{
 "metadata": {
  "name": "comparison_ordinal_logistic"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function\n",
      "import numpy as np\n",
      "from sklearn import datasets, metrics, cross_validation\n",
      "from minirank import ordinal_logistic_fit, ordinal_logistic_predict"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DOC = \"\"\"\n",
      "================================================================================\n",
      "Compare the prediction accuracy of different models on the boston dataset\n",
      "================================================================================\n",
      "\"\"\"\n",
      "print(DOC)\n",
      "boston = datasets.load_boston()\n",
      "X, y = boston.data, np.round(boston.target)\n",
      "X -= X.mean()\n",
      "y -= y.min()\n",
      "\n",
      "idx = np.argsort(y)\n",
      "X = X[idx]\n",
      "y = y[idx]\n",
      "cv = cross_validation.ShuffleSplit(y.size, n_iter=50, test_size=.1, random_state=0)\n",
      "score_logistic = []\n",
      "score_ordinal_logistic = []\n",
      "score_ridge = []\n",
      "for i, (train, test) in enumerate(cv):\n",
      "    if not np.all(np.unique(y[train]) == np.unique(y)):\n",
      "        # we need the train set to have all different classes\n",
      "        continue\n",
      "    assert np.all(np.unique(y[train]) == np.unique(y))\n",
      "    train = np.sort(train)\n",
      "    test = np.sort(test)\n",
      "    w, theta = ordinal_logistic_fit(X[train], y[train])\n",
      "    pred = ordinal_logistic_predict(w, theta, X[test], y)\n",
      "    s = metrics.mean_absolute_error(y[test], pred)\n",
      "    print('ERROR (ORDINAL)  fold %s: %s' % (i+1, s))\n",
      "    score_ordinal_logistic.append(s)\n",
      "\n",
      "    from sklearn import linear_model\n",
      "    clf = linear_model.LogisticRegression(C=1.)\n",
      "    clf.fit(X[train], y[train])\n",
      "    pred = clf.predict(X[test])\n",
      "    s = metrics.mean_absolute_error(y[test], pred)\n",
      "    print('ERROR (LOGISTIC) fold %s: %s' % (i+1, s))\n",
      "    score_logistic.append(s)\n",
      "\n",
      "    from sklearn import linear_model\n",
      "    clf = linear_model.Ridge(alpha=1.)\n",
      "    clf.fit(X[train], y[train])\n",
      "    pred = np.round(clf.predict(X[test]))\n",
      "    s = metrics.mean_absolute_error(y[test], pred)\n",
      "    print('ERROR (LOGISTIC) fold %s: %s' % (i+1, s))\n",
      "    score_ridge.append(s)\n",
      "\n",
      "\n",
      "print()\n",
      "print('MEAN ABSOLUTE ERROR (ORDINAL LOGISTIC):    %s' % np.mean(score_ordinal_logistic))\n",
      "print('MEAN ABSOLUTE ERROR (LOGISTIC REGRESSION): %s' % np.mean(score_logistic))\n",
      "print('MEAN ABSOLUTE ERROR (RIDGE REGRESSION):    %s' % np.mean(score_ridge))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "================================================================================\n",
        "Compare the prediction accuracy of different models on the boston dataset\n",
        "================================================================================\n",
        "\n",
        "ERROR (ORDINAL)  fold 2: 2.78431372549"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 2: 4.23529411765"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 2: 3.25490196078\n",
        "ERROR (ORDINAL)  fold 4: 3.88235294118"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 4: 4.60784313725"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 4: 3.58823529412\n",
        "ERROR (ORDINAL)  fold 5: 3.27450980392"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 5: 4.23529411765"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 5: 3.21568627451\n",
        "ERROR (ORDINAL)  fold 6: 3.50980392157"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 6: 4.03921568627"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 6: 3.47058823529\n",
        "ERROR (ORDINAL)  fold 7: 2.66666666667"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 7: 2.82352941176"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 7: 2.96078431373\n",
        "ERROR (ORDINAL)  fold 12: 4.03921568627"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 12: 4.70588235294"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 12: 4.50980392157\n",
        "ERROR (ORDINAL)  fold 13: 4.23529411765"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 13: 4.09803921569"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 13: 4.43137254902\n",
        "ERROR (ORDINAL)  fold 15: 3.1568627451"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 15: 4.74509803922"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 15: 4.09803921569\n",
        "ERROR (ORDINAL)  fold 23: 3.39215686275"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 23: 3.92156862745"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 23: 3.72549019608\n",
        "ERROR (ORDINAL)  fold 26: 3.54901960784"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 26: 5.25490196078"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 26: 4.03921568627\n",
        "ERROR (ORDINAL)  fold 29: 2.96078431373"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 29: 3.09803921569"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 29: 2.17647058824\n",
        "ERROR (ORDINAL)  fold 30: 2.80392156863"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 30: 3.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 30: 3.25490196078\n",
        "ERROR (ORDINAL)  fold 33: 3.27450980392"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 33: 3.90196078431"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 33: 3.62745098039\n",
        "ERROR (ORDINAL)  fold 34: 2.52941176471"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 34: 3.43137254902"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 34: 3.33333333333\n",
        "ERROR (ORDINAL)  fold 38: 2.78431372549"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 38: 3.66666666667"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 38: 2.64705882353\n",
        "ERROR (ORDINAL)  fold 39: 3.25490196078"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 39: 3.35294117647"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 39: 3.72549019608\n",
        "ERROR (ORDINAL)  fold 40: 3.56862745098"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 40: 3.72549019608"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 40: 3.72549019608\n",
        "ERROR (ORDINAL)  fold 41: 3.98039215686"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 41: 3.54901960784"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 41: 4.27450980392\n",
        "ERROR (ORDINAL)  fold 42: 4.03921568627"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 42: 3.21568627451"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 42: 4.13725490196\n",
        "ERROR (ORDINAL)  fold 45: 3.35294117647"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 45: 3.1568627451"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 45: 3.41176470588"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (ORDINAL)  fold 46: 2.92156862745"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 46: 4.50980392157"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 46: 3.47058823529\n",
        "ERROR (ORDINAL)  fold 48: 2.60784313725"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 48: 3.19607843137"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "ERROR (LOGISTIC) fold 48: 3.29411764706\n",
        "\n",
        "MEAN ABSOLUTE ERROR (ORDINAL LOGISTIC):    3.29857397504\n",
        "MEAN ABSOLUTE ERROR (LOGISTIC REGRESSION): 3.83957219251\n",
        "MEAN ABSOLUTE ERROR (RIDGE REGRESSION):    3.5623885918\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "\n",
      "pos = arange(3)+1.1    # the bar centers on the y axis\n",
      "val = map(np.mean, (score_ordinal_logistic, score_logistic, score_ridge))\n",
      "xerr = map(np.std, (score_ordinal_logistic, score_logistic, score_ridge))\n",
      "\n",
      "barh(pos,val, xerr=xerr, align='center', alpha=.5, ecolor='black')\n",
      "yticks(pos, ('Ordinal Logistic', 'Multiclass Logistic', 'Linear Regression'), rotation=45)\n",
      "grid(True)\n",
      "xlabel('Mean Absolute Error (lower is better)', fontsize='x-large')\n",
      "tight_layout()\n",
      "savefig('bars_ordinal.png')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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vrVq1Il++fHTr1o0GDRpID+oJ0G2cXLc8oF8m3fKAZLKGbnlAelJWiY6OZsOG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\nvXv3ZuPGjRw7dizL3iurSZHKZcqWLUu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      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}