3   16          8           304         150    3433          12.0    70   \n",
        "4   17          8           302         140    3449          10.5    70   \n",
        "\n",
        "   origin                       name  \n",
        "0       1  chevrolet chevelle malibu  \n",
        "1       1          buick skylark 320  \n",
        "2       1         plymouth satellite  \n",
        "3       1              amc rebel sst  \n",
        "4       1                ford torino  \n",
        "\n",
        "[5 rows x 9 columns]"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ax = auto_df.plot(x=\"horsepower\", y=\"mpg\", style=\"o\")\n",
      "ax.set_ylabel(\"mpg\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x57dccd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEPCAYAAABCyrPIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/P9EKrYLtb9CSQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x30a36d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Leave One Out Cross Validation (LOOCV) ###\n",
      "\n",
      "Instead of R's glm, we use Scikit-Learn's LinearRegression to arrive at very similar results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf = LinearRegression()\n",
      "loo = LeaveOneOut(len(auto_df))\n",
      "X = auto_df[[\"horsepower\"]].values\n",
      "y = auto_df[\"mpg\"].values\n",
      "n = np.shape(X)[0]\n",
      "mses = []\n",
      "for train, test in loo:\n",
      "    Xtrain, ytrain, Xtest, ytest = X[train], y[train], X[test], y[test]\n",
      "    clf.fit(Xtrain, ytrain)\n",
      "    ypred = clf.predict(Xtest)\n",
      "    mses.append(mean_squared_error(ytest, ypred))\n",
      "np.mean(mses)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "24.231513517929265"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def loo_shortcut(X, y):\n",
      "    \"\"\" implement one-pass LOOCV calculation for linear models from ISLR Page 180 (Eqn 5.2) \"\"\"\n",
      "    clf = LinearRegression()\n",
      "    clf.fit(X, y)\n",
      "    ypred = clf.predict(X)\n",
      "    xbar = np.mean(X, axis=0)\n",
      "    xsum = np.sum(np.power(X - xbar, 2))\n",
      "    nrows = np.shape(X)[0]\n",
      "    mses = []\n",
      "    for row in range(0, nrows):\n",
      "        hi = (1 / nrows) + (np.sum(X[row] - xbar) ** 2 / xsum)\n",
      "        mse = (y[row] - ypred[row]) ** 2 / (1 - hi)\n",
      "        mses.append(mse)\n",
      "    return np.mean(mses)\n",
      "\n",
      "loo_shortcut(auto_df[[\"horsepower\"]].values, auto_df[\"mpg\"].values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "24.086699242104974"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# LOOCV against models of different degrees\n",
      "auto_df[\"horsepower^2\"] = auto_df[\"horsepower\"] * auto_df[\"horsepower\"]\n",
      "auto_df[\"horsepower^3\"] = auto_df[\"horsepower^2\"] * auto_df[\"horsepower\"]\n",
      "auto_df[\"horsepower^4\"] = auto_df[\"horsepower^3\"] * auto_df[\"horsepower\"]\n",
      "auto_df[\"horsepower^5\"] = auto_df[\"horsepower^4\"] * auto_df[\"horsepower\"]\n",
      "auto_df[\"unit\"] = 1\n",
      "colnames = [\"unit\", \"horsepower\", \"horsepower^2\", \"horsepower^3\", \"horsepower^4\", \"horsepower^5\"]\n",
      "cv_errors = []\n",
      "for ncols in range(2, 6):\n",
      "    X = auto_df[colnames[0:ncols]]\n",
      "    y = auto_df[\"mpg\"]\n",
      "    clf = LinearRegression()\n",
      "    clf.fit(X, y)\n",
      "    cv_errors.append(loo_shortcut(X.values, y.values))\n",
      "plt.plot(range(1,5), cv_errors)\n",
      "plt.xlabel(\"degree\")\n",
      "plt.ylabel(\"cv.error\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x5d52b50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEPCAYAAABP1MOPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBCIiNqdCICJicyoEIiI29/8dhnMCxhyAEQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b92ed0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### K-Fold Cross Validation ###"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cv_errors = []\n",
      "for ncols in range(2, 6):\n",
      "    # each ncol corresponds to a polynomial model\n",
      "    X = auto_df[colnames[0:ncols]].values\n",
      "    y = auto_df[\"mpg\"].values\n",
      "    kfold = KFold(len(auto_df), n_folds=10)\n",
      "    mses = []\n",
      "    for train, test in kfold:\n",
      "        # each model is cross validated 10 times\n",
      "        Xtrain, ytrain, Xtest, ytest = X[train], y[train], X[test], y[test]   \n",
      "        clf = LinearRegression()\n",
      "        clf.fit(X, y)\n",
      "        ypred = clf.predict(Xtest)\n",
      "        mses.append(mean_squared_error(ypred, ytest))\n",
      "    cv_errors.append(np.mean(mses))\n",
      "plt.plot(range(1,5), cv_errors)\n",
      "plt.xlabel(\"degree\")\n",
      "plt.ylabel(\"cv.error\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x5f7c810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEPCAYAAABP1MOPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n0Br+GcEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5d6e390>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Bootstrap ###"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cv_errors = []\n",
      "for ncols in range(2, 6):\n",
      "    # each ncol corresponds to a polynomial model\n",
      "    X = auto_df[colnames[0:ncols]].values\n",
      "    y = auto_df[\"mpg\"].values\n",
      "    n = len(auto_df)\n",
      "    bs = Bootstrap(n, train_size=int(0.9*n), test_size=int(0.1*n), n_iter=10, random_state=0)\n",
      "    mses = []\n",
      "    for train, test in bs:\n",
      "        # each model is resampled 10 times\n",
      "        Xtrain, ytrain, Xtest, ytest = X[train], y[train], X[test], y[test]   \n",
      "        clf = LinearRegression()\n",
      "        clf.fit(X, y)\n",
      "        ypred = clf.predict(Xtest)\n",
      "        mses.append(mean_squared_error(ypred, ytest))\n",
      "    cv_errors.append(np.mean(mses))\n",
      "plt.plot(range(1,5), cv_errors)\n",
      "plt.xlabel(\"degree\")\n",
      "plt.ylabel(\"cv.error\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.text.Text at 0x5f9f810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEPCAYAAABP1MOPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5f88a90>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def alpha(x, y):\n",
      "    \"\"\" allocate alpha of your assets to x and (1-alpha) to y for optimum \"\"\"\n",
      "    vx = np.var(x)\n",
      "    vy = np.var(y)\n",
      "    cxy = np.cov(x, y)\n",
      "    return ((vy - cxy) / (vx + vy - 2 * cxy))[0, 1]\n",
      "\n",
      "# From ISLR package, retrieved with write.csv(Portfolio, \"portfolio.csv\", row.names=FALSE)\n",
      "portfolio_df = pd.read_csv(\"../data/Portfolio.csv\")\n",
      "portfolio_df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>X</th>\n",
        "      <th>Y</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>-0.895251</td>\n",
        "      <td>-0.234924</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>-1.562454</td>\n",
        "      <td>-0.885176</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>-0.417090</td>\n",
        "      <td> 0.271888</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1.044356</td>\n",
        "      <td>-0.734198</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>-0.315568</td>\n",
        "      <td> 0.841983</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 2 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "          X         Y\n",
        "0 -0.895251 -0.234924\n",
        "1 -1.562454 -0.885176\n",
        "2 -0.417090  0.271888\n",
        "3  1.044356 -0.734198\n",
        "4 -0.315568  0.841983\n",
        "\n",
        "[5 rows x 2 columns]"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha(portfolio_df[\"X\"].values, portfolio_df[\"Y\"].values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "0.57665115161041181"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Find the variance of alpha - shows that bootstrapping results in a near-normal distribution\n",
      "X = portfolio_df[\"X\"].values\n",
      "Y = portfolio_df[\"Y\"].values\n",
      "bs = Bootstrap(len(portfolio_df), n_iter=1000, train_size=99, random_state=0)\n",
      "alphas = []\n",
      "for train, test in bs:\n",
      "    xtrain, ytrain = X[train], Y[train]\n",
      "    alphas.append(alpha(xtrain, ytrain))\n",
      "plt.hist(alphas)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(array([   1.,    4.,   27.,  101.,  214.,  265.,  231.,  111.,   30.,   16.]),\n",
        " array([ 0.23030675,  0.2930067 ,  0.35570664,  0.41840658,  0.48110652,\n",
        "        0.54380646,  0.6065064 ,  0.66920634,  0.73190628,  0.79460622,\n",
        "        0.85730616]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncP8HmuYi7u9J6uQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b94d50>"
       ]
      }
     ],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}