Plurals (population learnability).ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Python27\\lib\\site-packages\\IPython\\extensions\\rmagic.py:693: UserWarning: The rmagic extension in IPython is deprecated in favour of rpy2.ipython. If available, that will be loaded instead.\n",
      "http://rpy.sourceforge.net/\n",
      "  warnings.warn(\"The rmagic extension in IPython is deprecated in favour of \"\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import pandas.rpy.common as com\n",
    "import numpy as np\n",
    "from sklearn.feature_extraction import DictVectorizer\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "%load_ext rmagic\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "%precision 2\n",
    "pd.set_option('display.precision', 3)\n",
    "\n",
    "import ndl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%R\n",
    "library(ndl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cues</th>\n",
       "      <th>Outcomes</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>Number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td>                 [size, shape, color, 1, exactly1]</td>\n",
       "      <td>  1</td>\n",
       "      <td> 455</td>\n",
       "      <td>  1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td>              [size, shape, color, 1, 2, exactly2]</td>\n",
       "      <td>  2</td>\n",
       "      <td> 205</td>\n",
       "      <td>  2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td>           [size, shape, color, 1, 2, 3, exactly3]</td>\n",
       "      <td>  3</td>\n",
       "      <td> 107</td>\n",
       "      <td>  3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td>        [size, shape, color, 1, 2, 3, 4, exactly4]</td>\n",
       "      <td>  4</td>\n",
       "      <td>  60</td>\n",
       "      <td>  4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td>     [size, shape, color, 1, 2, 3, 4, 5, exactly5]</td>\n",
       "      <td>  5</td>\n",
       "      <td>  50</td>\n",
       "      <td>  5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td>  [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]</td>\n",
       "      <td>  6</td>\n",
       "      <td>  36</td>\n",
       "      <td>  6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...</td>\n",
       "      <td>  7</td>\n",
       "      <td>  21</td>\n",
       "      <td>  7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...</td>\n",
       "      <td>  8</td>\n",
       "      <td>  20</td>\n",
       "      <td>  8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>  9</td>\n",
       "      <td>  13</td>\n",
       "      <td>  9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 10</td>\n",
       "      <td>  16</td>\n",
       "      <td> 10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 11</td>\n",
       "      <td>   3</td>\n",
       "      <td> 11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 12</td>\n",
       "      <td>   4</td>\n",
       "      <td> 12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 13</td>\n",
       "      <td>   2</td>\n",
       "      <td> 13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 14</td>\n",
       "      <td>   2</td>\n",
       "      <td> 14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> 15</td>\n",
       "      <td>   4</td>\n",
       "      <td> 15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 Cues Outcomes  Frequency  \\\n",
       "1                   [size, shape, color, 1, exactly1]        1        455   \n",
       "2                [size, shape, color, 1, 2, exactly2]        2        205   \n",
       "3             [size, shape, color, 1, 2, 3, exactly3]        3        107   \n",
       "4          [size, shape, color, 1, 2, 3, 4, exactly4]        4         60   \n",
       "5       [size, shape, color, 1, 2, 3, 4, 5, exactly5]        5         50   \n",
       "6    [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]        6         36   \n",
       "7   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...        7         21   \n",
       "8   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...        8         20   \n",
       "9   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...        9         13   \n",
       "10  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       10         16   \n",
       "11  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       11          3   \n",
       "12  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       12          4   \n",
       "13  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       13          2   \n",
       "14  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       14          2   \n",
       "15  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...       15          4   \n",
       "\n",
       "   Number  \n",
       "1       1  \n",
       "2       2  \n",
       "3       3  \n",
       "4       4  \n",
       "5       5  \n",
       "6       6  \n",
       "7       7  \n",
       "8       8  \n",
       "9       9  \n",
       "10     10  \n",
       "11     11  \n",
       "12     12  \n",
       "13     13  \n",
       "14     14  \n",
       "15     15  \n",
       "\n",
       "[15 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = com.load_data('numbers')\n",
    "data['Cues'] = [x.split('_') for x in data['Cues']]\n",
    "data['Number'] = data['Outcomes']\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def activation(W):\n",
    "    return pd.DataFrame([ndl.activation(c,W) for c in data.Cues],index=data.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular / plural distinction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cues</th>\n",
       "      <th>Outcomes</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>Number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td>                 [size, shape, color, 1, exactly1]</td>\n",
       "      <td> singular</td>\n",
       "      <td> 455</td>\n",
       "      <td>  1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td>              [size, shape, color, 1, 2, exactly2]</td>\n",
       "      <td>   plural</td>\n",
       "      <td> 205</td>\n",
       "      <td>  2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td>           [size, shape, color, 1, 2, 3, exactly3]</td>\n",
       "      <td>   plural</td>\n",
       "      <td> 107</td>\n",
       "      <td>  3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td>        [size, shape, color, 1, 2, 3, 4, exactly4]</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  60</td>\n",
       "      <td>  4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td>     [size, shape, color, 1, 2, 3, 4, 5, exactly5]</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  50</td>\n",
       "      <td>  5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td>  [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  36</td>\n",
       "      <td>  6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  21</td>\n",
       "      <td>  7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  20</td>\n",
       "      <td>  8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  13</td>\n",
       "      <td>  9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>  16</td>\n",
       "      <td> 10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>   3</td>\n",
       "      <td> 11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>   4</td>\n",
       "      <td> 12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>   2</td>\n",
       "      <td> 13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>   2</td>\n",
       "      <td> 14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td>   plural</td>\n",
       "      <td>   4</td>\n",
       "      <td> 15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 Cues  Outcomes  Frequency  \\\n",
       "1                   [size, shape, color, 1, exactly1]  singular        455   \n",
       "2                [size, shape, color, 1, 2, exactly2]    plural        205   \n",
       "3             [size, shape, color, 1, 2, 3, exactly3]    plural        107   \n",
       "4          [size, shape, color, 1, 2, 3, 4, exactly4]    plural         60   \n",
       "5       [size, shape, color, 1, 2, 3, 4, 5, exactly5]    plural         50   \n",
       "6    [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]    plural         36   \n",
       "7   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...    plural         21   \n",
       "8   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...    plural         20   \n",
       "9   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural         13   \n",
       "10  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural         16   \n",
       "11  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural          3   \n",
       "12  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural          4   \n",
       "13  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural          2   \n",
       "14  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural          2   \n",
       "15  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...    plural          4   \n",
       "\n",
       "   Number  \n",
       "1       1  \n",
       "2       2  \n",
       "3       3  \n",
       "4       4  \n",
       "5       5  \n",
       "6       6  \n",
       "7       7  \n",
       "8       8  \n",
       "9       9  \n",
       "10     10  \n",
       "11     11  \n",
       "12     12  \n",
       "13     13  \n",
       "14     14  \n",
       "15     15  \n",
       "\n",
       "[15 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Outcomes'] = 'plural'\n",
    "data['Outcomes'][1] = 'singular'\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>plural</th>\n",
       "      <th>singular</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td> 0.09</td>\n",
       "      <td> 0.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td> 0.13</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td> 0.16</td>\n",
       "      <td> 0.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> 0.14</td>\n",
       "      <td> 0.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    plural  singular\n",
       "1     0.09      0.29\n",
       "2     0.13      0.23\n",
       "3     0.16      0.22\n",
       "4     0.14      0.23\n",
       "5     0.14      0.23\n",
       "6     0.14      0.23\n",
       "7     0.14      0.23\n",
       "8     0.14      0.23\n",
       "9     0.14      0.23\n",
       "10    0.14      0.23\n",
       "11    0.14      0.23\n",
       "12    0.14      0.23\n",
       "13    0.14      0.23\n",
       "14    0.14      0.23\n",
       "15    0.14      0.23\n",
       "\n",
       "[15 rows x 2 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = ndl.rw(data,M=10)\n",
    "A = activation(W)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these associations, how many of the 15 items will the learner correctly label?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Truth</th>\n",
       "      <th>Prediction</th>\n",
       "      <th>Accurate?</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td> singular</td>\n",
       "      <td> singular</td>\n",
       "      <td>  True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>   plural</td>\n",
       "      <td> singular</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Truth Prediction Accurate?\n",
       "1   singular   singular      True\n",
       "2     plural   singular     False\n",
       "3     plural   singular     False\n",
       "4     plural   singular     False\n",
       "5     plural   singular     False\n",
       "6     plural   singular     False\n",
       "7     plural   singular     False\n",
       "8     plural   singular     False\n",
       "9     plural   singular     False\n",
       "10    plural   singular     False\n",
       "11    plural   singular     False\n",
       "12    plural   singular     False\n",
       "13    plural   singular     False\n",
       "14    plural   singular     False\n",
       "15    plural   singular     False\n",
       "\n",
       "[15 rows x 3 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame([data['Outcomes'], A.idxmax(1), A.idxmax(1) == data['Outcomes']], index = ['Truth', 'Prediction', 'Accurate?']).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(A.idxmax(1) == data['Outcomes'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How often are they correct (using relative item frequencies)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(sum(data['Frequency'] * (A.idxmax(1) == data['Outcomes']))) / float(sum(data['Frequency']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def accuracy(data, M):\n",
    "    W = ndl.rw(data, M=M)\n",
    "    A = activation(W)\n",
    "    return np.mean(A.idxmax(1) == data['Outcomes'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.00"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(data, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a population of 100 learners trying to acquire the number system, what proportion are able to successfully label all 15 items given M trials?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([accuracy(data, M=10) == 1 for i in xrange(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def population_accuracy(M=10, pop=100):\n",
    "    return np.mean([accuracy(data, M=M) == 1 for i in xrange(pop)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "MAX_TRIALS = 500\n",
    "P = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P['sg / pl'] = [population_accuracy(M=i) for i in xrange(1,MAX_TRIALS)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1789e780>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17766a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(range(1,len(P['sg / pl'])+1), P['sg / pl'], '-', linewidth=2)\n",
    "plt.title('Singular / plural distinction')\n",
    "plt.xlabel('Trial Number')\n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dual / non-dual distinction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cues</th>\n",
       "      <th>Outcomes</th>\n",
       "      <th>Frequency</th>\n",
       "      <th>Number</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td>                 [size, shape, color, 1, exactly1]</td>\n",
       "      <td> notdual</td>\n",
       "      <td> 455</td>\n",
       "      <td>  1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td>              [size, shape, color, 1, 2, exactly2]</td>\n",
       "      <td>    dual</td>\n",
       "      <td> 205</td>\n",
       "      <td>  2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td>           [size, shape, color, 1, 2, 3, exactly3]</td>\n",
       "      <td> notdual</td>\n",
       "      <td> 107</td>\n",
       "      <td>  3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td>        [size, shape, color, 1, 2, 3, 4, exactly4]</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  60</td>\n",
       "      <td>  4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td>     [size, shape, color, 1, 2, 3, 4, 5, exactly5]</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  50</td>\n",
       "      <td>  5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td>  [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  36</td>\n",
       "      <td>  6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  21</td>\n",
       "      <td>  7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  20</td>\n",
       "      <td>  8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  13</td>\n",
       "      <td>  9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>  16</td>\n",
       "      <td> 10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>   3</td>\n",
       "      <td> 11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>   4</td>\n",
       "      <td> 12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>   2</td>\n",
       "      <td> 13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>   2</td>\n",
       "      <td> 14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...</td>\n",
       "      <td> notdual</td>\n",
       "      <td>   4</td>\n",
       "      <td> 15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 Cues Outcomes  Frequency  \\\n",
       "1                   [size, shape, color, 1, exactly1]  notdual        455   \n",
       "2                [size, shape, color, 1, 2, exactly2]     dual        205   \n",
       "3             [size, shape, color, 1, 2, 3, exactly3]  notdual        107   \n",
       "4          [size, shape, color, 1, 2, 3, 4, exactly4]  notdual         60   \n",
       "5       [size, shape, color, 1, 2, 3, 4, 5, exactly5]  notdual         50   \n",
       "6    [size, shape, color, 1, 2, 3, 4, 5, 6, exactly6]  notdual         36   \n",
       "7   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, exac...  notdual         21   \n",
       "8   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, e...  notdual         20   \n",
       "9   [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual         13   \n",
       "10  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual         16   \n",
       "11  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual          3   \n",
       "12  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual          4   \n",
       "13  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual          2   \n",
       "14  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual          2   \n",
       "15  [size, shape, color, 1, 2, 3, 4, 5, 6, 7, 8, 9...  notdual          4   \n",
       "\n",
       "   Number  \n",
       "1       1  \n",
       "2       2  \n",
       "3       3  \n",
       "4       4  \n",
       "5       5  \n",
       "6       6  \n",
       "7       7  \n",
       "8       8  \n",
       "9       9  \n",
       "10     10  \n",
       "11     11  \n",
       "12     12  \n",
       "13     13  \n",
       "14     14  \n",
       "15     15  \n",
       "\n",
       "[15 rows x 4 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['Outcomes'] = 'notdual'\n",
    "data['Outcomes'][2] = 'dual'\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P['du / non-du'] = [population_accuracy(M=i) for i in xrange(1,MAX_TRIALS)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x178b8c88>"
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     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1773d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,len(P['du / non-du'])+1), P['du / non-du'], '-', linewidth=2)\n",
    "plt.title('Dual / non-dual distinction')\n",
    "plt.xlabel('Trial Number')\n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular, dual, plural"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['Outcomes'] = 'plural'\n",
    "data['Outcomes'][1] = 'singular'\n",
    "data['Outcomes'][2] = 'dual'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P['sg / du / pl'] = [population_accuracy(M=i) for i in xrange(1,MAX_TRIALS)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x17af5fd0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1789e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,len(P['sg / du / pl'])+1), P['sg / du / pl'], '-', linewidth=2)\n",
    "plt.title('Singular / dual / plural distinction')\n",
    "plt.xlabel('Trial Number')\n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular, dual, trial, plural"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['Outcomes'] = 'plural'\n",
    "data['Outcomes'][1] = 'singular'\n",
    "data['Outcomes'][2] = 'dual'\n",
    "data['Outcomes'][3] = 'trial'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P['sg / du / tr / pl'] = [population_accuracy(M=i) for i in xrange(1,MAX_TRIALS)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x17b12668>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "QoiBogBPCCEGigI8IYQYKArwhBBioP4fcPxhAIWpiKoAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x177742e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,len(P['sg / du / tr / pl'])+1), P['sg / du / tr / pl'], '-', linewidth=2)\n",
    "plt.title('Singular / dual / trial / plural distinction')\n",
    "plt.xlabel('Trial Number')\n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular, dual, trial, quadral, plural"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['Outcomes'] = 'plural'\n",
    "data['Outcomes'][1] = 'singular'\n",
    "data['Outcomes'][2] = 'dual'\n",
    "data['Outcomes'][3] = 'trial'\n",
    "data['Outcomes'][4] = '4ial'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "P['sg / du / tr / qu / pl'] = [population_accuracy(M=i) for i in xrange(1,MAX_TRIALS)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x17e23c50>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17b02518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1,len(P['sg / du / tr / qu / pl'])+1), P['sg / du / tr / qu / pl'], '-', linewidth=2)\n",
    "plt.title('Singular / dual / trial / quadral plural distinction')\n",
    "plt.xlabel('Trial Number')\n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A prediction is that the typology of number systems should roughly correspond to how learnable each type of number system is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17e436d8>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "iIhvvgGL1FKejmIn5AAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17e4d4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in ('sg / pl', 'sg / du / pl', 'sg / du / tr / pl', 'du / non-du', 'sg / du / tr / qu / pl'):\n",
    "    plt.plot(range(1,len(P[n])+1), P[n], '-', linewidth=1.5, label=n)\n",
    "    \n",
    "plt.suptitle('Proportion of 100 learners who label all 15 items correctly')\n",
    "plt.xlabel('Trials')\n",
    "plt.legend(loc=(-0.55,0.5))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}