Toy example of how to make a forecast for an Anki deck.

anki_forecast.ipynb

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   "cells": [
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import numpy as np\n",
      "import sqlite3\n",
      "import matplotlib\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "query_new = '''\n",
      "    select\n",
      "      count() as N,\n",
      "      sum(case when ease=1 then 1 else 0 end) as repeat,\n",
      "      sum(case when ease=2 then 1 else 0 end) as good,\n",
      "      sum(case when ease=3 then 1 else 0 end) as easy\n",
      "    from revlog\n",
      "    where type=0\n",
      "'''\n",
      "\n",
      "query_young = '''\n",
      "    select\n",
      "      count() as N,\n",
      "      sum(case when ease=1 then 1 else 0 end) as repeat,\n",
      "      sum(case when ease=2 then 1 else 0 end) as hard,\n",
      "      sum(case when ease=3 then 1 else 0 end) as good,\n",
      "      sum(case when ease=4 then 1 else 0 end) as easy\n",
      "    from revlog\n",
      "    where type=1 and lastIvl < 21\n",
      "'''\n",
      "\n",
      "query_mature = '''\n",
      "    select\n",
      "      count() as N,\n",
      "      sum(case when ease=1 then 1 else 0 end) as repeat,\n",
      "      sum(case when ease=2 then 1 else 0 end) as hard,\n",
      "      sum(case when ease=3 then 1 else 0 end) as good,\n",
      "      sum(case when ease=4 then 1 else 0 end) as easy\n",
      "    from revlog\n",
      "    where type=1 and lastIvl >= 21\n",
      "'''\n",
      "\n",
      "from os.path import expanduser\n",
      "db_fname = expanduser('~/Documents/Anki/User 1/collection.anki2')\n",
      "\n",
      "with sqlite3.connect(db_fname) as conn:\n",
      "    cursor = conn.cursor()\n",
      "    cursor.execute(query_new)\n",
      "    new_prob = np.array(cursor.fetchall()[0]).astype('f8')\n",
      "    # Add in some fake reviews. Makes outcome probabilities reasonable when there are\n",
      "    # very few reviews in the review log. This is essentially a prior.\n",
      "    new_prob[0] += 10  # Prior that half of new cards are answered correctly\n",
      "    new_prob[1] += 5\n",
      "    new_prob[2] += 5\n",
      "    new_prob = new_prob[1:] / np.sum(new_prob[1:])\n",
      "    \n",
      "    cursor = conn.cursor()\n",
      "    cursor.execute(query_young)\n",
      "    young_prob = np.array(cursor.fetchall()[0]).astype('f8')\n",
      "    young_prob[0] += 10  # Prior that 90% of young cards get \"good\" resonse\n",
      "    young_prob[1] += 1\n",
      "    young_prob[3] += 9\n",
      "    young_prob = young_prob[1:] / np.sum(young_prob[1:])\n",
      "    \n",
      "    cursor = conn.cursor()\n",
      "    cursor.execute(query_mature)\n",
      "    mature_prob = np.array(cursor.fetchall()[0]).astype('f8')\n",
      "    mature_prob[0] += 10  # Prior that 90% of mature cards get \"good\" resonse\n",
      "    mature_prob[1] += 1\n",
      "    mature_prob[3] += 9\n",
      "    mature_prob = mature_prob[1:] / np.sum(mature_prob[1:])\n",
      "\n",
      "outcome_pmf = [new_prob, young_prob, mature_prob]\n",
      "\n",
      "print new_prob, np.sum(new_prob)\n",
      "print young_prob, np.sum(young_prob)\n",
      "print mature_prob, np.sum(mature_prob)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.14796398  0.8451821   0.00685392] 1.0\n",
        "[ 0.07718062  0.19162996  0.72114537  0.01004405] 1.0\n",
        "[ 0.09411765  0.34117647  0.54529412  0.01941176] 1.0\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class CardType:\n",
      "    def __init__(self, ivl, ctype, due, factor=2.5):\n",
      "        self._ivl = ivl\n",
      "        self._ctype = ctype\n",
      "        self._due = due\n",
      "        self._factor = factor\n",
      "\n",
      "def draw_pmf(pmf):\n",
      "    v = np.random.random()\n",
      "    cmf = np.cumsum(pmf)\n",
      "    return np.searchsorted(cmf, v, side='right')\n",
      "\n",
      "def sim_single_review(c_type, c_ivl, c_factor):\n",
      "    outcome = draw_pmf(outcome_pmf[c_type])\n",
      "    \n",
      "    if c_type == 0:\n",
      "        if outcome <= 1:\n",
      "            c_ivl = 1\n",
      "        elif outcome == 2:\n",
      "            c_ivl = 4\n",
      "        else:\n",
      "            raise ValueError('Outcome should be <= 2 for new cards.')\n",
      "    elif c_type <= 2:\n",
      "        if outcome == 0:\n",
      "            c_ivl = 1\n",
      "        elif outcome == 1:\n",
      "            c_ivl *= 1.2\n",
      "        elif outcome == 2:\n",
      "            c_ivl *= 1.2 * c_factor\n",
      "        elif outcome == 3:\n",
      "            c_ivl *= 1.2 * 2. * c_factor\n",
      "        else:\n",
      "            raise ValueError('Outcome should be <= 3 for young/mature cards.')\n",
      "    else:\n",
      "        raise ValueError('Card type should be <= 2.')\n",
      "    \n",
      "    c_type = (1 if c_ivl <= 21 else 2)\n",
      "    correct = (outcome > 0)\n",
      "    \n",
      "    return c_type, c_ivl, correct\n",
      "\n",
      "def forecast_n_reviews(cards, n_time_bins=30, time_bin_length=1, max_add_per_day=5, n_smooth=1):\n",
      "    t_max = n_time_bins * time_bin_length\n",
      "\n",
      "    # Forecasted number of reviews\n",
      "    #   0 = Learn\n",
      "    #   1 = Young\n",
      "    #   2 = Mature\n",
      "    #   3 = Relearn\n",
      "    n_reviews = np.zeros((4, n_time_bins))\n",
      "    \n",
      "    # Forecasted final state of deck\n",
      "    n_cards = len(cards)\n",
      "    final_ivl = np.empty((n_smooth, n_cards), dtype='f8')\n",
      "    n_in_state = np.zeros(4, dtype='f8')\n",
      "    \n",
      "    for k in xrange(n_smooth):\n",
      "        n_added_today = 0\n",
      "        t_add = 0\n",
      "        \n",
      "        for l,card in enumerate(cards):\n",
      "            # Initiate time to next due date of card\n",
      "            t_elapsed = card._due\n",
      "            \n",
      "            # Rate-limit new cards by shifting starting time\n",
      "            if card._ctype == 0:\n",
      "                n_added_today += 1\n",
      "                t_elapsed += t_add\n",
      "                if n_added_today >= max_add_per_day:\n",
      "                    t_add += 1\n",
      "                    n_added_today = 0\n",
      "                    \n",
      "            \n",
      "            c_ivl = card._ivl    # card interval\n",
      "            c_type = card._ctype  # 0=new, 1=learn, 2=mature\n",
      "    \n",
      "            # Simulate reviews\n",
      "            while t_elapsed < t_max:\n",
      "                # Update the forecasted number of reviews\n",
      "                n_reviews[c_type, int(t_elapsed / time_bin_length)] += 1\n",
      "    \n",
      "                # Simulate response\n",
      "                c_type, c_ivl, correct = sim_single_review(c_type, c_ivl, card._factor)\n",
      "    \n",
      "                # If card failed, update \"relearn\" count\n",
      "                if correct == 0:\n",
      "                    n_reviews[3, int(t_elapsed / time_bin_length)] += 1\n",
      "    \n",
      "                # Advance time to next review\n",
      "                t_elapsed += c_ivl\n",
      "            \n",
      "            n_in_state[c_type] += 1\n",
      "            final_ivl[k, l] = c_ivl\n",
      "    \n",
      "    return (n_reviews / float(n_smooth),  # Number of reviews in each time bin\n",
      "            n_in_state / float(n_smooth), # Number of cards in each state (new, young, mature, relearn)\n",
      "            np.median(final_ivl, axis=0)) # Final interval of each card"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "query_cards = '''\n",
      "    select\n",
      "      reps,\n",
      "      due,\n",
      "      ivl,\n",
      "      factor,\n",
      "      did\n",
      "    from cards\n",
      "    where did=1383666618882\n",
      "'''\n",
      "\n",
      "db_fname = expanduser('~/Documents/Anki/User 1/collection.anki2')\n",
      "\n",
      "def calc_ctype(reps, ivl):\n",
      "    if reps == 0:\n",
      "        return 0\n",
      "    elif ivl <= 21:\n",
      "        return 1\n",
      "    else:\n",
      "        return 2\n",
      "\n",
      "with sqlite3.connect(db_fname) as conn:\n",
      "    cursor = conn.cursor()\n",
      "    cursor.execute(query_cards)\n",
      "    \n",
      "    cards = [CardType(ivl, calc_ctype(reps, ivl), due, factor=(factor/1000. if factor > 0 else 2.5)) for reps,due,ivl,factor,_ in cursor.fetchall()]\n",
      "\n",
      "# Fix due dates\n",
      "t_due = np.array([card._due for card in cards])\n",
      "ctype = np.array([card._ctype for card in cards])\n",
      "t_today = np.min(t_due[ctype != 0])\n",
      "\n",
      "n_new = 0\n",
      "\n",
      "for card in cards:\n",
      "    card._due -= t_today\n",
      "    if card._ctype == 0:\n",
      "        card._due = 0\n",
      "        n_new += 1\n",
      "\n",
      "print '{} total cards.'.format(len(cards))\n",
      "print '{} new cards.'.format(n_new)\n",
      "\n",
      "n_dummy_new = 500\n",
      "for k in xrange(n_dummy_new):\n",
      "    cards.append(CardType(0, 0, 0))\n",
      "\n",
      "print 'Added {} new dummy cards.'.format(n_dummy_new)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1674 total cards.\n",
        "28 new cards.\n",
        "Added 500 new dummy cards.\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#n_cards = 1650\n",
      "#cards = [CardType(0, 0, 0, 2.5) for k in xrange(n_cards)]\n",
      "time_bin_length = 1\n",
      "n_time_bins = 30\n",
      "\n",
      "from time import time\n",
      "t_start = time()\n",
      "\n",
      "n_reviews, final_ctype, final_ivl = forecast_n_reviews(\n",
      "    cards,\n",
      "    n_time_bins=n_time_bins,\n",
      "    time_bin_length=time_bin_length,\n",
      "    max_add_per_day=15,\n",
      "    n_smooth=1\n",
      ")\n",
      "\n",
      "t_end = time()\n",
      "print 'Time elapsed: {:.2f} ms'.format(1000.*(t_end-t_start))\n",
      "print '              {:.2f} us / card / sqrt(days)'.format(1.e6*(t_end-t_start)/float(len(cards))/np.sqrt(time_bin_length*n_time_bins))\n",
      "\n",
      "n_reviews /= float(time_bin_length)\n",
      "\n",
      "# Forecasted reviews\n",
      "fig = plt.figure(figsize=(14,7))\n",
      "ax = fig.add_subplot(1,1,1)\n",
      "\n",
      "x = time_bin_length * np.linspace(0., n_time_bins-1., n_reviews.shape[1])\n",
      "width = time_bin_length\n",
      "ax.bar(x, n_reviews[0], width, color='b', ec='none', label='new')\n",
      "ax.bar(x, n_reviews[1], width, bottom=n_reviews[0], color='chartreuse', ec='none', label='young')\n",
      "ax.bar(x, n_reviews[2], width, bottom=n_reviews[0]+n_reviews[1], color='green', ec='none', label='mature')\n",
      "ax.bar(x, n_reviews[3], width, bottom=n_reviews[0]+n_reviews[1]+n_reviews[2], color='r', ec='none', label='relearn')\n",
      "ax.set_xlim(0., n_time_bins*time_bin_length)\n",
      "ax.legend(loc='upper right')\n",
      "ax.set_xlabel('days', fontsize=18)\n",
      "ax.set_ylabel('reviews / day', fontsize=18)\n",
      "ax.set_title('Forecasted Reviews', fontsize=22)\n",
      "\n",
      "# Card intervals\n",
      "fig = plt.figure(figsize=(14,7))\n",
      "ax = fig.add_subplot(1,1,1)\n",
      "\n",
      "start_ivl = [card._ivl for card in cards]\n",
      "\n",
      "max_ivl = int(np.ceil(np.percentile(final_ivl, 96.)))\n",
      "n_bins = min(max_ivl, 60)\n",
      "bins = np.linspace(0., max_ivl, n_bins)\n",
      "#bins = time_bin_length * np.arange(0, n_time_bins+.01, 1)\n",
      "ax.hist(start_ivl, bins=bins, color='red', edgecolor='none', alpha=0.4, label='initial')\n",
      "ax.hist(final_ivl, bins=bins, color='blue', edgecolor='none', alpha=0.4, label='final')\n",
      "ax.set_xlim(bins[0], bins[-1])\n",
      "ax.legend()\n",
      "ax.set_xlabel('days', fontsize=18)\n",
      "ax.set_ylabel('# of cards', fontsize=18)\n",
      "ax.set_title('Card Intervals', fontsize=22)\n",
      "\n",
      "# Card types\n",
      "fig = plt.figure(figsize=(14,7))\n",
      "\n",
      "start_ctype = [0,0,0,0]\n",
      "for card in cards:\n",
      "    start_ctype[card._ctype] += 1\n",
      "\n",
      "labels = ['new', 'young', 'mature']\n",
      "colors = ['blue', 'chartreuse', 'green']\n",
      "\n",
      "ax = fig.add_subplot(1,2,1, aspect='equal')\n",
      "ax.pie(start_ctype[:3], labels=labels, colors=colors,\n",
      "       autopct='%1.1f%%', shadow=False, startangle=90)\n",
      "ax.set_title('Initial State', fontsize=22)\n",
      "\n",
      "ax = fig.add_subplot(1,2,2, aspect='equal')\n",
      "ax.pie(final_ctype[:3], labels=labels, colors=colors,\n",
      "       autopct='%1.1f%%', shadow=False, startangle=90)\n",
      "ax.set_title('Final State', fontsize=22)\n",
      "\n",
      "print ''"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time elapsed: 111.27 ms\n",
        "              9.34 us / card / sqrt(days)\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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99VZXlwsAAABck8LCwjRt2jS1aNFCfn5+uvfee3X48GH99a9/VbVq1dSzZ0+d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\nAAAACogmAACAAqIJAACgwP8DHbsvPvrqorYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5a2287d4d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f//ynCgoK9Prrr+vMmTOKjY117P/mm2/Utm1btxQJAAAAADXB6Ukapk2bpvj4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\nAQAAAIAPAQkAAAAAfP4GPlopbxeMdqIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5a22622e90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7vceM5xWMNzdiG4OYdXJ8sZHeTXA96or+uJ4aATUYMXwEHTt2lNYOJyfFhpNS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\nItZGcM/d90ihIZS74YYb8B/wwynVSYQQoURP07nqqqvCqtCAMPwIFx0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Xq04iQoYf3F+7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       "text": [
        "<matplotlib.figure.Figure at 0x7f5a227c57d0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}