{
 "cells": [
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   "source": [
    "# Spam classification using logistic regression\n",
    "\n",
    "We have 4601 email addresses with 57 features. The data can be found on [GitHub](https://github.com/probml/pmtk3/tree/master/data/spamData). The column names can be found [here](ftp://ftp.ics.uci.edu/pub/machine-learning-databases/spambase/spambase.names). We want to predict whether the email is spam or not, so we have a binary response, where 1 indicates spam and 0 indicates non-spam.\n",
    "\n",
    "You can find some utility functions on [GitHub](https://github.com/ppham27/MLaPP-solutions/blob/master/chap08/classifiers.py)."
   ]
  },
  {
   "cell_type": "code",
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>spam</th>\n",
       "      <th>word_freq_make</th>\n",
       "      <th>word_freq_address</th>\n",
       "      <th>word_freq_all</th>\n",
       "      <th>word_freq_3d</th>\n",
       "      <th>word_freq_our</th>\n",
       "      <th>word_freq_over</th>\n",
       "      <th>word_freq_remove</th>\n",
       "      <th>word_freq_internet</th>\n",
       "      <th>word_freq_order</th>\n",
       "      <th>...</th>\n",
       "      <th>word_freq_conference</th>\n",
       "      <th>char_freq_;</th>\n",
       "      <th>char_freq_(</th>\n",
       "      <th>char_freq_[</th>\n",
       "      <th>char_freq_!</th>\n",
       "      <th>char_freq_$</th>\n",
       "      <th>char_freq_#</th>\n",
       "      <th>capital_run_length_average</th>\n",
       "      <th>capital_run_length_longest</th>\n",
       "      <th>capital_run_length_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.00</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.132</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.372</td>\n",
       "      <td>0.180</td>\n",
       "      <td>0.048</td>\n",
       "      <td>5.114</td>\n",
       "      <td>101.0</td>\n",
       "      <td>1028.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.137</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.137</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3.537</td>\n",
       "      <td>40.0</td>\n",
       "      <td>191.0</td>\n",
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       "    <tr>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.63</td>\n",
       "      <td>0.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3.537</td>\n",
       "      <td>40.0</td>\n",
       "      <td>191.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.223</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3.000</td>\n",
       "      <td>15.0</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.92</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.054</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.164</td>\n",
       "      <td>0.054</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.671</td>\n",
       "      <td>4.0</td>\n",
       "      <td>112.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 58 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   spam  word_freq_make  word_freq_address  word_freq_all  word_freq_3d  \\\n",
       "0     1            0.21               0.28            0.5           0.0   \n",
       "1     1            0.00               0.00            0.0           0.0   \n",
       "2     1            0.00               0.00            0.0           0.0   \n",
       "3     1            0.00               0.00            0.0           0.0   \n",
       "4     1            0.00               0.00            0.0           0.0   \n",
       "\n",
       "   word_freq_our  word_freq_over  word_freq_remove  word_freq_internet  \\\n",
       "0           0.14            0.28              0.21                0.07   \n",
       "1           0.63            0.00              0.31                0.63   \n",
       "2           0.63            0.00              0.31                0.63   \n",
       "3           1.85            0.00              0.00                1.85   \n",
       "4           1.92            0.00              0.00                0.00   \n",
       "\n",
       "   word_freq_order            ...             word_freq_conference  \\\n",
       "0             0.00            ...                              0.0   \n",
       "1             0.31            ...                              0.0   \n",
       "2             0.31            ...                              0.0   \n",
       "3             0.00            ...                              0.0   \n",
       "4             0.00            ...                              0.0   \n",
       "\n",
       "   char_freq_;  char_freq_(  char_freq_[  char_freq_!  char_freq_$  \\\n",
       "0          0.0        0.132          0.0        0.372        0.180   \n",
       "1          0.0        0.137          0.0        0.137        0.000   \n",
       "2          0.0        0.135          0.0        0.135        0.000   \n",
       "3          0.0        0.223          0.0        0.000        0.000   \n",
       "4          0.0        0.054          0.0        0.164        0.054   \n",
       "\n",
       "   char_freq_#  capital_run_length_average  capital_run_length_longest  \\\n",
       "0        0.048                       5.114                       101.0   \n",
       "1        0.000                       3.537                        40.0   \n",
       "2        0.000                       3.537                        40.0   \n",
       "3        0.000                       3.000                        15.0   \n",
       "4        0.000                       1.671                         4.0   \n",
       "\n",
       "   capital_run_length_total  \n",
       "0                    1028.0  \n",
       "1                     191.0  \n",
       "2                     191.0  \n",
       "3                      54.0  \n",
       "4                     112.0  \n",
       "\n",
       "[5 rows x 58 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from classifiers import read_spam_data, transform_log, transform_binary\n",
    "#from sklearn.linear_model import LogisticRegression # reference sklearn implementation\n",
    "from classifiers import LogisticRegression\n",
    "\n",
    "train_data, test_data = read_spam_data()\n",
    "train_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In logistic regression, we let \n",
    "\n",
    "\\begin{equation}\n",
    "y \\mid \\mathbf{x} \\sim \\operatorname{Bernoulli}\\left(\\frac{1}{1 + \\exp\\left(-\\left(w_0 + \\mathbf{w}^\\intercal \\mathbf{x}\\right)\\right)}\\right),\n",
    "\\end{equation}\n",
    "\n",
    "so if we make $N$ observations the likelihood is\n",
    "\n",
    "\\begin{equation}\n",
    "L\\left(w_0, \\mathbf{w}\\right) = \\prod_{i=1}^N\\left(\\frac{1}{1 + \\exp\\left(-\\left(w_0 + \\mathbf{w}^\\intercal \\mathbf{x}\\right)\\right)}\\right)^{y_i}\\left(\\frac{1}{1 + \\exp\\left(w_0 + \\mathbf{w}^\\intercal \\mathbf{x}\\right)}\\right)^{1-y_i}.\n",
    "\\end{equation}\n",
    "\n",
    "Define $\\tilde{y}_i = 2y_i - 1.$ We want to minimize the negative log-likelihood, which is\n",
    "\n",
    "\\begin{equation}\n",
    "J\\left(w_0, \\mathbf{w}\\right) = \\sum_{i=1}^N\\log\\left(1 + \\exp\\left(-\\tilde{y}_i\\left(w_0 + \\mathbf{w}^\\intercal \\mathbf{x}\\right)\\right)\\right).\n",
    "\\end{equation}\n",
    "\n",
    "In practice, this function is not always convex, so we add some regularization. Now, we minimize\n",
    "\n",
    "\\begin{equation}\n",
    "J_\\lambda\\left(w_0, \\mathbf{w}\\right) = \\sum_{i=1}^N\\log\\left(1 + \\exp\\left(-\\tilde{y}_i\\left(w_0 + \\mathbf{w}^\\intercal \\mathbf{x}\\right)\\right)\\right) + \\frac{\\lambda}{2}\\mathbf{w}^\\intercal\\mathbf{w}.\n",
    "\\end{equation}\n",
    "\n",
    "Note that there is no penalty for $w_0$. One way to minimize this is with Newton's algorithm. To do so, we need to calculate the gradient $\\mathbf{g}$ and Hessian $\\mathbf{H}$. In exercise 3 (not shown), I show that\n",
    "\n",
    "\\begin{align}\n",
    "\\mathbf{g}\\left(w_0, \\mathbf{w}\\right) &= \\tilde{\\mathbf{X}}^\\intercal\\left(\\boldsymbol\\mu - \\mathbf{y}\\right) + \\lambda\\begin{pmatrix}0 \\\\ \\mathbf{w}\\end{pmatrix} \\\\\n",
    "\\mathbf{H}\\left(w_0, \\mathbf{w}\\right) &= \\tilde{\\mathbf{X}}^\\intercal \\mathbf{M} \\tilde{\\mathbf{X}} \n",
    "+ \\lambda\n",
    "\\begin{pmatrix}\n",
    "0 & \\mathbf{0} \\\\\n",
    "\\mathbf{0} & I\n",
    "\\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "where $\\tilde{\\mathbf{X}}$ is the data matrix with a column of 1s inserted as the first column. Also, we have defined\n",
    "\n",
    "\\begin{equation}\n",
    "\\boldsymbol\\mu = \\begin{pmatrix}\n",
    "\\left(1 + \\exp\\left(-\\left(w_0 + \\mathbf{w}^\\intercal\\mathbf{x}_1\\right)\\right)\\right)^{-1}\\\\\n",
    "\\left(1 + \\exp\\left(-\\left(w_0 + \\mathbf{w}^\\intercal\\mathbf{x}_2\\right)\\right)\\right)^{-1}\\\\\n",
    "\\vdots \\\\\n",
    "\\left(1 + \\exp\\left(-\\left(w_0 + \\mathbf{w}^\\intercal\\mathbf{x}_N\\right)\\right)\\right)^{-1}\\\\\n",
    "\\end{pmatrix},\n",
    "~\\text{and}~\n",
    "\\mathbf{M} = \\operatorname{diag}\\left(\n",
    "\\mu_1(1-\\mu_1), \\mu_2(1-\\mu_2), \\ldots,\\mu_N(1-\\mu_N)\n",
    "\\right).\n",
    "\\end{equation}\n",
    "\n",
    "Let $\\boldsymbol\\theta = (w_0,\\mathbf{w})^\\intercal$. Choose some initial estimate for $\\boldsymbol\\theta_0$. Then, by Newton's method,\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{H}\\left(\\boldsymbol\\theta_k\\right)\\left(\\boldsymbol\\theta_{k+1} - \\boldsymbol\\theta_{k}\\right) = -\\mathbf{g}\\left(\\boldsymbol\\theta_k\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.49981367068\n",
      "[ -1.26600248e-01  -1.56094390e-01   2.54708222e-01   8.58581226e-01\n",
      "   4.09630906e-01   8.96135831e-01   2.19302802e+00   7.60903407e-01\n",
      "   6.71931927e-01   1.01103996e-01  -2.82796444e-01  -1.83924290e-01\n",
      "  -1.11320045e-01   1.03485121e-01   5.54364725e-01   1.18430618e+00\n",
      "   1.06659155e+00   1.31293171e-01   1.43401894e-01   7.11353892e-01\n",
      "   2.31623776e-01   3.36640589e-01   1.87194517e+00   6.08773300e-01\n",
      "  -1.82320650e+00  -5.14474564e-01  -4.14759176e+00  -1.98631296e-01\n",
      "  -1.18020809e+00  -1.99879005e-01  -1.77496082e-01   1.48991710e-02\n",
      "  -7.45306456e-01  -1.68448134e-01  -5.55552499e-01   8.47931331e-01\n",
      "   3.72525690e-02  -6.12885760e-01  -1.00486600e+00  -1.36561188e-01\n",
      "  -1.16561300e+00  -1.59350006e+00  -9.86968673e-01  -1.38680860e+00\n",
      "  -7.55505052e-01  -1.82108130e+00  -6.55434252e-01  -1.61610798e+00\n",
      "  -1.18107595e+00  -3.44812567e-01  -3.76344925e-01   2.25717319e-01\n",
      "   4.05625095e+00   1.06168683e+00  -1.38267945e-02   8.02586523e-03\n",
      "   4.62754722e-04]\n",
      "0.0698205546493\n",
      "0.0703125\n"
     ]
    }
   ],
   "source": [
    "#logReg = LogisticRegression(solver='newton-cg', C=1) # sklearn implementation, only newton-cg converges\n",
    "logReg = LogisticRegression(regularization = 1)\n",
    "logReg.fit(train_data.drop('spam', axis = 1).as_matrix(), train_data['spam'].as_matrix())\n",
    "print(logReg.intercept_)\n",
    "print(logReg.coef_)\n",
    "print(1-logReg.score(train_data.drop('spam', axis = 1).as_matrix(), train_data['spam'].as_matrix()))\n",
    "print(1-logReg.score(test_data.drop('spam', axis = 1).as_matrix(), test_data['spam'].as_matrix()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default settings work pretty well and give us a 7% misclassification rate. Let us try various transformations.\n",
    "\n",
    "- Standardize, that is, $\\displaystyle\\frac{\\mathbf{x}_j - \\hat{\\mu}_j}{\\hat{\\sigma}_j}$\n",
    "- log, $\\log\\left(\\mathbf{x}_j + 0.1\\right)$\n",
    "- Binarize, $\\mathbb{I}\\left(\\mathbf{x}_j > 0\\right)$\n",
    "\n",
    "You can see the transformations and the logistic regression class that I wrote by hand on [GitHub](https://github.com/ppham27/MLaPP-solutions/blob/master/chap08/classifiers.py)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Regularization</th>\n",
       "      <th>Raw Train</th>\n",
       "      <th>Standard Train</th>\n",
       "      <th>Log Train</th>\n",
       "      <th>Binary Train</th>\n",
       "      <th>Raw Test</th>\n",
       "      <th>Standard Test</th>\n",
       "      <th>Log Test</th>\n",
       "      <th>Binary Test</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.070799</td>\n",
       "      <td>0.070147</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076172</td>\n",
       "      <td>0.086589</td>\n",
       "      <td>0.058594</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.069494</td>\n",
       "      <td>0.072431</td>\n",
       "      <td>0.051223</td>\n",
       "      <td>0.064274</td>\n",
       "      <td>0.070964</td>\n",
       "      <td>0.087891</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.072266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.069821</td>\n",
       "      <td>0.074062</td>\n",
       "      <td>0.050571</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.070312</td>\n",
       "      <td>0.087240</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.072266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.5</td>\n",
       "      <td>0.071126</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.049918</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.070312</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.060547</td>\n",
       "      <td>0.072917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.072757</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.050245</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.069661</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.061198</td>\n",
       "      <td>0.073568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.5</td>\n",
       "      <td>0.073409</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.050571</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.071615</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.072757</td>\n",
       "      <td>0.075693</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.063948</td>\n",
       "      <td>0.072266</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.5</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.051223</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.075521</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.075693</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.051223</td>\n",
       "      <td>0.063622</td>\n",
       "      <td>0.075521</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.5</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.051223</td>\n",
       "      <td>0.063295</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.075041</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.050897</td>\n",
       "      <td>0.063622</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5.5</td>\n",
       "      <td>0.074062</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.050897</td>\n",
       "      <td>0.063622</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.076998</td>\n",
       "      <td>0.050571</td>\n",
       "      <td>0.063948</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.076172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6.5</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.076998</td>\n",
       "      <td>0.050245</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.075521</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.058594</td>\n",
       "      <td>0.076172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.050245</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076172</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.058594</td>\n",
       "      <td>0.076172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>7.5</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.078303</td>\n",
       "      <td>0.050897</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076172</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.057943</td>\n",
       "      <td>0.076172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.078303</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.064927</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.057943</td>\n",
       "      <td>0.076172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>8.5</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.078630</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.064927</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.078630</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>9.5</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.079282</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.065253</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.083984</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10.0</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.078956</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>10.5</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.078956</td>\n",
       "      <td>0.052202</td>\n",
       "      <td>0.064600</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>11.0</td>\n",
       "      <td>0.074388</td>\n",
       "      <td>0.079282</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.065253</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>11.5</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.079282</td>\n",
       "      <td>0.051223</td>\n",
       "      <td>0.066232</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.074870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>12.0</td>\n",
       "      <td>0.075367</td>\n",
       "      <td>0.079608</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.069168</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.084635</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>12.5</td>\n",
       "      <td>0.075693</td>\n",
       "      <td>0.079608</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.069821</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>13.0</td>\n",
       "      <td>0.075693</td>\n",
       "      <td>0.079608</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.070147</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059245</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>13.5</td>\n",
       "      <td>0.075693</td>\n",
       "      <td>0.079608</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.070147</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.074219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>14.0</td>\n",
       "      <td>0.076020</td>\n",
       "      <td>0.080587</td>\n",
       "      <td>0.052202</td>\n",
       "      <td>0.070147</td>\n",
       "      <td>0.076823</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.059896</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>14.5</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.080587</td>\n",
       "      <td>0.052202</td>\n",
       "      <td>0.069821</td>\n",
       "      <td>0.077474</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.060547</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>15.0</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.080587</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.069821</td>\n",
       "      <td>0.079427</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.060547</td>\n",
       "      <td>0.075521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>15.5</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.080914</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.070473</td>\n",
       "      <td>0.079427</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.060547</td>\n",
       "      <td>0.078125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>16.0</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.080914</td>\n",
       "      <td>0.052202</td>\n",
       "      <td>0.071778</td>\n",
       "      <td>0.080078</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.061849</td>\n",
       "      <td>0.078776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>16.5</td>\n",
       "      <td>0.076346</td>\n",
       "      <td>0.081240</td>\n",
       "      <td>0.052202</td>\n",
       "      <td>0.071778</td>\n",
       "      <td>0.080078</td>\n",
       "      <td>0.085286</td>\n",
       "      <td>0.061849</td>\n",
       "      <td>0.078776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>17.0</td>\n",
       "      <td>0.077325</td>\n",
       "      <td>0.080914</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.071452</td>\n",
       "      <td>0.080078</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.061849</td>\n",
       "      <td>0.078776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>17.5</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.080914</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.071452</td>\n",
       "      <td>0.080729</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.078776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>18.0</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.080914</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.071452</td>\n",
       "      <td>0.080729</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.078776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>18.5</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.081240</td>\n",
       "      <td>0.051550</td>\n",
       "      <td>0.071452</td>\n",
       "      <td>0.080729</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.079427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>19.0</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.081566</td>\n",
       "      <td>0.051876</td>\n",
       "      <td>0.071452</td>\n",
       "      <td>0.081380</td>\n",
       "      <td>0.086589</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.079427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>19.5</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.081566</td>\n",
       "      <td>0.052529</td>\n",
       "      <td>0.071778</td>\n",
       "      <td>0.081380</td>\n",
       "      <td>0.086589</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.080078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>20.0</td>\n",
       "      <td>0.077651</td>\n",
       "      <td>0.081566</td>\n",
       "      <td>0.052529</td>\n",
       "      <td>0.072431</td>\n",
       "      <td>0.081380</td>\n",
       "      <td>0.086589</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>0.080078</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Regularization  Raw Train  Standard Train  Log Train  Binary Train  \\\n",
       "0              0.0   0.070799        0.070147   0.051876      0.064600   \n",
       "1              0.5   0.069494        0.072431   0.051223      0.064274   \n",
       "2              1.0   0.069821        0.074062   0.050571      0.063295   \n",
       "3              1.5   0.071126        0.075367   0.049918      0.063295   \n",
       "4              2.0   0.072757        0.076020   0.050245      0.063295   \n",
       "5              2.5   0.073409        0.075367   0.050571      0.063295   \n",
       "6              3.0   0.072757        0.075693   0.051876      0.063948   \n",
       "7              3.5   0.074715        0.075367   0.051223      0.063295   \n",
       "8              4.0   0.075693        0.076020   0.051223      0.063622   \n",
       "9              4.5   0.076020        0.076020   0.051223      0.063295   \n",
       "10             5.0   0.075041        0.076020   0.050897      0.063622   \n",
       "11             5.5   0.074062        0.076346   0.050897      0.063622   \n",
       "12             6.0   0.074388        0.076998   0.050571      0.063948   \n",
       "13             6.5   0.074388        0.076998   0.050245      0.064600   \n",
       "14             7.0   0.074388        0.077651   0.050245      0.064600   \n",
       "15             7.5   0.074388        0.078303   0.050897      0.064600   \n",
       "16             8.0   0.074388        0.078303   0.051550      0.064927   \n",
       "17             8.5   0.074715        0.078630   0.051550      0.064927   \n",
       "18             9.0   0.075367        0.078630   0.051876      0.064600   \n",
       "19             9.5   0.074715        0.079282   0.051876      0.065253   \n",
       "20            10.0   0.074715        0.078956   0.051876      0.064600   \n",
       "21            10.5   0.074715        0.078956   0.052202      0.064600   \n",
       "22            11.0   0.074388        0.079282   0.051550      0.065253   \n",
       "23            11.5   0.075367        0.079282   0.051223      0.066232   \n",
       "24            12.0   0.075367        0.079608   0.051550      0.069168   \n",
       "25            12.5   0.075693        0.079608   0.051550      0.069821   \n",
       "26            13.0   0.075693        0.079608   0.051550      0.070147   \n",
       "27            13.5   0.075693        0.079608   0.051550      0.070147   \n",
       "28            14.0   0.076020        0.080587   0.052202      0.070147   \n",
       "29            14.5   0.076346        0.080587   0.052202      0.069821   \n",
       "30            15.0   0.076346        0.080587   0.051876      0.069821   \n",
       "31            15.5   0.076346        0.080914   0.051876      0.070473   \n",
       "32            16.0   0.076346        0.080914   0.052202      0.071778   \n",
       "33            16.5   0.076346        0.081240   0.052202      0.071778   \n",
       "34            17.0   0.077325        0.080914   0.051876      0.071452   \n",
       "35            17.5   0.077651        0.080914   0.051876      0.071452   \n",
       "36            18.0   0.077651        0.080914   0.051550      0.071452   \n",
       "37            18.5   0.077651        0.081240   0.051550      0.071452   \n",
       "38            19.0   0.077651        0.081566   0.051876      0.071452   \n",
       "39            19.5   0.077651        0.081566   0.052529      0.071778   \n",
       "40            20.0   0.077651        0.081566   0.052529      0.072431   \n",
       "\n",
       "    Raw Test  Standard Test  Log Test  Binary Test  \n",
       "0   0.076172       0.086589  0.058594     0.074219  \n",
       "1   0.070964       0.087891  0.059245     0.072266  \n",
       "2   0.070312       0.087240  0.059896     0.072266  \n",
       "3   0.070312       0.085938  0.060547     0.072917  \n",
       "4   0.069661       0.084635  0.061198     0.073568  \n",
       "5   0.071615       0.085286  0.059896     0.074219  \n",
       "6   0.072266       0.084635  0.059896     0.074219  \n",
       "7   0.075521       0.085286  0.059896     0.074219  \n",
       "8   0.075521       0.083984  0.059896     0.074219  \n",
       "9   0.076823       0.084635  0.059896     0.074219  \n",
       "10  0.076823       0.085286  0.059896     0.074870  \n",
       "11  0.077474       0.085938  0.059896     0.075521  \n",
       "12  0.076823       0.085286  0.059896     0.076172  \n",
       "13  0.075521       0.083984  0.058594     0.076172  \n",
       "14  0.076172       0.084635  0.058594     0.076172  \n",
       "15  0.076172       0.084635  0.057943     0.076172  \n",
       "16  0.076823       0.083984  0.057943     0.076172  \n",
       "17  0.077474       0.083984  0.059245     0.075521  \n",
       "18  0.076823       0.083984  0.059245     0.075521  \n",
       "19  0.076823       0.083984  0.059245     0.075521  \n",
       "20  0.076823       0.085286  0.059245     0.075521  \n",
       "21  0.076823       0.084635  0.059245     0.075521  \n",
       "22  0.077474       0.084635  0.059245     0.074219  \n",
       "23  0.077474       0.084635  0.059245     0.074870  \n",
       "24  0.077474       0.084635  0.059245     0.075521  \n",
       "25  0.077474       0.085286  0.059245     0.074219  \n",
       "26  0.076823       0.085286  0.059245     0.074219  \n",
       "27  0.076823       0.085286  0.059896     0.074219  \n",
       "28  0.076823       0.085286  0.059896     0.075521  \n",
       "29  0.077474       0.085286  0.060547     0.075521  \n",
       "30  0.079427       0.085286  0.060547     0.075521  \n",
       "31  0.079427       0.085286  0.060547     0.078125  \n",
       "32  0.080078       0.085286  0.061849     0.078776  \n",
       "33  0.080078       0.085286  0.061849     0.078776  \n",
       "34  0.080078       0.085938  0.061849     0.078776  \n",
       "35  0.080729       0.085938  0.062500     0.078776  \n",
       "36  0.080729       0.085938  0.062500     0.078776  \n",
       "37  0.080729       0.085938  0.062500     0.079427  \n",
       "38  0.081380       0.086589  0.062500     0.079427  \n",
       "39  0.081380       0.086589  0.062500     0.080078  \n",
       "40  0.081380       0.086589  0.062500     0.080078  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "# transform the data\n",
    "ytrain = train_data['spam'].as_matrix()\n",
    "ytest = test_data['spam'].as_matrix()\n",
    "Xtrain_raw = train_data.drop('spam', axis = 1).as_matrix()\n",
    "Xtest_raw = test_data.drop('spam', axis = 1).as_matrix()\n",
    "Xtrain_standard = preprocessing.scale(Xtrain_raw, axis=0)\n",
    "Xtest_standard = preprocessing.scale(Xtest_raw, axis=0)\n",
    "Xtrain_log = np.apply_along_axis(transform_log, axis = 0, arr=Xtrain_raw)\n",
    "Xtest_log = np.apply_along_axis(transform_log, axis = 0, arr=Xtest_raw)\n",
    "Xtrain_binary = np.apply_along_axis(transform_binary, axis = 0, arr=Xtrain_raw)\n",
    "Xtest_binary = np.apply_along_axis(transform_binary, axis = 0, arr=Xtest_raw)\n",
    "\n",
    "data_transform = ['Raw', 'Standard', 'Log', 'Binary']\n",
    "Xtrain = [Xtrain_raw, Xtrain_standard, Xtrain_log, Xtrain_binary]\n",
    "Xtest = [Xtest_raw, Xtest_standard, Xtest_log, Xtest_binary]\n",
    "\n",
    "## now run lots of models to find regularization parameter\n",
    "regularization = np.linspace(0, 20, num=41)\n",
    "misclassification_rates = pd.DataFrame(dtype=np.float64,\n",
    "                                       index = np.arange(len(regularization)),\n",
    "                                       columns = ['Regularization'] + \n",
    "                                       list(map(lambda x : x + ' Train',  data_transform)) + \n",
    "                                       list(map(lambda x : x + ' Test',  data_transform)))\n",
    "for i in range(len(regularization)):\n",
    "    misclassification_rates.iloc[i]['Regularization'] = regularization[i]\n",
    "    if regularization[i] == 0:\n",
    "        regularization[i] += 0.01 # hack when there's no convergence.\n",
    "    logReg = LogisticRegression(regularization = regularization[i])\n",
    "    for j in range(len(data_transform)):\n",
    "        logReg.fit(Xtrain[j], ytrain)\n",
    "        misclassification_rates.iloc[i][data_transform[j] + ' Train'] = 1 - logReg.score(Xtrain[j], ytrain)\n",
    "        misclassification_rates.iloc[i][data_transform[j] + ' Test'] = 1 - logReg.score(Xtest[j], ytest)\n",
    "misclassification_rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot these results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JazCOLyjPmlJGspylZi90J8bQyEDnZ8jHq7V2Ydxo+KV57PPpOcQ1YNV6vf4N8H3z8/8E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\nBjWtqI8rfrNcsT5lZGSazjmD0mKxMGfOHA4ePIhSqSQjI6PO+Zea179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BDiuhMUFSDJlxCiXlT2ybulUmqSUmoucBcQCQxUSu27OqFVTdqwEVUeRugYHYU+Kqp49T9XVygs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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c374780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "colors = ['#e41a1c', '#377eb8', '#4daf4a', '#984ea3']\n",
    "plt.figure(figsize=(12,8))\n",
    "for i in range(len(data_transform)):\n",
    "    plt.plot(misclassification_rates['Regularization'], misclassification_rates[data_transform[i] + ' Train'],\n",
    "             color=colors[i], linestyle='--', linewidth=2, marker='.')\n",
    "    plt.plot(misclassification_rates['Regularization'], misclassification_rates[data_transform[i] + ' Test'],\n",
    "             color=colors[i], linestyle='-', linewidth=2, marker='.')\n",
    "plt.grid(True)\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1,0.5), title=\"Dataset\")\n",
    "plt.ylabel(\"Misclassification Rate\")\n",
    "plt.xlabel(\"Regularization Parameter ($\\lambda$)\")\n",
    "plt.title(\"Misclassification Rates for Various Transforms and Regularizations\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The problem tells us to select the regularization paramter with cross validation, but that seems pointless. We see that the log transform performs best with a misclassification rate of 5.8% when $\\lambda = 8$."
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}