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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   "source": [
    "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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       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "      <th>grnd-ry</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
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       "      <td>149</td>\n",
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       "      <td>170</td>\n",
       "      <td>175</td>\n",
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       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>170</td>\n",
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       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "    <tr>\n",
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       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </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  \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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   "execution_count": 4,
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     "name": "stdout",
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     "text": [
      "asl.df sample\n"
     ]
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       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>9</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",
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       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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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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     "execution_count": 4,
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   "source": [
    "from asl_utils import test_features_tryit\n",
    "# TODO 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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   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "[9, 113, -12, 119]"
      ]
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     "execution_count": 5,
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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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   "execution_count": 6,
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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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       "        [ -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",
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       "      <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",
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       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  left-x-mean  \n",
       "video frame                                                   \n",
       "98    0          113        9      119      -12   164.661438  \n",
       "      1          113        9      119      -12   164.661438  \n",
       "      2          113        9      119      -12   164.661438  \n",
       "      3          113        9      119      -12   164.661438  \n",
       "      4          113        9      119      -12   164.661438  "
      ]
     },
     "execution_count": 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",
       "    <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",
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       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "      <th>left-x-mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\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",
       "      <td>6.654573</td>\n",
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       "      <td>15.080360</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>woman-1</th>\n",
       "      <td>17.573442</td>\n",
       "      <td>26.594521</td>\n",
       "      <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",
       "      <td>27.117393</td>\n",
       "      <td>17.328941</td>\n",
       "      <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",
    "# TODO Create a dataframe named `df_std` with standard deviations grouped by speaker\n",
    "\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": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.686534848552704"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df['left-x'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO 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",
    "right_x_mean = asl.df['speaker'].map(df_means['right-x'])\n",
    "right_x_std = asl.df['speaker'].map(df_std['right-x'])\n",
    "\n",
    "right_y_mean = asl.df['speaker'].map(df_means['right-y'])\n",
    "right_y_std = asl.df['speaker'].map(df_std['right-y'])\n",
    "\n",
    "left_x_mean = asl.df['speaker'].map(df_means['left-x'])\n",
    "left_x_std = asl.df['speaker'].map(df_std['left-x'])\n",
    "\n",
    "left_y_mean = asl.df['speaker'].map(df_means['left-y'])\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\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx','norm-ly']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO 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",
    "# Initially, I was attempting to use np.sqrt(var1**2 + var2**2) but found np.hypot is equivalent\n",
    "asl.df['polar-rr'] = np.hypot(asl.df['right-x'] - asl.df['nose-x'],asl.df['right-y'] - asl.df['nose-y'])\n",
    "asl.df['polar-rtheta'] = np.arctan2(asl.df['right-x'] - asl.df['nose-x'],asl.df['right-y'] - asl.df['nose-y'])\n",
    "asl.df['polar-lr'] = np.hypot(asl.df['left-x'] - asl.df['nose-x'],asl.df['left-y'] - asl.df['nose-y'])\n",
    "asl.df['polar-ltheta'] = np.arctan2(asl.df['left-x'] - asl.df['nose-x'],asl.df['left-y'] - asl.df['nose-y'])\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO 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",
    "asl.df['delta-rx'] = asl.df['right-x'].diff().fillna(value=0)\n",
    "asl.df['delta-ry'] = asl.df['right-y'].diff().fillna(value=0)\n",
    "asl.df['delta-lx'] = asl.df['left-x'].diff().fillna(value=0)\n",
    "asl.df['delta-ly'] = asl.df['left-y'].diff().fillna(value=0)\n",
    "\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO 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",
    "# TODO define a list named 'features_custom' for building the training set\n",
    "\n",
    "# Mean normalisation\n",
    "\n",
    "asl_speaker_group = asl.df.groupby('speaker')\n",
    "\n",
    "asl.df['norm-mean-rx'] = asl_speaker_group['right-x'].transform(lambda x: (x-x.mean())/x.max()-x.min())\n",
    "asl.df['norm-mean-ry'] = asl_speaker_group['right-y'].transform(lambda y: (y-y.mean())/y.max()-y.min())\n",
    "asl.df['norm-mean-lx'] = asl_speaker_group['left-x'].transform(lambda x: (x-x.mean())/x.max()-x.min())\n",
    "asl.df['norm-mean-ly'] = asl_speaker_group['left-y'].transform(lambda y: (y-y.mean())/y.max()-y.min())\n",
    "\n",
    "features_custom = ['norm-mean-rx', 'norm-mean-ry', 'norm-mean-lx','norm-mean-ly']\n"
   ]
  },
  {
   "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:**   I chose to use mean normalisation because some learning algorithms do not work as effectively with high data variance.  Utilizing this technique helps model data more realistically and can potentially lead to faster convergence. "
   ]
  },
  {
   "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": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 0.041s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 16,
     "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": 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",
      "logL = -2331.1138127433205\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": 18,
   "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 =  [ -3.46504869  50.66686933  14.02391587  52.04731066]\n",
      "variance =  [ 49.12346305  43.04799144  39.35109609  47.24195772]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [ -11.45300909   94.109178     19.03512475  102.2030162 ]\n",
      "variance =  [  77.403668    203.35441965   26.68898447  156.12444034]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [ -1.12415027  69.44164191  17.02866283  77.7231196 ]\n",
      "variance =  [ 19.70434594  16.83041492  30.51552305  11.03678246]\n",
      "\n"
     ]
    }
   ],
   "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": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHOCOLATE is 4\n",
      "hidden state #0\n",
      "mean =  [   0.58333258   87.91666611   12.75000001  108.49999882]\n",
      "variance =  [  39.4105671    18.74389523    9.85499958  144.41752618]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [ -9.23835975  55.307463     6.92298661  71.30538347]\n",
      "variance =  [ 16.30887738  45.97071639   3.76856896  15.98215464]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [  -6.37712306   51.09867416    3.64009161  104.46268173]\n",
      "variance =  [  10.28220014   12.44316166   27.33390004  106.91029392]\n",
      "\n",
      "hidden state #3\n",
      "mean =  [ -4.93681705  64.73171915   1.62598519  84.91459657]\n",
      "variance =  [  6.1617479   28.36616959   5.47102461  13.11696032]\n",
      "\n",
      "logL = -565.1243334331187\n"
     ]
    }
   ],
   "source": [
    "my_testword = 'CHOCOLATE'\n",
    "model, logL = train_a_word(my_testword, 4, 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": 20,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kCCdPnqRt27aVjguFhoZy0003lZ8//fTTDBkyxGFYEfjqm1V07BjN5Pv/CcDg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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f723c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7JwV4uVh2i8ttctA9qBrZsWhn18XKZ4ila5sV/oZjWta5POAsh+MvHcpgCJDo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\npz766KO6b9++PHGAzp07t8D6btiwQStXrpzjb9u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53A+kdk+ZMhy+COesP4b/AFDby1/L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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a97ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+fhfbZp8bX86x4/O2fSnvtFJmx5nkYh+Bde5WdK14kppqjDMdVTWyWpbVvUO4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c3ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tassX2mE6zyw2xiq7rsp4bVKROsaZtqrapEwpVa3wgVXR/wnsAZ6z740GRtvn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\nzCEYhmEYLuYQDMMwDMAcgmEYhuHy/8Qi0J+oDynpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112dc2eb8>"
      ]
     },
     "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": 22,
   "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": 23,
   "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": 24,
   "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": 25,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# autoreload for automatically reloading changes made in my_model_selectors and my_recognizer\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 13 states with time 0.4253648680023616 seconds\n",
      "Training complete for BOOK with 2 states with time 1.8489230920022237 seconds\n",
      "Training complete for VEGETABLE with 14 states with time 0.9291535000011208 seconds\n",
      "Training complete for FUTURE with 2 states with time 1.6821549189990037 seconds\n",
      "Training complete for JOHN with 12 states with time 26.261220239997783 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": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.3723322360019665 seconds\n",
      "Training complete for BOOK with 8 states with time 2.1757402180010104 seconds\n",
      "Training complete for VEGETABLE with 15 states with time 0.7782322439961717 seconds\n",
      "Training complete for FUTURE with 9 states with time 2.3811681659935857 seconds\n",
      "Training complete for JOHN with 14 states with time 25.10130008499982 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorBIC in module my_model_selectors.py\n",
    "import importlib\n",
    "import my_model_selectors\n",
    "importlib.reload(my_model_selectors)\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": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 3 states with time 0.4183853629947407 seconds\n",
      "Training complete for BOOK with 15 states with time 2.875323718006257 seconds\n",
      "Training complete for VEGETABLE with 15 states with time 1.0956263839980238 seconds\n",
      "Training complete for FUTURE with 15 states with time 3.3576061600033427 seconds\n",
      "Training complete for JOHN with 15 states with time 27.579075854999246 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:**  If we observe the states and time it took train each word; there are clear advantages and disadvantages for the various model selectors implemented.  For instance, when we select best model based on average log Likelihood of cross-validation folds it's possible to achieve training with fewer states.  The disadvantage of the CV model is that it took longer to train on certain words.  When we select best model based on Discriminative Information Criterion (DIC), it appears the model may be overfitting due to the large number of states for each word.  However, this model trains some word at a reasonably fast speed.  Lastly, when we select the model with the lowest Bayesian Information Criterion(BIC) score, some words have a low number of hidden states and a quickly train each word.  However, some words have high number of states which can be a sign of overfitting"
   ]
  },
  {
   "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": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 27.806s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 43,
     "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": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "def train_all_words(features, model_selector):\n",
    "    training = asl.build_training(features)  # Experiment here with different feature sets defined in part 1\n",
    "    sequences = training.get_all_sequences()\n",
    "    Xlengths = training.get_all_Xlengths()\n",
    "    model_dict = {}\n",
    "    for word in training.words:\n",
    "        model = model_selector(sequences, Xlengths, word, \n",
    "                        n_constant=3).select()\n",
    "        model_dict[word]=model\n",
    "    return model_dict\n",
    "\n",
    "models = train_all_words(features_ground, SelectorConstant)\n",
    "print(\"Number of word models returned = {}\".format(len(models)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "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": 49,
   "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": 70,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO implement the recognize method in my_recognizer\n",
    "import importlib\n",
    "import my_recognizer\n",
    "importlib.reload(my_recognizer)\n",
    "from my_recognizer import recognize\n",
    "from asl_utils import show_errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SelectorBIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6348314606741573\n",
      "Total correct: 65 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *LOVE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN *BOX *GIVE1 *ARRIVE                                      JOHN CAN GO CAN\n",
      "   12: JOHN *BOX *LOVE CAN                                           JOHN CAN GO CAN\n",
      "   21: *MARY *MARY *LOVE *MARY *CAR *ARRIVE *FUTURE *MARY            JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *MARY IX IX                                          JOHN LIKE IX IX IX\n",
      "   28: JOHN *MARY *JOHN IX *SHOULD                                   JOHN LIKE IX IX IX\n",
      "   30: JOHN *IX IX *JOHN IX                                          JOHN LIKE IX IX IX\n",
      "   36: *JOHN *JOHN *JOHN IX *MARY *MARY                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY IX *JOHN MARY *MARY                                     JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX *FINISH HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN JOHN BUY CAR *MARY                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *JOHN *IX *IX                                           JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *MARY VISIT MARY                                         JOHN WILL VISIT MARY\n",
      "   74: JOHN *JOHN *IX MARY                                           JOHN NOT VISIT MARY\n",
      "   77: *JOHN *CAR MARY                                               ANN BLAME MARY\n",
      "   84: *JOHN *CAR *IX BOOK                                           IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *JOHN *IX *IX *JOHN *WHAT *CAN                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *JOHN *JOHN *IX *IX *JOHN                                JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX *JOHN *IX WOMAN BOOK                                 JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *JOHN NEW CAR *BOOK                                           POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  107: JOHN *JOHN *CAR *JOHN *MARY                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  113: *JOHN CAR *MARY *MARY *GIVE1                                  IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *GIVE1 IX CAR *MARY                                     SUE BUY IX CAR BLUE\n",
      "  122: JOHN *ARRIVE *WHAT                                            JOHN READ BOOK\n",
      "  139: JOHN *GIVE1 WHAT *JOHN *MARY                                  JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY *FUTURE WHAT *MARY                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *GIVE1 JOHN *JOHN                                             LOVE JOHN WHO\n",
      "  167: JOHN IX *IX *BOOK *WHAT                                       JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "  174: *GIVE1 *MARY GIVE1 *MARY *FINISH                              PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *IX *JOHN *GIVE1 *WHO *MARY                                   ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *JOHN *JOHN *ARRIVE                                      JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX *WOMAN BOX                                           JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *WHAT *MARY                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *IX MARY *IX BUY HOUSE                                   JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_delta # 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": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5674157303370787\n",
      "Total correct: 77 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "    7: *SOMETHING-ONE CAN GO *WHAT                                   JOHN CAN GO CAN\n",
      "   12: *IX *WHAT *CAN CAN                                            JOHN CAN GO CAN\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *NEW-YORK *WHAT *CHICAGO *MARY      JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   28: JOHN *WHO IX *FUTURE *LOVE                                    JOHN LIKE IX IX IX\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "   36: *VISIT *VISIT *GIVE *GO *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 JOHN BUY CAR *JOHN                                      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: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *VISIT *MARY MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *NEW-YORK                                         ANN BLAME MARY\n",
      "   84: *NEW-YORK *NEW-YORK *VISIT BOOK                               IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY IX *IX *IX IX *ARRIVE *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *TOY1 IX *TOY1 *VISIT *ARRIVE                            JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX *SEARCH-FOR BOOK                              JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *IX NEW CAR *ARRIVE                                           POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *GO *NEW-YORK *ARRIVE *JOHN                              JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *IX *NEW-YORK                                                 WOMAN ARRIVE\n",
      "  113: IX CAR *GO *MARY *TOY1                                        IX CAR BLUE SUE BUY\n",
      "  119: *VISIT *ARRIVE IX *BOX *GO                                    SUE BUY IX CAR BLUE\n",
      "  122: JOHN *CHICAGO BOOK                                            JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *NEW-YORK BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *GIVE1 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 ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *TOY1 *SEARCH-FOR *GIVE1 TEACHER *YESTERDAY                   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 *ARRIVE *GO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *LOVE *LOVE BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# 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": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6179775280898876\n",
      "Total correct: 68 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *ARRIVE *ARRIVE                                          JOHN WRITE HOMEWORK\n",
      "    7: *MARY *BUY GO *WHAT                                           JOHN CAN GO CAN\n",
      "   12: JOHN *WHAT *WHAT CAN                                          JOHN CAN GO CAN\n",
      "   21: *MARY *NEW *VISIT *GO *CAR *CAR *FUTURE CHICKEN               JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *GO *LIKE IX                                        JOHN LIKE IX IX IX\n",
      "   28: *ANN LIKE *GO *MARY IX                                        JOHN LIKE IX IX IX\n",
      "   30: *SHOOT *IX *MARY IX IX                                        JOHN LIKE IX IX IX\n",
      "   36: MARY *MARY *GIVE3 *VISIT LIKE *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY *JOHN *FUTURE1 *VEGETABLE *MARY                         JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *POSS *SEE BUY CAR *IX                                        FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *FUTURE *MAN *ARRIVE HOUSE                               JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *IX *IX *VISIT                                            JOHN DECIDE VISIT MARY\n",
      "   67: *MARY *IX *JOHN BUY HOUSE                                     JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *BILL *MARY MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME MARY                                                ANN BLAME MARY\n",
      "   84: *JOHN *WHAT *VISIT BOOK                                       IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *FUTURE IX *IX *IX IX NEW *BREAK-DOWN                         JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SELF *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 *HOUSE BREAK-DOWN                                    POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *POSS                                                    JOHN LEG\n",
      "  107: *MARY POSS *BOX *MARY *MARY                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *IX *JOHN                                                     WOMAN ARRIVE\n",
      "  113: *SHOULD CAR *IX *JOHN *BOX                                    IX CAR BLUE SUE BUY\n",
      "  119: *PREFER *BUY1 IX *JOHN *FINISH                                SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *CAR *JOHN BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY *POSS WHAT BOOK                                      JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *IX WHO                                                  LOVE JOHN WHO\n",
      "  167: JOHN IX *SAY-1P LOVE *IX                                      JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *NEW *GIVE1 GIVE1 *YESTERDAY *CAR                             PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *BOX                                                     JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *MARY *YESTERDAY *ARRIVE                                JOHN GIVE GIRL BOX\n",
      "  193: *IX *YESTERDAY *YESTERDAY BOX                                 JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *ARRIVE *JOHN                                           LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE1 *IX *WOMAN BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_norm # 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": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5617977528089888\n",
      "Total correct: 78 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *GO *BROTHER *GIVE1                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN *BOX GO *ARRIVE                                          JOHN CAN GO CAN\n",
      "   12: JOHN *WHAT *JOHN CAN                                          JOHN CAN GO CAN\n",
      "   21: JOHN *ARRIVE WONT *PREFER *GIVE1 *WHAT *FUTURE *WHO           JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE IX *WHO IX                                          JOHN LIKE IX IX IX\n",
      "   28: JOHN *FUTURE IX *FUTURE *LOVE                                 JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: *IX *VISIT *GIVE *GIVE *MARY *MARY                            MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GO *GIVE *JOHN *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN 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 *GO *GO MARY                                            JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   74: *IX *CORN *GO *VISIT                                          JOHN NOT VISIT MARY\n",
      "   77: *JOHN *GIVE1 MARY                                             ANN BLAME MARY\n",
      "   84: *HOMEWORK *GIVE1 *GIVE1 *COAT                                 IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: JOHN *SHOULD GIVE *IX IX *ARRIVE *BOOK                        JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *HAVE IX SOMETHING-ONE *GO *CHOCOLATE                    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: JOHN *IX *HAVE *GO *MARY                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *LOVE                                                   WOMAN ARRIVE\n",
      "  113: IX CAR *IX *MARY *BUY1                                        IX CAR BLUE SUE BUY\n",
      "  119: *MARY *BUY1 IX *BLAME *GO                                     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 *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "  171: *IX MARY BLAME                                                JOHN MARY BLAME\n",
      "  174: *JOHN *JOHN GIVE1 *YESTERDAY *JOHN                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *GO ARRIVE                                                    JOHN ARRIVE\n",
      "  184: *GO BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *JOHN *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  193: JOHN *HAVE *YESTERDAY BOX                                     JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *STUDENT *GO                                            LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *LOVE *WOMAN BUY HOUSE                             JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_polar # 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": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5224719101123596\n",
      "Total correct: 85 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *PAST WRITE HOMEWORK                                          JOHN WRITE HOMEWORK\n",
      "    7: JOHN *PEOPLE *JOHN CAN                                        JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN FISH WONT *CORN1 BUT *PARTY *CHICKEN *EAT                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *ANN *CORN1 *ANN                                    JOHN LIKE IX IX IX\n",
      "   28: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *LIKE *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: MARY *JANA *GIVE1 *VISIT LIKE *MARY                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *CORN *VEGETABLE *MARY                            JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *FRANK *WRITE *WHAT SHOULD                              FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *FUTURE *CHOCOLATE HOUSE                          JOHN SHOULD NOT BUY HOUSE\n",
      "   57: JOHN *VEGETABLE VISIT *GIVE2                                  JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *FUTURE *ARRIVE HOUSE                             JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL *BLAME MARY                                         JOHN WILL VISIT MARY\n",
      "   74: JOHN *WHO *MARY MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME *ANN                                                ANN BLAME MARY\n",
      "   84: *JOHN *STUDENT *FUTURE BOOK                                   IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *POSS *SOMETHING-ONE *SOMETHING-ONE *SOMETHING-ONE *NEW-YORK COAT  JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *WHO *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *SOMETHING-ONE IX *IX WOMAN BOOK                         JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  107: *MARY POSS FRIEND *MARY *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *THINK *LAST-WEEK                                             WOMAN ARRIVE\n",
      "  113: *SHOOT CAR BLUE *JOHN *BUY1                                   IX CAR BLUE SUE BUY\n",
      "  119: *WHO *BUY1 IX *TOY *POSS                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *TOY YESTERDAY 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 *JOHN *MARY LOVE *LOVE                                   JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *GROUP GROUP GIVE1 *WHO TOY                                   PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *FRIEND                                                  JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *SELF *CORN *TOY                                        JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SELF *CORN BOX                                          JOHN GIVE GIRL BOX\n",
      "  199: *FRANK CHOCOLATE *TELL                                        LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *WOMAN *WOMAN BUY HOUSE                            JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_custom # 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": "markdown",
   "metadata": {},
   "source": [
    "### SelectorDIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6235955056179775\n",
      "Total correct: 67 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *GIVE1 *ARRIVE                                           JOHN WRITE HOMEWORK\n",
      "    7: JOHN *BOX *GIVE1 *ARRIVE                                      JOHN CAN GO CAN\n",
      "   12: JOHN *BOX *JOHN CAN                                           JOHN CAN GO CAN\n",
      "   21: JOHN *MARY *LOVE *MARY *BUY *FUTURE *FUTURE *MARY             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *JOHN IX IX                                          JOHN LIKE IX IX IX\n",
      "   28: JOHN *MARY *JOHN IX *SHOULD                                   JOHN LIKE IX IX IX\n",
      "   30: JOHN *IX *SHOULD *JOHN IX                                     JOHN LIKE IX IX IX\n",
      "   36: *JOHN *JOHN *JOHN IX *MARY *MARY                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY IX *JOHN MARY *MARY                                     JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "   50: *JOHN JOHN BUY CAR *MARY                                      FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *JOHN *IX *IX                                           JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *MARY VISIT MARY                                         JOHN WILL VISIT MARY\n",
      "   74: JOHN *JOHN *IX MARY                                           JOHN NOT VISIT MARY\n",
      "   77: *JOHN *ARRIVE MARY                                            ANN BLAME MARY\n",
      "   84: *GO *CAR *IX BOOK                                             IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *JOHN *IX *IX *JOHN *WHAT *ARRIVE                       JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *JOHN *JOHN *IX WOMAN *MARY                              JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX *JOHN *IX *IX BOOK                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *JOHN NEW CAR *BOOK                                           POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  107: JOHN *JOHN *CAR *MARY *JOHN                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  113: *JOHN CAR *MARY *IX *GIVE1                                    IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 IX CAR *MARY                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *ARRIVE *WHAT                                            JOHN READ BOOK\n",
      "  139: JOHN *GIVE1 WHAT *JOHN *WHAT                                  JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY *FUTURE WHAT *WHAT                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *ARRIVE JOHN *JOHN                                            LOVE JOHN WHO\n",
      "  167: JOHN IX *IX *BOOK MARY                                        JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "  174: *GIVE1 *MARY GIVE1 *JOHN *CAR                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *IX *JOHN *GIVE1 TEACHER *MARY                                ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *JOHN *JOHN *ARRIVE                                      JOHN GIVE GIRL BOX\n",
      "  193: JOHN *IX *IX BOX                                              JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *WHAT *MARY                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *IX *IX *JOHN BUY HOUSE                                  JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_delta # change as needed\n",
    "model_selector = SelectorDIC # 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": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5730337078651685\n",
      "Total correct: 76 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "    7: *SOMETHING-ONE *CAR *ARRIVE *WHAT                             JOHN CAN GO CAN\n",
      "   12: *IX *WHAT *WHAT *CAR                                          JOHN CAN GO CAN\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *CAR *CAR *FUTURE *MARY             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   28: JOHN *WHO IX *FUTURE *LOVE                                    JOHN LIKE IX IX IX\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "   36: *VISIT *VISIT *IX *GO *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 JOHN *GIVE1 CAR *JOHN                                   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: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *IX *GO *MARY MARY                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *GIVE1 *VISIT BOOK                                      IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY IX *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 *IX IX *IX *IX BOOK                                      JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *IX NEW CAR *ARRIVE                                           POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  107: JOHN *IX *HAVE *ARRIVE *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *IX ARRIVE                                                    WOMAN ARRIVE\n",
      "  113: IX CAR *IX *MARY *BOX                                         IX CAR BLUE SUE BUY\n",
      "  119: *VISIT *BUY1 IX *BOX *IX                                      SUE BUY IX CAR BLUE\n",
      "  122: JOHN *BUY BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 WHAT *MARY 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 *MARY *GO LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "  174: *CAR *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             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 *ARRIVE *GO                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *LOVE *LOVE *GIVE1 HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_ground # change as needed\n",
    "model_selector = SelectorDIC # 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": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6235955056179775\n",
      "Total correct: 67 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN WRITE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "    7: *MARY *CAR GO *WHAT                                           JOHN CAN GO CAN\n",
      "   12: JOHN *CAR *WHAT CAN                                           JOHN CAN GO CAN\n",
      "   21: *MARY *BOX *JOHN *BLAME *CAR *CAR *FUTURE CHICKEN             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE IX *MARY IX                                         JOHN LIKE IX IX IX\n",
      "   28: *ANN *ANN *ANN *ANN *ANN                                      JOHN LIKE IX IX IX\n",
      "   30: *IX-1P *CHOCOLATE *MARY *LOVE *LOVE                           JOHN LIKE IX IX IX\n",
      "   36: MARY *MARY *GIVE3 *WOMAN LIKE *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY *JOHN *SEE MARY *MARY                                   JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *POSS *SEE *BOX CAR *IX                                       FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *FUTURE *MAN *ARRIVE HOUSE                               JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *LOVE *IX *JOHN *VISIT                                        JOHN DECIDE VISIT MARY\n",
      "   67: *MARY *IX *JOHN *ARRIVE HOUSE                                 JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: *GO *VISIT VISIT MARY                                         JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *BOX *VISIT BOOK                                        IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *POSS *IX *IX IX *ARRIVE *BREAK-DOWN                    JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SELF *IX IX *IX WOMAN BOOK                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX *LOVE BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *POSS                                                    JOHN LEG\n",
      "  107: *MARY POSS *BOX *MARY *TOY1                                   JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *JOHN                                                   WOMAN ARRIVE\n",
      "  113: *SHOULD CAR *IX *JOHN *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 *CAR *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 *SAY-1P LOVE *IX                                      JOHN IX SAY LOVE MARY\n",
      "  171: *LIKE *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *CAR *GIVE1 GIVE1 *YESTERDAY *CAR                             PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *BOX                                                     JOHN ARRIVE\n",
      "  184: *IX *IX *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *MARY *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  193: *IX *YESTERDAY *YESTERDAY BOX                                 JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *BOX *JOHN                                              LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE1 *IX *WOMAN *ARRIVE HOUSE                          JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_norm # change as needed\n",
    "model_selector = SelectorDIC # 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": 78,
   "metadata": {
    "collapsed": false
   },
   "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 *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "   12: JOHN *WHAT *JOHN CAN                                          JOHN CAN GO CAN\n",
      "   21: JOHN *NEW *JOHN *PREFER *CAR *WHAT *FUTURE *WHO               JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   28: JOHN *FUTURE IX *FUTURE *LOVE                                 JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: *IX *VISIT *GIVE *GIVE *MARY *MARY                            MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GO *GIVE *JOHN *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 NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *MARY *GO *GO MARY                                            JOHN DECIDE VISIT MARY\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   74: *IX *GO *GO *VISIT                                            JOHN NOT VISIT MARY\n",
      "   77: *JOHN *GIVE1 MARY                                             ANN BLAME MARY\n",
      "   84: *HOMEWORK *GIVE1 *POSS *COAT                                  IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE *GIVE *IX *IX IX *ARRIVE *BOOK                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN GIVE IX SOMETHING-ONE WOMAN *ARRIVE                      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 POSS *HAVE HAVE *MARY                                    JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *LOVE                                                   WOMAN ARRIVE\n",
      "  113: IX CAR *IX *MARY *JOHN                                        IX CAR BLUE SUE BUY\n",
      "  119: *MARY *BUY1 IX *BLAME *IX                                     SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *ARRIVE WHAT *MARY *ARRIVE                               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 *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "  171: *IX MARY BLAME                                                JOHN MARY BLAME\n",
      "  174: *JOHN *JOHN GIVE1 *YESTERDAY *JOHN                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *EAT ARRIVE                                                   JOHN ARRIVE\n",
      "  184: *GO BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *GO *YESTERDAY BOX                                      JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GO *YESTERDAY BOX                                       JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *STUDENT *GO                                            LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE *LOVE *JOHN BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_polar # change as needed\n",
    "model_selector = SelectorDIC # 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": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5168539325842697\n",
      "Total correct: 86 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *PAST WRITE HOMEWORK                                          JOHN WRITE HOMEWORK\n",
      "    7: JOHN *TOY *JOHN CAN                                           JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN FISH WONT *CORN1 BUT *PARTY *CHICKEN *EAT                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *ANN *CORN1 *ANN                                    JOHN LIKE IX IX IX\n",
      "   28: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *MARY *LIKE *MARY                                   JOHN LIKE IX IX IX\n",
      "   36: MARY *JANA *GIVE1 *VISIT LIKE *MARY                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *CORN *VEGETABLE *MARY                            JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *FRANK *WRITE *WHAT SHOULD                              FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *FUTURE BUY HOUSE                                 JOHN SHOULD NOT BUY HOUSE\n",
      "   57: JOHN *VEGETABLE VISIT *GIVE2                                  JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *FUTURE *ARRIVE HOUSE                             JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN WILL *BLAME MARY                                         JOHN WILL VISIT MARY\n",
      "   74: JOHN *WHO *MARY MARY                                          JOHN NOT VISIT MARY\n",
      "   77: ANN BLAME *ANN                                                ANN BLAME MARY\n",
      "   84: *JOHN *STUDENT *FUTURE BOOK                                   IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *POSS *SOMETHING-ONE *SOMETHING-ONE *SOMETHING-ONE *NEW-YORK COAT  JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *WHO *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *SOMETHING-ONE IX *IX WOMAN BOOK                         JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  107: *MARY POSS FRIEND *MARY *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *THINK *LAST-WEEK                                             WOMAN ARRIVE\n",
      "  113: *SHOOT CAR BLUE *JOHN *BUY1                                   IX CAR BLUE SUE BUY\n",
      "  119: *WHO *BUY1 IX *BLAME *POSS                                    SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *TOY YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *STUDENT YESTERDAY WHAT BOOK                             JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN *JOHN *MARY LOVE MARY                                    JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *GROUP GROUP GIVE1 *WHO TOY                                   PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SUE *HAVE                                                    JOHN ARRIVE\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "  189: *MARY *SELF *CORN *TOY                                        JOHN GIVE GIRL BOX\n",
      "  193: JOHN *SELF *CORN BOX                                          JOHN GIVE GIRL BOX\n",
      "  199: *FRANK CHOCOLATE *TELL                                        LIKE CHOCOLATE WHO\n",
      "  201: JOHN *MARY *WOMAN *WOMAN BUY HOUSE                            JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_custom # change as needed\n",
    "model_selector = SelectorDIC # 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": "markdown",
   "metadata": {},
   "source": [
    "### SelectorCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.651685393258427\n",
      "Total correct: 62 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *WHAT *GO1                                               JOHN WRITE HOMEWORK\n",
      "    7: JOHN *HAVE *GIVE1 *GO                                         JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *MARY *GO1 *MARY *BUY *GO *FUTURE *MARY                  JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *LOVE *GIVE IX                                       JOHN LIKE IX IX IX\n",
      "   28: JOHN *MARY IX *WHAT *WOMAN                                    JOHN LIKE IX IX IX\n",
      "   30: JOHN *IX *LOVE *JOHN *WOMAN                                   JOHN LIKE IX IX IX\n",
      "   36: *IX *IX *GIVE IX *MARY *IX                                    MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: *MARY IX *JOHN *IX *IX                                        JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *WOMAN BUY HOUSE                                         JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *WHAT BUY CAR *WHAT                                     FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *MARY *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: JOHN *LOVE *IX *IX                                            JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *JOHN *LOVE BUY *BOOK                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *MARY VISIT *BOOK                                        JOHN WILL VISIT MARY\n",
      "   74: JOHN *IX *IX MARY                                             JOHN NOT VISIT MARY\n",
      "   77: *JOHN *CAR MARY                                               ANN BLAME MARY\n",
      "   84: *JOHN *GO *WHAT *WHAT                                         IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: JOHN *GIVE GIVE *IX *VISIT *CAR COAT                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *MARY *JOHN *JOHN *IX WOMAN *WHAT                             JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: *JOHN NEW CAR *CAN                                            POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *IX                                                      JOHN LEG\n",
      "  107: JOHN *JOHN *LOVE *GIVE1 *MARY                                 JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  113: *JOHN *GIVE1 *MARY *IX *BUY1                                  IX CAR BLUE SUE BUY\n",
      "  119: *JOHN *BUY1 *GIVE1 *GIVE1 *WHAT                               SUE BUY IX CAR BLUE\n",
      "  122: JOHN *HAVE BOOK                                               JOHN READ BOOK\n",
      "  139: JOHN *NEW WHAT *JOHN BOOK                                     JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN BUY *WHAT WHAT *VIDEOTAPE                                JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *NEW *MARY *MARY                                              LOVE JOHN WHO\n",
      "  167: JOHN IX *IX *BOOK *BOOK                                       JOHN IX SAY LOVE MARY\n",
      "  171: *IX *JOHN BLAME                                               JOHN MARY BLAME\n",
      "  174: *GIVE1 *WHAT GIVE1 *JOHN *BOOK                                PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: JOHN *NEW                                                     JOHN ARRIVE\n",
      "  184: *GIVE *JOHN *GIVE1 TEACHER *WHAT                              ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *IX *JOHN *BOOK                                          JOHN GIVE GIRL BOX\n",
      "  193: JOHN *JOHN *WOMAN BOX                                         JOHN GIVE GIRL BOX\n",
      "  199: *JOHN *BOOK *MARY                                             LIKE CHOCOLATE WHO\n",
      "  201: JOHN *IX MARY *WOMAN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_delta # change as needed\n",
    "model_selector = SelectorCV # 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": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6123595505617978\n",
      "Total correct: 69 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: JOHN *BOOK *BLAME                                             JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "   12: JOHN *CAR *CAN CAN                                            JOHN CAN GO CAN\n",
      "   21: JOHN *VIDEOTAPE *FUTURE *JOHN *BLAME *CAR *VISIT *WHO         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 *LOVE                                          JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE IX IX *GO                                           JOHN LIKE IX IX IX\n",
      "   36: MARY VEGETABLE *GIVE *GO *IX *IX                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *GIVE *JOHN *JOHN *GO                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *SHOULD BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN JOHN BUY CAR *SOMETHING-ONE                             FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *VISIT VISIT *IX                                          JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *POSS *WHO *ARRIVE HOUSE                                 JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GO MARY                                         JOHN WILL VISIT MARY\n",
      "   74: *IX *VISIT *MARY *GO                                          JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *LOVE *ARRIVE *GO BOOK                                        IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *MARY *POSS GIVE *SOMETHING-ONE *SOMETHING-ONE *BUY *BOOK     JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *SOMETHING-ONE *SOMETHING-ONE SOMETHING-ONE WOMAN *ARRIVE  JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN GIVE *SOMETHING-ONE *WOMAN *GIVE1 BOOK                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW CAR *BOOK                                            POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  107: JOHN *MARY *CAN *GO *WHO                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *MARY *LOVE                                                   WOMAN ARRIVE\n",
      "  113: *MARY *CAN *GIVE *MARY *BLUE                                  IX CAR BLUE SUE BUY\n",
      "  119: *VEGETABLE *LOVE *BLUE *CAN *MARY                             SUE BUY IX CAR BLUE\n",
      "  122: JOHN *HOUSE BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *LOVE *CAN YESTERDAY *ARRIVE                             JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *NEW *FUTURE *CAR BOOK                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN *VISIT *JANA *WOMAN *GO                                  JOHN IX SAY LOVE MARY\n",
      "  171: *MARY *VISIT *MARY                                            JOHN MARY BLAME\n",
      "  174: *CAN *NEW GIVE1 *GO *CAN                                      PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *BLUE *SOMETHING-ONE                                          JOHN ARRIVE\n",
      "  184: *SOMETHING-ONE *GO *HOUSE TEACHER *GO                         ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *VISIT *VISIT *CAN                                       JOHN GIVE GIRL BOX\n",
      "  193: *MARY *GIVE1 *VISIT BOX                                       JOHN GIVE GIRL BOX\n",
      "  199: *LOVE *NEW WHO                                                LIKE CHOCOLATE WHO\n",
      "  201: JOHN *SHOULD *GIVE *JOHN BUY HOUSE                            JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_ground # change as needed\n",
    "model_selector = SelectorCV # 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": 81,
   "metadata": {
    "collapsed": false
   },
   "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: JOHN *BUY *ARRIVE                                             JOHN WRITE HOMEWORK\n",
      "    7: JOHN *NEW GO *ARRIVE                                          JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: *LIKE *NEW *HAVE *GO *BLAME *CAR *FUTURE *HAVE                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *GO LIKE *LIKE *LIKE *GO                                      JOHN LIKE IX IX IX\n",
      "   28: JOHN LIKE *LIKE *LIKE *GO                                     JOHN LIKE IX IX IX\n",
      "   30: *IX-1P LIKE *LOVE *LIKE *MARY                                 JOHN LIKE IX IX IX\n",
      "   36: *VISIT *SHOULD *YESTERDAY *VISIT *LEAVE *LIKE                 MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *SELF *SHOULD LOVE                                JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *POSS *SEE *NEW CAR *HAVE                                     FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN *TELL NOT *HAVE HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: JOHN *WHO *MARY MARY                                          JOHN DECIDE VISIT MARY\n",
      "   67: JOHN *SOMETHING-ONE *JOHN *ARRIVE *CAN                        JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   74: JOHN *VISIT VISIT *VISIT                                      JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *ARRIVE *POSS *NEW                                      IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *TELL *HAVE *SOMETHING-ONE *SOMETHING-ONE *SOMETHING-ONE NEW COAT  JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *SELF *GIVE1 *SOMETHING-ONE *GIVE1 WOMAN *VIDEOTAPE           JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *GIVE1 *WOMAN *WOMAN WOMAN BOOK                          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS NEW *HOUSE BREAK-DOWN                                    POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *POSS                                                    JOHN LEG\n",
      "  107: JOHN *IX *GIVE1 *LIKE *FUTURE                                 JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *JOHN                                                   WOMAN ARRIVE\n",
      "  113: IX *CAN *IX SUE *HAVE                                         IX CAR BLUE SUE BUY\n",
      "  119: *WHO *BUY1 *HAVE *ARRIVE *FUTURE                              SUE BUY IX CAR BLUE\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *CAR YESTERDAY *NEW                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *ARRIVE *GO WHAT *COAT                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *GIVE1 *MARY *CORN                                            LOVE JOHN WHO\n",
      "  167: JOHN *VISIT *VISIT *MARY *LOVE                                JOHN IX SAY LOVE MARY\n",
      "  171: *JANA *JOHN BLAME                                             JOHN MARY BLAME\n",
      "  174: *NEW *GIVE1 GIVE1 *WHO *VISIT                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *SOMETHING-ONE *GIVE1                                         JOHN ARRIVE\n",
      "  184: *IX BOY *GIVE1 TEACHER *WHO                                   ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *GIVE1 *FINISH *ARRIVE                                  JOHN GIVE GIRL BOX\n",
      "  193: JOHN *YESTERDAY *FINISH BOX                                   JOHN GIVE GIRL BOX\n",
      "  199: *JOHN CHOCOLATE *TELL                                         LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE1 *WOMAN *WOMAN BUY HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_norm # change as needed\n",
    "model_selector = SelectorCV # 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": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6404494382022472\n",
      "Total correct: 64 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *POSS *BROTHER *GO                                            JOHN WRITE HOMEWORK\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "   12: *IX *CAR *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN *JOHN *GIVE1 *JOHN *CAR *CAR *FUTURE *WHO                JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *LOVE *JOHN IX                                       JOHN LIKE IX IX IX\n",
      "   28: JOHN *JOHN *LOVE IX *LOVE                                     JOHN LIKE IX IX IX\n",
      "   30: JOHN LIKE *GO *LIKE *GO                                       JOHN LIKE IX IX IX\n",
      "   36: *VISIT *VISIT *GIVE *GIVE *MARY *IX                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *VISIT *VISIT *JOHN *MARY                                JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *POSS BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *SEE BUY CAR SHOULD                                     FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *VISIT VISIT MARY                                         JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *WHO BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *FINISH *GO *BLAME                                       JOHN WILL VISIT MARY\n",
      "   74: *GO *VISIT *MARY *GO                                          JOHN NOT VISIT MARY\n",
      "   77: *JOHN BLAME *LOVE                                             ANN BLAME MARY\n",
      "   84: *LOVE *BLAME *POSS BOOK                                       IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE1 *GIVE *SOMETHING-ONE *SOMETHING-ONE *SOMETHING-ONE *ARRIVE COAT  JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: JOHN *HAVE *SOMETHING-ONE SOMETHING-ONE *VISIT *ARRIVE        JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN GIVE *SOMETHING-ONE SOMETHING-ONE *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 *JOHN                                                    JOHN LEG\n",
      "  107: JOHN *GIVE *HAVE *GO *GO                                      JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *MARY *LOVE                                                   WOMAN ARRIVE\n",
      "  113: IX *HAVE *MARY *JOHN *BUY1                                    IX CAR BLUE SUE BUY\n",
      "  119: *VISIT *BUY1 *GO *VISIT *VISIT                                SUE BUY IX CAR BLUE\n",
      "  122: JOHN *BOOK BOOK                                               JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *DECIDE YESTERDAY *ARRIVE                          JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *NEW *GO *CAR BOOK                                       JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "  167: JOHN *MARY *VISIT LOVE *GO                                    JOHN IX SAY LOVE MARY\n",
      "  171: *IX *VISIT *SOMETHING-ONE                                     JOHN MARY BLAME\n",
      "  174: *CAN *VISIT GIVE1 *GO *VISIT                                  PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *YESTERDAY *SOMETHING-ONE                                     JOHN ARRIVE\n",
      "  184: *GIVE *GIVE *GO TEACHER *GIRL                                 ALL BOY GIVE TEACHER APPLE\n",
      "  189: JOHN *VISIT *VISIT *CAN                                       JOHN GIVE GIRL BOX\n",
      "  193: JOHN *HAVE *VISIT BOX                                         JOHN GIVE GIRL BOX\n",
      "  199: *LOVE *NEW *JOHN                                              LIKE CHOCOLATE WHO\n",
      "  201: JOHN *SHOULD *WOMAN *JOHN BUY HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_polar # change as needed\n",
    "model_selector = SelectorCV # 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": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.6179775280898876\n",
      "Total correct: 68 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "    2: *IX-1P *NEW-YORK *WHO                                         JOHN WRITE HOMEWORK\n",
      "    7: JOHN *HAVE GO CAN                                             JOHN CAN GO CAN\n",
      "   12: JOHN CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   21: JOHN FISH WONT *CORN1 BUT *CAR *CHICKEN *EAT                  JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *MARY LIKE *LOVE *LIKE *MARY                                  JOHN LIKE IX IX IX\n",
      "   28: *MARY LIKE *LOVE *LIKE *MARY                                  JOHN LIKE IX IX IX\n",
      "   30: *IX *IX IX IX IX                                              JOHN LIKE IX IX IX\n",
      "   36: MARY *JOHN *GIVE1 *VISIT *MARY *JOHN                          MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "   40: JOHN *MARY *CORN *JANA *IX                                    JOHN IX THINK MARY LOVE\n",
      "   43: JOHN *SHOULD BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "   50: *JOHN *FRANK BUY CAR SHOULD                                   FUTURE JOHN BUY CAR SHOULD\n",
      "   54: JOHN SHOULD *GIVE1 *CHOCOLATE *COAT                           JOHN SHOULD NOT BUY HOUSE\n",
      "   57: *IX *WHO VISIT MARY                                           JOHN DECIDE VISIT MARY\n",
      "   67: JOHN FUTURE *SHOULD BUY HOUSE                                 JOHN FUTURE NOT BUY HOUSE\n",
      "   71: JOHN *GIVE1 VISIT MARY                                        JOHN WILL VISIT MARY\n",
      "   74: *IX *WHO *MARY MARY                                           JOHN NOT VISIT MARY\n",
      "   77: *MARY BLAME MARY                                              ANN BLAME MARY\n",
      "   84: *JOHN *ARRIVE *FUTURE *NEW-YORK                               IX-1P FIND SOMETHING-ONE BOOK\n",
      "   89: *GIVE1 *POSS *WILL MAN *SOMETHING-ONE NEW *BREAK-DOWN         JOHN IX GIVE MAN IX NEW COAT\n",
      "   90: *JANA *GIVE1 *BOY *GIVE1 WOMAN *VIDEOTAPE                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   92: JOHN *GIVE1 *SOMETHING-ONE SOMETHING-ONE WOMAN BOOK           JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "  100: POSS *NEW-YORK *HOUSE BREAK-DOWN                              POSS NEW CAR BREAK-DOWN\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  107: *MARY *BLUE *HAVE *JOHN *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "  108: *LOVE *LOVE                                                   WOMAN ARRIVE\n",
      "  113: IX *HAVE BLUE *JOHN *BUY1                                     IX CAR BLUE SUE BUY\n",
      "  119: *WHO *BUY1 *BLUE *CAN *SELF                                   SUE BUY IX CAR BLUE\n",
      "  122: JOHN READ BOOK                                                JOHN READ BOOK\n",
      "  139: JOHN *BUY1 *CAN YESTERDAY *VIDEOTAPE                          JOHN BUY WHAT YESTERDAY BOOK\n",
      "  142: JOHN *ARRIVE *GO *CAR *NEW-YORK                               JOHN BUY YESTERDAY WHAT BOOK\n",
      "  158: *STOLEN *MARY WHO                                             LOVE JOHN WHO\n",
      "  167: JOHN *MARY *MARY LOVE *LOVE                                   JOHN IX SAY LOVE MARY\n",
      "  171: JOHN *JOHN *DECIDE                                            JOHN MARY BLAME\n",
      "  174: *DECIDE *GIVE1 GIVE1 *CORN *DECIDE                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  181: *GIRL *HAVE                                                   JOHN ARRIVE\n",
      "  184: *GIVE1 BOY *TEACHER TEACHER *CORN                             ALL BOY GIVE TEACHER APPLE\n",
      "  189: *JANA *JOHN *CORN *BUY1                                       JOHN GIVE GIRL BOX\n",
      "  193: JOHN *GIVE1 *CORN BOX                                         JOHN GIVE GIRL BOX\n",
      "  199: *JOHN CHOCOLATE *TELL                                         LIKE CHOCOLATE WHO\n",
      "  201: JOHN *GIVE1 *WOMAN *LOVE BUY HOUSE                            JOHN TELL MARY IX-1P BUY HOUSE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "features = features_custom # change as needed\n",
    "model_selector = SelectorCV # 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": "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",
    "\n",
    "##### WER Table\n",
    "| Features       | BIC Selector       | DIC Selector        | CV Selector  |\n",
    "| ------------- |:------------------:|:-------------------:| ------------:|\n",
    "| Delta|.63|.62|.65|\n",
    "| Ground|.56|.57|.61|\n",
    "| Norm|.61|.62|.66|\n",
    "| Polar|.56|.55|.64|\n",
    "| Custom|.52|.51|.61|\n",
    "\n",
    "After reviewing the table, it's clear to see that BIC Selector and DIC Selector are very close in WER.  This may be true due to the fact that both of these selectors leverage all samples when training models.  Additionally, it appears that my custom feature outperforms all other individual features -- These examples display the power of mean normalisation.  CV Selector appears to have scored worst for WER; this may be due to the fact of generalization and that CV does not use the entire training set to train models.  Leveraging CV Selector will often avoid overfitting during training.  DIC Selector achieved the lowest WER at .51 when using custom features -- predicting 86 out of 178 correctly.  DIC outperformed BIC when using custom features because DIC uses more comparisons and works greats for classification problems.  To improve WER, I'd recommend leveraging N-Grams and transition probabilities.  With sufficient training data it's possible to improve the WER by eliminating improbable word transitions."
   ]
  },
  {
   "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": 66,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "..\n",
      "----------------------------------------------------------------------\n",
      "Ran 2 tests in 30.095s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=2 errors=0 failures=0>"
      ]
     },
     "execution_count": 66,
     "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": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# create a DataFrame of log likelihoods for the test word items\n",
    "df_probs = pd.DataFrame(data=probabilities)\n",
    "df_probs.head()"
   ]
  }
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