{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 50 POINTS COS 324: Text Classification\n",
    "\n",
    "In this exercise, we'll use the **Weighted Majority** algorithm for text classification.\n",
    "\n",
    "Before we begin solving the exercise, unzip the provided ```data.zip``` (available [here](http://iml.cs.princeton.edu/PA1/data.zip)) file into a new folder named ```data``` so that the folder contains the files ```released_data``` and ```tokenized_data```. After you're done, this is what the directory structure should look like.\n",
    "\n",
    "![img](http://iml.cs.princeton.edu/PA1/file-struct.png)\n",
    "\n",
    "The code provided below does it for you. The filesize is large. So this might take a while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os.path\n",
    "\n",
    "if not os.path.isfile('data/released_data') or not os.path.isfile('data/tokenized_data'):\n",
    "    import urllib.request\n",
    "    url_data = 'http://iml.cs.princeton.edu/PA1/data.zip'\n",
    "    urllib.request.urlretrieve(url_data, \"data.zip\")\n",
    "    \n",
    "    import zipfile\n",
    "    with zipfile.ZipFile(\"data.zip\",\"r\") as zip_ref:\n",
    "        zip_ref.extractall(\".\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 36 POINTS Part A: Got2look's Spam Filtering\n",
    "\n",
    "It's 2100 AD. You're an employee at Boongle, a [Mariner](https://mars.jpl.nasa.gov/gallery/atlas/valles-marineris.html) [Valley](https://en.wikipedia.org/wiki/Geography_of_Mars) based web company that offers an email service called Got2look. Got2look, aiming to provide the Martians the best quality of service, has its own share of challenges. One of these is that it must differentiate __spam__ from __not-spam__.\n",
    "\n",
    "## 6 POINTS Loading the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "assert(os.path.isfile('data/released_data'))\n",
    "\n",
    "email, label = pickle.load(open('data/released_data', 'rb'))\n",
    "\n",
    "# The var email is a list of strings -- each string is an email.\n",
    "# The var label is a list of {-1,+1} -- +1 is indicator for spam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique Labels\n",
      " [-1.  1.] \n",
      "\n",
      "Number of Instances\n",
      " 2000 \n",
      "\n",
      "Number of Spam Instances\n",
      " 917 \n",
      "\n",
      "Number of Not-Spam Instances\n",
      " 1083 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 1 POINT ACT (1) How many instances are there in total? \n",
    "num_email = len(label)\n",
    "\n",
    "# 1 POINT ACT (2) List out all the distinct entries present in the var label.\n",
    "uniq_label = np.unique(label)\n",
    "\n",
    "print('Unique Labels\\n', uniq_label, '\\n')\n",
    "print('Number of Instances\\n', num_email, '\\n')\n",
    "\n",
    "# 1 POINT ACT (3) How many instances are labelled as spam?\n",
    "num_spam = sum(label == 1)\n",
    "print('Number of Spam Instances\\n', num_spam, '\\n')\n",
    "\n",
    "# 1 POINT ACT (4) How many instances are labelled as not-spam?\n",
    "num_not_spam = sum(label == -1)\n",
    "print('Number of Not-Spam Instances\\n', num_not_spam, '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(num_email == num_spam + num_not_spam)\n",
    "assert(len(uniq_label) == 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example of Spam (First 1000 characters) \n",
      " Pmy Pmy LLtq nE KdVr JeSig QJXbg rMuLb MW dAsnf qAJK Hwxvf hKYdn it u#fhv r#icI GcOdlP hFJrmV @c bx TL dIjhy Hdfj rTGhRP OKXexeU pobbcO PxGgVVQ KcXhlG JeSig #KgyBV aEKydNR ykYoD hUjUW cTEvEpF UYiyec Pmy h#l nkBzH u#fhv KcXhlG urJJS@w SZklMqH il dAsnf QW MhlYPc YbxnIE Hp#zkmI hDJs dHW UtimR JeSig dUm ynEZej dAsnf Pmy Pmy pZtF A#UOU hDJs SFXfCei ADSwO xQuxG Q@z wDQ nsKFMi dAsnf vX WE#mU UYiyec HfRGEu u#fhv QH JeSig FHVXm@ urJJS@w Pmy yBMRXvO AjKlYGv Pmy Hp#zkmI Pmy Pmy JeSig dyPRm BffQzk MLbbpB hKYdn tzbBHB mEF JeSig #Md aEKydNR Pmy JeSig @O Pmy wBASmD Hd gJhJB urJJS@w JeSig mfERJxP HvepX FbkiUv gIM hUjUW gJhJB llHkOz dAsnf hDJs Kfe wR IYp SFFq JeSig uC@KbJ HkE aEKydNR Pmy nsKFMi w#OBYAP Pmy JeSig ujmZEBx OKXexeU XkWAOZs tzbBHB mysN aEKydNR UYiyec JeSig JeSig dAsnf Pmy QJXbg rMuLb iyaKHZ aEKydNR HkE OKXexeU aEKydNR m@jS zsa urJJS@w OKXexeU KFd dAsnf dWaQ ajra Pmy ZoDko@ IRjede Pmy DhA jh u#fhv ZxlybjA iTHY Pmy gJhJB iTHY gJhJB jdO QSggdRg JeSig ZxhBzm dAsnf aEKydNR mql JeSig UYiyec YZbNK \n",
      "\n",
      "The Label of this document \n",
      " 1.0 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (5) Find the index of the first spam.\n",
    "first_spam_index = np.argmax(label)\n",
    "\n",
    "print('Example of Spam (First 1000 characters) \\n', email[first_spam_index][:1000], '\\n')\n",
    "print('The Label of this document \\n', label[first_spam_index], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(label[first_spam_index] == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example of Not-Spam (First 1000 characters) \n",
      " aEKydNR OKXexeU nGLM wBASmD dAsnf gJhJB zsa JeSig aEKydNR UYiyec bfSzR Nk QfA#e PmC id Pmy nVU JeSig dWaQ sJw oU hKYdn tp qcmZER dCMuDtC Vms Qa lq BJFWSeg nhVEq Yf# vvBNc aEKydNR rRQju rMuLb J@Y@fLF u#fhv w#OBYAP ZoDko@ iwrA BH UYiyec PWPwr urJJS@w UYiyec lT JeSig OKXexeU Pmy JyNnOsv urJJS@w J@Y@fLF TL SgZoR JeSig JVA mysN @RouL wDQ Ya dAsnf rMQbzT dAsnf JeSig mnZni Awnj dAsnf JeSig nkBzH Pmy iWCcWh AtUlnx EO hUjUW Pmy yo MLbbpB HxdAPn tzbBHB yt dAsnf tBo@e jrSem kUQ Pmy gN# BhNlwV bFgQ qk##Mt vluPO dAsnf dAsnf JeSig JeSig wBASmD wDQ ocD aEKydNR dAsnf JeSig WoWcj UYiyec dAsnf wNuecw caI FqurF Scj UPK#C DidYV QsfDE hUjUW nhVEq Pmy J@Y@fLF Pmy Hp#zkmI Pmy G#GF Kfe Kfe tzbBHB FT BOBqTIP oU eM@KmM dAsnf dWaQ Kph# nsKFMi wBASmD RuWFr Pmy WFGXkOO aEKydNR Hp#zkmI JeSig Pmy dWaQ WoWcj JfBj wNZR eJtcon SgZoR DtHwUhc Ha SgZoR JeSig JeSig pJIQEyt EWh dAsnf Ix QNvXj Pmy Scj jh jh treRYeg Hp#zkmI hKYdn Pmy u#fhv laOiUo dWaQ npnUm OKXexeU AzsuU phjO Kfe WEoK JeSig OKXexeU gIM dAsnf YC yluOa gJhJB UY \n",
      "\n",
      "The Label of this document \n",
      " -1.0 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (6) Find the index of the first not-spam.\n",
    "first_not_spam_index = np.argmin(label)\n",
    "\n",
    "print('Example of Not-Spam (First 1000 characters) \\n', email[first_not_spam_index][:1000], '\\n')\n",
    "print('The Label of this document \\n', label[first_not_spam_index], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(label[first_not_spam_index] == -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11 POINTS Bag-of-Words Representation\n",
    "\n",
    "Dealing with raw text directly can be challenging. First, you'll convert the raw text into the bag-of-words representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 1 POINT ACT (7) Design a function that takes in a text string and converts it to a list of words.\n",
    "def Tokenize(mail):\n",
    "    return mail.split()\n",
    "\n",
    "# Checks\n",
    "assert(Tokenize('ab de er de') == ['ab', 'de', 'er', 'de'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 2 POINTS ACT (8) Design a function that takes in a list of strings and outputs a list of unique words in this list.\n",
    "def Dictionary(email):\n",
    "    return list(set(word for mail in email for word in Tokenize(mail)))\n",
    "    \n",
    "# Checks\n",
    "assert(set(Dictionary(['ab cd', 'cd cd de'])) == set(['ab', 'cd', 'de']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Unique Words\n",
      " 9561 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (9) Create a list of unique words in the var email.\n",
    "words_found = Dictionary(email)\n",
    "num_words = len(words_found)\n",
    "\n",
    "print('Number of Unique Words\\n', num_words, '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(num_words == 9561)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 5 POINTS ACT (10) Design a function that outputs a matrix of dimension -- (num_docs, num_words) -- \n",
    "# such that matrix(i,j) == 1 if and only if email i contains word words_found[j]\n",
    "# and -1 otherwise.\n",
    "def MakeBow():\n",
    "    word_to_index = {w: i for (i, w) in enumerate(words_found)}\n",
    "    data = -1*np.ones((num_email, num_words))\n",
    "    for (i, mail) in enumerate(email):\n",
    "        for w in Tokenize(mail):\n",
    "            data[i, word_to_index[w]] = 1\n",
    "    return data\n",
    "\n",
    "data = MakeBow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(#Docs, #Words)\n",
      " (2000, 9561) \n",
      "\n",
      "The index of the word \"Pmy\"\n",
      " 3422 \n",
      "\n",
      "Checking if it is present in email 0.\n",
      " 1.0 \n",
      "\n",
      "Sample from the Dictionary\n",
      " ['IpGcSPr', 'AmpmxWW', 'odV', 'krr', 'XDx', 'eE', 'lZ#zUt', 'eyxdMQP', 'NUoX', '@cKRJ'] \n",
      "\n",
      "Sample (vector, label)\n",
      " (array([ 1.,  1., -1., ...,  1.,  1., -1.]), 1.0) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('(#Docs, #Words)\\n', data.shape, '\\n')\n",
    "\n",
    "# 1 POINT ACT (11) Get the first word from the first email.\n",
    "first_word = Tokenize(email[0])[0]\n",
    "\n",
    "# 1 POINT ACT (12) Get the index of first_word in words_found.\n",
    "index_first = words_found.index(first_word)\n",
    "\n",
    "print('The index of the word \"%s\"\\n'%first_word, index_first, '\\n')\n",
    "print('Checking if it is present in email 0.\\n', data[0, index_first], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert((num_email, num_words) == data.shape)\n",
    "assert(data[0, index_first] == 1)\n",
    "\n",
    "print('Sample from the Dictionary\\n', words_found[0:len(words_found):1000], '\\n')\n",
    "print('Sample (vector, label)\\n', (data[0,], label[0]), '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8 PONITS Weighted Majority\n",
    "In this section, you'll implement the Weighted Majority algorithm, as described in the [lecture slides](http://www.cs.princeton.edu/courses/archive/fall17/cos324/lectures/lect2.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 7 POINTS ACT (13) Implement the Weighted Majority algorithm. The input is -\n",
    "# (1) Arg 1 - a matrix -- (n, d) shape\n",
    "# (2) Arg 2 - an array -- (n) dimensional\n",
    "# (3) Arg 3 - a float -- eta\n",
    "# WM outputs -\n",
    "# (1) weight vector -- (d) dimensional\n",
    "# (2) mistakes -- an list of int containing 1 for rounds on which WM errs and 0 for others.\n",
    "def WeightedMajority(data, label, eta):\n",
    "    num_docs, num_words = data.shape\n",
    "    weight, mistakes = np.ones(num_words), []\n",
    "    \n",
    "    for (x, y) in zip(data, label):\n",
    "        prediction = np.sign(weight.dot(x))\n",
    "        prediction = np.random.choice([-1, 1]) if prediction == 0 else prediction\n",
    "        mistakes.append(0 if prediction == y else 1)\n",
    "        weight[x!=y] *= (1-eta)\n",
    "    \n",
    "    return weight, mistakes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x127571940>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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noY3Md3fgKLDiLKpcztJFWPAfH0POwgOUbMlQ5tAJOj8yDI2PHml3UvxHOtoA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\nzMyszknBzMzqnBTMzKzOScHMzOr+AwYPRxbys7CxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12756bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "eta_set = [0.01, 0.03, 0.1, 0.3, 0.9, 0.999999, 1.0]\n",
    "mistake_set = []\n",
    "for eta in eta_set:\n",
    "    weight, mistakes = WeightedMajority(data, label , eta)\n",
    "    cumsum_mistakes = np.cumsum(mistakes)/range(1,num_email+1)\n",
    "    mistake_set.append(sum(mistakes))\n",
    "    plt.plot(cumsum_mistakes, label=str(eta))\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Number of Mistakes');\n",
    "plt.xlabel('Number of Rounds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x127433c88>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12742c2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eta_set, mistake_set)\n",
    "plt.ylabel('Number of Mistakes');\n",
    "plt.xlabel('Eta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Mistakes\n",
      " 93 \n",
      "\n",
      "Error Rate\n",
      " 0.0465 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (14) Choose eta.\n",
    "eta = 0.9\n",
    "weight, mistakes = WeightedMajority(data, label , eta)\n",
    "\n",
    "print('Number of Mistakes\\n', sum(mistakes), '\\n')\n",
    "print('Error Rate\\n', sum(mistakes)/num_email, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11 POINTS Sanity Check\n",
    "Now that you've successfully built a classifier, you want to know if this is the maximum mileage one can hope to extract from the WM algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of weights\n",
      " 1e-84 \n",
      "\n",
      "Max weight, Argmax weight, Leading Weight\n",
      " 1e-84 , 7424 , vWs# \n",
      "\n",
      "Min mistake, Argmin mistake, Best Word\n",
      " 84.0 , 7424 , vWs# \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (15) Get the sum of the weight vector.\n",
    "sum_weight = sum(weight)\n",
    "\n",
    "print('Sum of weights\\n', sum_weight, '\\n')\n",
    "\n",
    "# 1 POINT ACT (16) List the maximum weight, the coordinate that achieves this maximum, and the word it corresponds to.\n",
    "max_weight = max(weight)\n",
    "index_max_weight = np.argmax(weight)\n",
    "max_word = words_found[index_max_weight]\n",
    "\n",
    "print('Max weight, Argmax weight, Leading Weight\\n', \n",
    "      max_weight, ',', index_max_weight, ',', max_word, '\\n')\n",
    "\n",
    "# 3 POINTS Does this make sense?\n",
    "# ACT (17) Create an array that for the i^th coordinate represents \n",
    "# the number of mistakes made if following the recommendation of word i all through.\n",
    "mistake_for_words = (num_email-label.dot(data))/2\n",
    "\n",
    "# 1 POINT ACT (18) List the minimum value at any coordinate of mistake_for_words, the coordinate that achieves it,\n",
    "# and the word it corresponds to.\n",
    "mis_weight = min(mistake_for_words)\n",
    "index_mis_weight = np.argmin(mistake_for_words)\n",
    "mis_word = words_found[index_mis_weight]\n",
    "print('Min mistake, Argmin mistake, Best Word\\n', \n",
    "      mis_weight, ',', index_mis_weight, ',', mis_word, '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(mis_word == max_word)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Words for Spam\n",
      " ['vWs#' '@OMBQ' 'NJm'] \n",
      "\n",
      "Words for Not-Spam\n",
      " ['kX' 'Frn' 'HX'] \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12756f080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# 2 POINTS ACT (19) Plot a histogram using mistake_for_words -- x axis is the number of mistakes, y is the number of words.\n",
    "# Preferably, the y axis should have a logarithmic scaling.\n",
    "plt.hist(mistake_for_words, normed=False, bins=30)\n",
    "plt.ylabel('Number of Words');\n",
    "plt.xlabel('Number of Mistakes')\n",
    "plt.yscale('log', nonposy='clip')\n",
    "\n",
    "# 3 POINTS ACT (20) Find the 3 words that make the most mistakes, and the 3 words that make the least number of mistakes.\n",
    "good_words = np.array(words_found)[np.argsort(mistake_for_words)[:3]]\n",
    "bad_words = np.array(words_found)[np.argsort(mistake_for_words)[-3:]]\n",
    "print('Words for Spam\\n', good_words, '\\n')\n",
    "print('Words for Not-Spam\\n', bad_words, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14 POINTS Part B: Earthly Delights\n",
    "Encouraged by your successes with machine learning, you decide to return back to the earth, and start your own consultancy. In the first week, you are contacted by a digital archaeologist. She has a collection of valuable documents from 1995 or earlier; remember that this is 2100 AD. Each document is about one of the two old modes of transport -- automobiles and motorcycles. Your job is to classify each document as belonging to exactly one of the two categories.\n",
    "\n",
    "This section asks you to repeat the steps in Part A on a different (_arguably_ more interesting) dataset.\n",
    "\n",
    "## 6 POINTS Loading the Dataset\n",
    "First, we load download the dataset, and load it into the memory. Fortunately, [scikit-learn](http://scikit-learn.org/stable/) has modules that automate this process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "newsgroups = fetch_20newsgroups(subset='all', categories=['rec.autos', 'rec.motorcycles'])\n",
    "\n",
    "# The var newsgroups.data is a list of strings -- each string is a document.\n",
    "# The var newsgroups.target is a list of {0,1} -- +1 is an indicator for motorcycles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique Labels\n",
      " [0 1] \n",
      "\n",
      "Number of Instances\n",
      " 1986 \n",
      "\n",
      "Number of Moto Instances\n",
      " 996 \n",
      "\n",
      "Number of Auto Instances\n",
      " 990 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 1 POINT ACT (1) How many instances are there in total?\n",
    "num_docs = len(newsgroups.target)\n",
    "\n",
    "# 1 POINT ACT (2) List out all the distinct entries present in the var label.\n",
    "uniq_label = np.unique(newsgroups.target)\n",
    "\n",
    "print('Unique Labels\\n', uniq_label, '\\n')\n",
    "print('Number of Instances\\n', num_docs, '\\n')\n",
    "\n",
    "# 1 POINT ACT (3) How many instances are labelled as motorcycles?\n",
    "num_moto = sum(newsgroups.target == 1)\n",
    "\n",
    "print('Number of Moto Instances\\n', num_moto, '\\n')\n",
    "\n",
    "# 1 POINT ACT (4) How many instances are labelled as autos?\n",
    "num_auto = sum(newsgroups.target == 0)\n",
    "print('Number of Auto Instances\\n', num_auto, '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(num_docs == num_moto + num_auto)\n",
    "assert(len(uniq_label) == 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example of document on Motorcycles \n",
      " From: davet@interceptor.cds.tek.com (Dave Tharp CDS)\n",
      "Subject: Re: Happy Easter!\n",
      "Organization: Tektronix - Colorado Data Systems, Englewood, CO\n",
      "Lines: 17\n",
      "\n",
      "In article <1993Apr15.171757.10890@i88.isc.com> jeq@lachman.com (Jonathan E. Quist) writes:\n",
      ">Rolls-Royce owned by a non-British firm?\n",
      ">\n",
      ">Ye Gods, that would be the end of civilization as we know it.\n",
      "\n",
      "  Why not?  Ford owns Aston-Martin and Jaguar, General Motors owns Lotus\n",
      "and Vauxhall.  Rover is only owned 20% by Honda.\n",
      "\n",
      "-----------------------------------------------------------------------------\n",
      "| Dave Tharp                      | DoD #0751   | \"You can't wear out       |\n",
      "| davet@interceptor.CDS.TEK.COM   | MRA #151    |   an Indian Scout,        |\n",
      "| '88 K75S  '48 Indian Chief      | AHRMA #751  |  Or its brother the Chief.|\n",
      "| '75 R90S(#151) '72 TR-2B(#751)  | AMA #524737 |  They're built like rocks |\n",
      "| '65 R50/2/Velorex  '57 NSU Max  |             |   to take the knocks,     |\n",
      "|       1936 BMW R12              | (Compulsive | It's the Harleys that     |\n",
      "| My employer has no idea.        |   Joiner)   |   give you grief.\"        |\n",
      "-----------------------------------------------------------------------------\n",
      " \n",
      "\n",
      "The Label of this document \n",
      " 1 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (5) Find the index of the moto doc.\n",
    "first_moto_index = np.argmax(newsgroups.target)\n",
    "\n",
    "print('Example of document on Motorcycles \\n', newsgroups.data[first_moto_index], '\\n')\n",
    "print('The Label of this document \\n', newsgroups.target[first_moto_index], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(newsgroups.target[first_moto_index] == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example of document on Autos \n",
      " From: cak3@ns1.cc.lehigh.edu (CHAD ANDREW KAUFFMAN)\n",
      "Subject: Car alarm info. (UNGO BOX)\n",
      "Organization: Lehigh University\n",
      "Lines: 12\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "    I want to get a car alarm and I am thinking about getting an Ungo Box.\n",
      "    Does anyone out there have any knowledge or experience with any of\n",
      "    these alarms?  How about price ranges for the different models?\n",
      "    Are these good car alarms?  Please email me any responces.\n",
      "\n",
      "                cak3@ns3.lehigh.edu\n",
      "\n",
      "                                        Chad\n",
      "                                                Chad\n",
      " \n",
      "\n",
      "The Label of this document \n",
      " 0 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (6) Find the index of the auto doc.\n",
    "first_auto_index = np.argmin(newsgroups.target)\n",
    "\n",
    "print('Example of document on Autos \\n', newsgroups.data[first_auto_index], '\\n')\n",
    "print('The Label of this document \\n', newsgroups.target[first_auto_index], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(newsgroups.target[first_auto_index] == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 POINT Bag-of-Words Representation\n",
    "\n",
    "You note that languages on earth seem more complex, and are riddled with punctuations. Dealing with raw text directly can be challenging. Fortunately, your archaeologist friend has already converted these to the bag-of-words representation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(#Docs, #Words)\n",
      " (1986, 24135) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "assert(os.path.isfile('data/tokenized_data'))\n",
    "data, label, words_found = pickle.load(open('data/tokenized_data', 'rb'))\n",
    "\n",
    "(num_docs, num_words) = data.shape\n",
    "print('(#Docs, #Words)\\n', data.shape, '\\n')\n",
    "# The var data is a matrix of dimension -- (num_docs, num_words) -- such that matrix(i,j) == 1 \n",
    "# if and only if email i contains word words_found[j] and -1 otherwise.\n",
    "# The var label is a list of {-1,+1} -- +1 is indicator for motos.\n",
    "# The var words_found is a list of words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The index of the word \"lehigh\"\n",
      " 13676 \n",
      "\n",
      "Checking if it is present in doc 0.\n",
      " 1 \n",
      "\n",
      "Sample from the Dictionary\n",
      " ['00', '19765', '387', '90s', 'anecdotal', 'bennett', 'calculated', 'comp', 'dealership', 'dweeb', 'fernando', 'grabbed', 'hurl', 'jt', 'loose', 'modulator', 'offerings', 'planning', 'rc', 'rwd', 'sliced', 'suit', 'trading', 'vickers', 'yjwon'] \n",
      "\n",
      "Sample (vector, label)\n",
      " (array([-1, -1, -1, ..., -1, -1, -1]), -1) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Sanity Check\n",
    "# 1 POINT ACT (7) Get the index of 'lehigh' in words_found.\n",
    "index_lehigh = words_found.index('lehigh')\n",
    "\n",
    "print('The index of the word \"lehigh\"\\n', index_lehigh, '\\n')\n",
    "print('Checking if it is present in doc 0.\\n', data[0, index_lehigh], '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(data[0, index_lehigh] == 1)\n",
    "\n",
    "print('Sample from the Dictionary\\n', words_found[0:len(words_found):1000], '\\n')\n",
    "print('Sample (vector, label)\\n', (data[0,], label[0]), '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 POINT Weighted Majority\n",
    "In this section, you'll implement the Weighted Majority algorithm, as described in the [lecture slides](http://www.cs.princeton.edu/courses/archive/fall17/cos324/lectures/lect2.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1277090b8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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I3kNNHKz3MzTFSXlDgKl5yYxIdzHOacO1v5Ed/iBmj42KBDN//rSQ3YeaALCaNEJRnY3F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\nUDAMwzBiTKFgGIZhxPx/vWxROZTvi5YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12752f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "eta_set = [0.01, 0.03, 0.1, 0.3, 0.9, 0.999999, 1.0]\n",
    "mistake_set = []\n",
    "for eta in eta_set:\n",
    "    weight, mistakes = WeightedMajority(data, label , eta)\n",
    "    cumsum_mistakes = np.cumsum(mistakes)/range(1,num_docs+1)\n",
    "    mistake_set.append(sum(mistakes))\n",
    "    plt.plot(cumsum_mistakes, label=str(eta))\n",
    "plt.legend()\n",
    "\n",
    "plt.ylabel('Number of Mistakes');\n",
    "plt.xlabel('Number of Rounds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1274b3eb8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w1EunOdN/mdqKJWGHI5LRRsdjvNgVnUoWL53oI+awJD+X7euqeHBbPTs31HDD\n8jLVLdJIySMEkx12D3b1UbtJyUMkkbvz+tnBqWTxQnsvl8fidYvNdRE+eU8jOxpraKqPUJinukVY\nlDxCsLG2nIK8HA6d6OO9m2rDDkckdKf6LseTxdFunjvWTffFUQAalpZM3RF1e0O11sLJIEoeISjI\ny+HmleXqsCuLVv/lMZ4P6hZ727pp747XLWpKC6fmWuxorGFlRCPzTBVK8jCzCPA14GbAgY8BbwDf\nBdYCHcADk+uHmNnniC9/OwF8yt1/nP6o51dTfSXf2tfJ2ESM/Fw1MJaFbWR8ghc7+9jTdoE9bT28\ncjJetyguyOW2dVX85m1v1S3UcTo7hDXy+EvgR+7+ATMrAIqBPwCedvcvmdkjwCPAZ81sI/AgcBOw\nEvj/zOxt7j4RUuzzoqk+wl/vOc7rZwbZtLoi7HBE5lUs5rx2dmDq9tn9x3sYHouRm2NsqYvw79+1\ngZ2NNWypi1CQpy9P2SjtycPMKoC7gd8GcPdRYNTM7gfeGez2GPCvwGeB+4HH3X0EOG5mbcB24Pm0\nBj7PttQFkwVPRJU8ZEE4Gb00lSyea+umZyhet2hcVsqD2+qDukUVZUWqWywEYYw81gEXgL8xs81A\nK/BpYLm7nwn2OQssD16vAvYlfP5ksO0XmNnDwMMA9fX18x/5PFoVWcLSskIOdvXx4TvCjkZk7vou\njfL8sZ6p2dwdPZcAWFZWyDvetnSqbrGioijkSCUVwkgeecCtwO+7+wtm9pfEL1FNcXc3M5/rL3b3\nXcAugObm5jl/Pp3MjKa6iIrmkjWGxyZ4sTMab1ne1s0rp/pxh5KCXG5vqObDd6xl54YaNiwrVd1i\nEQgjeZwETrr7C8H7J4knj3NmVuvuZ8ysFjgf/PwUUJfw+dXBtqzXVF/JT46co3dolKoStXyWzBKL\nOUfODEyNLPYf72VkPF63aKqL8Ol743WLzXUR3fSxCKU9ebj7WTM7YWY3uPsbwL3AkeDxEeBLwfMP\ng488BXzbzP6CeMF8A7A/3XGnQlPQJPGPfniYz9y7gQ3Ly0KOSBa7E72XpkYWz7V1E700BsDblpfG\n74hqrGH7OtUtJLy7rX4f+NvgTqt24KNADvCEmT0EdAIPALj7q2b2BPHkMg58MtvvtJq0fW0VD+1c\nx9++0Mk/vnyGe29cxsN3N7B9XZWG/ZIW0aFRnkuoW3T1xusWy8sLuefGZdy1oYY719ewvFx1C/l5\n5p7RpYGqZTq4AAAML0lEQVRr1tzc7C0tLWGHkZSeiyN88/lOvvl8B9FLY2yui/CJuxt4900ryFWv\nHplHw2MTtHREp5LF4dPxukVpYR63N1Szs7GanRtqWL9UdYvFysxa3b35qvspeWSOy6MTPNl6gq/t\nOU5nzyXWVBfzOzvX8YGtdVp1UK7JRMw5cnqAZ9susLetmwMdUUbHY+TlGLfWV8a70G6oYfPqCvJU\ntxCUPLIyeUyaiDk/fvUsj+5u56UTfVSVFPCh29fw4TvWUF1aGHZ4ksHcna6gbrG3rZvnjvXQF9Qt\nblxRNtWyfPu6KkoK1Z1IfpGSRxYnj0nuzv7jveza3c7Tr5+nKD+HD2xdze/sbGBtTUnY4UmG6B0a\n5blj8aaCe9q6ORm9DEBtRdHPrW+xrEx1C7k6JY8FkDwSHT03yFefbecHB08zFotx380rePju9VMz\n1WXxuDw6wYGO3qmW5a+eHgCgrDCPO9bHaxY7GmtoqClR3ULmTMljgSWPSecHhvmb5zr41r5OBofH\n2b6uik/c3cA9NyzTQjgL1ETMOXyqP34L7dFuWjujjE7EyM+N1y12NtawY0MNt6xS3UKun5LHAk0e\nky6OjPP4/i6+vuc4p/uHaVxWysN3NXB/00otkJPl3J2OnqBuEaxvMTA8DsDba8vZ2VjNjqBuUVyg\nuoXMLyWPBZ48Jo1NxPjHl8/w6O52XjszwLKyQn57x1p+67Y1Wjgni3RfHOG5Yz3sDeoWp/ridYuV\nFUVTl6HuXF/D0jLdMCGppeSxSJLHJHdnT1s3jz7Tzp62bkoKcnlwez0f27mOVVpQJ+NcGh1n//He\nqS60r50J6hZFedy5vpqdG5ays7GGtdXFqltIWil5LLLkkejwqX6++mw7//DyGQz4N7fU8vDd69m4\nsjzs0Bat8YkYr5zqnypyv9jZx+hEjILcHLauqZwaXWxaVaGJoRIqJY9FnDwmnYxe4ut7Onj8QBeX\nRie4a0MNn7h7PTsaq/VtNsXcnePdQ1NF7ufbexgM6hYba8u5K0gW29ZWaQKoZBQlDyWPKf2XxvjW\nC51847kOLgyOsLG2nE+8o4H3bqpVN9R5dGFwZGq+xd62bk73DwPxtVvumqpbVGuip2Q0JQ8lj18w\nMj7BDw6eYtfudo5dGGJVZAkf27mOB7fVabbxNRgaGWd/R+9Usnj97CAAFUvyg7pFfIJefZXqFpI9\nlDyUPGYUizk/e/08u3a3s7+jl/KiPD54+xp+e8dazUKexfhEjJdOvlW3ONgVZWzCKcjLYdvayqnZ\n3DetVN1CspeSh5JHUl7sirLrmXZ+fOQs+Tk5/LumVXz87gYal5WGHVro3J1jF4amksW+Yz0Mjoxj\nBjetLGdHYw13NS6leW0lRfmqW8jCoOSh5DEnx7uH+Nqz7TzZepKR8Ri/9PblfOIdDTSvqVxUl1zO\nDwyz91g3e472sLetm7MD8bpFXdUSdjbGb5+9Y321Vn6UBUvJQ8njmnQHa4v89+fja4s01cfXFvnl\njQtzbZGLI+PsP97DnqM97Gm7wJvnLgIQKc5nx/qaqUtR9dXFIUcqkh5KHkoe1+Xy6ATfaz3B1549\nTlfvJdZWF/M7dzXwga2rs/oSzdhEjJdO9E21LD/Y1cd4zCnMy2H7uqqpZLGxtly9wmRRUvJQ8pgX\nEzHnR4fPsmv3MV462U91SQEfvmMtH75jDZVZcOnG3Wk7f3EqWexr7+ViULfYtKpiKllsXaO6hQgo\neSh5zDN354VgbZGfBWuLPNBcx+/sbMi4Szpn+4fZGySLPW3dnB8cAWBNdTE7g2Rxx/pqIsWZn/xE\n0i3Z5KGb+yUpZsbtDdXc3lDNm+cG2bW7ne/s7+Jb+zq57+ZaHr67gc0hrS0yODzGC+29U6OLo+fj\ndYuqkoL4fIvGeO2iriqzkpxINtPIQ67Z2f5h/ua543x7XxeDI+Pctq6KT7yjgXe+LbVri4xNxDh0\noo9ng8l5h070MRFzivJz2La2amo299tXqG4hMle6bKXkkTaDw2M8vv8EX997nDP9w7xteSkfv6uB\n+7esoiDv+tufuDtvnnurbvFCew9DoxPkGGxaHZla3+LWetUtRK6XkoeSR9qNTcT4+5dOs2t3O6+f\nHWR5eSEf3bGO37ytnvKiua0tcqb/8lTbj73HergQ1C3W1ZSwo7GanY1LuaOhmopirVkiMp+UPJQ8\nQuPu7D7aza7dx9jb1kNpYR6/sb2Oj+1cR23FldcWGRgeY9+xnqki97ELQwBUlxRM3RF1Z2M1qytV\ntxBJJSUPJY+McPhUP7t2t/OPr8TXFnnf5pV8/O4G1i8t5WBXlL1t3Tzb1s3LJ/uZiDlL8nPZvq4q\nflfUhhpuWF6muoVIGil5KHlklBO9l/j63uN898AJLo1OUJSfw/BYjByDzXWRqTuimuojWoNdJERK\nHkoeGanv0ijf3t/F+YER7lgfv/VXa62LZA7N85CMFCku4Pfe2Rh2GCJynbSMnIiIzJmSh4iIzJmS\nh4iIzJmSh4iIzJmSh4iIzJmSh4iIzJmSh4iIzJmSh4iIzNmCnWFuZheAzjl8pAboTlE4mWoxnjMs\nzvNejOcMi/O8r/ec17j70qvttGCTx1yZWUsyU/IXksV4zrA4z3sxnjMszvNO1znrspWIiMyZkoeI\niMyZksdbdoUdQAgW4znD4jzvxXjOsDjPOy3nrJqHiIjMmUYeIiIyZ4sqeZjZe8zsDTNrM7NHrvBz\nM7MvBz9/2cxuDSPO+ZbEef9WcL6vmNlzZrY5jDjn09XOOWG/bWY2bmYfSGd8qZLMeZvZO83skJm9\nambPpDvG+ZbEf98VZvb3ZvZScM4fDSPO+WRmXzez82Z2eIafp/5vmbsvigeQCxwDGoAC4CVg47R9\n3gv8M2DA7cALYcedpvO+E6gMXt+X7eedzDkn7Pcz4J+AD4Qdd5r+rSPAEaA+eL8s7LjTcM5/APxZ\n8Hop0AsUhB37dZ733cCtwOEZfp7yv2WLaeSxHWhz93Z3HwUeB+6fts/9wDc9bh8QMbPadAc6z656\n3u7+nLtHg7f7gNVpjnG+JfNvDfD7wN8B59MZXAolc96/CXzf3bsA3D3bzz2Zc3agzMwMKCWePMbT\nG+b8cvfdxM9jJin/W7aYkscq4ETC+5PBtrnuk23mek4PEf/Gks2ues5mtgr4d8BfpTGuVEvm3/pt\nQKWZ/auZtZrZh9MWXWokc87/FXg7cBp4Bfi0u8fSE15oUv63TGuYyxQzu4d48tgZdixp8H8Dn3X3\nWPwL6aKRB2wF7gWWAM+b2T53fzPcsFLq3cAh4F3AeuCnZvasuw+EG1Z2W0zJ4xRQl/B+dbBtrvtk\nm6TOycxuAb4G3OfuPWmKLVWSOedm4PEgcdQA7zWzcXf/QXpCTIlkzvsk0OPuQ8CQme0GNgPZmjyS\nOeePAl/yeDGgzcyOAzcC+9MTYihS/rdsMV22OgBsMLN1ZlYAPAg8NW2fp4APB3cq3A70u/uZdAc6\nz6563mZWD3wf+NAC+QZ61XN293Xuvtbd1wJPAr+X5YkDkvtv/IfATjPLM7Ni4DbgtTTHOZ+SOecu\n4iMtzGw5cAPQntYo0y/lf8sWzcjD3cfN7N8DPyZ+h8bX3f1VM/vd4Of/jfhdN+8F2oBLxL+xZLUk\nz/uPgWrgK8E38XHP4mZySZ7zgpPMebv7a2b2I+BlIAZ8zd2veLtnNkjy3/pPgW+Y2SvE7z76rLtn\ndaddM/sO8E6gxsxOAp8H8iF9f8s0w1xEROZsMV22EhGReaLkISIic6bkISIic6bkISIic6bkISIi\nc6bkIZICZjYRdK6dfDwSbP9MML9CJKvpVl2RFDCzi+5eeoXtHUBzts8zENHIQyRNzOxTwErgX8zs\nX4Jtf2VmLcE6E38SboQiydPIQyQFzGyCeAfXSV909+9OH3mYWZW795pZLvA08Cl3fzn9EYvMzaJp\nTyKSZpfdfUsS+z1gZg8T//9iLbCReOsQkYym5CESEjNbB/wnYJu7R83sG0BRuFGJJEc1D5H0GgTK\ngtflwBDQH3R7vS+0qETmSCMPkdRYYmaHEt7/yN0fAXYBPzKz0+5+j5kdBF4nvurb3jACFbkWKpiL\niMic6bKViIjMmZKHiIjMmZKHiIjMmZKHiIjMmZKHiIjMmZKHiIjMmZKHiIjMmZKHiIjM2f8PO1+v\nvjeJcncAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x127705550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eta_set, mistake_set)\n",
    "plt.ylabel('Number of Mistakes');\n",
    "plt.xlabel('Eta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 1 POINT ACT (8) Choose eta.\n",
    "eta = 0.7\n",
    "weight, mistakes = WeightedMajority(data, label , eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Mistakes\n",
      " 505 \n",
      "\n",
      "Error Rate\n",
      " 0.2542799597180262 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Number of Mistakes\\n', sum(mistakes), '\\n')\n",
    "print('Error Rate\\n', sum(mistakes)/num_docs, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 PONITS Sanity Check\n",
    "As before, we want to know if this is the best one can hope to do with WM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of weights\n",
      " 4.48892491307e-260 \n",
      "\n",
      "Max weight, Argmax weight, Leading Weight\n",
      " 4.48892491307e-260 , 8711 , dod \n",
      "\n",
      "Min mistake, Argmin mistake, Best Word\n",
      " 496.0 , 8711 , dod \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1 POINT ACT (9) Get the sum of the weight vector.\n",
    "sum_weight = sum(weight)\n",
    "\n",
    "print('Sum of weights\\n', sum_weight, '\\n')\n",
    "\n",
    "# 1 POINT ACT (10) List the maximum weight, the coordinate that achieves this maximum, and the word it corresponds to.\n",
    "max_weight = max(weight)\n",
    "index_max_weight = np.argmax(weight)\n",
    "max_word = words_found[index_max_weight]\n",
    "\n",
    "print('Max weight, Argmax weight, Leading Weight\\n', \n",
    "      max_weight, ',', index_max_weight, ',', max_word, '\\n')\n",
    "\n",
    "# Does this make sense?\n",
    "# 1 POINT ACT (11) Create an array that for the i^th coordinate represents \n",
    "# the number of mistakes made if following the recommendation of word i all through.\n",
    "mistake_for_words = (num_docs-label.dot(data))/2\n",
    "\n",
    "# 1 POINT ACT (12) List the minimum value at any coordinate of mistake_for_words, the coordinate that achieves it,\n",
    "# and the word it corresponds to.\n",
    "mis_weight = min(mistake_for_words)\n",
    "index_mis_weight = np.argmin(mistake_for_words)\n",
    "mis_word = words_found[index_mis_weight]\n",
    "print('Min mistake, Argmin mistake, Best Word\\n', \n",
    "      mis_weight, ',', index_mis_weight, ',', mis_word, '\\n')\n",
    "\n",
    "# Checks\n",
    "assert(mis_word == max_word)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Words for Motorcycles\n",
      " ['dod' 'bike' 'ride'] \n",
      "\n",
      "Words for Autos\n",
      " ['they' 'cars' 'car'] \n",
      "\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1276b8b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# 1 POINT ACT (13) Plot a histogram using mistake_for_words -- x axis is the number of mistakes, y is the number of words.\n",
    "# Preferably, the y axis should have a logarithmic scaling.\n",
    "plt.hist(mistake_for_words, normed=False, bins=30)\n",
    "plt.ylabel('Number of Words');\n",
    "plt.xlabel('Number of Mistakes')\n",
    "plt.yscale('log', nonposy='clip')\n",
    "\n",
    "# 1 POINT ACT (14) Find the 3 words that make the most mistakes, and the 3 words that make the least number of mistakes.\n",
    "good_words = np.array(words_found)[np.argsort(mistake_for_words)[:3]]\n",
    "bad_words = np.array(words_found)[np.argsort(mistake_for_words)[-3:]]\n",
    "print('Words for Motorcycles\\n', good_words, '\\n')\n",
    "print('Words for Autos\\n', bad_words, '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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