4_asl_recognizer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Sign Language Recognition System"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notebook version of the project [Sign Language Recognition System](https://github.com/udacity/AIND-Recognizer) from [Udacity's Artificial Intelligence Nanodegree](https://www.udacity.com/course/artificial-intelligence-nanodegree--nd889) <br> \n",
    "\n",
    "The 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. The project comprises three parts: <br>\n",
    "<ol>\n",
    "<li>[Create a variety of feature sets](#part1)</li>\n",
    "<li>[Implement three different model selection criterion to determine the optimal number of hidden states for each word model](#part2)</li>\n",
    "<li>[Implement the recognizer and compare the effects the different combinations of feature sets and model selection criteria](#part3)</li> \n",
    "</ol>\n",
    "\n",
    "\n",
    "This project requires Python 3 and the following Python libraries installed:\n",
    "\n",
    "[NumPy](http://www.numpy.org/), [SciPy](https://www.scipy.org/), [scikit-learn](http://scikit-learn.org/0.17/install.html), [pandas](http://pandas.pydata.org/), [matplotlib](http://matplotlib.org/), [jupyter](http://ipython.org/notebook.html), [hmmlearn](http://hmmlearn.readthedocs.io/en/latest/)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1'></a>\n",
    "# 1: Data and Features\n",
    "\n",
    "The data handler class `AslDb` creates the initial pandas dataframe as well as dictionaries suitable for extracting data to the [hmmlearn](https://hmmlearn.readthedocs.io/en/latest/) library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
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       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
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       "      <td>170</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "    <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",
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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"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from asl_recognizer.asl_data import AslDb\n",
    "\n",
    "asl = AslDb()  # initializes the database\n",
    "asl.df.head()  # displays the first rows of the asl database, indexed by video and frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "left-x         149\n",
       "left-y         181\n",
       "right-x        170\n",
       "right-y        175\n",
       "nose-x         161\n",
       "nose-y          62\n",
       "speaker    woman-1\n",
       "Name: (98, 1), dtype: object"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df.loc[98, 1]  # look at the data available for an individual frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame represented by video 98, frame 1 is shown here:\n",
    "![Video 98](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/098-start.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Features example: ground position (hand relative to nose)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "      <th>grnd-lx</th>\n",
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       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>-12</td>\n",
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       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>119</td>\n",
       "      <td>9</td>\n",
       "      <td>-12</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>119</td>\n",
       "      <td>9</td>\n",
       "      <td>-12</td>\n",
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       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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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-ly  grnd-rx  grnd-lx  \n",
       "video frame                                      \n",
       "98    0          113      119        9      -12  \n",
       "      1          113      119        9      -12  \n",
       "      2          113      119        9      -12  \n",
       "      3          113      119        9      -12  \n",
       "      4          113      119        9      -12  "
      ]
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     "execution_count": 3,
     "metadata": {},
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   "source": [
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-ly'] = asl.df['left-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-rx'] = asl.df['right-x'] - asl.df['nose-x']\n",
    "asl.df['grnd-lx'] = asl.df['left-x'] - asl.df['nose-x']\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 113, -12, 119]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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.loc[98, 1][v] for v in features_ground]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training words: ['JOHN', 'WRITE', 'HOMEWORK', 'IX-1P', 'SEE', 'YESTERDAY', 'IX', 'LOVE', 'MARY', 'CAN', 'GO', 'GO1', 'FUTURE', 'GO2', 'PARTY', 'FUTURE1', 'HIT', 'BLAME', 'FRED', 'FISH', 'WONT', 'EAT', 'BUT', 'CHICKEN', 'VEGETABLE', 'CHINA', 'PEOPLE', 'PREFER', 'BROCCOLI', 'LIKE', 'LEAVE', 'SAY', 'BUY', 'HOUSE', 'KNOW', 'CORN', 'CORN1', 'THINK', 'NOT', 'PAST', 'LIVE', 'CHICAGO', 'CAR', 'SHOULD', 'DECIDE', 'VISIT', 'MOVIE', 'WANT', 'SELL', 'TOMORROW', 'NEXT-WEEK', 'NEW-YORK', 'LAST-WEEK', 'WILL', 'FINISH', 'ANN', 'READ', 'BOOK', 'CHOCOLATE', 'FIND', 'SOMETHING-ONE', 'POSS', 'BROTHER', 'ARRIVE', 'HERE', 'GIVE', 'MAN', 'NEW', 'COAT', 'WOMAN', 'GIVE1', 'HAVE', 'FRANK', 'BREAK-DOWN', 'SEARCH-FOR', 'WHO', 'WHAT', 'LEG', 'FRIEND', 'CANDY', 'BLUE', 'SUE', 'BUY1', 'STOLEN', 'OLD', 'STUDENT', 'VIDEOTAPE', 'BORROW', 'MOTHER', 'POTATO', 'TELL', 'BILL', 'THROW', 'APPLE', 'NAME', 'SHOOT', 'SAY-1P', 'SELF', 'GROUP', 'JANA', 'TOY1', 'MANY', 'TOY', 'ALL', 'BOY', 'TEACHER', 'GIRL', 'BOX', 'GIVE2', 'GIVE3', 'GET', 'PUTASIDE']\n"
     ]
    }
   ],
   "source": [
    "training = asl.build_training(features_ground)\n",
    "print(\"Training words: {}\".format(training.words))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training data in `training` is an object of class `WordsData` defined in the `asl_data` module.  in addition to the `words` list, data can be accessed with the `get_all_sequences`, `get_all_Xlengths`, `get_word_sequences`, and `get_word_Xlengths` methods. 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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-23,  53,  39,  85],\n",
       "        [-26,  49,  41,  87],\n",
       "        [-25,  41,  38,  84],\n",
       "        [-25,  43,  35,  88],\n",
       "        [-17,  33,  28,  91],\n",
       "        [ -8,  27,  21,  91],\n",
       "        [ -2,  26,  18,  93],\n",
       "        [ -2,  26,  15,  92]]), [8])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.get_word_Xlengths('GET')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Features Implementation \n",
    "\n",
    "- normalized Cartesian coordinates\n",
    "- polar coordinates\n",
    "- delta difference\n",
    "- custom features: delta2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_means = asl.df.groupby('speaker').mean()  # Dataframe with mean grouped by speaker\n",
    "df_std = asl.df.groupby(\n",
    "    'speaker').std()  # Dataframe with standard deviations grouped by speaker\n",
    "\n",
    "# Add features for normalized by speaker values using Z-score scaling (X-Xmean)/Xstd\n",
    "asl.df['left-x-mean'] = asl.df['speaker'].map(df_means['left-x'])\n",
    "asl.df['left-y-mean'] = asl.df['speaker'].map(df_means['left-y'])\n",
    "asl.df['right-x-mean'] = asl.df['speaker'].map(df_means['right-x'])\n",
    "asl.df['right-y-mean'] = asl.df['speaker'].map(df_means['right-y'])\n",
    "\n",
    "asl.df['left-x-std'] = asl.df['speaker'].map(df_std['left-x'])\n",
    "asl.df['left-y-std'] = asl.df['speaker'].map(df_std['left-y'])\n",
    "asl.df['right-x-std'] = asl.df['speaker'].map(df_std['right-x'])\n",
    "asl.df['right-y-std'] = asl.df['speaker'].map(df_std['right-y'])\n",
    "\n",
    "asl.df['norm-rx'] = (asl.df['right-x'] - asl.df['right-x-mean']) / asl.df['right-x-std']\n",
    "asl.df['norm-ry'] = (asl.df['right-y'] - asl.df['right-y-mean']) / asl.df['right-y-std']\n",
    "asl.df['norm-lx'] = (asl.df['left-x'] - asl.df['left-x-mean']) / asl.df['left-x-std']\n",
    "asl.df['norm-ly'] = (asl.df['left-y'] - asl.df['left-y-mean']) / asl.df['left-y-std']\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx', 'norm-ly']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Add features for polar coordinate values where the nose is the origin\n",
    "# Note that 'polar-rr' and 'polar-rtheta' refer to the radius and angle\n",
    "asl.df['polar-rr'] = (asl.df['grnd-rx']**2 + asl.df['grnd-ry']**2)**0.5\n",
    "asl.df['polar-rtheta'] = np.arctan2(asl.df['grnd-rx'], asl.df['grnd-ry'])\n",
    "asl.df['polar-lr'] = (asl.df['grnd-lx']**2 + asl.df['grnd-ly']**2)**0.5\n",
    "asl.df['polar-ltheta'] = np.arctan2(asl.df['grnd-lx'], asl.df['grnd-ly'])\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Add features for left, right, x, y differences by one time step\n",
    "asl.df['delta-rx'] = asl.df['right-x'].diff().fillna(method='bfill')\n",
    "asl.df['delta-ry'] = asl.df['right-y'].diff().fillna(method='bfill')\n",
    "asl.df['delta-lx'] = asl.df['left-x'].diff().fillna(method='bfill')\n",
    "asl.df['delta-ly'] = asl.df['left-y'].diff().fillna(method='bfill')\n",
    "\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Custom feature: delta2\n",
    "\n",
    "We chose Delta difference by two-time steps of cartesian coordinates (delta2)  empirically . We obtained better results at the end of the project with delta2. In particular, it gave better performance than other combinations of the above features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th>...</th>\n",
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       "             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-ly  grnd-rx    ...        polar-lr  polar-ltheta  \\\n",
       "video frame                               ...                                 \n",
       "98    0          113      119        9    ...      119.603512     -0.100501   \n",
       "      1          113      119        9    ...      119.603512     -0.100501   \n",
       "      2          113      119        9    ...      119.603512     -0.100501   \n",
       "      3          113      119        9    ...      119.603512     -0.100501   \n",
       "      4          113      119        9    ...      119.603512     -0.100501   \n",
       "\n",
       "             delta-rx  delta-ry  delta-lx  delta-ly  delta2-rx  delta2-ry  \\\n",
       "video frame                                                                 \n",
       "98    0           0.0       0.0       0.0       0.0        0.0        0.0   \n",
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       "\n",
       "             delta2-lx  delta2-ly  \n",
       "video frame                        \n",
       "98    0            0.0        0.0  \n",
       "      1            0.0        0.0  \n",
       "      2            0.0        0.0  \n",
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       "\n",
       "[5 rows x 35 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# delta2: features for left, right, x, y differences by TWO time steps\n",
    "asl.df['delta2-rx'] = asl.df['right-x'].diff(periods=2).fillna(method='bfill')\n",
    "asl.df['delta2-ry'] = asl.df['right-y'].diff(periods=2).fillna(method='bfill')\n",
    "asl.df['delta2-lx'] = asl.df['left-x'].diff(periods=2).fillna(method='bfill')\n",
    "asl.df['delta2-ly'] = asl.df['left-y'].diff(periods=2).fillna(method='bfill')\n",
    "\n",
    "features_custom = ['delta2-rx', 'delta2-ry', 'delta2-lx', 'delta2-ly']\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='part2'></a>\n",
    "## 2: Model Selection\n",
    "\n",
    "Here we find the best number of states for each word HMM prior to testing on unseen data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train a single word\n",
    "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHICKEN is 3\n",
      "logL = -133.30792481639244\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "import sklearn\n",
    "from hmmlearn.hmm import GaussianHMM\n",
    "\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",
    "\n",
    "testword = 'CHICKEN'\n",
    "model, logL = train_a_word(testword, 3, features_custom)\n",
    "print(\"Number of states trained in model for {} is {}\".format(testword, model.n_components))\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The HMM model has been trained and information can be pulled from the model, including means and variances for each feature and hidden state.  The [log likelihood](http://math.stackexchange.com/questions/892832/why-we-consider-log-likelihood-instead-of-likelihood-in-gaussian-distribution) for any individual sample or group of samples can also be calculated with the `score` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHICKEN is 3\n",
      "hidden state #0\n",
      "mean =  [ 0.          0.         -0.21428348  1.42857051]\n",
      "variance =  [  7.14288533e-04   7.14288533e-04   1.69080359e-01   2.67418817e+00]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [ 2.19999683  1.59999768 -4.09999441  4.99999798]\n",
      "variance =  [  4.96099985  13.24098473   7.69101097   4.20099767]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [ 2.49998724 -3.24998338 -2.12499415  1.12499927]\n",
      "variance =  [ 5.00125634  4.43878134  3.860612    1.61061695]\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",
    "\n",
    "show_model_stats(testword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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aVaxgC6cykHx6WX9HFLArwYg7tlPCRyxkDdvJogNXcASZpEfbLANIIZmf0J+h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\nF3BQ3K/D3QH0BDpx8M7NJ+4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hmYm70fjMmgWnnw6nnQZbt7rhbHPmuN+G0Vj07u1GX337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\nZ5cI5X1ozgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc806263d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aRktmPdt5jVnspYYLOIEBdE22SQ3SjhyuYBgfsZgvKWUT5VzACbTBPk/bGrFb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\nkToAWV7+IqAK+BbIBfp585u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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc8060e84a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iCemkkkYKgrCPQ5RTyQEqOMjRJ/5TENqRTSdy6Eou3cilKenxKJZhJAxm3I2Y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\n7o7jOD2IO3fHcZwe5L9zVBberwIwlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc805fb6ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Bl3QXAdtqyzMfzBB0AUI5BPpCO8qqpPxh9pLmhKJy2+9NuY8Btvsod4rzYOYA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\n3J1zLoQ8uTvnXAj9H0QMksVjwqWdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc805e8d320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "from matplotlib import (cm, pyplot as plt, mlab)\n",
    "\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",
    "\n",
    "visualize(testword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Model Selectors\n",
    "Three methods are explored here: \n",
    "\n",
    "- `SelectorCV `: Log likelihood with Cross-Validation folds\n",
    "- `SelectorBIC`: Baysian Information Criterion\n",
    "- `SelectorDIC`: Discriminative Information Criterion\n",
    "\n",
    "Each word in the training set will be trained with a range of values for the number of hidden states, and then scored with the model selector, choosing the \"best\" according to each strategy.\n",
    "\n",
    "#### 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.  Only the \"left out\" fold is scored.  This gives us a proxy method of finding the best model to use on \"unseen data\". "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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. [reference](http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf)\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": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import statistics\n",
    "import warnings\n",
    "\n",
    "import numpy as np\n",
    "from hmmlearn.hmm import GaussianHMM\n",
    "from sklearn.model_selection import KFold\n",
    "from asl_recognizer.asl_utils import combine_sequences\n",
    "\n",
    "\n",
    "class ModelSelector(object):\n",
    "    '''\n",
    "    base class for model selection (strategy design pattern)\n",
    "    '''\n",
    "\n",
    "    def __init__(self,\n",
    "                 all_word_sequences: dict,\n",
    "                 all_word_Xlengths: dict,\n",
    "                 this_word: str,\n",
    "                 n_constant=3,\n",
    "                 min_n_components=2,\n",
    "                 max_n_components=10,\n",
    "                 random_state=14,\n",
    "                 verbose=False):\n",
    "        self.words = all_word_sequences\n",
    "        self.hwords = all_word_Xlengths\n",
    "        self.sequences = all_word_sequences[this_word]\n",
    "        self.X, self.lengths = all_word_Xlengths[this_word]\n",
    "        self.this_word = this_word\n",
    "        self.n_constant = n_constant\n",
    "        self.min_n_components = min_n_components\n",
    "        self.max_n_components = max_n_components\n",
    "        self.random_state = random_state\n",
    "        self.verbose = verbose\n",
    "\n",
    "    def select(self):\n",
    "        raise NotImplementedError\n",
    "\n",
    "    def base_model(self, num_states):\n",
    "        # with warnings.catch_warnings():\n",
    "        warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "        # warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
    "        try:\n",
    "            hmm_model = GaussianHMM(\n",
    "                n_components=num_states,\n",
    "                covariance_type=\"diag\",\n",
    "                n_iter=1000,\n",
    "                random_state=self.random_state,\n",
    "                verbose=False).fit(self.X, self.lengths)\n",
    "            if self.verbose:\n",
    "                print(\"model created for {} with {} states\".format(self.this_word, num_states))\n",
    "            return hmm_model\n",
    "        except:\n",
    "            if self.verbose:\n",
    "                print(\"failure on {} with {} states\".format(self.this_word, num_states))\n",
    "            return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SelectorConstant(ModelSelector):\n",
    "    \"\"\" select the model with value self.n_constant\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    def select(self):\n",
    "        \"\"\" select based on n_constant value\n",
    "\n",
    "        :return: GaussianHMM object\n",
    "        \"\"\"\n",
    "        best_num_components = self.n_constant\n",
    "        return self.base_model(best_num_components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Log Likelihood of cross-Validation folds (CV)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SelectorCV(ModelSelector):\n",
    "    \"\"\" select best model based on average log Likelihood of cross-validation folds \"\"\"\n",
    "\n",
    "    def select(self):\n",
    "        \"\"\" :return: GaussianHMM object \"\"\"\n",
    "\n",
    "        warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "\n",
    "        #  Sequences of size lower than 3 must be considered:\n",
    "        if len(self.sequences) >= 3:\n",
    "            n_splits = 3\n",
    "        elif len(self.sequences) == 2:\n",
    "            n_splits = 2\n",
    "        else:\n",
    "            # print(\"No CV possible for word: \", self.this_word, \"only has 1 occurrence\")\n",
    "            return None\n",
    "\n",
    "        best_score = float('-inf')  # hold the highest avg of cross-validation scores found\n",
    "        best_model = None  # hold the model with the highest avg of CV score found\n",
    "\n",
    "        # main loop: get model and score for different number of hidden states \n",
    "        #             and update best_score and best_model\n",
    "        for n_components in range(self.min_n_components, self.max_n_components + 1):\n",
    "\n",
    "            split_method = KFold(n_splits=n_splits)\n",
    "            logL = []  # list of cross validation scores obtained\n",
    "\n",
    "            # get the model for the combined cross-validation training sequences and score with\n",
    "            #  their combined validation sequences filling the list 'logL'\n",
    "            for cv_train_idx, cv_test_idx in split_method.split(self.sequences):\n",
    "\n",
    "                self.X, self.lengths = combine_sequences(cv_train_idx, self.sequences)\n",
    "                model = self.base_model(\n",
    "                    n_components)  # avoid code duplication using the inherited method\n",
    "                if model is None:  # failed\n",
    "                    continue\n",
    "\n",
    "                test_X, test_lengths = combine_sequences(cv_test_idx, self.sequences)\n",
    "                try:  # hmmlearn stability issues\n",
    "                    logL.append(model.score(test_X, test_lengths))\n",
    "                except:\n",
    "                    continue\n",
    "\n",
    "            if model is None or logL == []:\n",
    "                continue\n",
    "\n",
    "            score = np.mean(logL)  # The higher the better\n",
    "            if score > best_score:\n",
    "                best_score = score\n",
    "                best_model = model\n",
    "\n",
    "        return best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Baysian Information Criterion (BIC)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SelectorBIC(ModelSelector):\n",
    "    \"\"\" select the model with the lowest Baysian Information Criterion(BIC) score\n",
    "\n",
    "    http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf\n",
    "    Bayesian information criteria: BIC = -2 * logL + p * logN\n",
    "    \"\"\"\n",
    "\n",
    "    def select(self):\n",
    "        \"\"\" select the best model for self.this_word based on\n",
    "        BIC score for n between self.min_n_components and self.max_n_components\n",
    "        :return: GaussianHMM object\n",
    "        \"\"\"\n",
    "        warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "\n",
    "        best_BIC = float('inf')  # hold the lowest BIC found\n",
    "        best_model = None  # hold the model with the lowest BIC found\n",
    "\n",
    "        # main loop: get model and score for different number of hidden states \n",
    "        #             and update best_BIC and best_model\n",
    "        for n_components in range(self.min_n_components, self.max_n_components + 1):\n",
    "            logL = None\n",
    "            model = self.base_model(\n",
    "                n_components)  # avoid code duplication using the inherited method\n",
    "            if model is None:  # failed\n",
    "                continue\n",
    "            try:  # hmmlearn stability issues\n",
    "                logL = model.score(self.X, self.lengths)\n",
    "            except:\n",
    "                continue\n",
    "\n",
    "            # BIC = -2 log L + p log N  (the lower the better)\n",
    "            # p = num free params = transistion probs(n*n) + means(n*f) + covars(n*f)  \n",
    "            p = n_components**2 + (2 * len(self.X[0]) * n_components)\n",
    "            BIC = -2 * logL + p * np.log(len(self.X))\n",
    "            if BIC < best_BIC:\n",
    "                best_BIC = BIC\n",
    "                best_model = model\n",
    "\n",
    "        return best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Discriminative Information Criterion (DIC)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SelectorDIC(ModelSelector):\n",
    "    \"\"\" select best model based on Discriminative Information Criterion\n",
    "\n",
    "    Biem, Alain. \"A model selection criterion for classification: Application to hmm topology \n",
    "    optimization.\" Document Analysis and Recognition, 2003. Proceedings. Seventh International \n",
    "    Conference on. IEEE, 2003.\n",
    "    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf\n",
    "    DIC = log(P(X(i)) - 1/(M-1)SUM(log(P(X(all but i))\n",
    "    \"\"\"\n",
    "\n",
    "    def select(self):\n",
    "        warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "\n",
    "        best_DIC = float('-inf')  # hold the highest BIC found\n",
    "        best_model = None  # hold the model with the highest BIC found\n",
    "        my_word = self.this_word  # word to evaluate\n",
    "\n",
    "        # main loop: get model and score for different number of hidden states \n",
    "        #             and update best_DIC and best_model\n",
    "        for n_components in range(self.min_n_components, self.max_n_components + 1):\n",
    "            logL = None  # likelihood of the trained model\n",
    "            anti_logL = []  # list containing all the anti likelihoods of the trained model\n",
    "            self.this_word = my_word\n",
    "\n",
    "            # train the model for current word (self.this_word)\n",
    "            model = self.base_model(\n",
    "                n_components)  # avoid code duplication using the inherited method\n",
    "            if model is None:  # failed\n",
    "                continue\n",
    "            # get the likelihood of the model\n",
    "            try:  # hmmlearn stability issues\n",
    "                logL = model.score(self.X, self.lengths)\n",
    "            except:\n",
    "                continue\n",
    "\n",
    "            # get the anti-likehoods (score every other word for the current model)\n",
    "            for other_word in self.hwords:\n",
    "                if other_word == my_word:\n",
    "                    continue\n",
    "                X, lengths = self.hwords[other_word]\n",
    "                try:  # stability issues for hmmlearn v<0.2.1\n",
    "                    anti_logL.append(model.score(X, lengths))\n",
    "                except:\n",
    "                    continue\n",
    "\n",
    "            # I found the docstring formula a bit confusing: \n",
    "            # DIC = log(P(X(i)) - 1/(M-1)SUM(log(P(X(all but i)) \n",
    "            # The size of anti_logL is M-1, as the word evaluated is not included in anti_logL.\n",
    "            # Biem, Alain: \"DIC = Difference between the likelihood of the data an the the \n",
    "            # average of anti-likelihood\"\n",
    "            # From the paper we can state: DIC = log(P(X(i)) - average(log(P(X(all but i))\n",
    "            DIC = logL - np.average(anti_logL)  # the higher the better\n",
    "            if DIC > best_DIC:\n",
    "                best_DIC = DIC\n",
    "                best_model = model\n",
    "\n",
    "        return best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Training example\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHICKEN is 3\n"
     ]
    }
   ],
   "source": [
    "training = asl.build_training(features_ground)\n",
    "word = 'CHICKEN'\n",
    "model = SelectorConstant(\n",
    "    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": {},
   "source": [
    "<a id='part2_submission'></a>\n",
    "### Model Selectors Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "words_to_train = ['FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train(features, model_selector):\n",
    "    training = asl.build_training(features)\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 = model_selector(\n",
    "            sequences,\n",
    "            Xlengths,\n",
    "            word,\n",
    "            min_n_components=2,\n",
    "            max_n_components=15,\n",
    "            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(\n",
    "                word, model.n_components, end))\n",
    "        else:\n",
    "            print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class '__main__.SelectorCV'>:\n",
      "Training complete for FISH with 11 states with time 0.36364252299972577 seconds\n",
      "Training complete for BOOK with 6 states with time 4.421584876999987 seconds\n",
      "Training complete for VEGETABLE with 2 states with time 2.0113580120014376 seconds\n",
      "Training complete for FUTURE with 2 states with time 4.179233299000771 seconds\n",
      "Training complete for JOHN with 12 states with time 42.61958790699646 seconds\n",
      "<class '__main__.SelectorBIC'>:\n",
      "Training complete for FISH with 5 states with time 0.36513492399899405 seconds\n",
      "Training complete for BOOK with 8 states with time 2.3213795779993234 seconds\n",
      "Training complete for VEGETABLE with 9 states with time 0.8410732449992793 seconds\n",
      "Training complete for FUTURE with 9 states with time 2.4961920649984677 seconds\n",
      "Training complete for JOHN with 13 states with time 23.01789991700207 seconds\n",
      "<class '__main__.SelectorDIC'>:\n",
      "Training complete for FISH with 3 states with time 0.9269850839991705 seconds\n",
      "Training complete for BOOK with 15 states with time 4.616702977997193 seconds\n",
      "Training complete for VEGETABLE with 15 states with time 3.940272883999569 seconds\n",
      "Training complete for FUTURE with 15 states with time 4.799144736000017 seconds\n",
      "Training complete for JOHN with 15 states with time 25.007601143999636 seconds\n"
     ]
    }
   ],
   "source": [
    "selector = [SelectorCV, SelectorBIC, SelectorDIC]\n",
    "\n",
    "for i in selector:\n",
    "    print(\"{}:\".format(i))\n",
    "    train(features_ground, i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Advantages and disadvantages of the model selectors implemented:\n",
    "\n",
    "**CV**: Common in supervised learning to avoid partitioning the training set for validation. Among the tree model selectors, CV is the only one (cross)validated with sequences different from the training sets. However, the running time needed is higher than direct selectors like BIC. For each word, several models are created for cross-validation (combinations of training-validation sequences).\n",
    "\n",
    "**BIC**: a simple selector penalizing the resulted likelihood with the complexity of the model. It reduces the risk of overfitting. The running time is lower than CV and DIC, as only one model and one score are computed per number of hidden nodes.\n",
    "\n",
    "**DIC**: The penalty term in DIC is based on the average likelihood for the other words, thus having higher computational cost than BIC.\n",
    "Further comparisons discussed together with the results of part 3 of the project\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3'></a>\n",
    "## 3: Recognizer\n",
    "Here we perform experiments training all the words for the 4 feature sets and the 3 model selectors.  \n",
    "\n",
    "### Train the full training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_all_words(features, model_selector):\n",
    "    training = asl.build_training(features)\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_constant=3).select()\n",
    "        model_dict[word] = model\n",
    "    return model_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following example trains the entire set with the example `features_ground` and `SelectorConstant` features and model selector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "models = train_all_words(features_ground, SelectorConstant)\n",
    "print(\"Number of word models returned = {}\".format(len(models)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of test set items: 178\n",
      "Number of test set sentences: 40\n"
     ]
    }
   ],
   "source": [
    "test_set = asl.build_test(features_ground)\n",
    "print(\"Number of test set items: {}\".format(test_set.num_items))\n",
    "print(\"Number of test set sentences: {}\".format(len(test_set.sentences_index)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recognizer Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "from asl_recognizer.asl_data import SinglesData\n",
    "\n",
    "\n",
    "def recognize(models: dict, test_set: SinglesData):\n",
    "    \"\"\" Recognize test word sequences from word models set\n",
    "\n",
    "   :param models: dict of trained models\n",
    "       {'SOMEWORD': GaussianHMM model object, 'SOMEOTHERWORD': GaussianHMM model object, ...}\n",
    "   :param test_set: SinglesData object\n",
    "   :return: (list, list)  as probabilities, guesses\n",
    "       both lists are ordered by the test set word_id\n",
    "       probabilities is a list of dictionaries where each key a word and value is Log Liklehood\n",
    "           [{SOMEWORD': LogLvalue, 'SOMEOTHERWORD' LogLvalue, ... },\n",
    "            {SOMEWORD': LogLvalue, 'SOMEOTHERWORD' LogLvalue, ... },\n",
    "            ]\n",
    "       guesses is a list of the best guess words ordered by the test set word_id\n",
    "           ['WORDGUESS0', 'WORDGUESS1', 'WORDGUESS2',...]\n",
    "   \"\"\"\n",
    "    warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "    probabilities = []\n",
    "    guesses = []\n",
    "\n",
    "    test_sequences = list(\n",
    "        test_set.get_all_Xlengths().values())  # extract X and Xlength lists in a variable\n",
    "\n",
    "    # Main loop: iterate for each word sequence and fill the lists probabilities and guesses\n",
    "    for test_X, test_Xlength in test_sequences:\n",
    "\n",
    "        best_score = float(\n",
    "            '-inf')  # hold the highest likelihood found for the current sequence\n",
    "        best_word = None  # hold the word with the highest likelihood for the current sequence\n",
    "        prob_dict = {\n",
    "        }  # dictionary to fill before being added to the probabilities list {word: LogL}\n",
    "\n",
    "        # Score the models avaliable for different words for the current sequence, \n",
    "        # fill prob_dict, and update best_score and best_word found\n",
    "        for word, model in models.items():\n",
    "            try:  # hmmlearn stability issues\n",
    "                logL = model.score(test_X, test_Xlength)\n",
    "            except:\n",
    "                logL = None\n",
    "\n",
    "            prob_dict[word] = logL\n",
    "            if logL is not None:\n",
    "                if logL > best_score:\n",
    "                    best_score = logL\n",
    "                    best_word = word\n",
    "\n",
    "        probabilities.append(prob_dict)\n",
    "        guesses.append(best_word)\n",
    "\n",
    "    return probabilities, guesses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from asl_recognizer.asl_utils import show_errors\n",
    "\n",
    "\n",
    "def evaluate(features, model_selector):\n",
    "\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6685393258426966\n",
      "Total correct: 59 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *GO WRITE *ARRIVE                                             JOHN WRITE HOMEWORK\n",
      "    7: *SOMETHING-ONE *GO1 *IX CAN                                   JOHN CAN GO CAN\n",
      "   12: JOHN *HAVE *WHAT CAN                                          JOHN CAN GO CAN\n",
      "   21: JOHN *HOMEWORK *NEW *PREFER *CAR *CAR *FUTURE *EAT            JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *FRANK *TELL *LOVE *TELL *LOVE                                JOHN LIKE IX IX IX\n",
      "   28: *FRANK *TELL *LOVE *TELL *LOVE                                JOHN LIKE IX IX IX\n",
      "   30: *SHOULD LIKE *GO *GO *GO                                      JOHN LIKE IX IX IX\n",
      "   36: *VISIT VEGETABLE *YESTERDAY *GIVE *MARY *MARY                 MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *SUE *GIVE *CORN *VEGETABLE *GO                               JOHN IX THINK MARY LOVE\n",
      "   43: *FRANK *GO BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *SEE BUY CAR *SOMETHING-ONE                            FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *VISIT VISIT *VISIT                                     JOHN DECIDE VISIT MARY\n",
      "   67: *LIKE FUTURE NOT BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *VISIT *GO *GO                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *LOVE *ARRIVE *HOMEWORK BOOK                                  IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE *GIVE GIVE *IX IX *ARRIVE *BOOK                         JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SOMETHING-ONE *SOMETHING-ONE IX *IX WOMAN *COAT              JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: *FRANK GIVE *WOMAN *WOMAN WOMAN BOOK                          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: *FRANK *VEGETABLE                                             JOHN LEG\n",
      "  107: *SHOULD *IX FRIEND *GO *JANA                                  JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *GIVE *LOVE                                                   WOMAN ARRIVE\n",
      "  113: IX CAR *CAR *IX *IX                                           IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 IX *BLAME *IX                                   SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 *COAT                                             JOHN READ BOOK\n",
      "  139: *SHOULD *BUY1 *CAR *BLAME BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: *FRANK *STUDENT YESTERDAY *TEACHER BOOK                       JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: *MARY IX *VISIT *WOMAN *LOVE                                  JOHN IX SAY LOVE MARY\n",
      "  171: *VISIT *VISIT BLAME                                           JOHN MARY BLAME\n",
      "  174: *CAN *GIVE3 GIVE1 *APPLE *WHAT                                PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *BLAME ARRIVE                                                 JOHN ARRIVE\n",
      "  184: *GIVE1 BOY *GIVE1 TEACHER APPLE                               ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *SOMETHING-ONE *YESTERDAY *WHAT                         JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SOMETHING-ONE *YESTERDAY BOX                            JOHN GIVE GIRL BOX\n",
      "  199: *LOVE CHOCOLATE WHO                                           LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE *GIVE *LOVE *ARRIVE HOUSE                          JOHN TELL MARY IX-1P BUY HOUSE\n",
      "CPU times: user 33.4 s, sys: 440 ms, total: 33.9 s\n",
      "Wall time: 23.3 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#  BASE COMBINATION:  SelectorConstant with features_ground.  WER = 0.669\n",
    "evaluate(features_ground, SelectorConstant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6067415730337079\n",
      "Total correct: 70 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *POSS *BROTHER *NEW                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN *HAVE GO *WHAT                                           JOHN CAN GO CAN\n",
      "   12: *IX *WHAT *WHAT CAN                                           JOHN CAN GO CAN\n",
      "   21: JOHN *NEW *POSS *JOHN *CAR *CAR *VISIT *FUTURE                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE *LOVE *JOHN IX                                      JOHN LIKE IX IX IX\n",
      "   28: JOHN *JOHN *MARY *JOHN IX                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX *LIKE IX                                         JOHN LIKE IX IX IX\n",
      "   36: MARY VEGETABLE *GIRL *GIVE *MARY *MARY                        MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GIVE *CORN *JOHN *IX                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *FRANK *SEE BUY CAR *WHAT                                     FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *SEE *GIVE *IX                                            JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *JOHN NOT BUY HOUSE                                      JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GO *BLAME                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *IX *MARY *GO                                             JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *SOMETHING-ONE                                    ANN BLAME MARY\n",
      "   84: *FRANK *ARRIVE *POSS BOOK                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE IX *WOMAN *IX IX *ARRIVE *BOOK                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *GIVE1 *WOMAN *WOMAN WOMAN *CHOCOLATE                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *WOMAN IX *WOMAN *SOMETHING-ONE BOOK                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *GIVE *HAVE *GO *WHO                                     JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *MARY *LOVE                                                   WOMAN ARRIVE\n",
      "  113: *GO *HAVE *SUE SUE *BUY1                                      IX CAR BLUE SUE BUY\n",
      "  119: *VEGETABLE *BUY1 *GO *HAVE *GIVE                              SUE BUY IX CAR BLUE\n",
      "  122: JOHN *HOUSE BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *DECIDE YESTERDAY *CHOCOLATE                       JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *NEW YESTERDAY *TEACHER BOOK                             JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "  167: JOHN *MARY *MARY *WOMAN *GO                                   JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *SUE BLAME                                               JOHN MARY BLAME\n",
      "  174: *CAN *GIVE1 GIVE1 *GIRL *WHAT                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *BOX                                                     JOHN ARRIVE\n",
      "  184: *WOMAN BOY *BLAME TEACHER *GIRL                               ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN GIVE *YESTERDAY *CAN                                     JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  199: *FRANK CHOCOLATE *FRANK                                       LIKE CHOCOLATE WHO\n",
      "  201: JOHN *SHOULD *WOMAN *LOVE BUY HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n",
      "CPU times: user 5min 57s, sys: 5.16 s, total: 6min 2s\n",
      "Wall time: 1min 59s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#  COMBINATION 1:   SelectorCV with features_polar.\n",
    "evaluate(features_polar, SelectorCV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
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    {
     "name": "stdout",
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     "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",
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      "CPU times: user 3min 31s, sys: 2.92 s, total: 3min 33s\n",
      "Wall time: 1min 18s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#  COMBINATION 2:  SelectorBIC with features_polar.\n",
    "evaluate(features_polar, SelectorBIC)"
   ]
  },
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      "\n",
      "**** WER = 0.5393258426966292\n",
      "Total correct: 82 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *IX *ARRIVE                                              JOHN WRITE HOMEWORK\n",
      "    7: JOHN *HAVE GO *TEACHER                                        JOHN CAN GO CAN\n",
      "   12: JOHN CAN *FUTURE CAN                                          JOHN CAN GO CAN\n",
      "   21: JOHN *NOT *GIVE1 *JOHN *NEW *VISIT *MARY *MARY                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *MARY IX IX IX                                           JOHN LIKE IX IX IX\n",
      "   28: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   30: JOHN *IX IX IX IX                                             JOHN LIKE IX IX IX\n",
      "   36: *JOHN *MARY *IX *LIKE *MARY *JOHN                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN IX *JOHN *JOHN *JOHN                                     JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *MARY *GO HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *NOT BUY CAR *FUTURE                                    FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *IX BUY HOUSE                                      JOHN SHOULD NOT BUY HOUSE\n",
      "   57: JOHN *FUTURE *IX *IX                                          JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *MARY *IX BUY HOUSE                                      JOHN FUTURE NOT BUY HOUSE\n",
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      "   74: JOHN *MARY *IX MARY                                           JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *FUTURE                                           ANN BLAME MARY\n",
      "   84: *JOHN *NEW *IX BOOK                                           IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: JOHN IX *IX *IX IX NEW COAT                                   JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *IX IX *IX WOMAN *MARY                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX WOMAN *NEW                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
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      "  105: JOHN *JOHN                                                    JOHN LEG\n",
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      "  108: *IX ARRIVE                                                    WOMAN ARRIVE\n",
      "  113: *JOHN CAR *JOHN *IX *BUY1                                     IX CAR BLUE SUE BUY\n",
      "  119: *MARY *BUY1 *GO CAR *MARY                                     SUE BUY IX CAR BLUE\n",
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      "  142: JOHN BUY *IX WHAT *VISIT                                      JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *NEW JOHN *JOHN                                               LOVE JOHN WHO\n",
      "  167: JOHN IX *IX LOVE *COAT                                        JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *NEW *IX GIVE1 *JOHN *CAN                                     PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *GIVE *JOHN *GIVE1 TEACHER *MARY                              ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *JOHN *ARRIVE                                        JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX *IX BOX                                              JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE *JOHN                                           LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE *JOHN *JOHN BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "CPU times: user 6min 23s, sys: 5.5 s, total: 6min 28s\n",
      "Wall time: 2min 6s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#  COMBINATION 3:  SelectorCV with features_custom(delta2).\n",
    "evaluate(features_custom, SelectorCV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Results:**\n",
    "\n",
    "| Selector | features |Word Error Rate  | wall time (s) |\n",
    "|----------|----------|------|---------------|\n",
    "| CV | polar | 0.607 |  119  |\n",
    "| BIC | polar | 0.545 | 78   |\n",
    "| CV | delta2 | 0.539 | 126 |\n",
    "\n",
    "\n",
    "More tests were performed, leading to the following conclusions:\n",
    "\n",
    "- Best combination found: SelectorCV + \"delta_2\" custom features\n",
    "- DIC and BIC never improves 0.6 WER\n",
    "- Normalized features perform worse than the rest. \n",
    "- Delta features never improves 0..6 WER (best: 0.612 with selectorCV)\n",
    "- After using \"delta2\" custom features, we easily obtained WER lower than 0.6 for the three model selectors. It gave us a better comparison. SelectorCV had a better performance with \"delta2\" than BIC and DIC, just opposite to  polar features)\n",
    "\n",
    "About the running time, BIC model selector is the fastest for all tests for the reasons discussed in part 2, followed by Cross-Validation (~1.5 times longer). We rejected DIC earlier for similar or worse performance and higher running time.\n",
    "\n",
    "To improve WER we suggest enhancing \"delta2\" or \"polar\" with a linear function of combinations of features. Other variables like zoom and hand orientations, unavailable in this project, could help to elaborate more accurate features.\n",
    "\n",
    "A better option is to include statistical data with information about the occurrence of a word in a sentence. We could also use the probability of the word to appear next to other words (biased priors could be created before training). By using semantics rules, for example, a heuristic strategy using previous sequences could focus the search for meaningful words. \n",
    "\n",
    "Moreover, as all sequences are ordered, a Recurrent Neural Network (GRU or LSTM) could be used to improve the models here.\n",
    "\n"
   ]
  }
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