asl_recognizer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Project: Sign Language Recognition System\n",
    "- [Introduction](#intro)\n",
    "- [Part 1 Data investigation and feature engineering](#part1)\n",
    "- [Part 2 Model selection](#part2)\n",
    "- [Part 3 Recognizer system](#part3)\n",
    "- [Part 4 Improving the WER with Language Models](#part4)\n",
    "- [Conclusion](#conclusion)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='intro'></a>\n",
    "## Introduction\n",
    "The overall goal of this project is to build a word recognizer for American Sign Language video sequences by making use of probabalistic models.  In particular, this project employs  [hidden Markov models (HMM's)](https://en.wikipedia.org/wiki/Hidden_Markov_model) to analyze a series of measurements taken from videos of American Sign Language (ASL) collected for research (see the [RWTH-BOSTON-104 Database](http://www-i6.informatik.rwth-aachen.de/~dreuw/database-rwth-boston-104.php)).  In this video, the right-hand x and y locations are plotted as the speaker signs the sentence. Click the picture to see a video example.\n",
    "[![ASLR demo](http://www-i6.informatik.rwth-aachen.de/~dreuw/images/demosample.png)](https://drive.google.com/open?id=0B_5qGuFe-wbhUXRuVnNZVnMtam8)\n",
    "\n",
    "The raw data, train, and test sets are pre-defined.  In part 1, a variety of feature sets is constructed to be tested later on. In part 2, three different model selection techniques are used to determine the optimal number of hidden states for each word model. Finally, in Part 3 a recognizer system is built and the different combinations of feature sets and model selection criteria are compared."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1'></a>\n",
    "## PART 1: Data investigation & feature engineering\n",
    "\n",
    "### Loading the initial database\n",
    "A data handler designed for this database is provided as the `AslDb` class in the `asl_data` module. This handler creates the initial [pandas](http://pandas.pydata.org/pandas-docs/stable/) dataframe from the corpus of data included in the `data` directory as well as dictionaries suitable for extracting data in a format friendly to the [hmmlearn](https://hmmlearn.readthedocs.io/en/latest/) library. Those are used to create models in part 2.\n",
    "\n",
    "To start, let's set up the initial database and select an example set of features for the training set.  At the end of Part 1, additional feature sets will be created for experimentation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    },
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "      <th>1</th>\n",
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       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker\n",
       "video frame                                                           \n",
       "98    0         149     181      170      175     161      62  woman-1\n",
       "      1         149     181      170      175     161      62  woman-1\n",
       "      2         149     181      170      175     161      62  woman-1\n",
       "      3         149     181      170      175     161      62  woman-1\n",
       "      4         149     181      170      175     161      62  woman-1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from asl_data import AslDb\n",
    "import copy\n",
    "\n",
    "# Settings to make test iterations faster and easier\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "asl = AslDb() # initializes the database\n",
    "asl.df.head() # displays the first five rows of the asl database, indexed by video and frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "left-x         149\n",
       "left-y         181\n",
       "right-x        170\n",
       "right-y        175\n",
       "nose-x         161\n",
       "nose-y          62\n",
       "speaker    woman-1\n",
       "Name: (98, 1), dtype: object"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df.ix[98,1]  # look at the data available for an individual frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame represented by video 98, frame 1 is shown here:\n",
    "\n",
    "![Video 98](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/098-start.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature selection for training the model\n",
    "The objective of feature selection when training a model is to choose the most relevant variables while keeping the model as simple as possible, thus reducing training time.  The already provided raw features can be used, or custom features can be derived and added to the pandas dataframe `asl.df` for selection. In the next cell the ground features are added. These features stand for the difference between each hand and the nose in both x and y directions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
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       "      <th>video</th>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>-12</td>\n",
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       "      <td>-12</td>\n",
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       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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       "      <th>4</th>\n",
       "      <td>149</td>\n",
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       "      <td>170</td>\n",
       "      <td>175</td>\n",
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       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  \n",
       "video frame                                      \n",
       "98    0          113        9      119      -12  \n",
       "      1          113        9      119      -12  \n",
       "      2          113        9      119      -12  \n",
       "      3          113        9      119      -12  \n",
       "      4          113        9      119      -12  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-rx'] = asl.df['right-x'] - asl.df['nose-x']\n",
    "asl.df['grnd-ly'] = asl.df['left-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-lx'] = asl.df['left-x'] - asl.df['nose-x']\n",
    "asl.df.head()  # the new features are now in the frames dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 113, -12, 119]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# collect the features into a list\n",
    "features_ground = ['grnd-rx','grnd-ry','grnd-lx','grnd-ly']\n",
    " #show a single set of features for a given (video, frame) tuple\n",
    "[asl.df.ix[98,1][v] for v in features_ground]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the training set\n",
    "Now that a feature list is defined, the list can be passed to the `build_training` method to collect the features for all the words in the training set. Each word in the training set has multiple examples from various videos. Below are the unique words that are loaded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training words: ['JOHN', 'WRITE', 'HOMEWORK', 'IX-1P', 'SEE', 'YESTERDAY', 'IX', 'LOVE', 'MARY', 'CAN', 'GO', 'GO1', 'FUTURE', 'GO2', 'PARTY', 'FUTURE1', 'HIT', 'BLAME', 'FRED', 'FISH', 'WONT', 'EAT', 'BUT', 'CHICKEN', 'VEGETABLE', 'CHINA', 'PEOPLE', 'PREFER', 'BROCCOLI', 'LIKE', 'LEAVE', 'SAY', 'BUY', 'HOUSE', 'KNOW', 'CORN', 'CORN1', 'THINK', 'NOT', 'PAST', 'LIVE', 'CHICAGO', 'CAR', 'SHOULD', 'DECIDE', 'VISIT', 'MOVIE', 'WANT', 'SELL', 'TOMORROW', 'NEXT-WEEK', 'NEW-YORK', 'LAST-WEEK', 'WILL', 'FINISH', 'ANN', 'READ', 'BOOK', 'CHOCOLATE', 'FIND', 'SOMETHING-ONE', 'POSS', 'BROTHER', 'ARRIVE', 'HERE', 'GIVE', 'MAN', 'NEW', 'COAT', 'WOMAN', 'GIVE1', 'HAVE', 'FRANK', 'BREAK-DOWN', 'SEARCH-FOR', 'WHO', 'WHAT', 'LEG', 'FRIEND', 'CANDY', 'BLUE', 'SUE', 'BUY1', 'STOLEN', 'OLD', 'STUDENT', 'VIDEOTAPE', 'BORROW', 'MOTHER', 'POTATO', 'TELL', 'BILL', 'THROW', 'APPLE', 'NAME', 'SHOOT', 'SAY-1P', 'SELF', 'GROUP', 'JANA', 'TOY1', 'MANY', 'TOY', 'ALL', 'BOY', 'TEACHER', 'GIRL', 'BOX', 'GIVE2', 'GIVE3', 'GET', 'PUTASIDE']\n"
     ]
    }
   ],
   "source": [
    "training = asl.build_training(features_ground)\n",
    "print(\"Training words: {}\".format(training.words))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training data in `training` is an object of class `WordsData` defined in the `asl_data` module. In addition to the `words` list, data can be accessed with the `get_all_sequences`, `get_all_Xlengths`, `get_word_sequences`, and `get_word_Xlengths` methods. The `get_word_Xlengths` method is needed to train multiple sequences with the `hmmlearn` library. In the following example, notice that there are two lists; the first is a concatenation of all the sequences(the X portion) and the second is a list of the sequence lengths(the Lengths portion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-11,  48,   7, 120],\n",
       "        [-11,  48,   8, 109],\n",
       "        [ -8,  49,  11,  98],\n",
       "        [ -7,  50,   7,  87],\n",
       "        [ -4,  54,   7,  77],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [-10,  59,   7,  71],\n",
       "        [-15,  64,   9,  77],\n",
       "        [-17,  75,  13,  81],\n",
       "        [ -4,  48,  -4, 113],\n",
       "        [ -2,  53,  -4, 113],\n",
       "        [ -4,  55,   2,  98],\n",
       "        [ -4,  58,   2,  98],\n",
       "        [ -1,  59,   2,  89],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -2,  73,   5,  90],\n",
       "        [ -3,  79,  -4,  96],\n",
       "        [-15,  98,  13, 135],\n",
       "        [ -6,  93,  12, 128],\n",
       "        [ -2,  89,  14, 118],\n",
       "        [  5,  90,  10, 108],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,  13, 100],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  7,  85,  17, 111]], dtype=int64), [17, 20, 12])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.get_word_Xlengths('CHOCOLATE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More feature sets\n",
    "So far we have a simple feature set that is enough to get started modeling. However, better results might be achieved if the raw values are manipulated a bit more, so several feature sets are defined below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pandas [map](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.map.html) method is used to create a new feature based on the speaker."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
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       "      <th>left-x</th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
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       "      <td>170</td>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  left-x-mean  \n",
       "video frame                                                   \n",
       "98    0          113        9      119      -12   164.661438  \n",
       "      1          113        9      119      -12   164.661438  \n",
       "      2          113        9      119      -12   164.661438  \n",
       "      3          113        9      119      -12   164.661438  \n",
       "      4          113        9      119      -12   164.661438  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select the means and std's per speaker\n",
    "df_means = asl.df.groupby('speaker').mean()\n",
    "df_stds = asl.df.groupby('speaker').std()\n",
    "# Map the means on the left-x feature\n",
    "asl.df['left-x-mean']= asl.df['speaker'].map(df_means['left-x'])\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This method is extended to create 4 additional feature sets:\n",
    "- normalized Cartesian coordinates:\n",
    "    - to account for speakers with different heights and arm lengths, the *mean* and *standard deviation* statistics and the [standard score](https://en.wikipedia.org/wiki/Standard_score) equation are used.\n",
    "- polar coordinates:\n",
    "    - the [Cartesian to polar equations](https://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates) are used to convert to polar coordinates\n",
    "    - the [np.arctan2](https://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.arctan2.html) function is used and *the x and y axes are swapped* to move the $0$ to $2\\pi$ discontinuity to 12 o'clock instead of 3 o'clock;  in other words, the normal break in radians value from $0$ to $2\\pi$ occurs directly to the left of the speaker's nose, which may be in the signing area and interfere with results.  By swapping the x and y axes, that discontinuity move to directly above the speaker's head, an area not generally used in signing.\n",
    "- delta difference:\n",
    "    - the difference in values between one frame and the next frames is used as feature\n",
    "    - pandas [diff method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.diff.html) and [fillna method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.fillna.html) are helpful for this\n",
    "- combination\n",
    "    - the polar coordinates are scaled resulting in a new feature\n",
    "    - after trial and error, a combination of this feature with the ground and normalized distance features was used. These were added according to experimentally defined weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding features for normalized by speaker values of left, right, x, y\n",
    "# Z-score scaling is used: (X-Xmean)/Xstd\n",
    "asl.df['norm-rx']= (asl.df['right-x'] - asl.df['speaker'].map(df_means['right-x'])) / asl.df['speaker'].map(df_stds['right-x'])\n",
    "asl.df['norm-ry']= (asl.df['right-y'] - asl.df['speaker'].map(df_means['right-y'])) / asl.df['speaker'].map(df_stds['right-y'])\n",
    "asl.df['norm-lx']= (asl.df['left-x'] - asl.df['speaker'].map(df_means['left-x'])) / asl.df['speaker'].map(df_stds['left-x'])\n",
    "asl.df['norm-ly']= (asl.df['left-y'] - asl.df['speaker'].map(df_means['left-y'])) / asl.df['speaker'].map(df_stds['left-y'])\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx','norm-ly']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Adding features for polar coordinate values where the nose is the origin\n",
    "asl.df['polar-rr'] = np.sqrt(asl.df['grnd-rx']**2 + asl.df['grnd-ry']**2)\n",
    "asl.df['polar-rtheta'] = np.arctan2(asl.df['grnd-rx'], asl.df['grnd-ry'])\n",
    "asl.df['polar-lr'] = np.sqrt(asl.df['grnd-lx']**2 + asl.df['grnd-ly']**2)\n",
    "asl.df['polar-ltheta'] = np.arctan2(asl.df['grnd-lx'], asl.df['grnd-ly'])\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Adding features for left, right, x, y differences by one time step\n",
    "asl.df['delta-rx'] = asl.df['grnd-rx'].diff()\n",
    "asl.df['delta-rx'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-ry'] = asl.df['grnd-ry'].diff()\n",
    "asl.df['delta-ry'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-lx'] = asl.df['grnd-lx'].diff()\n",
    "asl.df['delta-lx'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-ly'] = asl.df['grnd-ly'].diff()\n",
    "asl.df['delta-ly'].fillna(value=0.0, axis=0, inplace=True)\n",
    "\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Adding combined features\n",
    "\n",
    "#Delta's of polar coordinates\n",
    "asl.df['delta-rr'] = asl.df['polar-rr'].diff()\n",
    "asl.df['delta-rr'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-rtheta'] = asl.df['polar-rtheta'].diff()\n",
    "asl.df['delta-rtheta'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-lr'] = asl.df['polar-lr'].diff()\n",
    "asl.df['delta-lr'].fillna(value=0.0, axis=0, inplace=True)\n",
    "asl.df['delta-ltheta'] = asl.df['polar-ltheta'].diff()\n",
    "asl.df['delta-ltheta'].fillna(value=0.0, axis=0, inplace=True)\n",
    "\n",
    "#Feature scaling\n",
    "asl.df['scaled_polar-rr'] = asl.df['delta-rr'] / asl.df['delta-rr'].max()\n",
    "asl.df['scaled_polar-rtheta'] = (asl.df['delta-rtheta'] + np.pi)/ (2 * np.pi)\n",
    "asl.df['scaled_polar-lr'] = asl.df['delta-lr'] / asl.df['delta-lr'].max()\n",
    "asl.df['scaled_polar-ltheta'] = (asl.df['delta-ltheta'] + np.pi) / (2 * np.pi)\n",
    "\n",
    "# Scaling function\n",
    "def scale(f):\n",
    "    return (asl.df[f] - asl.df[f].min()) / (asl.df[f].max() - asl.df[f].min())\n",
    "\n",
    "asl.df['features_combination-r1'] = scale('grnd-rx') + 0.5*scale('norm-rx') + asl.df['scaled_polar-rr']\n",
    "asl.df['features_combination-r2'] = scale('grnd-ry') + 0.5*scale('norm-ry') + asl.df['scaled_polar-rtheta']\n",
    "asl.df['features_combination-l1'] = scale('grnd-lx') + 0.5*scale('norm-lx') + asl.df['scaled_polar-lr']\n",
    "asl.df['features_combination-l2'] = scale('grnd-ly') + 0.5*scale('norm-ly') + asl.df['scaled_polar-ltheta']\n",
    "\n",
    "features_combination = ['features_combination-r1', 'features_combination-r2', 'features_combination-l1', 'features_combination-l2']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Further work can include making use of principle component analysis to automatically define a promising feature set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='part2'></a>\n",
    "## PART 2: Model Selection\n",
    "\n",
    "The objective of Model Selection is to tune the number of states for each word HMM prior to testing on unseen data. Three models will be explored:\n",
    "- Log likelihood using cross-validation folds (CV)\n",
    "- Bayesian Information Criterion (BIC)\n",
    "- Discriminative Information Criterion (DIC) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training a single word\n",
    "Now that a training set with sequence data has been built, models can be 'trained' for each word. First a single word is trained using Gaussian hidden Markov models (HMM). By using the `fit` method during training, the [Baum-Welch Expectation-Maximization](https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm) (EM) algorithm is invoked iteratively to find the best estimate for the model *for the number of hidden states specified* from a group of sample sequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "logL = -2331.113812743319\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "from hmmlearn.hmm import GaussianHMM\n",
    "\n",
    "def train_a_word(word, num_hidden_states, features):\n",
    "    \n",
    "    warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "    training = asl.build_training(features)  \n",
    "    X, lengths = training.get_word_Xlengths(word)\n",
    "    model = GaussianHMM(n_components=num_hidden_states, n_iter=1000).fit(X, lengths)\n",
    "    logL = model.score(X, lengths)\n",
    "    return model, logL\n",
    "\n",
    "demoword = 'BOOK'\n",
    "model, logL = train_a_word(demoword, 3, features_ground) # The number of hidden states, 3, is guessed here\n",
    "print(\"Number of states trained in model for {} is {}\".format(demoword, model.n_components))\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The HMM model has been trained and information can be pulled from the model, including means and variances for each feature and hidden state.  The [log likelihood](http://math.stackexchange.com/questions/892832/why-we-consider-log-likelihood-instead-of-likelihood-in-gaussian-distribution) for any individual sample or group of samples can also be calculated with the `score` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "hidden state #0\n",
      "mean =  [ -3.46504869  50.66686933  14.02391587  52.04731066]\n",
      "variance =  [ 49.12346305  43.04799144  39.35109609  47.24195772]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [ -11.45300909   94.109178     19.03512475  102.2030162 ]\n",
      "variance =  [  77.403668    203.35441965   26.68898447  156.12444034]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [ -1.12415027  69.44164191  17.02866283  77.7231196 ]\n",
      "variance =  [ 19.70434594  16.83041492  30.51552305  11.03678246]\n",
      "\n",
      "logL = -2331.113812743319\n"
     ]
    }
   ],
   "source": [
    "def show_model_stats(word, model):\n",
    "    print(\"Number of states trained in model for {} is {}\".format(word, model.n_components))    \n",
    "    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])    \n",
    "    for i in range(model.n_components):  # for each hidden state\n",
    "        print(\"hidden state #{}\".format(i))\n",
    "        print(\"mean = \", model.means_[i])\n",
    "        print(\"variance = \", variance[i])\n",
    "        print()\n",
    "    \n",
    "show_model_stats(demoword, model)\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the hidden states\n",
    "The means and variances for each state and feature can be plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WMDBM2Fzcm3OQnbjCMBLTVXWSqpbjaoS9I/gbCdyrqltVdQ0wPuA2EGcIHlTV\nUlX9B675tpJo8jBeVb/FvWi8BfSJoKMU16zXQVX3qer0SBlT1S2q+rqq7lHVXbhawZBI/nG1mFWq\n+oyqlqnqXOB14LII8U9R1VbAm8AKXFPqKiBPVVup6odVpNUoMYMQPybUwO8WIK+y0KqCV/2Ne3AL\ncd+M65APpT2u4Nrm06pq9HJl22SkeKJpu7wWWKSq8/zxC8BVIpIZRdhK8kLyGs0owQm4wueNgMFc\nhCu08kUkXUTuE5HlIrITVxhAFEauCjap6r7AcWfgzhCj3Qn3Nh1KCa6NOnivtMQ140QiOHp+D9A0\nwn3TgcOHeK8OcVur/nUzjHs0eajUMcHriDTe5Ve4ZshZIrJARG6M4A8RaSYij4vIav/7TANa+Q9a\nw9EZ98FrUOfVuL64cPEXez9X+rxs9HGsE5EHIumqh9SkbIkJMwhxQt3w2GiZgXsDuzDGZCcT/u1o\nJK6pZ4/3019EOkaIYzGuXfyweEQkDVednxKFjlHA0SKyXkTWAw/gCt1zo8pFLfHXfA0wPMSYNFXV\ntcBVuA8gz+ZQBy4cGgQbbkTFHlwTRiWhhU1omDW4N/Ng+s1U9aUwcS8AjsY1q1TS25+PlXW4QryS\no0LcCkQOG/AbdI86D9Xd56q6XlVvUtUOwE+Av4pItwje78R1HA9Q1RbAGf58pN9nDa75M6gzV1V/\nGkFLR1zz7GRVbYYrWG/x4X5eVT7qEzUsW2LCDEISUNUdwP8Aj4jIhf5NKVNEhovI/TWI6rfAaSJy\nr58bqrmI3IYroH/t05qM64R7Q0T6ikiG9zdGRG70b42/AO4RkatEpKmItAOexL3NBlcdFu8e3E4F\nuuK+aO/jtxOAF6l5s1FteAy4V0Q6e4FHiMgI79YcZ3i34Ar5P4SE3YAroIPMw9Vu0kVkGFU3YQA8\nAYwRkQF+Tq8cETlPRL7TDKSqS3z8Y/21uxg3wur1qHMbmVeB34hIa2/8bwu4zcD1ffzM32cX436v\nGuehOkTkssDLxzZcoV7hj0Ovd3PcgIftItIGGBsSXaj/t4FjRORan49METmlmubFvrjOdICTcf1O\noZrTRaQprl8izf82NandNhjMICQJVf0T8HPgHtwoizW4obtv1iCOpcAg3FvmKtyb4CXAD1T144DX\nS4FJuNEhO3Adjv1wtQdU9RVcs88duMJzIa7D9HRV3RKI5zTcAxzcfgT8S1W/9G+H61V1PfAQcL5/\n0KNhu4gDQO7YAAAgAElEQVSUBLZo3+AeAiYC74vILlwHc+XX8M/jmkbW+jzNDAn7FNDTNz9UXvfb\ngQtwnY5XU83voaqzgZuAh3EF4DJcB3wkrsBd+224TuJLVXVTtbmsnt/i8roSeB/X31Cp8QBwsde1\nFTfC558x5KEqTgE+FZES3O9yu/qpa3B9OM/56z0S18mfjWuWnAm8GxLXQ7j+oG0iMt73M5yDu4bf\n4pqxKjv4I9EX+NzXjnoQvjZ2Le5efhQY7PefqFGuGwjVfodgGIZhNA6shmAYhmEAZhAMwzAMjxkE\nwzAMAzCDYBiGYXjqxfTX0ZKXl6eFhYXJlhGW3bt3k5OTk2wZtSJVtZvuuidVtaeqboiP9jlz5mzW\nKCa3SymDUFhYyOzZ3xlGXC+Ido77+kiqajfddU+qak9V3RAf7SIS1SzRKWUQDKMuUJQlbOAL1pJL\nE9rTgva0JJ8WSHClH8NoYJhBMAyPosxnLR+znM2UkEsTDlDObD/tT0/aM4LeZBJpqh3DSG3MIBgG\nzhh8wCJmspJ8mnMxfehJewRhK3tYwLcUsYTt7OFy+tGcpsmWbBhxx0YZGQbwMcuZyUpOoTOjGcwJ\nFJBGGoLQlhzOoDuX04/NlPAk09lY5QSlhpGamEEwGj1zWM1/WEwvOjCM4yP2ExxLPjdwGgq8xhwO\nhF310jBSl5gMgogME5HFIrJM3LrIoe4iIuO9+3wROTnEPV1E5orI27HoMIzasoLNvMNXdOdIfkjv\najuN82nBRfRhC7t5j4V1pNIw6oZaGwS/iMUjwHCgJ3CliPQM8TYc6O630bjZBIPcjlvQxDDqnFLK\neZv5tCWHSzmZ9Cgfhy7kcTpdmcsaFlW5GJ1hpBax1BD6A8tUdYWfXvdl3GIkQUYAz6tjJm41pPYA\nfs7083Dz7htGnfMhS9nOXs6jV41HDg3lGDrQkrf4kh3sTZBCw6hbYhllVMDhS/YVc2ge+qr8FODm\n7X8Qt9xelYtwiMhoXO2C/Px8ioqKYpCcOEpKSuqttupIVe2x6C7JqeDzfnvJX5/BqsVfHlxbsyYU\nZFewvl8pf9/6IccviH7UUapeb0hd7amqG+pWe1KGnYrI+cBGVZ0jIkOr8uuXj5sA0K9fP62vXxs2\n9i8hk0FtdVegPMMnNKOca9sPoVn7rFpryGEpRUcsocvQE+lMdGsBper1htTVnqq6oW61x9JktJbD\n13Dt6M9F4+d04IcisgrX1HSWiPw9Bi2GETVfsIa1bOccjqMZtTcGAKdyNM1pwmQWoWGXaDaM1CEW\ng/AZ0F1EuohIFm5Zu4khfiYCo/xoo4HADlVdp6q/UdWOqlrow/1HVa+JQYthREUZ5XzIUgpoRS8K\nYo4vk3SGcixr2c5C62A2UpxaGwRVLcOtAfwebqTQq6q6wC/ePsZ7mwSswK3R+gRwc4x6DSMmPmcN\nO9nHmRwbt3mJetORI2nOf1hMGeVxidMwkkFMfQiqOglX6AfPPRbYV+CWauIoAopi0WEY0VBKOdNZ\nxlG0oQtt4xZvGsLZ9OBFPmM23zCQLnGL2zDqEvtS2Wg0zGY1JeznTI6J+6ylXTmCQtryCcsptVqC\nkaKYQTAaBfsp42OWczR5dI5j7aASQTiD7pSwn3mHjbQ2jNTBDILRKPiMVezhAGdybMLS6EwbOtKa\nT1hBORUJS8cwEoUZBKPBU0o5n7KSrhxBAa0Slo4gDKYbO9jL/O+MwDaM+o8ZBKPB8wXF7OYAp9M1\n4Wl14wja04KPWUaF1RKMFMMMgtGgqaCCT1hOAa2i/pI4FlwtoTtb2WPfJRgphxkEo0GzgHVsZy+D\n6FZn6yEfSz5HkMt0ltvXy0ZKYQbBaLAoyscs5whyOYYj6yxdQTiNrmxkF8vYVGfpGkasmEEwGixL\n2chGdnEaXeusdlDJCXSgBU35mOV1mq5hxIIZBKPB8jHLaUk2J9ChztNOJ42BHM03bKWYbXWevmHU\nBjMIRoPkG7ayhm0MpEvUK6HFm5PpRFMy+cRqCUaKYAbBaJB8wnKyyeSkw2Zfr1uyyOAUOvM1G9hM\nSdJ0GEa0mEEwGhwb2cUSNtKfQrKSswbUQfpTSAZpzGBFUnUYRjSYQTAaHJ+wnEzSOYXCZEshhyac\nRCe+oNjWXjbqPWYQjAbFDvbyFd9yMp1iXg0tXpzK0QDMtFqCUc8xg2A0KCqbZgb6Qrg+0Ipm9KKA\nOXzDbvYnW45hRCQmgyAiw0RksYgsE5G7wriLiIz37vNF5GR/vpOITBWRhSKyQERuj0WHYQDsYh+f\n8w29KKAl2cmWcxin05UyKviUlcmWYhgRqbVBEJF04BFgONATuFJEeoZ4Gw5099to4FF/vgy4U1V7\nAgOBW8KENYwaMYMVlKMMpluypXyHPHLpSXs+YzVlGTadhVE/iaWG0B9YpqorVPUA8DIwIsTPCOB5\ndcwEWolIe1Vdp6qfA6jqLtyazLGveG40WkrYz2xW04sOtCEn2XLCMoiu7KeMbzuUJluKYYQlljF5\nBXDY0lDFwIAo/BTAoWkgRaQQOAn4NFwiIjIaV7sgPz+foqKiGCQnjpKSknqrrTpSVXtQ94qjD1DW\nqYKsWVsp2luUVF1V0aZXOms6HmDyR1PJKK/b6TTiQUO4V1KNutSe1EHaIpILvA78l6ruDOdHVScA\nEwD69eunQ4cOrTuBNaCoqIj6qq06UlV7pe7d7GcGU+lFB84dcFKyZVXJMezgSaaTMbiAoRyTbDk1\nJtXvlVSkLrXH0mS0Fg77DLSjPxeVHxHJxBmDF1T1nzHoMBo5M1hJKeUMqod9B6F0oCV5G9OZyQob\ncWTUO2IxCJ8B3UWki4hkAVcAE0P8TARG+dFGA4EdqrpORAR4Clikqg/EoMFo5OxgL7NYSS86cATN\nky0nKgpXZVFKuc2EatQ7am0QVLUMuBV4D9cp/KqqLhCRMSIyxnubBKwAlgFPADf786cD1wJnicg8\nv51bWy1G42Uqi1HgTI5NtpSoabYnjd505DNWs9O+XjbqETH1IajqJFyhHzz3WGBfgVvChJsOdTxB\nvdHg2JVbznzWchpdaUWzZMupEWfQnS/5lmks5XxOTLYcwwDsS2UjRVGUFV0PkE0mg+iabDk1phXN\n6MdRzGUN69mRbDmGAZhBMFKUpWxkR+sKhnAMTclMtpxacQbHkE0W7/CVrb1s1AvMIBgpRynlvM9C\nsvcIfTkq2XJqTTaZfJ/jWMt25h72uY5hJAczCEbKMZXFbGUP3ZY0SdpqaPHiRAo4ijZM4Wv2cCDZ\ncoxGTmo/TUajo5htfMpK+nIUrbenJ1tOzAjCuZzAfsqYwtfJlmM0cswgGClDGeVMZD7NacrZ9Ei2\nnLhxJM0ZQBfmsoYlbEi2HKMRYwbBSBmmsZTNlHA+vWiSoh3JkTiTY2hHC/7FF/ZtgpE0zCAYKcFi\nNjCd5fShI904Mtly4k4G6VzCSZRRwT+ZRwUVyZZkNELMIBj1nk3s4g3m0Z6WDOeEZMtJGG3J5Xx6\n8Q1b+ZClyZZjNELMIBj1mr2U8gqzySSdy+lLJqnfkVwVvSigDx35iGXMpzjZcoxGRlKnvzaMqiil\nnH8whx3sYxQDaFHPlsVMFOd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3hzgtDWkY8cQMgmEkihdfhK1b4Wc/O+z0unPPhblz4fPP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x235417f89b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8kRHt7xLchIftItIXuCkqu+j4zwFHicjFvhyFInJyC92L43GD6QDjgEUxbM73\n/5MCIM//T1rTuu0wmCDkCFW9HbgGuBE3y2IdburuM63IYyVwOq5feQ3uTvBrwBdU9c1A1POA+bjZ\nITtwA44TcK0HVPUJXLfPD3GV5zLcgOlpqro1kM+puB9wcPsW8GdV/dDfHdaoag3wa+Ac/0MPw3YR\nqQ9sYe/gfg3MA14UkV24AebI0/AP4bpGNvgyLYxK+1tgrO9+iPj9auBLuEHHi2jh/6Gqi4DvAHfi\nKsAq3AB8PO7D+e0C3ODrXpzvU+VmXFk/AV7EjTdEbNwPfNXbtQ03w+dPKZQhEScDb4tIPe7/crX6\npWtwYzgPen/PxA3yd8d1Sy4Eno/K69e48aA6EbnDjzN8HvgGbrpsDYcH+OMxHnjft47G4GZqRXMx\n7v9wN/BZv39fq0rdQWjxOQTDMAyjc2AtBMMwDAMwQTAMwzA8JgiGYRgGYIJgGIZheNrE8tdhKS0t\n1WHDhuXajJTZvXs3RUVFuTajzWD+aI75oznmj+Yk44/33nuvVkMsbteuBGHYsGEsWvSpacTtjoyu\nZ94OMX80x/zRHPNHc5Lxh4iEWiXauowMI0d8RA3PsJh1bENb8wYdw8gQ7aqFYBgdhW3s5hkWs5+D\nfMAGBtGbzzGKo2K/SdYwsoK1EAwjyxykiadZTB7CPzKF6RzLXvbzOIuopT7X5hmdGBMEw8gyC1jJ\nBrbzRY6nlGJOZhiXcyr55LGQ1S1nYBgZwgTBMLLI39nGG1RxIoM5NrC6dDFdOYnB/I0N7O/SlCAH\nw8gcJgiGkUUq+ZgSujGNsZ8KO4URHKSJDeUtvTfJMDKDCYJhZImd7GMNWzmJIXTl06sr96WIYxjA\nxvIDNGCiYGQfEwTDyBLL2AjAcQlepnYqIzlYAO/z92yZZRiHMEEwjCyxhI0MpBelcd8+CeX0pldd\nHm/zCQexsQQju5ggGEYW2MpuNrIjYesgwqANhexkH39nWxYsM4zDmCAYRhZY4ruLjmVgi3H71uWT\nTx4fsznTZhlGM0wQDCPDKMoSNjCUvvSke4vx8w8Kw+nHx2yyJS2MrGKCYBgZpoadbGU3x1EeOs1R\nlFHHHnty2cgqJgiGkWGWsJE8hGMYEDrNURwBYN1GRlZJSRBEZJqIrBCRKhG5Pka4iMgdPvwDERnn\njw8RkVdFZJmILBWRq1OxwzDaMh+zieGU0oMuodP0pDsD6ckKNmXQMsNoTtKCICL5wF3AdGAscIGI\nRD9+OR3fpZocAAAdRElEQVQY7bdZwN3+eCNwraqOBSYDV8ZIaxjtnjr2sJXdjKLFd5N8iqMoYz11\n7KYhA5YZxqdJpYUwEahS1dWquh94HJgRFWcG8JA6FgK9RWSgqlar6vsAqroLWA6t6GA1jHbCKrYA\nJC0IACut28jIEqm8D6EcWBf4vh6YFCJOOVAdOSAiw4DPAG/HOomIzMK1LigrK6OysjIFk9sG9fX1\nHaIc6aIj+2PpcfvoWiR88Pa7CBIqTcQfitJlsvDmrqVsX7oqw5a2XTry9ZEMmfRHTl+QIyLFwFPA\nD1R1Z6w4qjoXmAswYcIE7Qiv0rNXAjano/rjIE0s5EWOZwhTK44PnS7oj718yN+6beD0is9SQH6G\nLG3bdNTrI1ky6Y9Uuow2AEMC3wf7Y6HiiEghTgweUdU/pWCHYbRJ1lHHfg4yMonuogijKeMAB1lr\nTy0bWSAVQXgXGC0iw0WkC/ANYF5UnHnAJX620WRgh6pWi4gAvwWWq+ovU7DBMNosq9hCHu4hs2QZ\nSl/yyTs0FmEYmSTpLiNVbRSRq4AXgHzgflVdKiKzffg9wHzgbKAK2ANc7pOfBlwMfCgii/2xf1HV\n+cnaYxhtjVVsYQh9Yi51HZYuFHAkfVhNbRotM4zYpDSG4Cvw+VHH7gnsK3BljHRvQMgRNsNoh9Sz\njxp28g8cnXJeI+jPK3zELvZRQrc0WGcYsbEnlQ0jA6zyd/SpjB9EiORh3UZGpjFBMIwMsIotFNGV\nAfRMOa8ySiiiq3UbGRnHBMEw0kwTyiq2MJLS0M8eJEIQRlLKampt9VMjo5ggGEaa2ch29nIgqaeT\n4zGCUvawn2p2pC1Pw4jGBMEw0kwVWxDcYHC6ODyOYN1GRuYwQTCMNFPFZgbRu1Wrm7ZEZDzCBpaN\nTGKCYBhpZDcNbGQHo/z7DNLJCPqznjoaaEx73oYBJgiGkVYid/Cj09hdFGEU/WlC+cS6jYwMYYJg\nGGmkii0U0YWB9Ep73kPoQzcK7KU5RsYwQTCMNHF4umn/tEw3jSafPEZxBCvZTJNNPzUygAmCYaSJ\nTEw3jeZoytjDftZTl7FzGJ0XEwTDSBOZmG4azUj6k4dYt5GREUwQDCNNVLEl7dNNo+lGIcPox8cm\nCEYGMEEwjDSwnT1sZDtH+/cgZ5KjKWMru6mlPuPnMjoXJgiGkQaW+teEH8egjJ/rKC861m1kpBsT\nBMNIA0vYSDm96U2PjJ+rF90ZQE/rNjLSjgmCYaTIFnaxiZ1ZaR1EOIoy1lHHbhqydk6j42OCYBgp\nEukuGsvArJ1zjO82WubPbRjpwATBMFJAUZaykWH0y+rrLcvoyQB68j7r7B0JRtowQTCMFKhhJ1vZ\nndXuInAvzRnHkWxiJxvtHQlGmjBBMIwUWMJG8hDGMCDr5z6OQRSSz/v8PevnNjomJgiGkSQHaWIp\nGxlBaUYfRotHNwo5loEsYSMNHMj6+Y2OhwmCYSTJEjayk32MZ2jObBjHkRzgIEvYmDMbjI6DCYJh\nJEETyhtUUUZPjsrAy3DCUk5vyiixbiMjLZggGEYSLKearezms4zKyFLXYYkMLlezkw1sz5kdRsfA\nBMEwWomivE4VpRTlZDA5muMppzuFvMJHNgXVSAkTBMNoJR+zmc3s4nRGkZfD1kGEbhQylaNZw1Z7\nUM1ICRMEw2gFrnWwkt50z/qzB4kYx5EMoCcvsZz9NObaHKOdYoJgGK1gASvZyA4qOIq8NvTzyUOY\nzrHsZB+vU5Vrc4x2Stu5og2jjVPFZl5jJScymOMpz7U5n2IIfTmRwbzFantXgpEUJgiGEYLt7OFp\nFlNGCWdzXE5nFiXiDMbQlQIe4R3q2JNrc4x2hgmCYbTAbhr4A+/RhHI+4ykkP9cmxaWYrnyTSTTQ\nyIO8ZaJgtAoTBMNIQBVbuIfX2Uw953ISfSnKtUktMpBeXMwkDnCQB3mLTezMtUlGOyElQRCRaSKy\nQkSqROT6GOEiInf48A9EZFzYtIaRS3awl+dZyqO8Qw8K+TanZeV9yenCicJkGmniXl7nGRazjd25\nNsto4xQkm1BE8oG7gLOA9cC7IjJPVZcFok0HRvttEnA3MClkWsPIGvs4QC31VLODpVTzd7YBcDJD\nOZNj2nQ3UTwG0JN/ZApvsop3WcMSNjKS/gylL0PpxxGUtMtyGZkjaUEAJgJVqroaQEQeB2YAwUp9\nBvCQqiqwUER6i8hAYFiItGnjQzawlq2ZyDopNh7VQD0f5NqMNkO6/aHN9g8/u9uE0kQTB2mikSb2\n0UgDB9jDfnaz/1CaUoqo4CiOY1C76CJKRA+6cBbHMJnh/IXVVLGZlWw+FN6NQkroSne6UEg+heSR\nTx55SODPET2Qnq1hdfu9OCYynCMoyeg5UhGEcmBd4Pt6XCugpTjlIdMCICKzgFkAZWVlVFZWttrQ\nT4bvZ9OAtvOwjvZtYlvD+lyb0WbItD9ED3+KgjRBngoFjVDQKJQcEI7YW0iPPXn02JNHt71KExv4\ngA0ZsykR9fX1SV3nLdEVOBbY36U7O3o1sbd7E/u7Kg1d9rKjYA9N+dCUpzTlgYrbwAtsDidV2e/F\n0bh8C72352fs+gBAVZPagPOA3wS+XwzcGRXnOeD0wPdXgAlh0sbaxo8frx2BV199NdcmtCla44+a\nmhr97Gc/q8XFxXrNNddkzqgcEvHHTTfdpBdddFHceGPHjo3ru1dffVXLy8vjpr300kv1hhtuSMXM\nrGG/l+Yk4w9gkYao11MZVN4ADAl8H+yPhYkTJm2H59FHH2XChAkUFxczcOBApk+fzhtvvAHAnDlz\n+OY3v/mpNCJCVdXhJ1GXLVvGl7/8ZXr16kVJSQlTp07lL3/5S7M0+/fvZ86cOYwePZqioiKGDRvG\nFVdcwZo1aw7Fee6555g4cSJFRUX069ePiy66iPXrD9+VPfDAA5x++ukJy3PZZZdRUFBAdfXh9XRm\nz55NcXExxcXFdOnShcLCwkPfp0+fzpo1a5g6deqhY5HtiSeeiHmOuXPnUlpays6dO7n99tsT2tMS\nl112GTfeeGNKebSWf/3Xf+X444+noKCAOXPmpJTX0qVLqaioSItd2SD62m2JiooKfvOb36Tl3DNn\nzuTFF1+koaGBAQOaL0h43XXXMXr0aEpKShgzZgwPPfRQWs7ZHhEnHkkkFCkAPgbOwFXm7wIXqurS\nQJwvAlcBZ+O6hO5Q1Ylh0sY55xZgbVIGty1KgXxgAK48O3Et855ACa4LbRCulf9JVNrxwBKgwYcf\nA2wBanwepbguuY/h0LSSUUChP9cef+6+Pn4t0Ac3rrMWqPPhg70ty4CDQD+f94o4ZcoDTvR5VgOb\nYsSJVaYuwPHAe3HyjWYocADS8kaYYcD+NOUVln44+/sDe+OcuxT3f4l3DYShBBgOcTvfh5H9sgev\n3TAcDYcG/2pTPPdxwHKcPwfjfh8RBgHbgH1AEW4SzEpos9OyItdHaxiqqv1bjBWmGRFvw1X0HwOr\ngBv8sdnAbL8vuNlEq4APgQmJ0naWDfgrUA+cnyDOHODhGMcVGOX3fw/MjxHnbmCB3z8TV/EMiXMe\nwQnBj6KO5+F+vD/13y8D3khg7yW4caGrgSVhy4SrmBQoCOG3B3CV6X7vvzO9ndf762gr8CTQN5Dm\nDzix3AEsAI71x2dF5fVstH8D5/yZ36/AifWPfZ6/98fPARYD24G/ACeEKMvDwJw4YYsC/noSeAjY\nBSyN+g2tAc70+929rXU4Ef9nYH0g7meA930+TwCPR8rVUhn8ea7DicsOn75bHNtHAa/5eLXAE/74\nAu/b3d7fX8fdiDyHu6Gp8/uDffxbcDci+/znnf74GOAlXAW+ApgZwtd9gNV+/3vAbS3Enwdcm636\noLUbIbt/kso714XrjBtOCBtJUAkSThBqgMtjxJnqf0TdgVuB1xKcZ4zPc3iMsJuBt/z+ZSQWhFeA\n24AyX7bxYcpEKwTBx38gqiK7GliIu+vrCtwLPBYIvwJ3t9wV+BWwOF5e0f6NjoMThEbgFz6/7riK\ndjOuBZwPXIqrQLu2UI6wgrAPd/OUD/wHsDAQbw2HBeFW4HVcy28ITszX+7AuONH/Ia6leB5ODCPl\nSlgGv/8O7k66L+5Oe3Yc2x8DbsAJdTeajyFG+7Yf8DWgh/8f/QF4JhBeCXw74I8i3E3H5bgJMZ/B\nic7YOLacgRO4epzwb/efu/3+lBhpuuNauNOyWSe0ZiODgmBPKueGAqBWVVua+jRTRLYHt6jwUoi5\nAH417gfZF/ejS7RIfmkgTax8SmMcb4aIHIkToUdVdRNOHC5pKV0UtVFlPSZkutm4FuZ6VW3AVaLn\n+W5JVPV+Vd0VCDtRRHq10rYgTcBNqtqgqntxLY17VfVtVT2oqg/iukQmp3COIG+o6nxVPYhrEZ4Y\nJ95M4BZV3aaq64A7AmGTcULwK1U9oKp/xHXTRghThjtUdaOqbgOeBU6KY8cBXLfeIFXdp6pvxCuY\nqm5V1adUdY+q7sK1CqbEi49rxaxR1d+paqOq/hV4Cjg/Tv6vqGpv4BkfpxwnbqWq2ltVX4uR7B7g\nb8ALCezosJgg5IZngdJIpZWAJ/2Fe2iLCq8FBsZINxBXcdXhulFixQnmQZw4AwnXV3kxsFxVF/vv\njwAXikhhiLQRSqPKujxkuqHA0wHBXI5rHZWJSL6I3Coiq0RkJ64ygBAil4Atqrov6vzXRon2EEjp\nZQlzA/s1gf09QLc4180gmk/lXhsVtkH97WWM8DBliLajOI7tP8J1Q74jIktF5Io48RCRHiJyr4is\n9f+fBUBv/+BqkIg/huIebA3aeRHEfm2diKz3cS4AHsS1goYC1SLyyxjx/xM31jAzyldtjbktR0kO\nE4Tc8G+4O7BzU8znZWLfHc3EdfXs8XEmisjgOHmswPWLN8tHRPJwzflXQthxCTBCRGpEpAb4Ja7S\nPTtUKVJjHTA9Sky6qeoG4ELcA49nAr1w3VNweFZ9rB/9HlwXRoToyiY6zTrcnXnw/D1U9bFkC6Sq\nyfzgq2k+c+/IqLByEZE44Wkrg6rWqOp3VHUQ8F3gf0RkVJzo1+IGjiepak/gc/54s/9PwB/rcN2f\nQTuLVfV7cWwZDEwDXvY3U3OBK326a4JxReRm3MoKn1fVNr34U5LXRyhMEHKAqu7AicJdInKuv1Mq\nFJHpInJbK7K6GThVRG4Rkb4iUiIi38dV0D/253oZNwj3tIiMF5ECH2+2iFzh74SuA24UkQtFpJuI\nDAB+g5v19N+B84kPD26nACNxT66f5LfjgEdpfbdRMtwD3CIiQ72B/UVkhg8rwQnvVlwl//OotJuA\nEVHHFuNaN/kiMo3EXRgA9wGzRWSSX7urSES+KCIxHyn1/+duuN9egfdhOtaPeBL4iYj08eL//UDY\nW7ixj3/y5/8q7v+VVBkSISLnB24+6nCVepP/Hu3vEtyEh+0i0he4KSq76PjPAUeJyMW+HIUicnIL\n3YvjcYPpAOOARTFs/gnu5uFMVW07SxrkABOEHKGqtwPXADfiZlmsw03RfaYVeawETsf1K6/B3Ql+\nDfiCqr4ZiHoeMB83O2QHbsBxAq71gKo+gev2+SGu8lyGG1w7LeoHciruBxzcvgX8WVU/9HeHNapa\nA/waOMf/0MOwXUTqA9s1LScBf555wIsisgs3wBx56v0hXNfIBl+mhVFpfwuM9d0PEb9fDXwJN+h4\nES38P1R1EfAd4E5cBViFG4CPx304v12AG3zdi/N9qtyMK+snwIu48YaIjfuBr3q7tuFm+PwphTIk\n4mTgbRGpx/1frla/RA1uDOdB7++ZuEH+7rhuyYXA81F5/Ro3HlQnInf4cYbPA9/ATZet4fAAfzzG\nA+/71tEY3EytaH6OazFVBa6/f2ltwTsCST+HYBiGYXQsrIVgGIZhAJl/H8IYEXlLRBpE5LrWpDUM\nwzCySypLV+TjHrA69E4D4AINvNNARI7ATfM6F6hT1f8Km9YwDMPILqm0EA69D8EPWkXeaXAIVd2s\nqu/iHlZpVVrDMAwju2T6fQgpp5XA+xC6d+8+fsiQIbGitSuamprIy7Phmwjmj+aYP5pj/mhOMv74\n+OOPazXE4napCEJW8A9hzAWYMGGCLlr0qWnE7Y7Kysp2tWxxpjF/NMf80RzzR3OS8YeIhFolOtPv\nQ8hEWsNoO0ydCnMz9uCoYWSVVAThXWC0iAwXkS64h0XmZSGtYbQNtm2Dykp4I+76bYbRrki6y0hV\nG0XkKtyqgPnA/aq6VERm+/B7/BIIi3BLIDSJyA9wS9XujJU21cIYRlZZ7tffq6lJHM8w2gkpjSGo\n6nzckgjBY/cE9mtw3UGh0hpGuyIiCNWJVhc3jPaDDd0bRrJYC8HoYJggGEayLPPPUdbWwoHoR20M\no/1hgmAYybJ8OUTmg2/enFtbDCMNmCAYRjLs3g1r18K4ce67dRsZHQATBMNIhhUr3OfUqe7TBMHo\nAJggGEYyRAaU/+Ef3KcJgtEBMEEwjGRYtgzy8+G009x3EwSjA2CCYBjJsHw5jB4NJSXQp489i2B0\nCEwQDCMZli+HY/y73QcMsBaC0SEwQTCM1rJ/P1RVmSAYHQ4TBMNoLVVV0NhogmB0OEwQDKO1RGYY\nmSAYHQwTBMNoLRFBGDPGfQ4Y4B5Uq6/PnU2GkQZMEAyjtSxfDkOHQlGR+z5ggPu0VoLRzjFBMIzW\nsmzZ4e4iMEEwOgwmCIbRGpqa3LIVsQTBnkUw2jkmCIbRGrZuhb17Ydiww8cGDnSf1kIw2jkmCIbR\nGiKtgIgIAPTr55axMEEw2jkmCIbRGmIJQl4elJWZIBjtHhMEw2gNEUEYNKj5cXsWwegAmCAYRmuI\n1UIAEwSjQ5CSIIjINBFZISJVInJ9jHARkTt8+AciMi4QtkZEPhSRxSKyKBU7DCNrbNwIvXpB9+7N\nj5sgGB2AgmQTikg+cBdwFrAeeFdE5qnqskC06cBov00C7vafEaaqam2yNhhG1qmu/nTrAJwgbNrk\npqXmWcPbaJ+kcuVOBKpUdbWq7gceB2ZExZkBPKSOhUBvEYnxazKMdkIiQTh4EGrt/sZovyTdQgDK\ngXWB7+tpfvcfL045UA0o8LKIHATuVdW5sU4iIrOAWQBlZWVUVlamYHLboL6+vkOUI120J39M+uQT\ndo4dy/Ioe/tv3cqxwLvPPsvukSNTOkd78kc2MH80J5P+SEUQUuV0Vd0gIkcAL4nIR6q6IDqSF4q5\nABMmTNCKioosm5l+Kisr6QjlSBftxh+qUFdH95NOoiza3oICuPlmTh4yBFIsS7vxR5YwfzQnk/5I\npctoAzAk8H2wPxYqjqpGPjcDT+O6oAyj7bJjB+zb9+kpp2DrGRkdglQE4V1gtIgMF5EuwDeAeVFx\n5gGX+NlGk4EdqlotIkUiUgIgIkXA54ElKdhiGJkn3pRTMEEwOgRJdxmpaqOIXAW8AOQD96vqUhGZ\n7cPvAeYDZwNVwB7gcp+8DHhaRCI2PKqqzyddCsPIBokEobjYLYdtgmC0Y1IaQ1DV+bhKP3jsnsC+\nAlfGSLcaODGVcxtG1tm40X3GEoTI8fXrs2ePYaQZmzBtGGFJ1EIAGDECVq/Onj2GkWZMEAwjLNXV\n0KMHlJTEDh81Cqqq3Gwkw2iHmCAYRlgiD6W5sa9PM3Kkm4m0bVt27TKMNGGCYBhhqa6OPeU0wqhR\n7nPVquzYYxhpxgTBMMISb9mKCJEnlKuqsmOPYaQZEwTDCEtLgjBihPu0FoLRTjFBMIww1NfDrl2J\nBaF7dygvtxaC0W4xQTCMMLQ05TTCqFHWQjDaLSYIhhGGsIIwcqS1EIx2iwmCYYShNS2ETZtcF5Nh\ntDNMEAwjDBFBSDTtFA7PNLJuI6MdYoJgGGGoroauXaFPn8Tx7FkEox1jgmAYYaiudktcx3tKOYK1\nEIx2jAmCYYShpWcQIvTqBf362cCy0S4xQTCMMGzcGE4QwKaeGu0WEwTDCEPYFgLY1FOj3WKCYBgt\nsW8f1NW1PMMowqhRsG4dNDRk1i7DSDMmCIbREq+84j7Hjg0Xf+RIaGqCNWsyZpJhZAITBMNoiTvv\ndN1F55wTLr5NPTXaKSYIhpGIlSvh+edh9mwoLAyXxpbBNtopJgiGkYi77nJCMGtW+DRHHAHFxdZC\nMNodJgiGEY/6evjd7+D8891DaWERgaOPhv/9X9iyJXP2GUaaSUkQRGSaiKwQkSoRuT5GuIjIHT78\nAxEZFzatYeSchx+GnTvhqqtan/b222HDBjjrLHvHstFuSFoQRCQfuAuYDowFLhCR6GkY04HRfpsF\n3N2KtIaRGxoaYPly+H//D8aNg8mTW5/HlCnw5z+7fL7wBdixI/12GkaaKUgh7USgSlVXA4jI48AM\nYFkgzgzgIVVVYKGI9BaRgcCwEGnTx5w58MgjGck6GSbu3evermUAbcAfqm4D2L/fPZXc1OS+P/JI\ny+sXxePzn4ennoKvfvXwuEKPHtClS/M8o/LPuT/aGOYPz29/C5/7XEZPkYoglAPrAt/XA5NCxCkP\nmRYAEZmFa11QVlZGZWVlqw0dsHcvfYYObXW6TNHY2MiuglRc37FoE/4QQUUgL499Z5zBnvJydg8f\nzu5BgyCJa+4QxcX0uu02+r39NnkNDeTv3UteY+Ph8IgQBWgT/mhDmD8cf//4Y3Y3NVFfX59UPRiG\nNu9lVZ0LzAWYMGGCVlRUtD6TZNJkkMrKSpIqRwelw/ujlWXr8P5oJeYPR5n/zKQ/UhGEDcCQwPfB\n/liYOIUh0hqGYRhZJBVBeBcYLSLDcZX5N4ALo+LMA67yYwSTgB2qWi0iW0Kk/RTvvfderYisTcHm\ntkIpUJtrI9oQ5o/mmD+aY/5oTjL+CNVnnrQgqGqjiFwFvADkA/er6lIRme3D7wHmA2cDVcAe4PJE\naUOcs3+y9rYlRGSRqk7ItR1tBfNHc8wfzTF/NCeT/khpDEFV5+Mq/eCxewL7ClwZNq1hGIaRO+xJ\nZcMwDAMwQcgVc3NtQBvD/NEc80dzzB/NyZg/RGPMgzYMwzA6H9ZCMAzDMAATBMMwDMNjgpBhROR8\nEVkqIk0iMiEq7Cd+tdcVIvKFwPHxIvKhD7tDJNnFdNo+nXHVWxG5X0Q2i8iSwLG+IvKSiKz0n30C\nYTGvk46AiAwRkVdFZJn/nVztj3dWf3QTkXdE5G/eHzf749nxh6ralsENOAY4GqgEJgSOjwX+BnQF\nhgOrgHwf9g4wGRDg/4DpuS5HhnyT78s9Auji/TE213ZlodyfA8YBSwLHbgOu9/vXA79o6TrpCBsw\nEBjn90uAj32ZO6s/BCj2+4XA274uyIo/rIWQYVR1uaquiBE0A3hcVRtU9RPcw3sT/WqwPVV1obr/\n+EPAuVk0OZscWjFXVfcDkVVvOzSqugCIfknCDOBBv/8gh//nMa+TrBiaBVS1WlXf9/u7gOW4xS87\nqz9UVev910K/KVnyhwlC7ki0Euz6GMc7IvF80BkpU9Vqv1/D4bXMOo2PRGQY8BncXXGn9YeI5IvI\nYmAz8JKqZs0fbX610/aAiLwMxHrH4g2q+uds22O0b1RVRaRTzQcXkWLgKeAHqrozOGzW2fyhqgeB\nk0SkN/C0iBwXFZ4xf5ggpAFVPTOJZPFWgt3g96OPd0TCrJjbWdgkIgPVLf44EHd3CJ3ARyJSiBOD\nR1T1T/5wp/VHBFXdLiKvAtPIkj+syyh3zAO+ISJd/aqvo4F3fLNwp4hM9rOLLgE6aivj0Iq5ItIF\nt+rtvBzblCvmAZf6/Us5/D+PeZ3kwL6M4K/x3wLLVfWXgaDO6o/+vmWAiHQHzgI+Ilv+yPWoekff\ngK/g+vUagE3AC4GwG3CzAlYQmEkETACW+LA78U+Ud8QNtxrux76sN+TaniyV+TGgGjjgr41vAf2A\nV4CVwMtA35auk46wAafjBk0/ABb77exO7I8TgL96fywB/s0fz4o/bOkKwzAMA7AuI8MwDMNjgmAY\nhmEAJgiGYRiGxwTBMAzDAEwQDMMwDI8JgmEYhgGYIBiGYRie/w9Kc0wSHcf2HQAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x235406a6240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EUdWlQM8oYW4ETimPsoYRi12b4O1fwAE93J4GNYWMA+Dsce7bhKl3wcA/Bq2RYeyPfals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\nzsIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23540a5ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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I8F3gv0VkdIzgP8QNHE9S1V5A5Jt3sa7PBlz3Z9DOHqr6vRi2DcN1z76qqt1x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\neIqxp3LcWk0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x235409a4eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from matplotlib import (cm, pyplot as plt, mlab)\n",
    "\n",
    "def visualize(word, model):\n",
    "    \"\"\" visualize the input model for a particular word \"\"\"\n",
    "    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])\n",
    "    figures = []\n",
    "    for parm_idx in range(len(model.means_[0])):\n",
    "        xmin = int(min(model.means_[:,parm_idx]) - max(variance[:,parm_idx]))\n",
    "        xmax = int(max(model.means_[:,parm_idx]) + max(variance[:,parm_idx]))\n",
    "        fig, axs = plt.subplots(model.n_components, sharex=True, sharey=False)\n",
    "        colours = cm.rainbow(np.linspace(0, 1, model.n_components))\n",
    "        for i, (ax, colour) in enumerate(zip(axs, colours)):\n",
    "            x = np.linspace(xmin, xmax, 100)\n",
    "            mu = model.means_[i,parm_idx]\n",
    "            sigma = math.sqrt(np.diag(model.covars_[i])[parm_idx])\n",
    "            ax.plot(x, mlab.normpdf(x, mu, sigma), c=colour)\n",
    "            ax.set_title(\"{} feature {} hidden state #{}\".format(word, parm_idx, i))\n",
    "\n",
    "            ax.grid(True)\n",
    "        figures.append(plt)\n",
    "    for p in figures:\n",
    "        p.show()\n",
    "        \n",
    "visualize('CHOCOLATE', model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part2_submission'></a>\n",
    "### Model Selection Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  ModelSelector class\n",
    "`SelectorModel` is designed to be a strategy pattern for choosing different model selectors. Subclasses from `SelectorModel` are implemented to create several model selectors:\n",
    "- `SelectorCV `:  Log likelihood with CV\n",
    "- `SelectorBIC`: BIC \n",
    "- `SelectorDIC`: DIC\n",
    "\n",
    "Each word in the training set is trained with a range of values for the number of hidden states, and then scored with the model selector, choosing the \"best\" model according to each strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "words_to_train = ['CHICKEN', 'FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross-validation folds\n",
    "If the model is simply scored with the Log Likelihood calculated from the feature sequences it has been trained on, it is expected that more complex models will have higher likelihoods. However, that doesn't determine which would have a better likelihood score on unseen data. The model will likely be overfit as complexity is added. To estimate which topology model is better using only the training data, scores can be compared using cross-validation. One technique for cross-validation is to break the training set into \"folds\" and rotate which fold is left out of training. The \"left out\" fold is used as testing data to determine the score. This is a proxy method of finding the best model to use on \"unseen data\". In the following example, a set of word sequences is broken into three folds using the [scikit-learn Kfold](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) class object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train fold indices:[2 3 4 5] Test fold indices:[0 1]\n",
      "Train fold indices:[0 1 4 5] Test fold indices:[2 3]\n",
      "Train fold indices:[0 1 2 3] Test fold indices:[4 5]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "training = asl.build_training(features_ground)\n",
    "word = 'VEGETABLE'\n",
    "word_sequences = training.get_word_sequences(word)\n",
    "all_seq = training.get_all_sequences()\n",
    "split_method = KFold()\n",
    "for cv_train_idx, cv_test_idx in split_method.split(word_sequences):\n",
    "    print(\"Train fold indices:{} Test fold indices:{}\".format(cv_train_idx, cv_test_idx))  # view indices of the folds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A helper utility is used in the `asl_utils` module named `combine_sequences` to retrieve the correct sequences from the split indices list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for CHICKEN with 3 states with time 0.7268389291475614 seconds\n",
      "Training complete for FISH with 4 states with time 0.4670965633576998 seconds\n",
      "Training complete for BOOK with 13 states with time 5.485285816159376 seconds\n",
      "Training complete for VEGETABLE with 3 states with time 2.218377775652698 seconds\n",
      "Training complete for FUTURE with 14 states with time 4.661069005029276 seconds\n",
      "Training complete for JOHN with 6 states with time 56.81728309505979 seconds\n"
     ]
    }
   ],
   "source": [
    "# The SelectorCV class is implemented in my_model_selector.py\n",
    "from my_model_selectors import SelectorCV\n",
    "\n",
    "training = asl.build_training(features_combination)\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorCV(sequences, Xlengths, word, min_n_components=2, max_n_components=15, random_state = 14, verbose=False).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scoring models with other criteria\n",
    "Scoring model topologies with **BIC** balances fit and complexity within the training set for each word. In the BIC equation, a penalty term penalizes complexity to avoid overfitting, so that it is not necessary to also use cross-validation in the selection process. There are a number of references on the internet for this criterion.  These [slides](http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf) include a formula that was used for this implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for CHICKEN with 2 states with time 0.3987755046746315 seconds\n",
      "Training complete for FISH with 3 states with time 0.33281878199977655 seconds\n",
      "Training complete for BOOK with 6 states with time 2.1379755716761792 seconds\n",
      "Training complete for VEGETABLE with 3 states with time 0.8036213466002664 seconds\n",
      "Training complete for FUTURE with 5 states with time 2.577051119990756 seconds\n",
      "Training complete for JOHN with 12 states with time 26.461044290143036 seconds\n"
     ]
    }
   ],
   "source": [
    "# The SelectorBIC class is implemented in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "training = asl.build_training(features_combination)\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorBIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The advantages of scoring model topologies with **DIC** over BIC are presented by Alain Biem in this [reference](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf) (also found [here](https://pdfs.semanticscholar.org/ed3d/7c4a5f607201f3848d4c02dd9ba17c791fc2.pdf)). DIC scores the discriminant ability of a training set for one word against competing words. Instead of a penalty term for complexity, it provides a penalty if model liklihoods for non-matching words are too similar to model likelihoods for the correct word in the word set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for CHICKEN with 2 states with time 2.6359390568677554 seconds\n",
      "Training complete for FISH with 2 states with time 2.6330935606229104 seconds\n",
      "Training complete for BOOK with 15 states with time 4.314156990432821 seconds\n",
      "Training complete for VEGETABLE with 3 states with time 3.1747383485935643 seconds\n",
      "Training complete for FUTURE with 13 states with time 4.722612355226374 seconds\n",
      "Training complete for JOHN with 15 states with time 28.165780228830045 seconds\n"
     ]
    }
   ],
   "source": [
    "# The SelectorDIC class is implemented in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorDIC\n",
    "\n",
    "training = asl.build_training(features_combination)\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorDIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comparison between the 3 presented model selection techniques\n",
    "- Cross validation:\n",
    "    - Advantage: the score is checked using the regular score() function. This is easy to use and relatively inexpensive.    \n",
    "    - Disadvantage: you need enough samples to be able to split the data into meaningful folds.\n",
    "- BIC:\n",
    "    - Advantage: it is quite inexpensive compared to the other techniques and therefore faster.\n",
    "    - Disadvantage: the formula to be calculated isn't as easy to implement, especially the calculation of the number of free parameters.\n",
    "- DIC:\n",
    "    - Advantage: theoretically, it is a more suitable technique for classification tasks than BIC because both of the formula's terms reward better classification performance, unlike BIC (it rewards good scores but punishes for complexity).\n",
    "    - Disadvantage: it is more expensive to calculate sinds all words need to be scored for either the first or the second term of the formula. To overcome this, I suggest using only a portion of the 'other words' in the second term of the formula if the data allows it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3'></a>\n",
    "## PART 3: Recognizer system\n",
    "The objective of this section is to \"put it all together\".  Using the presented four feature sets and the three model selectors, several experiments are conducted. This time, the entire test set is used for training.\n",
    "### Training the full training set\n",
    "The following code is used to train all words with a given feature set and model selector.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "def train_all_words(features, model_selector):\n",
    "    training = asl.build_training(features)  # Experiment here with different feature sets defined in part 1\n",
    "    sequences = training.get_all_sequences()\n",
    "    Xlengths = training.get_all_Xlengths()\n",
    "    model_dict = {}\n",
    "    for word in training.words:\n",
    "        model = model_selector(sequences, Xlengths, word, \n",
    "                        n_constant=3).select()\n",
    "        model_dict[word]=model\n",
    "    return model_dict\n",
    "\n",
    "models = train_all_words(features_ground, SelectorConstant)\n",
    "print(\"Number of word models returned = {}\".format(len(models)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the test set\n",
    "The `build_test` method in `ASLdb` is similar to the `build_training` method already presented, but there are a few differences:\n",
    "- the object is type `SinglesData`\n",
    "- the internal dictionary keys are the index of the test word rather than the word itself (because we don't know the word... yet)\n",
    "- the getter methods are `get_all_sequences`, `get_all_Xlengths`, `get_item_sequences` and `get_item_Xlengths`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of test set items: 178\n",
      "Number of test set sentences: 40\n"
     ]
    }
   ],
   "source": [
    "test_set = asl.build_test(features_ground)\n",
    "print(\"Number of test set items: {}\".format(test_set.num_items))\n",
    "print(\"Number of test set sentences: {}\".format(len(test_set.sentences_index)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_submission'></a>\n",
    "### Recognizer Implementation\n",
    "The recognizer is implemented below, together with the `recognize` function in the `my_recognizer.py` module. Several similar experiments are conducted where different combinations of features and model selectors are tested.\n",
    "\n",
    "The `show_errors` function is used to display the test results of each experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from my_recognizer import recognize\n",
    "from asl_utils import show_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5337078651685393\n",
      "Total correct: 83 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *CORN1 *BUY *NEW-YORK                                         JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN *MARY CAN                                            JOHN CAN GO CAN\n",
      "   12: *IX *DECIDE *GO1 CAN                                          JOHN CAN GO CAN\n",
      "   21: *POSS FISH WONT *SHOULD BUT *CAR *FUTURE *EAT                 JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *FRANK LIKE IX IX IX                                          JOHN LIKE IX IX IX\n",
      "   28: *FRANK *IX IX IX IX                                           JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX *LIKE IX                                         JOHN LIKE IX IX IX\n",
      "   36: *IX VEGETABLE KNOW *BILL *MARY *JOHN                          MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *SOMETHING-ONE *MARY *SELF *NOT *MARY                         JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *IX-1P *SEE BUY *TEACHER SHOULD                               FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *PREFER *LEAVE MARY                                       JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *TELL BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL VISIT MARY                                          JOHN WILL VISIT MARY\n",
      "   74: *IX *MARY *TELL MARY                                          JOHN NOT VISIT MARY\n",
      "   77: *CORN1 BLAME MARY                                             ANN BLAME MARY\n",
      "   84: *JOHN *NEW-YORK *POSS BOOK                                    IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MAN *POSS *WOMAN *GO *WOMAN NEW COAT                         JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SEE *GIVE1 *ALL SOMETHING-ONE WOMAN BOOK                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *MAN *SOMETHING-ONE SOMETHING-ONE WOMAN BOOK             JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS *NEW-YORK CAR BREAK-DOWN                                 POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *POSS                                                    JOHN LEG\n",
      "  107: *LIKE *SUE *NEW *MARY *TELL                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: WOMAN *BUY1                                                   WOMAN ARRIVE\n",
      "  113: *SOMETHING-ONE CAR *SUE SUE *BUY1                             IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 *FUTURE1 *WHAT *GIVE                            SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT YESTERDAY *CHOCOLATE                          JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *FRANK BUY *POSS *DECIDE BOOK                                 JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY *NOT                                               LOVE JOHN WHO\n",
      "  167: JOHN *SOMETHING-ONE *LEAVE LOVE MARY                          JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *SOMETHING-ONE BLAME                                     JOHN MARY BLAME\n",
      "  174: *GIVE1 *GIVE1 GIVE1 *GIRL *WHAT                               PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *NEW                                                     JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER *GIRL                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *SELF *CORN BOX                                         JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *GIVE1 BOX                                        JOHN GIVE GIRL BOX\n",
      "  199: *CORN1 *ARRIVE *FRANK                                         LIKE CHOCOLATE WHO\n",
      "  201: JOHN *SHOULD *WOMAN *WOMAN BUY HOUSE                          JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "features = features_combination\n",
    "model_selector = SelectorCV\n",
    "\n",
    "models = train_all_words(features, model_selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize(models, test_set)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.48314606741573035\n",
      "Total correct: 92 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE HOMEWORK                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO *TOY                                              JOHN CAN GO CAN\n",
      "   12: *TOY *HAVE *PEOPLE CAN                                        JOHN CAN GO CAN\n",
      "   21: *ANN FISH WONT *FUTURE BUT *MANY *CHICKEN CHICKEN             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN *WHO *GO *ANN IX                                         JOHN LIKE IX IX IX\n",
      "   28: *ANN *ANN *GO *ANN IX                                         JOHN LIKE IX IX IX\n",
      "   30: *IX LIKE *MARY *LIKE IX                                       JOHN LIKE IX IX IX\n",
      "   36: *SAY-1P *SUE *YESTERDAY *BILL LIKE *MARY                      MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *SELF *SAY *MARY                                  JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *FRANK *WRITE CAR SHOULD                                FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *THINK BUY HOUSE                                  JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *VISIT VISIT *GIVE2                                       JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *WHO BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL VISIT MARY                                          JOHN WILL VISIT MARY\n",
      "   74: *IX *JOHN VISIT MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME MARY                                                ANN BLAME MARY\n",
      "   84: *CHOCOLATE *LAST-WEEK *VISIT BOOK                             IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MAN *POSS *IX *IX IX NEW COAT                                JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *GIVE1 IX SOMETHING-ONE WOMAN *ARRIVE                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX SOMETHING-ONE WOMAN BOOK                          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  107: *MARY *SUE FRIEND *GO CANDY                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *OLD *BUY1                                                    WOMAN ARRIVE\n",
      "  113: IX CAR *IX *SOMETHING-ONE *BUY1                               IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 IX *WHAT *GO                                    SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *ANN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN *LEAVE *SAY-1P LOVE MARY                                 JOHN IX SAY LOVE MARY\n",
      "  171: *TOY1 *TOY1 BLAME                                             JOHN MARY BLAME\n",
      "  174: *NEW GROUP GIVE1 *APPLE TOY                                   PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *BOX                                                     JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *SELF *FUTURE1 *CAN                                     JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *GIVE1 BOX                                        JOHN GIVE GIRL BOX\n",
      "  199: *ANN *BORROW *ANN                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *THINK *IX *LIKE BUY HOUSE                               JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "features = features_combination\n",
    "model_selector = SelectorBIC\n",
    "\n",
    "models = train_all_words(features, model_selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize(models, test_set)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.47191011235955055\n",
      "Total correct: 94 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE HOMEWORK                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO *TOY                                              JOHN CAN GO CAN\n",
      "   12: *HAVE *DECIDE *GO1 CAN                                        JOHN CAN GO CAN\n",
      "   21: *ANN FISH WONT *PREFER BUT *MANY *CHICKEN CHICKEN             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN *WHO *GO *ANN *ANN                                       JOHN LIKE IX IX IX\n",
      "   28: *ANN *ANN *GO *ANN IX                                         JOHN LIKE IX IX IX\n",
      "   30: *IX LIKE *MARY *MARY *MARY                                    JOHN LIKE IX IX IX\n",
      "   36: *SAY-1P *SAY-1P *YESTERDAY *GIVE *MARY *MARY                  MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *CORN MARY *MARY                                  JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *POSS BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *SEE BUY CAR *FRIEND                                   FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *VISIT VISIT MARY                                         JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *WHO BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL VISIT MARY                                          JOHN WILL VISIT MARY\n",
      "   74: *IX *JOHN VISIT MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME MARY                                                ANN BLAME MARY\n",
      "   84: *CHOCOLATE *STUDENT *VISIT BOOK                               IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE *POSS *IX MAN *GIVE NEW COAT                            JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *GIVE1 IX SOMETHING-ONE WOMAN *ARRIVE                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX SOMETHING-ONE WOMAN BOOK                          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  107: *LIKE *SUE FRIEND *GO CANDY                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *OLD ARRIVE                                                   WOMAN ARRIVE\n",
      "  113: IX CAR BLUE *SOMETHING-ONE *BUY1                              IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 IX *BLAME *GO                                   SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *ANN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN *MARY *SAY-1P LOVE MARY                                  JOHN IX SAY LOVE MARY\n",
      "  171: *TOY1 *TOY1 BLAME                                             JOHN MARY BLAME\n",
      "  174: *GROUP GROUP GIVE1 *GIRL TOY                                  PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *NEW                                                     JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *SELF *FUTURE1 *BUY1                                    JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *GIVE1 BOX                                        JOHN GIVE GIRL BOX\n",
      "  199: *ANN *BORROW *ANN                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *THINK *WOMAN *WOMAN BUY HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "features = features_combination\n",
    "model_selector = SelectorDIC\n",
    "\n",
    "models = train_all_words(features, model_selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize(models, test_set)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison\n",
    "Only the 3 cases with the best results are shown above. Their WER scores are:\n",
    "- features_combination + SelectorCV: 53,37%\n",
    "- features_combination + SelectorBIC: 48,31%\n",
    "- features_combination + SelectorDIC: 47,19%\n",
    "\n",
    "From running all 12 combinations, it shows that there isn't one best model selector that fits all. The BIC technique was superior for 2 of the 4 used feature sets. DIC was superior for the other 2 sets.\n",
    "Regarding running time, the DIC technique clearly takes a lot longer to compute, which confirms the expectations from part 2.\n",
    "The best combo was achieved by using the DIC selector. The difference in WER with the BIC selector for the combination feature set is 1,12%. Depending on the requirements, a choice must be made between WER and running time.\n",
    "\n",
    "The proposed combination for this problem is based on performance alone:\n",
    "- Feature list: features_combination\n",
    "- Model selector: SelectorDIC\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part4_info'></a>\n",
    "## PART 4: Improving the WER with Language Models\n",
    "To further improve the WER, [statistical language models (SLM)](https://en.wikipedia.org/wiki/Language_model) are used.  The basic idea is that each word has some probability of occurrence within the set, and some probability that it is adjacent to specific other words. That additional information can be used to make better choices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# For information purpose\n",
    "#for k in test_set.sentences_index.keys():\n",
    "#    print(k, test_set.sentences_index[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trying to improve the WER with information from the 3-gram language model took 103.07966208457947 seconds\n"
     ]
    }
   ],
   "source": [
    "from my_recognizer import *\n",
    "import copy\n",
    "import arpa\n",
    "import time\n",
    "\n",
    "# Load the provided language model (created for this corpus)\n",
    "models = arpa.loadf(r\"lm\\ukn.3.lm\")\n",
    "lm = models[0]\n",
    "\n",
    "verbose = False # Set this to true to see all intermediate results\n",
    "\n",
    "# Deepcopy guesses to compare results afterwards\n",
    "g = copy.deepcopy(guesses)\n",
    "\n",
    "# Normalize probabilities [0:1] because it can contain positive and negative scores\n",
    "prob_norm = normalize_probabilities(probabilities, verbose=verbose)\n",
    "\n",
    "start = time.time()\n",
    "for k in test_set.sentences_index.keys():\n",
    "    sentence = test_set.sentences_index[k]  # For testing: the longest sentence is the one from video 21.\n",
    "    \n",
    "    # For each word in the sentence, get the words with high probabilities\n",
    "    candidates = get_candidates(prob_norm, g, sentence, test_set, threshold_score=0.98, threshold_number=0, verbose=verbose)\n",
    "    \n",
    "    # Build sentences with all candidate words and score the sentences\n",
    "    sentence_scores = score_sentences(candidates, g, sentence, lm, verbose=verbose)\n",
    "    \n",
    "    # Combine the individual word scores with the top rated sentence scores according to the passed weights\n",
    "    winner, scores = combine_scores(sentence_scores, candidates, sentence, word_weight=1.0, sentence_weight=0.1, verbose=verbose)\n",
    "\n",
    "    # Modify the guesses with the winner's words\n",
    "    for i, idx in enumerate(sentence):\n",
    "        if g[idx] != winner[0][i]:\n",
    "            g[idx] = winner[0][i]\n",
    "\n",
    "    if verbose:\n",
    "        print(\"Winner without SLM:\")\n",
    "        print([guesses[i] for i in sentence])\n",
    "        print(\"Winner with SLM:\")\n",
    "        print(winner[0])\n",
    "        print(\"Correct sentence:\")\n",
    "        print([test_set.wordlist[i] for i in sentence])\n",
    "        print()\n",
    "        print(\"===========================================================================\")\n",
    "        print()\n",
    "\n",
    "end = time.time()\n",
    "print(\"Trying to improve the WER with information from the 3-gram language model took {} seconds\".format(end-start))"
   ]
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     "text": [
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "WRITE      --> WRITE        Correct:WRITE     \n",
      "HOMEWORK   --> HOMEWORK     Correct:HOMEWORK  \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "CAN        --> CAN          Correct:CAN       \n",
      "GO         --> GO           Correct:GO        \n",
      "TOY        --> CAN          Correct:CAN        ---> WIN\n",
      "HAVE       --> JOHN         Correct:JOHN       ---> WIN\n",
      "DECIDE     --> CAN          Correct:CAN        ---> WIN\n",
      "GO1        --> GO1          Correct:GO        \n",
      "CAN        --> CAN          Correct:CAN       \n",
      "ANN        --> JOHN         Correct:JOHN       ---> WIN\n",
      "FISH       --> FISH         Correct:FISH      \n",
      "WONT       --> WONT         Correct:WONT      \n",
      "PREFER     --> PREFER       Correct:EAT       \n",
      "BUT        --> BUT          Correct:BUT       \n",
      "MANY       --> PARTY        Correct:CAN       \n",
      "CHICKEN    --> FUTURE       Correct:EAT       \n",
      "CHICKEN    --> CHICKEN      Correct:CHICKEN   \n",
      "ANN        --> JOHN         Correct:JOHN       ---> WIN\n",
      "WHO        --> LIKE         Correct:LIKE       ---> WIN\n",
      "GO         --> IX           Correct:IX         ---> WIN\n",
      "ANN        --> IX           Correct:IX         ---> WIN\n",
      "ANN        --> IX           Correct:IX         ---> WIN\n",
      "ANN        --> JOHN         Correct:JOHN       ---> WIN\n",
      "ANN        --> LIKE         Correct:LIKE       ---> WIN\n",
      "GO         --> IX           Correct:IX         ---> WIN\n",
      "ANN        --> IX           Correct:IX         ---> WIN\n",
      "IX         --> IX           Correct:IX        \n",
      "IX         --> JOHN         Correct:JOHN       ---> WIN\n",
      "LIKE       --> LIKE         Correct:LIKE      \n",
      "MARY       --> IX           Correct:IX         ---> WIN\n",
      "MARY       --> IX           Correct:IX         ---> WIN\n",
      "MARY       --> IX           Correct:IX         ---> WIN\n",
      "SAY-1P     --> MARY         Correct:MARY       ---> WIN\n",
      "SAY-1P     --> VEGETABLE    Correct:VEGETABLE  ---> WIN\n",
      "YESTERDAY  --> KNOW         Correct:KNOW       ---> WIN\n",
      "GIVE       --> GIVE         Correct:IX        \n",
      "MARY       --> IX           Correct:LIKE      \n",
      "MARY       --> IX           Correct:CORN1     \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "VISIT      --> GIVE2        Correct:IX        \n",
      "CORN       --> GIRL         Correct:THINK     \n",
      "MARY       --> SAY          Correct:MARY       ---> FAIL\n",
      "MARY       --> MARY         Correct:LOVE      \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "POSS       --> POSS         Correct:MUST      \n",
      "BUY        --> BUY          Correct:BUY       \n",
      "HOUSE      --> HOUSE        Correct:HOUSE     \n",
      "FRANK      --> FRANK        Correct:FUTURE    \n",
      "SEE        --> POSS         Correct:JOHN      \n",
      "BUY        --> NEW          Correct:BUY        ---> FAIL\n",
      "CAR        --> CAR          Correct:CAR       \n",
      "FRIEND     --> SHOULD       Correct:SHOULD     ---> WIN\n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "SHOULD     --> SHOULD       Correct:SHOULD    \n",
      "NOT        --> NOT          Correct:NOT       \n",
      "BUY        --> BUY          Correct:BUY       \n",
      "HOUSE      --> HOUSE        Correct:HOUSE     \n",
      "IX         --> IX           Correct:JOHN      \n",
      "VISIT      --> GIVE1        Correct:DECIDE    \n",
      "VISIT      --> VISIT        Correct:VISIT     \n",
      "MARY       --> MARY         Correct:MARY      \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "FUTURE     --> FUTURE       Correct:FUTURE    \n",
      "WHO        --> WHO          Correct:NOT       \n",
      "BUY        --> BUY          Correct:BUY       \n",
      "HOUSE      --> HOUSE        Correct:HOUSE     \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "WILL       --> WILL         Correct:WILL      \n",
      "VISIT      --> VISIT        Correct:VISIT     \n",
      "MARY       --> MARY         Correct:MARY      \n",
      "IX         --> IX           Correct:JOHN      \n",
      "JOHN       --> JOHN         Correct:NOT       \n",
      "VISIT      --> VISIT        Correct:VISIT     \n",
      "MARY       --> MARY         Correct:MARY      \n",
      "ANN        --> ANN          Correct:ANN       \n",
      "BLAME      --> BLAME        Correct:BLAME     \n",
      "MARY       --> MARY         Correct:MARY      \n",
      "CHOCOLATE  --> LOVE         Correct:IX-1P     \n",
      "STUDENT    --> JOHN         Correct:FIND      \n",
      "VISIT      --> GO           Correct:SOMETHING-ONE\n",
      "BOOK       --> NEW-YORK     Correct:BOOK       ---> FAIL\n",
      "GIVE       --> GIVE         Correct:JOHN      \n",
      "POSS       --> POSS         Correct:IX        \n",
      "IX         --> IX           Correct:GIVE      \n",
      "MAN        --> MAN          Correct:MAN       \n",
      "GIVE       --> IX           Correct:IX         ---> WIN\n",
      "NEW        --> NEW          Correct:NEW       \n",
      "COAT       --> COAT         Correct:COAT      \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "GIVE1      --> GIVE1        Correct:GIVE      \n",
      "IX         --> IX           Correct:IX        \n",
      "SOMETHING-ONE --> SOMETHING-ONE   Correct:SOMETHING-ONE\n",
      "WOMAN      --> WOMAN        Correct:WOMAN     \n",
      "ARRIVE     --> BOOK         Correct:BOOK       ---> WIN\n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "IX         --> GIVE         Correct:GIVE       ---> WIN\n",
      "IX         --> IX           Correct:IX        \n",
      "SOMETHING-ONE --> SOMETHING-ONE   Correct:SOMETHING-ONE\n",
      "WOMAN      --> WOMAN        Correct:WOMAN     \n",
      "BOOK       --> BOOK         Correct:BOOK      \n",
      "POSS       --> POSS         Correct:POSS      \n",
      "NEW        --> NEW          Correct:NEW       \n",
      "CAR        --> CAR          Correct:CAR       \n",
      "BREAK-DOWN --> BREAK-DOWN   Correct:BREAK-DOWN\n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "SEE        --> MARY         Correct:LEG       \n",
      "LIKE       --> JOHN         Correct:JOHN       ---> WIN\n",
      "SUE        --> POSS         Correct:POSS       ---> WIN\n",
      "FRIEND     --> FRIEND       Correct:FRIEND    \n",
      "GO         --> MARY         Correct:HAVE      \n",
      "CANDY      --> MARY         Correct:CANDY      ---> FAIL\n",
      "OLD        --> WOMAN        Correct:WOMAN      ---> WIN\n",
      "ARRIVE     --> ARRIVE       Correct:ARRIVE    \n",
      "IX         --> IX           Correct:IX        \n",
      "CAR        --> CAR          Correct:CAR       \n",
      "BLUE       --> BLUE         Correct:BLUE      \n",
      "SOMETHING-ONE --> SUE          Correct:SUE        ---> WIN\n",
      "BUY1       --> BUY1         Correct:BUY       \n",
      "PREFER     --> SUE          Correct:SUE        ---> WIN\n",
      "BUY1       --> BUY1         Correct:BUY       \n",
      "IX         --> IX           Correct:IX        \n",
      "BLAME      --> BLAME        Correct:CAR       \n",
      "GO         --> IX           Correct:BLUE      \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "READ       --> READ         Correct:READ      \n",
      "BOOK       --> BOOK         Correct:BOOK      \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "BUY1       --> BUY1         Correct:BUY       \n",
      "WHAT       --> WHAT         Correct:WHAT      \n",
      "YESTERDAY  --> YESTERDAY    Correct:YESTERDAY \n",
      "BOOK       --> BOOK         Correct:BOOK      \n",
      "ANN        --> JOHN         Correct:JOHN       ---> WIN\n",
      "BUY        --> BUY          Correct:BUY       \n",
      "YESTERDAY  --> YESTERDAY    Correct:YESTERDAY \n",
      "WHAT       --> WHAT         Correct:WHAT      \n",
      "BOOK       --> BOOK         Correct:BOOK      \n",
      "LOVE       --> LOVE         Correct:LOVE      \n",
      "MARY       --> JOHN         Correct:JOHN       ---> WIN\n",
      "WHO        --> WHO          Correct:WHO       \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "MARY       --> IX           Correct:IX         ---> WIN\n",
      "SAY-1P     --> SAY-1P       Correct:SAY       \n",
      "LOVE       --> LOVE         Correct:LOVE      \n",
      "MARY       --> MARY         Correct:MARY      \n",
      "TOY1       --> JOHN         Correct:JOHN       ---> WIN\n",
      "TOY1       --> MARY         Correct:MARY       ---> WIN\n",
      "BLAME      --> BLAME        Correct:BLAME     \n",
      "GROUP      --> JOHN         Correct:PEOPLE    \n",
      "GROUP      --> GIVE1        Correct:GROUP      ---> FAIL\n",
      "GIVE1      --> GIVE1        Correct:GIVE1     \n",
      "GIRL       --> EAT          Correct:JANA      \n",
      "TOY        --> WHAT         Correct:TOY        ---> FAIL\n",
      "SUE        --> JOHN         Correct:JOHN       ---> WIN\n",
      "NEW        --> ARRIVE       Correct:ARRIVE     ---> WIN\n",
      "ALL        --> ALL          Correct:ALL       \n",
      "BOY        --> BOY          Correct:BOY       \n",
      "GIVE1      --> GIVE1        Correct:GIVE      \n",
      "TEACHER    --> TEACHER      Correct:TEACHER   \n",
      "APPLE      --> APPLE        Correct:APPLE     \n",
      "JANA       --> MARY         Correct:JOHN      \n",
      "SELF       --> SELF         Correct:GIVE      \n",
      "FUTURE1    --> PREFER       Correct:GIRL      \n",
      "BUY1       --> ARRIVE       Correct:BOX       \n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "GIVE1      --> GIVE1        Correct:GIVE      \n",
      "GIVE1      --> GIVE1        Correct:GIRL      \n",
      "BOX        --> BOX          Correct:BOX       \n",
      "ANN        --> JOHN         Correct:LIKE      \n",
      "BORROW     --> ARRIVE       Correct:CHOCOLATE \n",
      "ANN        --> WHO          Correct:WHO        ---> WIN\n",
      "JOHN       --> JOHN         Correct:JOHN      \n",
      "THINK      --> MARY         Correct:TELL      \n",
      "WOMAN      --> IX           Correct:MARY      \n",
      "WOMAN      --> WOMAN        Correct:IX-1P     \n",
      "BUY        --> BUY          Correct:BUY       \n",
      "HOUSE      --> HOUSE        Correct:HOUSE     \n",
      "\n",
      "37 samples were changed for the better for a total score inscrease of 0.20786516853932585!\n",
      "6 samples were changed for the worse for a total score decrease of 0.033707865168539325!\n",
      "\n",
      "**** WER = 0.29775280898876405\n",
      "Total correct: 125 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE HOMEWORK                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN FISH WONT *PREFER BUT *PARTY *FUTURE CHICKEN             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE IX IX IX                                            JOHN LIKE IX IX IX\n",
      "   28: JOHN LIKE IX IX IX                                            JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX IX IX                                            JOHN LIKE IX IX IX\n",
      "   36: MARY VEGETABLE KNOW *GIVE *IX *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GIVE2 *GIRL *SAY *MARY                                  JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *POSS BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *POSS *NEW CAR SHOULD                                  FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *GIVE1 VISIT MARY                                         JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *WHO BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL VISIT MARY                                          JOHN WILL VISIT MARY\n",
      "   74: *IX *JOHN VISIT MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME MARY                                                ANN BLAME MARY\n",
      "   84: *LOVE *JOHN *GO *NEW-YORK                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE *POSS *IX MAN IX NEW COAT                               JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *GIVE1 IX SOMETHING-ONE WOMAN BOOK                       JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN GIVE IX SOMETHING-ONE WOMAN BOOK                         JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *MARY                                                    JOHN LEG\n",
      "  107: JOHN POSS FRIEND *MARY *MARY                                  JOHN POSS FRIEND HAVE CANDY\n",
      "  108: WOMAN ARRIVE                                                  WOMAN ARRIVE\n",
      "  113: IX CAR BLUE SUE *BUY1                                         IX CAR BLUE SUE BUY\n",
      "  119: SUE *BUY1 IX *BLAME *IX                                       SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "  167: JOHN IX *SAY-1P LOVE MARY                                     JOHN IX SAY LOVE MARY\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE1 GIVE1 *EAT *WHAT                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *SELF *PREFER *ARRIVE                                   JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *GIVE1 BOX                                        JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *IX *WOMAN BUY HOUSE                               JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "total_samples = 0\n",
    "corrected_samples = 0\n",
    "worsened_samples = 0\n",
    "\n",
    "for i in range(len(guesses)):\n",
    "    if guesses[i] != g[i] and g[i] == test_set.wordlist[i]:\n",
    "        total_samples += 1\n",
    "        corrected_samples += 1\n",
    "        print(\"{0:10} --> {1:10}   Correct:{2:10} ---> WIN\".format(guesses[i], g[i], test_set.wordlist[i]))\n",
    "    elif guesses[i] != g[i] and guesses[i] == test_set.wordlist[i]:\n",
    "        total_samples += 1\n",
    "        worsened_samples += 1\n",
    "        print(\"{0:10} --> {1:10}   Correct:{2:10} ---> FAIL\".format(guesses[i], g[i], test_set.wordlist[i]))\n",
    "    else:\n",
    "        total_samples += 1\n",
    "        print(\"{0:10} --> {1:10}   Correct:{2:10}\".format(guesses[i], g[i], test_set.wordlist[i]))\n",
    "print()\n",
    "print(\"{} samples were changed for the better for a total score inscrease of {}!\".format(corrected_samples, float(corrected_samples)/total_samples))\n",
    "print(\"{} samples were changed for the worse for a total score decrease of {}!\".format(worsened_samples, float(worsened_samples)/total_samples))\n",
    "show_errors(g, test_set)"
   ]
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    "<a id='conclusion'></a>\n",
    "## Conclusion\n",
    "The impact from implementing a 3-gram SLM is significant. The WER is increased from <50% to <30%.\n",
    "\n",
    "Further improvements that are planned in this project:\n",
    "- Applying PCA to define a better feature set\n",
    "- Implementing combinations of different n-gram models"
   ]
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