linear-classifier-regularization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression with L2 regularization\n",
    "\n",
    "In this notebook, we'll implement logistic regression classifier with L2 regularization. We shall do the following:\n",
    "\n",
    " * Extract features from Amazon product reviews.\n",
    " * Convert an SFrame into a NumPy array.\n",
    " * Write a function to compute the derivative of log likelihood function with an L2 penalty with respect to a single coefficient.\n",
    " * Implement gradient ascent with an L2 penalty.\n",
    " * Empirically explore how the L2 penalty can ameliorate overfitting.\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up GraphLab Create\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import graphlab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and process review dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will use the subset of the Amazon product review dataset. The subset was chosen to contain similar numbers of positive and negative reviews, as the original dataset consisted of mostly positive reviews."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: C:\\Users\\Nan\\AppData\\Local\\Temp\\graphlab_server_1529807768.log.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to nanlee_89@yahoo.com and will expire on December 07, 2018.\n"
     ]
    }
   ],
   "source": [
    "products = graphlab.SFrame('amazon_baby_subset.gl/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data transformations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#  feature processing \n",
    "# ---------------------------------------------------------------\n",
    "import json\n",
    "with open('important_words.json', 'r') as f: # Reads the list of most frequent words\n",
    "    important_words = json.load(f)\n",
    "important_words = [str(s) for s in important_words]\n",
    "\n",
    "\n",
    "def remove_punctuation(text):\n",
    "    import string\n",
    "    return text.translate(None, string.punctuation) \n",
    "\n",
    "# Remove punctuation.\n",
    "products['review_clean'] = products['review'].apply(remove_punctuation)\n",
    "\n",
    "# Split out the words into individual columns\n",
    "for word in important_words:\n",
    "    products[word] = products['review_clean'].apply(lambda s : s.split().count(word))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Take a look at what the dataset looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">product</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">good</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">daughter</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">much</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">loves</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stroller</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">put</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">months</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">car</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">still</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">back</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">used</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">recommend</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">first</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">even</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
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       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">perfect</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">nice</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">...</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[53072 rows x 198 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\treview\tstr\n",
       "\trating\tfloat\n",
       "\tsentiment\tint\n",
       "\treview_clean\tstr\n",
       "\tbaby\tint\n",
       "\tone\tint\n",
       "\tgreat\tint\n",
       "\tlove\tint\n",
       "\tuse\tint\n",
       "\twould\tint\n",
       "\tlike\tint\n",
       "\teasy\tint\n",
       "\tlittle\tint\n",
       "\tseat\tint\n",
       "\told\tint\n",
       "\twell\tint\n",
       "\tget\tint\n",
       "\talso\tint\n",
       "\treally\tint\n",
       "\tson\tint\n",
       "\ttime\tint\n",
       "\tbought\tint\n",
       "\tproduct\tint\n",
       "\tgood\tint\n",
       "\tdaughter\tint\n",
       "\tmuch\tint\n",
       "\tloves\tint\n",
       "\tstroller\tint\n",
       "\tput\tint\n",
       "\tmonths\tint\n",
       "\tcar\tint\n",
       "\tstill\tint\n",
       "\tback\tint\n",
       "\tused\tint\n",
       "\trecommend\tint\n",
       "\tfirst\tint\n",
       "\teven\tint\n",
       "\tperfect\tint\n",
       "\tnice\tint\n",
       "\tbag\tint\n",
       "\ttwo\tint\n",
       "\tusing\tint\n",
       "\tgot\tint\n",
       "\tfit\tint\n",
       "\taround\tint\n",
       "\tdiaper\tint\n",
       "\tenough\tint\n",
       "\tmonth\tint\n",
       "\tprice\tint\n",
       "\tgo\tint\n",
       "\tcould\tint\n",
       "\tsoft\tint\n",
       "\tsince\tint\n",
       "\tbuy\tint\n",
       "\troom\tint\n",
       "\tworks\tint\n",
       "\tmade\tint\n",
       "\tchild\tint\n",
       "\tkeep\tint\n",
       "\tsize\tint\n",
       "\tsmall\tint\n",
       "\tneed\tint\n",
       "\tyear\tint\n",
       "\tbig\tint\n",
       "\tmake\tint\n",
       "\ttake\tint\n",
       "\teasily\tint\n",
       "\tthink\tint\n",
       "\tcrib\tint\n",
       "\tclean\tint\n",
       "\tway\tint\n",
       "\tquality\tint\n",
       "\tthing\tint\n",
       "\tbetter\tint\n",
       "\twithout\tint\n",
       "\tset\tint\n",
       "\tnew\tint\n",
       "\tevery\tint\n",
       "\tcute\tint\n",
       "\tbest\tint\n",
       "\tbottles\tint\n",
       "\twork\tint\n",
       "\tpurchased\tint\n",
       "\tright\tint\n",
       "\tlot\tint\n",
       "\tside\tint\n",
       "\thappy\tint\n",
       "\tcomfortable\tint\n",
       "\ttoy\tint\n",
       "\table\tint\n",
       "\tkids\tint\n",
       "\tbit\tint\n",
       "\tnight\tint\n",
       "\tlong\tint\n",
       "\tfits\tint\n",
       "\tsee\tint\n",
       "\tus\tint\n",
       "\tanother\tint\n",
       "\tplay\tint\n",
       "\tday\tint\n",
       "\tmoney\tint\n",
       "\tmonitor\tint\n",
       "\ttried\tint\n",
       "\tthought\tint\n",
       "\tnever\tint\n",
       "\titem\tint\n",
       "\thard\tint\n",
       "\tplastic\tint\n",
       "\thowever\tint\n",
       "\tdisappointed\tint\n",
       "\treviews\tint\n",
       "\tsomething\tint\n",
       "\tgoing\tint\n",
       "\tpump\tint\n",
       "\tbottle\tint\n",
       "\tcup\tint\n",
       "\twaste\tint\n",
       "\treturn\tint\n",
       "\tamazon\tint\n",
       "\tdifferent\tint\n",
       "\ttop\tint\n",
       "\twant\tint\n",
       "\tproblem\tint\n",
       "\tknow\tint\n",
       "\twater\tint\n",
       "\ttry\tint\n",
       "\treceived\tint\n",
       "\tsure\tint\n",
       "\ttimes\tint\n",
       "\tchair\tint\n",
       "\tfind\tint\n",
       "\thold\tint\n",
       "\tgate\tint\n",
       "\topen\tint\n",
       "\tbottom\tint\n",
       "\taway\tint\n",
       "\tactually\tint\n",
       "\tcheap\tint\n",
       "\tworked\tint\n",
       "\tgetting\tint\n",
       "\tordered\tint\n",
       "\tcame\tint\n",
       "\tmilk\tint\n",
       "\tbad\tint\n",
       "\tpart\tint\n",
       "\tworth\tint\n",
       "\tfound\tint\n",
       "\tcover\tint\n",
       "\tmany\tint\n",
       "\tdesign\tint\n",
       "\tlooking\tint\n",
       "\tweeks\tint\n",
       "\tsay\tint\n",
       "\twanted\tint\n",
       "\tlook\tint\n",
       "\tplace\tint\n",
       "\tpurchase\tint\n",
       "\tlooks\tint\n",
       "\tsecond\tint\n",
       "\tpiece\tint\n",
       "\tbox\tint\n",
       "\tpretty\tint\n",
       "\ttrying\tint\n",
       "\tdifficult\tint\n",
       "\ttogether\tint\n",
       "\tthough\tint\n",
       "\tgive\tint\n",
       "\tstarted\tint\n",
       "\tanything\tint\n",
       "\tlast\tint\n",
       "\tcompany\tint\n",
       "\tcome\tint\n",
       "\treturned\tint\n",
       "\tmaybe\tint\n",
       "\ttook\tint\n",
       "\tbroke\tint\n",
       "\tmakes\tint\n",
       "\tstay\tint\n",
       "\tinstead\tint\n",
       "\tidea\tint\n",
       "\thead\tint\n",
       "\tsaid\tint\n",
       "\tless\tint\n",
       "\twent\tint\n",
       "\tworking\tint\n",
       "\thigh\tint\n",
       "\tunit\tint\n",
       "\tseems\tint\n",
       "\tpicture\tint\n",
       "\tcompletely\tint\n",
       "\twish\tint\n",
       "\tbuying\tint\n",
       "\tbabies\tint\n",
       "\twon\tint\n",
       "\ttub\tint\n",
       "\talmost\tint\n",
       "\teither\tint\n",
       "\n",
       "Rows: 53072\n",
       "\n",
       "Data:\n",
       "+-------------------------------+-------------------------------+--------+-----------+\n",
       "|              name             |             review            | rating | sentiment |\n",
       "+-------------------------------+-------------------------------+--------+-----------+\n",
       "| Stop Pacifier Sucking with... | All of my kids have cried ... |  5.0   |     1     |\n",
       "| Nature's Lullabies Second ... | We wanted to get something... |  5.0   |     1     |\n",
       "| Nature's Lullabies Second ... | My daughter had her 1st ba... |  5.0   |     1     |\n",
       "|  Lamaze Peekaboo, I Love You  | One of baby's first and fa... |  4.0   |     1     |\n",
       "| SoftPlay Peek-A-Boo Where'... | Very cute interactive book... |  5.0   |     1     |\n",
       "|   Our Baby Girl Memory Book   | Beautiful book, I love it ... |  5.0   |     1     |\n",
       "| Hunnt&reg; Falling Flowers... | Try this out for a spring ... |  5.0   |     1     |\n",
       "| Blessed By Pope Benedict X... | very nice Divine Mercy Pen... |  5.0   |     1     |\n",
       "| Cloth Diaper Pins Stainles... | We bought the pins as my 6... |  4.0   |     1     |\n",
       "| Cloth Diaper Pins Stainles... | It has been many years sin... |  5.0   |     1     |\n",
       "+-------------------------------+-------------------------------+--------+-----------+\n",
       "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
       "|          review_clean         | baby | one | great | love | use | would | like |\n",
       "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
       "| All of my kids have cried ... |  0   |  0  |   1   |  0   |  0  |   0   |  0   |\n",
       "| We wanted to get something... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
       "| My daughter had her 1st ba... |  1   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
       "| One of babys first and fav... |  0   |  0  |   0   |  0   |  0  |   0   |  1   |\n",
       "| Very cute interactive book... |  0   |  0  |   1   |  0   |  0  |   0   |  0   |\n",
       "| Beautiful book I love it t... |  0   |  0  |   1   |  1   |  0  |   0   |  0   |\n",
       "| Try this out for a spring ... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
       "| very nice Divine Mercy Pen... |  0   |  0  |   0   |  0   |  0  |   0   |  0   |\n",
       "| We bought the pins as my 6... |  0   |  1  |   0   |  0   |  1  |   0   |  0   |\n",
       "| It has been many years sin... |  0   |  1  |   0   |  0   |  0  |   0   |  1   |\n",
       "+-------------------------------+------+-----+-------+------+-----+-------+------+\n",
       "+------+--------+------+-----+------+-----+------+--------+-----+\n",
       "| easy | little | seat | old | well | get | also | really | ... |\n",
       "+------+--------+------+-----+------+-----+------+--------+-----+\n",
       "|  1   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  1  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  1  |  0   |  1  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  0  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   0    |  0   |  1  |  0   |  0  |  0   |   0    | ... |\n",
       "|  0   |   1    |  0   |  0  |  0   |  1  |  0   |   0    | ... |\n",
       "+------+--------+------+-----+------+-----+------+--------+-----+\n",
       "[53072 rows x 198 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "products"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train-Validation split\n",
    "\n",
    "We split the data into a train-validation split with 80% of the data in the training set and 20% of the data in the validation set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set   : 42361 data points\n",
      "Validation set : 10711 data points\n"
     ]
    }
   ],
   "source": [
    "train_data, validation_data = products.random_split(.8, seed=2)\n",
    "\n",
    "print 'Training set   : %d data points' % len(train_data)\n",
    "print 'Validation set : %d data points' % len(validation_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert SFrame to NumPy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def get_numpy_data(data_sframe, features, label):\n",
    "    \n",
    "    # function that extracts columns from an SFrame and converts them into a NumPy array.\n",
    "    # returned: one representing features and another representing class labels. \n",
    "    # Note: The feature matrix includes an additional column 'intercept' filled with 1's to take account of the intercept term.\n",
    "\n",
    "    data_sframe['intercept'] = 1\n",
    "    features = ['intercept'] + features\n",
    "    features_sframe = data_sframe[features]\n",
    "    feature_matrix = features_sframe.to_numpy()\n",
    "    label_sarray = data_sframe[label]\n",
    "    label_array = label_sarray.to_numpy()\n",
    "    return(feature_matrix, label_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We convert both the training and validation sets into NumPy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "feature_matrix_train, sentiment_train = get_numpy_data(train_data, important_words, 'sentiment')\n",
    "feature_matrix_valid, sentiment_valid = get_numpy_data(validation_data, important_words, 'sentiment') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building on logistic regression with no L2 penalty assignment\n",
    "\n",
    "The link function for logistic regression can be defined as:\n",
    "\n",
    "$$\n",
    "P(y_i = +1 | \\mathbf{x}_i,\\mathbf{w}) = \\frac{1}{1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))},\n",
    "$$\n",
    "\n",
    "where the feature vector $h(\\mathbf{x}_i)$ is given by the word counts of **important_words** in the review $\\mathbf{x}_i$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "'''\n",
    "produces probablistic estimate for P(y_i = +1 | x_i, w).\n",
    "estimate ranges between 0 and 1.\n",
    "'''\n",
    "def predict_probability(feature_matrix, coefficients):\n",
    "    # Take dot product of feature_matrix and coefficients  \n",
    "    scores = np.dot(feature_matrix, coefficients)\n",
    "    \n",
    "    # Compute P(y_i = +1 | x_i, w) using the link function\n",
    "    predictions = 1 / (1 + np.exp(-scores))\n",
    "    \n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding  L2 penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For logistic regression without an L2 penalty, the derivative of the log likelihood function is:\n",
    "$$\n",
    "\\frac{\\partial\\ell}{\\partial w_j} = \\sum_{i=1}^N h_j(\\mathbf{x}_i)\\left(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})\\right)\n",
    "$$\n",
    "\n",
    "** Adding L2 penalty to the derivative** \n",
    "\n",
    "It takes only a small modification to add a L2 penalty. All terms indicated in **red** refer to terms that were added due to an **L2 penalty**.\n",
    "\n",
    "* The link function is still the sigmoid:\n",
    "$$\n",
    "P(y_i = +1 | \\mathbf{x}_i,\\mathbf{w}) = \\frac{1}{1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))},\n",
    "$$\n",
    "* We add the L2 penalty term to the per-coefficient derivative of log likelihood:\n",
    "$$\n",
    "\\frac{\\partial\\ell}{\\partial w_j} = \\sum_{i=1}^N h_j(\\mathbf{x}_i)\\left(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})\\right) \\color{red}{-2\\lambda w_j }\n",
    "$$\n",
    "\n",
    "The **per-coefficient derivative for logistic regression with an L2 penalty** is as follows:\n",
    "$$\n",
    "\\frac{\\partial\\ell}{\\partial w_j} = \\sum_{i=1}^N h_j(\\mathbf{x}_i)\\left(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})\\right) \\color{red}{-2\\lambda w_j }\n",
    "$$\n",
    "and for the intercept term, we have\n",
    "$$\n",
    "\\frac{\\partial\\ell}{\\partial w_0} = \\sum_{i=1}^N h_0(\\mathbf{x}_i)\\left(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w})\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: We do not apply the L2 penalty on the intercept. A large intercept does not necessarily indicate overfitting because the intercept is not associated with any particular feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following function computes the derivative of log likelihood with respect to a single coefficient $w_j$. The function accepts five arguments:\n",
    " * `errors` vector containing $(\\mathbf{1}[y_i = +1] - P(y_i = +1 | \\mathbf{x}_i, \\mathbf{w}))$ for all $i$\n",
    " * `feature` vector containing $h_j(\\mathbf{x}_i)$  for all $i$\n",
    " * `coefficient` containing the current value of coefficient $w_j$.\n",
    " * `l2_penalty` representing the L2 penalty constant $\\lambda$\n",
    " * `feature_is_constant` telling whether the $j$-th feature is constant or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def feature_derivative_with_L2(errors, feature, coefficient, l2_penalty, feature_is_constant): \n",
    "    \n",
    "    # Compute the dot product of errors and feature\n",
    "    derivative = np.dot(errors, feature)\n",
    "\n",
    "    # add L2 penalty term for any feature that isn't the intercept.\n",
    "    if not feature_is_constant: \n",
    "        derivative = np.dot(errors, feature) - 2*l2_penalty*coefficient\n",
    "        \n",
    "    return derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify the correctness of the gradient ascent algorithm, we will use a function for computing log likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\ell\\ell(\\mathbf{w}) = \\sum_{i=1}^N \\Big( (\\mathbf{1}[y_i = +1] - 1)\\mathbf{w}^T h(\\mathbf{x}_i) - \\ln\\left(1 + \\exp(-\\mathbf{w}^T h(\\mathbf{x}_i))\\right) \\Big) \\color{red}{-\\lambda\\|\\mathbf{w}\\|_2^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def compute_log_likelihood_with_L2(feature_matrix, sentiment, coefficients, l2_penalty):\n",
    "    indicator = (sentiment==+1)\n",
    "    scores = np.dot(feature_matrix, coefficients)\n",
    "    \n",
    "    lp = np.sum((indicator-1)*scores - np.log(1. + np.exp(-scores))) - l2_penalty*np.sum(coefficients[1:]**2)\n",
    "    \n",
    "    return lp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic regression function with a minor modification for the L2 penalty shows as follow: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def logistic_regression_with_L2(feature_matrix, sentiment, initial_coefficients, step_size, l2_penalty, max_iter):\n",
    "    coefficients = np.array(initial_coefficients) # make sure it's a numpy array\n",
    "    for itr in xrange(max_iter):\n",
    "        # Predict P(y_i = +1|x_i,w) using your predict_probability() function\n",
    "        predictions = predict_probability(feature_matrix, coefficients)\n",
    "        \n",
    "        # Compute indicator value for (y_i = +1)\n",
    "        indicator = (sentiment==+1)\n",
    "        \n",
    "        # Compute the errors as indicator - predictions\n",
    "        errors = indicator - predictions\n",
    "        for j in xrange(len(coefficients)): # loop over each coefficient\n",
    "            is_intercept = (j == 0)\n",
    "            # Recall that feature_matrix[:,j] is the feature column associated with coefficients[j].\n",
    "            # Compute the derivative for coefficients[j]. Save it in a variable called derivative\n",
    "            derivative = feature_derivative_with_L2(errors, feature_matrix[:,j], coefficients[j], l2_penalty, is_intercept)\n",
    "            \n",
    "            # add the step size times the derivative to the current coefficient\n",
    "            coefficients[j] = coefficients[j] + step_size*derivative\n",
    "        \n",
    "        # Checking whether log likelihood is increasing\n",
    "        if itr <= 15 or (itr <= 100 and itr % 10 == 0) or (itr <= 1000 and itr % 100 == 0) \\\n",
    "        or (itr <= 10000 and itr % 1000 == 0) or itr % 10000 == 0:\n",
    "            lp = compute_log_likelihood_with_L2(feature_matrix, sentiment, coefficients, l2_penalty)\n",
    "            print 'iteration %*d: log likelihood of observed labels = %.8f' % \\\n",
    "                (int(np.ceil(np.log10(max_iter))), itr, lp)\n",
    "    return coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Explore effects of L2 regularization\n",
    "\n",
    "Here, we'll explore the benefits of using **L2 regularization** in analyzing sentiment for product reviews. **As iterations pass, the log likelihood will increase**.\n",
    "\n",
    "Below, we train models with increasing amounts of regularization, starting with no L2 penalty, which is equivalent to our previous logistic regression implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29179.39138303\n",
      "iteration   1: log likelihood of observed labels = -29003.71259047\n",
      "iteration   2: log likelihood of observed labels = -28834.66187288\n",
      "iteration   3: log likelihood of observed labels = -28671.70781507\n",
      "iteration   4: log likelihood of observed labels = -28514.43078198\n",
      "iteration   5: log likelihood of observed labels = -28362.48344665\n",
      "iteration   6: log likelihood of observed labels = -28215.56713122\n",
      "iteration   7: log likelihood of observed labels = -28073.41743783\n",
      "iteration   8: log likelihood of observed labels = -27935.79536396\n",
      "iteration   9: log likelihood of observed labels = -27802.48168669\n",
      "iteration  10: log likelihood of observed labels = -27673.27331484\n",
      "iteration  11: log likelihood of observed labels = -27547.98083656\n",
      "iteration  12: log likelihood of observed labels = -27426.42679977\n",
      "iteration  13: log likelihood of observed labels = -27308.44444728\n",
      "iteration  14: log likelihood of observed labels = -27193.87673876\n",
      "iteration  15: log likelihood of observed labels = -27082.57555831\n",
      "iteration  20: log likelihood of observed labels = -26570.43059938\n",
      "iteration  30: log likelihood of observed labels = -25725.48742389\n",
      "iteration  40: log likelihood of observed labels = -25055.53326910\n",
      "iteration  50: log likelihood of observed labels = -24509.63590026\n",
      "iteration  60: log likelihood of observed labels = -24054.97906083\n",
      "iteration  70: log likelihood of observed labels = -23669.51640848\n",
      "iteration  80: log likelihood of observed labels = -23337.89167628\n",
      "iteration  90: log likelihood of observed labels = -23049.07066021\n",
      "iteration 100: log likelihood of observed labels = -22794.90974921\n",
      "iteration 200: log likelihood of observed labels = -21283.29527353\n",
      "iteration 300: log likelihood of observed labels = -20570.97485473\n",
      "iteration 400: log likelihood of observed labels = -20152.21466944\n",
      "iteration 500: log likelihood of observed labels = -19876.62333410\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 0\n",
    "coefficients_0_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                     initial_coefficients=np.zeros(194),\n",
    "                                                     step_size=5e-6, l2_penalty=0, max_iter=501)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29179.39508175\n",
      "iteration   1: log likelihood of observed labels = -29003.73417180\n",
      "iteration   2: log likelihood of observed labels = -28834.71441858\n",
      "iteration   3: log likelihood of observed labels = -28671.80345068\n",
      "iteration   4: log likelihood of observed labels = -28514.58077957\n",
      "iteration   5: log likelihood of observed labels = -28362.69830317\n",
      "iteration   6: log likelihood of observed labels = -28215.85663259\n",
      "iteration   7: log likelihood of observed labels = -28073.79071393\n",
      "iteration   8: log likelihood of observed labels = -27936.26093762\n",
      "iteration   9: log likelihood of observed labels = -27803.04751805\n",
      "iteration  10: log likelihood of observed labels = -27673.94684207\n",
      "iteration  11: log likelihood of observed labels = -27548.76901327\n",
      "iteration  12: log likelihood of observed labels = -27427.33612958\n",
      "iteration  13: log likelihood of observed labels = -27309.48101569\n",
      "iteration  14: log likelihood of observed labels = -27195.04624253\n",
      "iteration  15: log likelihood of observed labels = -27083.88333261\n",
      "iteration  20: log likelihood of observed labels = -26572.49874392\n",
      "iteration  30: log likelihood of observed labels = -25729.32604153\n",
      "iteration  40: log likelihood of observed labels = -25061.34245801\n",
      "iteration  50: log likelihood of observed labels = -24517.52091982\n",
      "iteration  60: log likelihood of observed labels = -24064.99093939\n",
      "iteration  70: log likelihood of observed labels = -23681.67373669\n",
      "iteration  80: log likelihood of observed labels = -23352.19298741\n",
      "iteration  90: log likelihood of observed labels = -23065.50180166\n",
      "iteration 100: log likelihood of observed labels = -22813.44844580\n",
      "iteration 200: log likelihood of observed labels = -21321.14164794\n",
      "iteration 300: log likelihood of observed labels = -20624.98634439\n",
      "iteration 400: log likelihood of observed labels = -20219.92048845\n",
      "iteration 500: log likelihood of observed labels = -19956.11341777\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 4\n",
    "coefficients_4_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                      initial_coefficients=np.zeros(194),\n",
    "                                                      step_size=5e-6, l2_penalty=4, max_iter=501)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29179.40062984\n",
      "iteration   1: log likelihood of observed labels = -29003.76654163\n",
      "iteration   2: log likelihood of observed labels = -28834.79322654\n",
      "iteration   3: log likelihood of observed labels = -28671.94687528\n",
      "iteration   4: log likelihood of observed labels = -28514.80571589\n",
      "iteration   5: log likelihood of observed labels = -28363.02048079\n",
      "iteration   6: log likelihood of observed labels = -28216.29071186\n",
      "iteration   7: log likelihood of observed labels = -28074.35036891\n",
      "iteration   8: log likelihood of observed labels = -27936.95892966\n",
      "iteration   9: log likelihood of observed labels = -27803.89576265\n",
      "iteration  10: log likelihood of observed labels = -27674.95647005\n",
      "iteration  11: log likelihood of observed labels = -27549.95042714\n",
      "iteration  12: log likelihood of observed labels = -27428.69905549\n",
      "iteration  13: log likelihood of observed labels = -27311.03455140\n",
      "iteration  14: log likelihood of observed labels = -27196.79890162\n",
      "iteration  15: log likelihood of observed labels = -27085.84308528\n",
      "iteration  20: log likelihood of observed labels = -26575.59697506\n",
      "iteration  30: log likelihood of observed labels = -25735.07304608\n",
      "iteration  40: log likelihood of observed labels = -25070.03447306\n",
      "iteration  50: log likelihood of observed labels = -24529.31188025\n",
      "iteration  60: log likelihood of observed labels = -24079.95349572\n",
      "iteration  70: log likelihood of observed labels = -23699.83199186\n",
      "iteration  80: log likelihood of observed labels = -23373.54108747\n",
      "iteration  90: log likelihood of observed labels = -23090.01500055\n",
      "iteration 100: log likelihood of observed labels = -22841.08995135\n",
      "iteration 200: log likelihood of observed labels = -21377.25595328\n",
      "iteration 300: log likelihood of observed labels = -20704.63995428\n",
      "iteration 400: log likelihood of observed labels = -20319.25685307\n",
      "iteration 500: log likelihood of observed labels = -20072.16321721\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 10\n",
    "coefficients_10_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                      initial_coefficients=np.zeros(194),\n",
    "                                                      step_size=5e-6, l2_penalty=10, max_iter=501)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29179.48385120\n",
      "iteration   1: log likelihood of observed labels = -29004.25177457\n",
      "iteration   2: log likelihood of observed labels = -28835.97382190\n",
      "iteration   3: log likelihood of observed labels = -28674.09410083\n",
      "iteration   4: log likelihood of observed labels = -28518.17112932\n",
      "iteration   5: log likelihood of observed labels = -28367.83774654\n",
      "iteration   6: log likelihood of observed labels = -28222.77708939\n",
      "iteration   7: log likelihood of observed labels = -28082.70799392\n",
      "iteration   8: log likelihood of observed labels = -27947.37595368\n",
      "iteration   9: log likelihood of observed labels = -27816.54738615\n",
      "iteration  10: log likelihood of observed labels = -27690.00588850\n",
      "iteration  11: log likelihood of observed labels = -27567.54970126\n",
      "iteration  12: log likelihood of observed labels = -27448.98991327\n",
      "iteration  13: log likelihood of observed labels = -27334.14912742\n",
      "iteration  14: log likelihood of observed labels = -27222.86041863\n",
      "iteration  15: log likelihood of observed labels = -27114.96648229\n",
      "iteration  20: log likelihood of observed labels = -26621.50201299\n",
      "iteration  30: log likelihood of observed labels = -25819.72803950\n",
      "iteration  40: log likelihood of observed labels = -25197.34035501\n",
      "iteration  50: log likelihood of observed labels = -24701.03698195\n",
      "iteration  60: log likelihood of observed labels = -24296.66378580\n",
      "iteration  70: log likelihood of observed labels = -23961.38842316\n",
      "iteration  80: log likelihood of observed labels = -23679.38088853\n",
      "iteration  90: log likelihood of observed labels = -23439.31824267\n",
      "iteration 100: log likelihood of observed labels = -23232.88192018\n",
      "iteration 200: log likelihood of observed labels = -22133.50726528\n",
      "iteration 300: log likelihood of observed labels = -21730.03957488\n",
      "iteration 400: log likelihood of observed labels = -21545.87572145\n",
      "iteration 500: log likelihood of observed labels = -21451.95551390\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 1e2\n",
    "coefficients_1e2_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                       initial_coefficients=np.zeros(194),\n",
    "                                                       step_size=5e-6, l2_penalty=1e2, max_iter=501)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29180.31606471\n",
      "iteration   1: log likelihood of observed labels = -29009.07176112\n",
      "iteration   2: log likelihood of observed labels = -28847.62378912\n",
      "iteration   3: log likelihood of observed labels = -28695.14439397\n",
      "iteration   4: log likelihood of observed labels = -28550.95060743\n",
      "iteration   5: log likelihood of observed labels = -28414.45771129\n",
      "iteration   6: log likelihood of observed labels = -28285.15124375\n",
      "iteration   7: log likelihood of observed labels = -28162.56976044\n",
      "iteration   8: log likelihood of observed labels = -28046.29387744\n",
      "iteration   9: log likelihood of observed labels = -27935.93902900\n",
      "iteration  10: log likelihood of observed labels = -27831.15045502\n",
      "iteration  11: log likelihood of observed labels = -27731.59955260\n",
      "iteration  12: log likelihood of observed labels = -27636.98108219\n",
      "iteration  13: log likelihood of observed labels = -27547.01092670\n",
      "iteration  14: log likelihood of observed labels = -27461.42422295\n",
      "iteration  15: log likelihood of observed labels = -27379.97375625\n",
      "iteration  20: log likelihood of observed labels = -27027.18208317\n",
      "iteration  30: log likelihood of observed labels = -26527.22737267\n",
      "iteration  40: log likelihood of observed labels = -26206.59048765\n",
      "iteration  50: log likelihood of observed labels = -25995.96903148\n",
      "iteration  60: log likelihood of observed labels = -25854.95710284\n",
      "iteration  70: log likelihood of observed labels = -25759.08109950\n",
      "iteration  80: log likelihood of observed labels = -25693.05688014\n",
      "iteration  90: log likelihood of observed labels = -25647.09929349\n",
      "iteration 100: log likelihood of observed labels = -25614.81468705\n",
      "iteration 200: log likelihood of observed labels = -25536.20998919\n",
      "iteration 300: log likelihood of observed labels = -25532.57691220\n",
      "iteration 400: log likelihood of observed labels = -25532.35543765\n",
      "iteration 500: log likelihood of observed labels = -25532.33970049\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 1e3\n",
    "coefficients_1e3_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                       initial_coefficients=np.zeros(194),\n",
    "                                                       step_size=5e-6, l2_penalty=1e3, max_iter=501)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration   0: log likelihood of observed labels = -29271.85955115\n",
      "iteration   1: log likelihood of observed labels = -29271.71006589\n",
      "iteration   2: log likelihood of observed labels = -29271.65738833\n",
      "iteration   3: log likelihood of observed labels = -29271.61189923\n",
      "iteration   4: log likelihood of observed labels = -29271.57079975\n",
      "iteration   5: log likelihood of observed labels = -29271.53358505\n",
      "iteration   6: log likelihood of observed labels = -29271.49988440\n",
      "iteration   7: log likelihood of observed labels = -29271.46936584\n",
      "iteration   8: log likelihood of observed labels = -29271.44172890\n",
      "iteration   9: log likelihood of observed labels = -29271.41670149\n",
      "iteration  10: log likelihood of observed labels = -29271.39403722\n",
      "iteration  11: log likelihood of observed labels = -29271.37351294\n",
      "iteration  12: log likelihood of observed labels = -29271.35492661\n",
      "iteration  13: log likelihood of observed labels = -29271.33809523\n",
      "iteration  14: log likelihood of observed labels = -29271.32285309\n",
      "iteration  15: log likelihood of observed labels = -29271.30905015\n",
      "iteration  20: log likelihood of observed labels = -29271.25729150\n",
      "iteration  30: log likelihood of observed labels = -29271.20657205\n",
      "iteration  40: log likelihood of observed labels = -29271.18775997\n",
      "iteration  50: log likelihood of observed labels = -29271.18078247\n",
      "iteration  60: log likelihood of observed labels = -29271.17819447\n",
      "iteration  70: log likelihood of observed labels = -29271.17723457\n",
      "iteration  80: log likelihood of observed labels = -29271.17687853\n",
      "iteration  90: log likelihood of observed labels = -29271.17674648\n",
      "iteration 100: log likelihood of observed labels = -29271.17669750\n",
      "iteration 200: log likelihood of observed labels = -29271.17666862\n",
      "iteration 300: log likelihood of observed labels = -29271.17666862\n",
      "iteration 400: log likelihood of observed labels = -29271.17666862\n",
      "iteration 500: log likelihood of observed labels = -29271.17666862\n"
     ]
    }
   ],
   "source": [
    "# run with L2 = 1e5\n",
    "coefficients_1e5_penalty = logistic_regression_with_L2(feature_matrix_train, sentiment_train,\n",
    "                                                       initial_coefficients=np.zeros(194),\n",
    "                                                       step_size=5e-6, l2_penalty=1e5, max_iter=501)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare coefficients\n",
    "\n",
    "We compare the **coefficients** for each of the models that were trained above. We will create a table of features and learned coefficients associated with each of the different L2 penalty values.\n",
    "\n",
    "Below is a simple helper function that will help us create this table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "table = graphlab.SFrame({'word': ['(intercept)'] + important_words})\n",
    "def add_coefficients_to_table(coefficients, column_name):\n",
    "    table[column_name] = coefficients\n",
    "    return table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now, let's run the function `add_coefficients_to_table` for each of the L2 penalty strengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">word</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=0]</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=4]</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=10]</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=1e2]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.0637421352275</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.0631430877074</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.06225594377</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.0504383651953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">baby</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0740730059216</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0739938541405</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0738773534804</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0723603602218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">one</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0127525057784</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0124949704481</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0121152529534</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0072472833187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">great</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.801624989778</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.796896933003</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.789935147221</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.701425073675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">love</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.05855398207</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.05085568099</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.03952851585</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.896644133101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">use</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.000104152191248</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000162857656177</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000555710975756</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00548103267946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">would</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.287021443534</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.286027202975</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.284564035562</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.265992746226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">like</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00338447399293</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00344208577045</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00352729444966</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00463499283253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">easy</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.984558819873</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.977600149782</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.967361836631</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.838244832955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">little</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.524419456364</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.521384726107</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.516917392491</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.460234577902</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=1e3]</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">coefficients [L2=1e5]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.38675326957e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0113617511844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0597516888364</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0017841492163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00876091762004</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00182685568023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.376011714222</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00894956049736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.418353644134</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0090417372977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0173264874461</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000417863934616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.188662422049</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.008127027099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.00704307584353</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.000826650270031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.401903971363</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0088076812121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.251220653959</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00594051364038</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[194 rows x 7 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tword\tstr\n",
       "\tcoefficients [L2=0]\tfloat\n",
       "\tcoefficients [L2=4]\tfloat\n",
       "\tcoefficients [L2=10]\tfloat\n",
       "\tcoefficients [L2=1e2]\tfloat\n",
       "\tcoefficients [L2=1e3]\tfloat\n",
       "\tcoefficients [L2=1e5]\tfloat\n",
       "\n",
       "Rows: 194\n",
       "\n",
       "Data:\n",
       "+-------------+---------------------+---------------------+----------------------+\n",
       "|     word    | coefficients [L2=0] | coefficients [L2=4] | coefficients [L2=10] |\n",
       "+-------------+---------------------+---------------------+----------------------+\n",
       "| (intercept) |   -0.0637421352275  |   -0.0631430877074  |    -0.06225594377    |\n",
       "|     baby    |   0.0740730059216   |   0.0739938541405   |   0.0738773534804    |\n",
       "|     one     |   0.0127525057784   |   0.0124949704481   |   0.0121152529534    |\n",
       "|    great    |    0.801624989778   |    0.796896933003   |    0.789935147221    |\n",
       "|     love    |    1.05855398207    |    1.05085568099    |    1.03952851585     |\n",
       "|     use     |  -0.000104152191248 |  0.000162857656177  |  0.000555710975756   |\n",
       "|    would    |   -0.287021443534   |   -0.286027202975   |   -0.284564035562    |\n",
       "|     like    |  -0.00338447399293  |  -0.00344208577045  |  -0.00352729444966   |\n",
       "|     easy    |    0.984558819873   |    0.977600149782   |    0.967361836631    |\n",
       "|    little   |    0.524419456364   |    0.521384726107   |    0.516917392491    |\n",
       "+-------------+---------------------+---------------------+----------------------+\n",
       "+-----------------------+-----------------------+-----------------------+\n",
       "| coefficients [L2=1e2] | coefficients [L2=1e3] | coefficients [L2=1e5] |\n",
       "+-----------------------+-----------------------+-----------------------+\n",
       "|    -0.0504383651953   |   5.38675326957e-05   |    0.0113617511844    |\n",
       "|    0.0723603602218    |    0.0597516888364    |    0.0017841492163    |\n",
       "|    0.0072472833187    |   -0.00876091762004   |   -0.00182685568023   |\n",
       "|     0.701425073675    |     0.376011714222    |    0.00894956049736   |\n",
       "|     0.896644133101    |     0.418353644134    |    0.0090417372977    |\n",
       "|    0.00548103267946   |    0.0173264874461    |   0.000417863934616   |\n",
       "|    -0.265992746226    |    -0.188662422049    |    -0.008127027099    |\n",
       "|   -0.00463499283253   |   -0.00704307584353   |   -0.000826650270031  |\n",
       "|     0.838244832955    |     0.401903971363    |    0.0088076812121    |\n",
       "|     0.460234577902    |     0.251220653959    |    0.00594051364038   |\n",
       "+-----------------------+-----------------------+-----------------------+\n",
       "[194 rows x 7 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add_coefficients_to_table(coefficients_0_penalty, 'coefficients [L2=0]')\n",
    "add_coefficients_to_table(coefficients_4_penalty, 'coefficients [L2=4]')\n",
    "add_coefficients_to_table(coefficients_10_penalty, 'coefficients [L2=10]')\n",
    "add_coefficients_to_table(coefficients_1e2_penalty, 'coefficients [L2=1e2]')\n",
    "add_coefficients_to_table(coefficients_1e3_penalty, 'coefficients [L2=1e3]')\n",
    "add_coefficients_to_table(coefficients_1e5_penalty, 'coefficients [L2=1e5]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using **the coefficients trained with L2 penalty 0**,  the 5 most positive words (with largest positive coefficients) and the 5 most negative words (with largest negative coefficients) .\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype: str\n",
       "Rows: 5\n",
       "['love', 'loves', 'easy', 'perfect', 'great']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "positive_words = table.topk('coefficients [L2=0]',5)['word']\n",
    "positive_words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype: str\n",
       "Rows: 5\n",
       "['disappointed', 'money', 'return', 'waste', 'returned']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "negative_words = table.topk('coefficients [L2=0]',5, reverse = True)['word']\n",
    "negative_words"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To observe the effect of increasing L2 penalty on the 10 words just selected, we use a utility function to  plot the coefficient path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = 10, 6\n",
    "\n",
    "def make_coefficient_plot(table, positive_words, negative_words, l2_penalty_list):\n",
    "    cmap_positive = plt.get_cmap('Reds')\n",
    "    cmap_negative = plt.get_cmap('Blues')\n",
    "    \n",
    "    xx = l2_penalty_list\n",
    "    plt.plot(xx, [0.]*len(xx), '--', lw=1, color='k')\n",
    "    \n",
    "    table_positive_words = table.filter_by(column_name='word', values=positive_words)\n",
    "    table_negative_words = table.filter_by(column_name='word', values=negative_words)\n",
    "    del table_positive_words['word']\n",
    "    del table_negative_words['word']\n",
    "    \n",
    "    for i in xrange(len(positive_words)):\n",
    "        color = cmap_positive(0.8*((i+1)/(len(positive_words)*1.2)+0.15))\n",
    "        plt.plot(xx, table_positive_words[i:i+1].to_numpy().flatten(),\n",
    "                 '-', label=positive_words[i], linewidth=4.0, color=color)\n",
    "        \n",
    "    for i in xrange(len(negative_words)):\n",
    "        color = cmap_negative(0.8*((i+1)/(len(negative_words)*1.2)+0.15))\n",
    "        plt.plot(xx, table_negative_words[i:i+1].to_numpy().flatten(),\n",
    "                 '-', label=negative_words[i], linewidth=4.0, color=color)\n",
    "        \n",
    "    plt.legend(loc='best', ncol=3, prop={'size':16}, columnspacing=0.5)\n",
    "    plt.axis([1, 1e5, -1, 2])\n",
    "    plt.title('Coefficient path')\n",
    "    plt.xlabel('L2 penalty ($\\lambda$)')\n",
    "    plt.ylabel('Coefficient value')\n",
    "    plt.xscale('log')\n",
    "    plt.rcParams.update({'font.size': 18})\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following cell to generate the plot. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3Li4uNG7cmKVLlzrchGPbtm0kJydfdyYKLy8vWrduzc6dO2nUqBEGQ+Ej+C5duoTZbMZo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7THPZCOc+JghqvHR3STmIhIEwNZnPXs2Rz/5Hce7PUw+p/z/tBfExjXhcr1x/rhn617KTMSbSgB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\nsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdc1a898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "make_coefficient_plot(table, positive_words, negative_words, l2_penalty_list=[0, 4, 10, 1e2, 1e3, 1e5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measuring accuracy\n",
    "\n",
    "Now, let us compute the accuracy of the classifier model. The accuracy is given by\n",
    "\n",
    "$$\n",
    "\\mbox{accuracy} = \\frac{\\mbox{# correctly classified data points}}{\\mbox{# total data points}}\n",
    "$$\n",
    "\n",
    "\n",
    "The class prediction is calculated using\n",
    "$$\n",
    "\\hat{y}_i = \n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "      +1 & h(\\mathbf{x}_i)^T\\mathbf{w} > 0 \\\\\n",
    "      -1 & h(\\mathbf{x}_i)^T\\mathbf{w} \\leq 0 \\\\\n",
    "\\end{array} \n",
    "\\right.\n",
    "$$\n",
    "\n",
    "**Note**: The model prediction code doesn't change even with the addition of an L2 penalty. The only thing that changes is the estimated coefficients used in this prediction.\n",
    "\n",
    "Based on the above, we will use following code to compute the model accuracy: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_classification_accuracy(feature_matrix, sentiment, coefficients):\n",
    "    scores = np.dot(feature_matrix, coefficients)\n",
    "    apply_threshold = np.vectorize(lambda x: 1. if x > 0  else -1.)\n",
    "    predictions = apply_threshold(scores)\n",
    "    \n",
    "    num_correct = (predictions == sentiment).sum()\n",
    "    accuracy = num_correct / len(feature_matrix)    \n",
    "    return accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we compare the accuracy on the **training data** and **validation data** for all the models that were trained in this assignment.  We first calculate the accuracy values and then build a simple report summarizing the performance for the various models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_accuracy = {}\n",
    "train_accuracy[0]   = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_0_penalty)\n",
    "train_accuracy[4]   = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_4_penalty)\n",
    "train_accuracy[10]  = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_10_penalty)\n",
    "train_accuracy[1e2] = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_1e2_penalty)\n",
    "train_accuracy[1e3] = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_1e3_penalty)\n",
    "train_accuracy[1e5] = get_classification_accuracy(feature_matrix_train, sentiment_train, coefficients_1e5_penalty)\n",
    "\n",
    "validation_accuracy = {}\n",
    "validation_accuracy[0]   = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_0_penalty)\n",
    "validation_accuracy[4]   = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_4_penalty)\n",
    "validation_accuracy[10]  = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_10_penalty)\n",
    "validation_accuracy[1e2] = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_1e2_penalty)\n",
    "validation_accuracy[1e3] = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_1e3_penalty)\n",
    "validation_accuracy[1e5] = get_classification_accuracy(feature_matrix_valid, sentiment_valid, coefficients_1e5_penalty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 penalty = 0\n",
      "train accuracy = 0.785156157787, validation_accuracy = 0.78143964149\n",
      "--------------------------------------------------------------------------------\n",
      "L2 penalty = 4\n",
      "train accuracy = 0.785108944548, validation_accuracy = 0.781533003454\n",
      "--------------------------------------------------------------------------------\n",
      "L2 penalty = 10\n",
      "train accuracy = 0.784990911452, validation_accuracy = 0.781719727383\n",
      "--------------------------------------------------------------------------------\n",
      "L2 penalty = 100\n",
      "train accuracy = 0.783975826822, validation_accuracy = 0.781066193633\n",
      "--------------------------------------------------------------------------------\n",
      "L2 penalty = 1000\n",
      "train accuracy = 0.775855149784, validation_accuracy = 0.771356549342\n",
      "--------------------------------------------------------------------------------\n",
      "L2 penalty = 100000\n",
      "train accuracy = 0.680366374731, validation_accuracy = 0.667818130893\n",
      "--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Build a simple report\n",
    "for key in sorted(validation_accuracy.keys()):\n",
    "    print \"L2 penalty = %g\" % key\n",
    "    print \"train accuracy = %s, validation_accuracy = %s\" % (train_accuracy[key], validation_accuracy[key])\n",
    "    print \"--------------------------------------------------------------------------------\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.tight_layout>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F+sGB84FPnXM7AcysEd5Vtw5AS6CemV0eeoCZ3QUUAFMindA5N9k5l+Wcy2ra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\nb3lOm6aWZ6JSSBMRESlNirY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SpEnR/t/85jfs2rWL7t2706tXLz744AOaNm3K5MmTufji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\naSIiIiIJSCFNREREJAH9Px4kXb9m0+E3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe14b3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot accuracy on training and validation sets over choice of L2 penalty.\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = 10, 6\n",
    "\n",
    "sorted_list = sorted(train_accuracy.items(), key=lambda x:x[0])\n",
    "plt.plot([p[0] for p in sorted_list], [p[1] for p in sorted_list], 'bo-', linewidth=4, label='Training accuracy')\n",
    "sorted_list = sorted(validation_accuracy.items(), key=lambda x:x[0])\n",
    "plt.plot([p[0] for p in sorted_list], [p[1] for p in sorted_list], 'ro-', linewidth=4, label='Validation accuracy')\n",
    "plt.xscale('symlog')\n",
    "plt.axis([0, 1e3, 0.78, 0.786])\n",
    "plt.legend(loc='lower left')\n",
    "plt.rcParams.update({'font.size': 18})\n",
    "plt.tight_layout"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}