asl_recognizer.ipynb

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    "# Artificial Intelligence Engineer Nanodegree - Probabilistic Models\n",
    "## Project: Sign Language Recognition System\n",
    "- [Introduction](#intro)\n",
    "- [Part 1 Feature Selection](#part1_tutorial)\n",
    "    - [Tutorial](#part1_tutorial)\n",
    "    - [Features Submission](#part1_submission)\n",
    "    - [Features Unittest](#part1_test)\n",
    "- [Part 2 Train the models](#part2_tutorial)\n",
    "    - [Tutorial](#part2_tutorial)\n",
    "    - [Model Selection Score Submission](#part2_submission)\n",
    "    - [Model Score Unittest](#part2_test)\n",
    "- [Part 3 Build a Recognizer](#part3_tutorial)\n",
    "    - [Tutorial](#part3_tutorial)\n",
    "    - [Recognizer Submission](#part3_submission)\n",
    "    - [Recognizer Unittest](#part3_test)\n",
    "- [Part 4 (OPTIONAL) Improve the WER with Language Models](#part4_info)"
   ]
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    "<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, demonstrating the power 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.\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.  You will derive a variety of feature sets (explored in Part 1), as well as implement three different model selection criterion to determine the optimal number of hidden states for each word model (explored in Part 2). Finally, in Part 3 you will implement the recognizer and compare the effects the different combinations of feature sets and model selection criteria.  \n",
    "\n",
    "At the end of each Part, complete the submission cells with implementations, answer all questions, and pass the unit tests.  Then submit the completed notebook for review!"
   ]
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    "<a id='part1_tutorial'></a>\n",
    "## PART 1: Data\n",
    "\n",
    "### Features Tutorial\n",
    "##### Load the initial database\n",
    "A data handler designed for this database is provided in the student codebase 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.  We'll use those 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, you will create additional feature sets for experimentation. "
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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",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </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",
       "    </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",
       "    </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",
       "    </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",
       "    </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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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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"
      ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from asl_data import AslDb\n",
    "\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"
   ]
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       "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"
      ]
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    "asl.df.ix[98,1]  # look at the data available for an individual frame"
   ]
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   "source": [
    "The frame represented by video 98, frame 1 is shown here:\n",
    "![Video 98](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/098-start.jpg)"
   ]
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    "##### 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.  We can use the raw features already provided or derive our own and add columns to the pandas dataframe `asl.df` for selection. As an example, in the next cell a feature named `'grnd-ry'` is added. This feature is the difference between the right-hand y value and the nose y value, which serves as the \"ground\" right y value. "
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       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
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       "    <tr>\n",
       "      <th>video</th>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "    <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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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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  \n",
       "video frame           \n",
       "98    0          113  \n",
       "      1          113  \n",
       "      2          113  \n",
       "      3          113  \n",
       "      4          113  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df.head()  # the new feature 'grnd-ry' is now in the frames dictionary"
   ]
  },
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   "source": [
    "##### Try it!"
   ]
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     "text": [
      "asl.df sample\n"
     ]
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       "      <th>grnd-lx</th>\n",
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       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>-12</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <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",
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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  "
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      "text/html": [
       "<font color=green>Correct!</font><br/>"
      ],
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       "<IPython.core.display.HTML object>"
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   "source": [
    "from asl_utils import test_features_tryit\n",
    "# DONE add df columns for 'grnd-rx', 'grnd-ly', 'grnd-lx' representing differences between hand and nose locations\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",
    "# test the code\n",
    "test_features_tryit(asl)"
   ]
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    {
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      "text/plain": [
       "[9, 113, -12, 119]"
      ]
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   "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]"
   ]
  },
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   "source": [
    "##### Build the training set\n",
    "Now that we have a feature list defined, we can pass that list 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 we can see the unique words that have been loaded into the training set:"
   ]
  },
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     "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": {
    "deletable": true,
    "editable": true
   },
   "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. We need the `get_word_Xlengths` method 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": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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",
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       "        [ -8,  51,   6,  69],\n",
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       "        [-17,  75,  13,  81],\n",
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       "        [ -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]]), [17, 20, 12])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.get_word_Xlengths('CHOCOLATE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "###### More feature sets\n",
    "So far we have a simple feature set that is enough to get started modeling.  However, we might get better results if we manipulate the raw values a bit more, so we will go ahead and set up some other options now for experimentation later.  For example, we could normalize each speaker's range of motion with grouped statistics using [Pandas stats](http://pandas.pydata.org/pandas-docs/stable/api.html#api-dataframe-stats) functions and [pandas groupby](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.groupby.html).  Below is an example for finding the means of all speaker subgroups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\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>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>man-1</th>\n",
       "      <td>206.248203</td>\n",
       "      <td>218.679449</td>\n",
       "      <td>155.464350</td>\n",
       "      <td>150.371031</td>\n",
       "      <td>175.031756</td>\n",
       "      <td>61.642600</td>\n",
       "      <td>88.728430</td>\n",
       "      <td>-19.567406</td>\n",
       "      <td>157.036848</td>\n",
       "      <td>31.216447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-1</th>\n",
       "      <td>164.661438</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>162.655120</td>\n",
       "      <td>57.245098</td>\n",
       "      <td>60.087364</td>\n",
       "      <td>-11.637255</td>\n",
       "      <td>104.026144</td>\n",
       "      <td>2.006318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>183.214509</td>\n",
       "      <td>176.527232</td>\n",
       "      <td>156.866295</td>\n",
       "      <td>119.835714</td>\n",
       "      <td>170.318973</td>\n",
       "      <td>58.022098</td>\n",
       "      <td>61.813616</td>\n",
       "      <td>-13.452679</td>\n",
       "      <td>118.505134</td>\n",
       "      <td>12.895536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x      left-y     right-x     right-y      nose-x  \\\n",
       "speaker                                                               \n",
       "man-1    206.248203  218.679449  155.464350  150.371031  175.031756   \n",
       "woman-1  164.661438  161.271242  151.017865  117.332462  162.655120   \n",
       "woman-2  183.214509  176.527232  156.866295  119.835714  170.318973   \n",
       "\n",
       "            nose-y    grnd-ry    grnd-rx     grnd-ly    grnd-lx  \n",
       "speaker                                                          \n",
       "man-1    61.642600  88.728430 -19.567406  157.036848  31.216447  \n",
       "woman-1  57.245098  60.087364 -11.637255  104.026144   2.006318  \n",
       "woman-2  58.022098  61.813616 -13.452679  118.505134  12.895536  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_means = asl.df.groupby('speaker').mean()\n",
    "df_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To select a mean that matches by speaker, use the pandas [map](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.map.html) method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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       "      <th>left-x-mean</th>\n",
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       "      <th>video</th>\n",
       "      <th>frame</th>\n",
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       "      <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": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df['left-x-mean']= asl.df['speaker'].map(df_means['left-x'])\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Try it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df_std\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <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",
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       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
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       "      <th>left-x-mean</th>\n",
       "    </tr>\n",
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       "      <th>speaker</th>\n",
       "      <th></th>\n",
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       "      <th>man-1</th>\n",
       "      <td>15.154425</td>\n",
       "      <td>36.328485</td>\n",
       "      <td>18.901917</td>\n",
       "      <td>54.902340</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>16.459943</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>3.549392</td>\n",
       "      <td>3.538330</td>\n",
       "      <td>33.972660</td>\n",
       "      <td>16.764706</td>\n",
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       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>15.388711</td>\n",
       "      <td>28.825025</td>\n",
       "      <td>14.890288</td>\n",
       "      <td>39.649111</td>\n",
       "      <td>4.099760</td>\n",
       "      <td>3.416167</td>\n",
       "      <td>39.128572</td>\n",
       "      <td>16.191324</td>\n",
       "      <td>29.320655</td>\n",
       "      <td>15.050938</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            left-x     left-y    right-x    right-y    nose-x    nose-y  \\\n",
       "speaker                                                                   \n",
       "man-1    15.154425  36.328485  18.901917  54.902340  6.654573  5.520045   \n",
       "woman-1  17.573442  26.594521  16.459943  34.667787  3.549392  3.538330   \n",
       "woman-2  15.388711  28.825025  14.890288  39.649111  4.099760  3.416167   \n",
       "\n",
       "           grnd-ry    grnd-rx    grnd-ly    grnd-lx  left-x-mean  \n",
       "speaker                                                           \n",
       "man-1    53.487999  20.269032  36.572749  15.080360          0.0  \n",
       "woman-1  33.972660  16.764706  27.117393  17.328941          0.0  \n",
       "woman-2  39.128572  16.191324  29.320655  15.050938          0.0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<font color=green>Correct!</font><br/>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_utils import test_std_tryit\n",
    "# DONE Create a dataframe named `df_std` with standard deviations grouped by speaker\n",
    "df_std = asl.df.groupby('speaker').std()\n",
    "\n",
    "# test the code\n",
    "test_std_tryit(df_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part1_submission'></a>\n",
    "### Features Implementation Submission\n",
    "Implement four feature sets and answer the question that follows.\n",
    "- normalized Cartesian coordinates\n",
    "    - use *mean* and *standard deviation* statistics and the [standard score](https://en.wikipedia.org/wiki/Standard_score) equation to account for speakers with different heights and arm length\n",
    "    \n",
    "- polar coordinates\n",
    "    - calculate polar coordinates with [Cartesian to polar equations](https://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates)\n",
    "    - use the [np.arctan2](https://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.arctan2.html) function and *swap the x and y axes* 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",
    "\n",
    "- delta difference\n",
    "    - as described in Thad's lecture, use the difference in values between one frame and the next frames as features\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) will be helpful for this one\n",
    "\n",
    "- custom features\n",
    "    - These are your own design; combine techniques used above or come up with something else entirely. We look forward to seeing what you come up with! \n",
    "    Some ideas to get you started:\n",
    "        - normalize using a [feature scaling equation](https://en.wikipedia.org/wiki/Feature_scaling)\n",
    "        - normalize the polar coordinates\n",
    "        - adding additional deltas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# DONE add features for normalized by speaker values of left, right, x, y\n",
    "# Name these 'norm-rx', 'norm-ry', 'norm-lx', and 'norm-ly'\n",
    "# using Z-score scaling (X-Xmean)/Xstd\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx','norm-ly']\n",
    "\n",
    "right_x_mean = asl.df['speaker'].map(df_means['right-x'])\n",
    "right_y_mean = asl.df['speaker'].map(df_means['right-y'])\n",
    "left_x_mean = asl.df['speaker'].map(df_means['left-x'])\n",
    "left_y_mean = asl.df['speaker'].map(df_means['left-y'])\n",
    "\n",
    "right_x_std = asl.df['speaker'].map(df_std['right-x'])\n",
    "right_y_std = asl.df['speaker'].map(df_std['right-y'])\n",
    "left_x_std = asl.df['speaker'].map(df_std['left-x'])\n",
    "left_y_std = asl.df['speaker'].map(df_std['left-y'])\n",
    "\n",
    "asl.df['norm-rx'] = (asl.df['right-x'] - right_x_mean) / right_x_std\n",
    "asl.df['norm-ry'] = (asl.df['right-y'] - right_y_mean) / right_y_std\n",
    "asl.df['norm-lx'] = (asl.df['left-x'] - left_x_mean) / left_x_std\n",
    "asl.df['norm-ly'] = (asl.df['left-y'] - left_y_mean) / left_y_std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# DONE add features for polar coordinate values where the nose is the origin\n",
    "# Name these 'polar-rr', 'polar-rtheta', 'polar-lr', and 'polar-ltheta'\n",
    "# Note that 'polar-rr' and 'polar-rtheta' refer to the radius and angle\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
    "\n",
    "grnd_rx = asl.df['grnd-rx']\n",
    "grnd_ry = asl.df['grnd-ry']\n",
    "grnd_lx = asl.df['grnd-lx']\n",
    "grnd_ly = asl.df['grnd-ly']\n",
    "\n",
    "asl.df['polar-rr'] = np.sqrt(np.power(grnd_rx, 2) + np.power(grnd_ry, 2))\n",
    "asl.df['polar-rtheta'] = np.arctan2(grnd_rx, grnd_ry)\n",
    "asl.df['polar-lr'] = np.sqrt(np.power(grnd_lx, 2) + np.power(grnd_ly, 2))\n",
    "asl.df['polar-ltheta'] = np.arctan2(grnd_lx, grnd_ly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# DONE add features for left, right, x, y differences by one time step, i.e. the \"delta\" values discussed in the lecture\n",
    "# Name these 'delta-rx', 'delta-ry', 'delta-lx', and 'delta-ly'\n",
    "\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
    "\n",
    "asl.df['delta-rx'] = asl.df['right-x'].diff().fillna(0)\n",
    "asl.df['delta-ry'] = asl.df['right-y'].diff().fillna(0)\n",
    "asl.df['delta-lx'] = asl.df['left-x'].diff().fillna(0)\n",
    "asl.df['delta-ly'] = asl.df['left-y'].diff().fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# DONE add features of your own design, which may be a combination of the above or something else\n",
    "# Name these whatever you would like\n",
    "\n",
    "# DONE define a list named 'features_custom' for building the training set\n",
    "\n",
    "features_custom = ['delta-polar-rr', 'delta-polar-rtheta', 'delta-polar-lr', 'delta-polar-ltheta']\n",
    "\n",
    "delta_rx = asl.df['delta-rx']\n",
    "delta_ry = asl.df['delta-ry']\n",
    "delta_lx = asl.df['delta-lx']\n",
    "delta_ly = asl.df['delta-ly']\n",
    "\n",
    "asl.df['delta-polar-rr'] = np.sqrt(np.power(delta_rx, 2) + np.power(delta_ry, 2))\n",
    "asl.df['delta-polar-rtheta'] = np.arctan2(delta_rx, delta_ry)\n",
    "asl.df['delta-polar-lr'] = np.sqrt(np.power(delta_lx, 2) + np.power(delta_ly, 2))\n",
    "asl.df['delta-polar-ltheta'] = np.arctan2(delta_lx, delta_ly)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Question 1:**  What custom features did you choose for the features_custom set and why?\n",
    "\n",
    "**Answer 1:** Added a delta-polar feature that takes the differences by one time step (\"delta\" values) and converts them to a polar coordinates. Combining features from #2 and #3 above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part1_test'></a>\n",
    "### Features Unit Testing\n",
    "Run the following unit tests as a sanity check on the defined \"ground\", \"norm\", \"polar\", and 'delta\"\n",
    "feature sets.  The test simply looks for some valid values but is not exhaustive.  However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 0.021s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import unittest\n",
    "# import numpy as np\n",
    "\n",
    "class TestFeatures(unittest.TestCase):\n",
    "\n",
    "    def test_features_ground(self):\n",
    "        sample = (asl.df.ix[98, 1][features_ground]).tolist()\n",
    "        self.assertEqual(sample, [9, 113, -12, 119])\n",
    "\n",
    "    def test_features_norm(self):\n",
    "        sample = (asl.df.ix[98, 1][features_norm]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [ 1.153,  1.663, -0.891,  0.742], 3)\n",
    "\n",
    "    def test_features_polar(self):\n",
    "        sample = (asl.df.ix[98,1][features_polar]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [113.3578, 0.0794, 119.603, -0.1005], 3)\n",
    "\n",
    "    def test_features_delta(self):\n",
    "        sample = (asl.df.ix[98, 0][features_delta]).tolist()\n",
    "        self.assertEqual(sample, [0, 0, 0, 0])\n",
    "        sample = (asl.df.ix[98, 18][features_delta]).tolist()\n",
    "        self.assertTrue(sample in [[-16, -5, -2, 4], [-14, -9, 0, 0]], \"Sample value found was {}\".format(sample))\n",
    "                         \n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestFeatures())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part2_tutorial'></a>\n",
    "## PART 2: Model Selection\n",
    "### Model Selection Tutorial\n",
    "The objective of Model Selection is to tune the number of states for each word HMM prior to testing on unseen data.  In this section you will explore three methods: \n",
    "- Log likelihood using cross-validation folds (CV)\n",
    "- Bayesian Information Criterion (BIC)\n",
    "- Discriminative Information Criterion (DIC) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Train a single word\n",
    "Now that we have built a training set with sequence data, we can \"train\" models for each word.  As a simple starting example, we train a single word 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 seequences. For this example, we *assume* the correct number of hidden states is 3, but that is just a guess.  How do we know what the \"best\" number of states for training is?  We will need to find some model selection technique to choose the best parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "logL = -2331.1138127433196\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)\n",
    "print(\"Number of states trained in model for {} is {}\".format(demoword, model.n_components))\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "hidden state #0\n",
      "mean =  [ -11.45300909   94.109178     19.03512475  102.2030162 ]\n",
      "variance =  [  77.403668    203.35441965   26.68898447  156.12444034]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [ -3.46504869  50.66686933  14.02391587  52.04731066]\n",
      "variance =  [ 49.12346305  43.04799144  39.35109609  47.24195772]\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"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Try it!\n",
    "Experiment by changing the feature set, word, and/or num_hidden_states values in the next cell to see changes in values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHOCOLATE is 3\n",
      "hidden state #0\n",
      "mean =  [ -9.30211403  55.32333876   6.92259936  71.24057775]\n",
      "variance =  [ 16.16920957  46.50917372   3.81388185  15.79446427]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [   0.58333333   87.91666667   12.75        108.5       ]\n",
      "variance =  [  39.41055556   18.74388889    9.855       144.4175    ]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [ -5.40587658  60.1652424    2.32479599  91.3095432 ]\n",
      "variance =  [   7.95073876   64.13103127   13.68077479  129.5912395 ]\n",
      "\n",
      "logL = -601.3291470028641\n"
     ]
    }
   ],
   "source": [
    "my_testword = 'CHOCOLATE'\n",
    "model, logL = train_a_word(my_testword, 3, features_ground) # Experiment here with different parameters\n",
    "show_model_stats(my_testword, model)\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Visualize the hidden states\n",
    "We can plot the means and variances for each state and feature.  Try varying the number of states trained for the HMM model and examine the variances.  Are there some models that are \"better\" than others?  How can you tell?  We would like to hear what you think in the classroom online."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dguy8EjcXFyr+dd7PFcDzuF5QV2CjiDwUzq46QqT6pdqYIMQJdctlwzED1wK7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\n5VsKKeIychv0Et36ivWXjXp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5be9509860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iAVWtUNXXcN3ANUSTh/GqukpVNwJvAf3C6KjAdQ92VNVdqjotXMZUtVRVX1fV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\nIlAEQRAElfwBm+ji+xOtRekAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5be9116e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ei8ijIrJeRPZjXnqAaVWQy5sdquq5KEJ74FavCrodpnXsExFJxijPhar6SCVp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\nhu/IoQWpXM4ptHQfFkWM9jT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OnaF7d+jRA847D/r2hQofoTocjlDgFL8j/KxZA5Mnw8sv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\ncMfvOI6TZ7jjdxzHyTPc8TuO4+QZ/wMBXr6rHUbrvgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5be8fd2d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7u51BuJFR0VyMO5fvA77g1x9MqtSthAbH8RuGYRitC6vxG4Zh5Bhm/IZhGDmG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\nwzCMHMOM3zAMI8f4/9JTPkbW4t0uAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5be8e8c668>"
      ]
     },
     "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(my_testword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#####  ModelSelector class\n",
    "Review the `ModelSelector` class from the codebase found in the `my_model_selectors.py` module.  It is designed to be a strategy pattern for choosing different model selectors.  For the project submission in this section, subclass `SelectorModel` to implement the following model selectors.  In other words, you will write your own classes/functions in the `my_model_selectors.py` module and run them from this notebook:\n",
    "\n",
    "- `SelectorCV `:  Log likelihood with CV\n",
    "- `SelectorBIC`: BIC \n",
    "- `SelectorDIC`: DIC\n",
    "\n",
    "You will train each word in the training set with a range of values for the number of hidden states, and then score these alternatives with the model selector, choosing the \"best\" according to each strategy. The simple case of training with a constant value for `n_components` can be called using the provided `SelectorConstant` subclass as follow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for VEGETABLE is 3\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "word = 'VEGETABLE' # Experiment here with different words\n",
    "model = SelectorConstant(training.get_all_sequences(), training.get_all_Xlengths(), word, n_constant=3).select()\n",
    "print(\"Number of states trained in model for {} is {}\".format(word, model.n_components))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Cross-validation folds\n",
    "If we simply score the model with the Log Likelihood calculated from the feature sequences it has been trained on, we should expect that more complex models will have higher likelihoods. However, that doesn't tell us 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, we can compare scores 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 scored.  This gives us 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. When you implement `SelectorCV`, you will use this technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": 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) # Experiment here with different feature sets\n",
    "word = 'VEGETABLE' # Experiment here with different words\n",
    "word_sequences = training.get_word_sequences(word)\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Tip:** In order to run `hmmlearn` training using the X,lengths tuples on the new folds, subsets must be combined based on the indices given for the folds.  A helper utility has been provided in the `asl_utils` module named `combine_sequences` for this purpose."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Scoring models with other criterion\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 you may find helpful for your implementation.\n",
    "\n",
    "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": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part2_submission'></a>\n",
    "### Model Selection Implementation Submission\n",
    "Implement `SelectorCV`, `SelectorBIC`, and `SelectorDIC` classes in the `my_model_selectors.py` module.  Run the selectors on the following five words. Then answer the questions about your results.\n",
    "\n",
    "**Tip:** The `hmmlearn` library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "words_to_train = ['FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 11 states with time 0.5612156479910482 seconds\n",
      "Training complete for BOOK with 2 states with time 2.0598022360063624 seconds\n",
      "Training complete for VEGETABLE with 14 states with time 1.1879597130027832 seconds\n",
      "Training complete for FUTURE with 2 states with time 1.96829090200481 seconds\n",
      "Training complete for JOHN with 12 states with time 30.645184734996292 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorCV in my_model_selector.py\n",
    "from my_model_selectors import SelectorCV\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\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, \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": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.44815071899211034 seconds\n",
      "Training complete for BOOK with 8 states with time 2.831645194994053 seconds\n",
      "Training complete for VEGETABLE with 9 states with time 0.9953727289976086 seconds\n",
      "Training complete for FUTURE with 9 states with time 2.9195479920017533 seconds\n",
      "Training complete for JOHN with 13 states with time 39.02189624300809 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorBIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\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": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 18.51256914899568 seconds\n",
      "Training complete for BOOK with 14 states with time 119.65364703501109 seconds\n",
      "Training complete for VEGETABLE with 14 states with time 117.18279409699608 seconds\n",
      "Training complete for FUTURE with 14 states with time 120.32522980599606 seconds\n",
      "Training complete for JOHN with 14 states with time 162.93097441500868 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorDIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorDIC\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Question 2:**  Compare and contrast the possible advantages and disadvantages of the various model selectors implemented.\n",
    "\n",
    "**Answer 2:**\n",
    "\n",
    "**Log Likelihood with Cross Validation (CV)**\n",
    "**Advantages**\n",
    "  - Using the cross validation technique helps produce generalized models\n",
    "  - Relatively simple technique\n",
    "**Disadvantages**\n",
    "  - Requires more input data (more data better results)\n",
    "\n",
    "**Bayesian Information Criterion (BIC)**\n",
    "**Advantages**\n",
    "  - Regularizing term helps prevent over-fitting without needing to split the data (like for cross validation) therefore it uses all the input data to train (possibly better performance than CV)\n",
    "**Disadvantages**\n",
    " - Could be more difficult to discern between words\n",
    "\n",
    "**Discrimative Information Criterion**\n",
    "**Advantages**\n",
    "  - better performance/accuracy (as advocated in research paper)\n",
    "**Disadvantages**\n",
    "  - component complexity is not penalized so the HMMs may have larger states than other techniques\n",
    "  - longer compute time for most implementations/data sets\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part2_test'></a>\n",
    "### Model Selector Unit Testing\n",
    "Run the following unit tests as a sanity check on the implemented model selectors.  The test simply looks for valid interfaces  but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 137.673s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_model_selectors import TestSelectors\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestSelectors())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part3_tutorial'></a>\n",
    "## PART 3: Recognizer\n",
    "The objective of this section is to \"put it all together\".  Using the four feature sets created and the three model selectors, you will experiment with the models and present your results.  Instead of training only five specific words as in the previous section, train the entire set with a feature set and model selector strategy.  \n",
    "### Recognizer Tutorial\n",
    "##### Train the full training set\n",
    "The following example trains the entire set with the example `features_ground` and `SelectorConstant` features and model selector.  Use this pattern for you experimentation and final submission cells.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "# autoreload for automatically reloading changes made in my_model_selectors and my_recognizer\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Load 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\n",
    "- the getter methods are `get_all_sequences`, `get_all_Xlengths`, `get_item_sequences` and `get_item_Xlengths`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part3_submission'></a>\n",
    "### Recognizer Implementation Submission\n",
    "For the final project submission, students must implement a recognizer following guidance in the `my_recognizer.py` module.  Experiment with the four feature sets and the three model selection methods (that's 12 possible combinations). You can add and remove cells for experimentation or run the recognizers locally in some other way during your experiments, but retain the results for your discussion.  For submission, you will provide code cells of **only three** interesting combinations for your discussion (see questions below). At least one of these should produce a word error rate of less than 60%, i.e. WER < 0.60 . \n",
    "\n",
    "**Tip:** The hmmlearn library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO implement the recognize method in my_recognizer\n",
    "from my_recognizer import recognize\n",
    "from asl_utils import show_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.550561797752809\n",
      "Total correct: 80 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *NEW                                               JOHN WRITE HOMEWORK\n",
      "    7: *SOMETHING-ONE *GO1 GO *ARRIVE                                JOHN CAN GO CAN\n",
      "   12: *IX *WHAT *CAN CAN                                            JOHN CAN GO CAN\n",
      "   21: JOHN *WRITE *JOHN *FUTURE *CAR *TEACHER *VISIT *WHO           JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *LIKE IX                                          JOHN LIKE IX IX IX\n",
      "   28: JOHN *WHO IX *LIKE *LOVE                                      JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: *VISIT *VISIT *IX *GIVE *MARY *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY *GO *GIVE MARY *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE BUY CAR *NEW                                       FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD *JOHN *WHO BUY HOUSE                                  JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *VISIT VISIT MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *JOHN *ARRIVE *GIVE1 BOOK                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *POSS *IX *IX IX *ARRIVE *BOOK                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *SOMETHING-ONE IX *IX *VISIT *ARRIVE                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *SHOULD IX *IX *IX BOOK                                  JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *IX NEW CAR BREAK-DOWN                                        POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *GO *ARRIVE HAVE *JOHN                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *WHO *LOVE                                                    WOMAN ARRIVE\n",
      "  113: IX CAR *CAR *MARY *BOX                                        IX CAR BLUE SUE BUY\n",
      "  119: *VISIT *BUY1 IX *BOX *GO                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *GIVE1 BOOK                                   JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *STUDENT YESTERDAY WHAT BOOK                             JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "  167: JOHN *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "  174: *CAN *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *BOX                                                     JOHN ARRIVE\n",
      "  184: *GIVE BOY *GIVE1 TEACHER APPLE                                ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *SOMETHING-ONE *VISIT BOX                                JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SOMETHING-ONE *VISIT BOX                                JOHN GIVE GIRL BOX\n",
      "  199: *JOHN CHOCOLATE *GO                                           LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *LOVE *JOHN BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "# TODO Choose a feature set and model selector\n",
    "features = features_ground # change as needed\n",
    "model_selector = SelectorBIC # change as needed\n",
    "\n",
    "# TODO Recognize the test set and display the result with the show_errors method\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": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5449438202247191\n",
      "Total correct: 81 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *GO WRITE *NEW                                                JOHN WRITE HOMEWORK\n",
      "    7: JOHN *PEOPLE GO *ARRIVE                                       JOHN CAN GO CAN\n",
      "   12: JOHN *WHAT *GO1 CAN                                           JOHN CAN GO CAN\n",
      "   21: JOHN *NEW WONT *NOT *GIVE1 *TEACHER *FUTURE *WHO              JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE *LOVE *WHO IX                                       JOHN LIKE IX IX IX\n",
      "   28: JOHN *WHO *FUTURE *WHO IX                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: *VISIT VEGETABLE *GIRL *GIVE *MARY *MARY                      MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *FUTURE1 *JOHN *MARY                              JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE *STUDENT CAR *JOHN                                 FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   74: *IX *VISIT *GIVE MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *HOMEWORK *GIVE1 *GIVE1 BOOK                                  IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE *GIVE *WOMAN *WOMAN IX *ARRIVE *BREAK-DOWN              JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *HAVE IX SOMETHING-ONE *VISIT *BREAK-DOWN                JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *WOMAN IX *WOMAN WOMAN BOOK                              JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *VEGETABLE                                               JOHN LEG\n",
      "  107: JOHN *IX *HAVE *GO *JANA                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN *HOMEWORK                                               WOMAN ARRIVE\n",
      "  113: IX CAR *IX *IX *BUY1                                          IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 *CAR CAR *GO                                    SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *BLAME *CHOCOLATE                             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 *VISIT LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *IX BLAME                                                JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE3 GIVE1 *YESTERDAY *JOHN                           PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *EAT ARRIVE                                                   JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *VISIT *VISIT BOX                                       JOHN GIVE GIRL BOX\n",
      "  193: JOHN *POSS *VISIT BOX                                         JOHN GIVE GIRL BOX\n",
      "  199: *HOMEWORK *VIDEOTAPE *JOHN                                    LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MAN *MAN *LIKE BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "# TODO Choose a feature set and model selector\n",
    "features = features_polar\n",
    "model_selector = SelectorBIC\n",
    "\n",
    "# TODO Recognize the test set and display the result with the show_errors method\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": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5561797752808989\n",
      "Total correct: 79 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE HOMEWORK                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN *PEOPLE GO *BOX                                          JOHN CAN GO CAN\n",
      "   12: JOHN *WHAT *PEOPLE CAN                                        JOHN CAN GO CAN\n",
      "   21: JOHN *HOMEWORK WONT *WHO *BLAME *TEACHER *FUTURE *WHO         JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *TELL IX *WHO IX                                         JOHN LIKE IX IX IX\n",
      "   28: JOHN *TELL IX *TELL *LOVE                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: *IX VEGETABLE *GIRL *GIVE *MARY *MARY                         MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GO *FUTURE1 *JOHN *MARY                                 JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *POSS BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *PREFER *GO MARY                                        JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD FUTURE NOT BUY HOUSE                                  JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL *GIVE1 MARY                                         JOHN WILL VISIT MARY\n",
      "   74: *IX *IX *GO *VISIT                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *BLAME                                            ANN BLAME MARY\n",
      "   84: *BLAME *STUDENT *HOMEWORK *COAT                               IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *THINK *MAN GIVE *IX IX *BUY *BOOK                            JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *HAVE IX SOMETHING-ONE *GO *ARRIVE                       JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN GIVE IX *IX *IX 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 POSS *HAVE *GO *MARY                                    JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *HOMEWORK                                               WOMAN ARRIVE\n",
      "  113: IX *HAVE *IX *MARY *BOX                                       IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 IX *JOHN *GO                                    SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *BLAME *ARRIVE                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *NEW YESTERDAY WHAT BOOK                                 JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "  167: JOHN *MARY *VISIT *BLAME MARY                                 JOHN IX SAY LOVE MARY\n",
      "  171: *IX MARY BLAME                                                JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE3 GIVE1 *YESTERDAY *JOHN                           PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *EAT ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *GO BOY *GIVE1 TEACHER *GIRL                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *JOHN *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  193: JOHN *POSS *YESTERDAY BOX                                     JOHN GIVE GIRL BOX\n",
      "  199: *HOMEWORK CHOCOLATE *TELL                                     LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MAN *MAN *JOHN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import FastSelectorDIC\n",
    "\n",
    "# TODO Choose a feature set and model selector\n",
    "features = features_polar\n",
    "model_selector = FastSelectorDIC\n",
    "\n",
    "# TODO Recognize the test set and display the result with the show_errors method\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Question 3:**  Summarize the error results from three combinations of features and model selectors.  What was the \"best\" combination and why?  What additional information might we use to improve our WER?  For more insight on improving WER, take a look at the introduction to Part 4.\n",
    "\n",
    "**Answer 3:**\n",
    "**Summary**\n",
    "The full results for every combination of features and selectors can be found in full_results.txt. The following is a graph of my main results.\n",
    "<img src=\"files/images/WER_comparison.jpg\">\n",
    "The results show a clear trend that certain features work better than other even across different selectors. The polar features generally worked the best and my custom features fared the worst. Also, the results show that BIC and DIC clearly work better than the Constant and CV selectors.\n",
    "\n",
    "**Best Combination**\n",
    "The DIC selector with the polar features showed the lowest WER and therefore the best result. Amoung the features used, the polar features were shown to contain the most relevant features (where the hands are on the polar plane) and then the DIC selector was able to select the number of stages that maximized the differences between the input data set.\n",
    "\n",
    "**How to improve WER**\n",
    "One potential way of improving the WER rate is to improve the features I'm using. One thing to evaluate is to try different combination of the features that are already being used. Another way of improving the WER rate would be to use Language Models. Language Models can take advantage of the fact that certain words are more likely to be used (for instance the word \"is\" is used more often than \"crate\" in everyday conversation) and certain words are more likely to follow other certain words. For instance, Language Models can take advantage of language syntax."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Improvement: Combine Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.4943820224719101\n",
      "Total correct: 90 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN *PEOPLE *MARY CAN                                        JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *JOHN *JOHN *JOHN *CAR *CAR *CHICKEN *FUTURE             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *JOHN *LOVE IX IX                                        JOHN LIKE IX IX IX\n",
      "   28: JOHN *MARY IX *JOHN IX                                        JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY IX IX                                         JOHN LIKE IX IX IX\n",
      "   36: MARY *JOHN *GIRL *MARY *MARY *JOHN                            MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *MARY *CORN MARY *MARY                                   JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *POSS *FRANK BUY CAR *JOHN                                    FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *JOHN *IX MARY                                            JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *MARY BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *JOHN VISIT MARY                                         JOHN WILL VISIT MARY\n",
      "   74: *IX *MARY *MARY MARY                                          JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *JOHN *CAR BOOK                                         IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *IX IX *IX *IX IX *ARRIVE *BREAK-DOWN                         JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *WOMAN IX *IX *IX 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: JOHN *IX *JOHN *MARY *MARY                                    JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN ARRIVE                                                  WOMAN ARRIVE\n",
      "  113: IX CAR *IX *JOHN *JOHN                                        IX CAR BLUE SUE BUY\n",
      "  119: *MARY *BUY1 IX *JOHN *IX                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *JOHN BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN IX *MARY LOVE MARY                                       JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "  174: *JOHN GROUP GIVE1 *JOHN *JOHN                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *JOHN                                                    JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER *IX                                    ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *JOHN *ARRIVE                                        JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX GIRL BOX                                             JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MAN *IX *WOMAN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import FastSelectorDIC\n",
    "\n",
    "# Choose a feature set and model selector\n",
    "features = features_norm + features_polar + features_delta\n",
    "model_selector = FastSelectorDIC\n",
    "\n",
    "# Recognize the test set and display the result with the show_errors method\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By using the DIC selector with a combination of features (normalized + polar + delta) the WER rate was improved by 3.4% (.49438 vs .52809) against just using the polar features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part3_test'></a>\n",
    "### Recognizer Unit Tests\n",
    "Run the following unit tests as a sanity check on the defined recognizer.  The test simply looks for some valid values but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "..\n",
      "----------------------------------------------------------------------\n",
      "Ran 2 tests in 1670.785s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=2 errors=0 failures=0>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_recognizer import TestRecognize\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestRecognize())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='part4_info'></a>\n",
    "## PART 4: (OPTIONAL)  Improve the WER with Language Models\n",
    "We've squeezed just about as much as we can out of the model and still only get about 50% of the words right! Surely we can do better than that.  Probability to the rescue again in the form of [statistical language models (SLM)](https://en.wikipedia.org/wiki/Language_model).  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. We can use that additional information to make better choices.\n",
    "\n",
    "##### Additional reading and resources\n",
    "- [Introduction to N-grams (Stanford Jurafsky slides)](https://web.stanford.edu/class/cs124/lec/languagemodeling.pdf)\n",
    "- [Speech Recognition Techniques for a Sign Language Recognition System, Philippe Dreuw et al](https://www-i6.informatik.rwth-aachen.de/publications/download/154/Dreuw--2007.pdf) see the improved results of applying LM on *this* data!\n",
    "- [SLM data for *this* ASL dataset](ftp://wasserstoff.informatik.rwth-aachen.de/pub/rwth-boston-104/lm/)\n",
    "\n",
    "##### Optional challenge\n",
    "The recognizer you implemented in Part 3 is equivalent to a \"0-gram\" SLM.  Improve the WER with the SLM data provided with the data set in the link above using \"1-gram\", \"2-gram\", and/or \"3-gram\" statistics. The `probabilities` data you've already calculated will be useful and can be turned into a pandas DataFrame if desired (see next cell).  \n",
    "Good luck!  Share your results with the class!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ALL</th>\n",
       "      <th>ANN</th>\n",
       "      <th>APPLE</th>\n",
       "      <th>ARRIVE</th>\n",
       "      <th>BILL</th>\n",
       "      <th>BLAME</th>\n",
       "      <th>BLUE</th>\n",
       "      <th>BOOK</th>\n",
       "      <th>BORROW</th>\n",
       "      <th>BOX</th>\n",
       "      <th>...</th>\n",
       "      <th>VIDEOTAPE</th>\n",
       "      <th>VISIT</th>\n",
       "      <th>WANT</th>\n",
       "      <th>WHAT</th>\n",
       "      <th>WHO</th>\n",
       "      <th>WILL</th>\n",
       "      <th>WOMAN</th>\n",
       "      <th>WONT</th>\n",
       "      <th>WRITE</th>\n",
       "      <th>YESTERDAY</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2735.278733</td>\n",
       "      <td>-2.139485e+05</td>\n",
       "      <td>-51217.977248</td>\n",
       "      <td>-767.260729</td>\n",
       "      <td>-118678.396694</td>\n",
       "      <td>-1013.623790</td>\n",
       "      <td>-6180.378072</td>\n",
       "      <td>-1634.891173</td>\n",
       "      <td>-6976.872182</td>\n",
       "      <td>-1510.331836</td>\n",
       "      <td>...</td>\n",
       "      <td>-2093.804725</td>\n",
       "      <td>-495.509247</td>\n",
       "      <td>-1689.079794</td>\n",
       "      <td>-803.987359</td>\n",
       "      <td>-280.131858</td>\n",
       "      <td>-14763.276744</td>\n",
       "      <td>-1536.998852</td>\n",
       "      <td>-807.533187</td>\n",
       "      <td>-1134.819056</td>\n",
       "      <td>-484.157370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-9569.334584</td>\n",
       "      <td>-1.893533e+05</td>\n",
       "      <td>-87886.917085</td>\n",
       "      <td>-280.944233</td>\n",
       "      <td>-204661.241248</td>\n",
       "      <td>-717.769027</td>\n",
       "      <td>-12848.060259</td>\n",
       "      <td>-368.492543</td>\n",
       "      <td>-3125.564672</td>\n",
       "      <td>-1176.335301</td>\n",
       "      <td>...</td>\n",
       "      <td>-516.309764</td>\n",
       "      <td>-1202.937168</td>\n",
       "      <td>-2091.318853</td>\n",
       "      <td>-633.792616</td>\n",
       "      <td>-785.172469</td>\n",
       "      <td>-20302.005771</td>\n",
       "      <td>-799.905823</td>\n",
       "      <td>-1188.525508</td>\n",
       "      <td>-204.563693</td>\n",
       "      <td>-868.073821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-12925.511998</td>\n",
       "      <td>-8.329347e+05</td>\n",
       "      <td>-132420.699469</td>\n",
       "      <td>-697.781054</td>\n",
       "      <td>-348303.393783</td>\n",
       "      <td>-1498.582549</td>\n",
       "      <td>-25020.167645</td>\n",
       "      <td>-1243.390757</td>\n",
       "      <td>-7293.793965</td>\n",
       "      <td>-1853.295279</td>\n",
       "      <td>...</td>\n",
       "      <td>-1314.111280</td>\n",
       "      <td>-1459.234495</td>\n",
       "      <td>-3357.501290</td>\n",
       "      <td>-1616.719049</td>\n",
       "      <td>-1460.226770</td>\n",
       "      <td>-26211.972948</td>\n",
       "      <td>-2320.123120</td>\n",
       "      <td>-1837.992873</td>\n",
       "      <td>-2006.094826</td>\n",
       "      <td>-1462.504656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-941.291144</td>\n",
       "      <td>-2.550592e+06</td>\n",
       "      <td>-4858.876577</td>\n",
       "      <td>-702.895218</td>\n",
       "      <td>-23315.016072</td>\n",
       "      <td>-1383.069165</td>\n",
       "      <td>-1888.131187</td>\n",
       "      <td>-2298.524416</td>\n",
       "      <td>-9504.383626</td>\n",
       "      <td>-1265.470321</td>\n",
       "      <td>...</td>\n",
       "      <td>-2914.296461</td>\n",
       "      <td>-597.793501</td>\n",
       "      <td>-5732.201474</td>\n",
       "      <td>-818.540698</td>\n",
       "      <td>-521.709007</td>\n",
       "      <td>-6363.847533</td>\n",
       "      <td>-670.521453</td>\n",
       "      <td>-1207.183177</td>\n",
       "      <td>-3303.561904</td>\n",
       "      <td>-1018.315059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2339.247381</td>\n",
       "      <td>-1.259154e+06</td>\n",
       "      <td>-74174.913397</td>\n",
       "      <td>-219.085323</td>\n",
       "      <td>-548207.403837</td>\n",
       "      <td>-216.866348</td>\n",
       "      <td>-2446.962533</td>\n",
       "      <td>-326.561255</td>\n",
       "      <td>-1979.452802</td>\n",
       "      <td>-198.689822</td>\n",
       "      <td>...</td>\n",
       "      <td>-837.673460</td>\n",
       "      <td>-168.732921</td>\n",
       "      <td>-772.193610</td>\n",
       "      <td>-215.135917</td>\n",
       "      <td>-482.761999</td>\n",
       "      <td>-17937.117138</td>\n",
       "      <td>-419.227242</td>\n",
       "      <td>-645.278865</td>\n",
       "      <td>-1109.893328</td>\n",
       "      <td>-467.313770</td>\n",
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      "text/plain": [
       "            ALL           ANN          APPLE      ARRIVE           BILL  \\\n",
       "0  -2735.278733 -2.139485e+05  -51217.977248 -767.260729 -118678.396694   \n",
       "1  -9569.334584 -1.893533e+05  -87886.917085 -280.944233 -204661.241248   \n",
       "2 -12925.511998 -8.329347e+05 -132420.699469 -697.781054 -348303.393783   \n",
       "3   -941.291144 -2.550592e+06   -4858.876577 -702.895218  -23315.016072   \n",
       "4  -2339.247381 -1.259154e+06  -74174.913397 -219.085323 -548207.403837   \n",
       "\n",
       "         BLAME          BLUE         BOOK       BORROW          BOX  \\\n",
       "0 -1013.623790  -6180.378072 -1634.891173 -6976.872182 -1510.331836   \n",
       "1  -717.769027 -12848.060259  -368.492543 -3125.564672 -1176.335301   \n",
       "2 -1498.582549 -25020.167645 -1243.390757 -7293.793965 -1853.295279   \n",
       "3 -1383.069165  -1888.131187 -2298.524416 -9504.383626 -1265.470321   \n",
       "4  -216.866348  -2446.962533  -326.561255 -1979.452802  -198.689822   \n",
       "\n",
       "      ...         VIDEOTAPE        VISIT         WANT         WHAT  \\\n",
       "0     ...      -2093.804725  -495.509247 -1689.079794  -803.987359   \n",
       "1     ...       -516.309764 -1202.937168 -2091.318853  -633.792616   \n",
       "2     ...      -1314.111280 -1459.234495 -3357.501290 -1616.719049   \n",
       "3     ...      -2914.296461  -597.793501 -5732.201474  -818.540698   \n",
       "4     ...       -837.673460  -168.732921  -772.193610  -215.135917   \n",
       "\n",
       "           WHO          WILL        WOMAN         WONT        WRITE  \\\n",
       "0  -280.131858 -14763.276744 -1536.998852  -807.533187 -1134.819056   \n",
       "1  -785.172469 -20302.005771  -799.905823 -1188.525508  -204.563693   \n",
       "2 -1460.226770 -26211.972948 -2320.123120 -1837.992873 -2006.094826   \n",
       "3  -521.709007  -6363.847533  -670.521453 -1207.183177 -3303.561904   \n",
       "4  -482.761999 -17937.117138  -419.227242  -645.278865 -1109.893328   \n",
       "\n",
       "     YESTERDAY  \n",
       "0  -484.157370  \n",
       "1  -868.073821  \n",
       "2 -1462.504656  \n",
       "3 -1018.315059  \n",
       "4  -467.313770  \n",
       "\n",
       "[5 rows x 112 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a DataFrame of log likelihoods for the test word items\n",
    "df_probs = pd.DataFrame(data=probabilities)\n",
    "df_probs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Language Model Approach\n",
    "In order to combine statistical language models (SLMs) to the word recognizer used above, the language model log probability (how likely the word or word combination is) times a scaling factor is added to the log likelihood probability from the HMM model. The scaling factor is there because the language model probabilities and the HMM probabilities are on very different scales. The difference can easily be seen by comparing the probabilities in the df_probs table above and the SLM probabilities in the SLM data link above (this data is what I used to get the results below). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Recognizer with Uni-gram Language Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------\n",
      "Features: ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly', 'polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta', 'delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "Model Selector: <class 'my_model_selectors.FastSelectorDIC'>\n",
      "Scale Factor: 30\n",
      "\n",
      "**** WER = 0.4943820224719101\n",
      "Total correct: 90 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN *JOHN *MARY CAN                                          JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *JOHN *JOHN *JOHN *JOHN *CAR *FUTURE *FUTURE             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *JOHN *LOVE IX IX                                        JOHN LIKE IX IX IX\n",
      "   28: JOHN *IX IX *JOHN IX                                          JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY IX IX                                         JOHN LIKE IX IX IX\n",
      "   36: MARY *JOHN *IX *MARY *MARY *JOHN                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *MARY *CORN MARY *MARY                                   JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *JOHN JOHN BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *JOHN *IX MARY                                            JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *JOHN BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *JOHN VISIT MARY                                         JOHN WILL VISIT MARY\n",
      "   74: JOHN *MARY *MARY MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *JOHN *CAR BOOK                                         IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *IX IX *IX *IX IX *ARRIVE *BOOK                               JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *IX IX *IX *MARY BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *WOMAN IX *IX *IX 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: JOHN *IX *JOHN *IX *JOHN                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN ARRIVE                                                  WOMAN ARRIVE\n",
      "  113: IX *JOHN *IX *JOHN *JOHN                                      IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 IX *JOHN *IX                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *JOHN 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 *IX LOVE MARY                                         JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE1 GIVE1 *JOHN *JOHN                                PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *JOHN                                                    JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER *JOHN                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *JOHN *ARRIVE                                        JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX GIRL BOX                                             JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *JOHN *IX *JOHN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_recognizer import recognize_unigram\n",
    "\n",
    "features = features_norm + features_polar + features_delta\n",
    "selector = FastSelectorDIC\n",
    "scale_factor = 30\n",
    "\n",
    "print(\"----------------------------------\")\n",
    "print(\"Features: {}\".format(features))\n",
    "print(\"Model Selector: {}\".format(selector))\n",
    "print(\"Scale Factor: {}\".format(scale_factor))\n",
    "models = train_all_words(features, selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize_unigram(models, test_set, scale_factor)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### Recognizer with Bi-gram Language Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------\n",
      "Features: ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly', 'polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta', 'delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "Model Selector: <class 'my_model_selectors.FastSelectorDIC'>\n",
      "Scale Factor: 40\n",
      "\n",
      "**** WER = 0.46629213483146065\n",
      "Total correct: 95 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN *IX CAN                                              JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *JOHN *FUTURE *JOHN *JOHN *GIVE1 *JOHN *FUTURE           JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   28: JOHN *IX IX *JOHN IX                                          JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX IX IX                                            JOHN LIKE IX IX IX\n",
      "   36: MARY *JOHN *IX IX *IX *IX                                     MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN IX *GIRL MARY *MARY                                      JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *JOHN BUY HOUSE                                   JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *IX *IX *IX                                               JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *JOHN BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *IX VISIT MARY                                           JOHN WILL VISIT MARY\n",
      "   74: JOHN *MARY *MARY MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *ARRIVE *CAR BOOK                                       IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: JOHN IX *IX *IX IX *ARRIVE *BOOK                              JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX *IX 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: JOHN *IX *JOHN *IX *JOHN                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN ARRIVE                                                  WOMAN ARRIVE\n",
      "  113: IX CAR *IX *IX *JOHN                                          IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 IX *JOHN *IX                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *JOHN *LOVE                                   JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN IX *IX LOVE MARY                                         JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *IX BLAME                                                JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE1 GIVE1 *JOHN *JOHN                                PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *BOX                                                     JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER *IX                                    ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *IX *ARRIVE                                          JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX GIRL BOX                                             JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *FUTURE *IX *WOMAN BUY HOUSE                             JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_recognizer import recognize_bigram\n",
    "\n",
    "features = features_norm + features_polar + features_delta\n",
    "selector = FastSelectorDIC\n",
    "scale_factor = 40\n",
    "\n",
    "print(\"----------------------------------\")\n",
    "print(\"Features: {}\".format(features))\n",
    "print(\"Model Selector: {}\".format(selector))\n",
    "print(\"Scale Factor: {}\".format(scale_factor))\n",
    "models = train_all_words(features, selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize_bigram(models, test_set, scale_factor)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Recognizer with Tri-gram Language Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------\n",
      "Features: ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly', 'polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta', 'delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "Model Selector: <class 'my_model_selectors.FastSelectorDIC'>\n",
      "Scale Factor: 40\n",
      "\n",
      "**** WER = 0.4606741573033708\n",
      "Total correct: 96 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN *IX CAN                                              JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *JOHN *JOHN *JOHN *JOHN *CAR *FUTURE *FUTURE             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *LOVE IX IX                                          JOHN LIKE IX IX IX\n",
      "   28: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX IX IX                                            JOHN LIKE IX IX IX\n",
      "   36: MARY *JOHN *IX IX *IX *IX                                     MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN IX *CORN MARY *MARY                                      JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *JOHN BUY HOUSE                                   JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *JOHN *IX *IX                                             JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *JOHN BUY HOUSE                                   JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *IX VISIT MARY                                           JOHN WILL VISIT MARY\n",
      "   74: JOHN *MARY *MARY MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *ARRIVE *CAR BOOK                                       IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: JOHN IX *IX *IX IX *ARRIVE *BOOK                              JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX *IX 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: JOHN *IX *JOHN *IX *JOHN                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN ARRIVE                                                  WOMAN ARRIVE\n",
      "  113: IX CAR *IX *IX *JOHN                                          IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 IX CAR *IX                                        SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *JOHN *LOVE                                   JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN IX *IX LOVE MARY                                         JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "  174: *JOHN *GIVE1 GIVE1 *JOHN *BOX                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *JOHN                                                    JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER *IX                                    ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *IX *ARRIVE                                          JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX GIRL BOX                                             JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *FUTURE *IX *WOMAN BUY HOUSE                             JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "from my_recognizer import recognize_trigram\n",
    "\n",
    "features = features_norm + features_polar + features_delta\n",
    "selector = FastSelectorDIC\n",
    "scale_factor = 40\n",
    "\n",
    "print(\"----------------------------------\")\n",
    "print(\"Features: {}\".format(features))\n",
    "print(\"Model Selector: {}\".format(selector))\n",
    "print(\"Scale Factor: {}\".format(scale_factor))\n",
    "models = train_all_words(features, selector)\n",
    "test_set = asl.build_test(features)\n",
    "probabilities, guesses = recognize_trigram(models, test_set, scale_factor)\n",
    "show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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