PCFG Demo

concepts_catalog.pickle

PCFG Demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro\n",
    "\n",
    "This is  a reimplimentation of the Rational Rules model of concept learning by [Noah Goodman et al. (2008)](http://web.mit.edu/cocosci/Papers/RRfinal3.pdf). At the end of the notebook, I use data provided by Jacob Feldman from his [2000 letter](http://ruccs.rutgers.edu/images/personal-jacob-feldman/papers/feldman_nature.pdf) to test the Rational Rules model. This code and Feldman's data are provided without guarantees of any kind and for academic purposes only.\n",
    "\n",
    "To my knowledge, Noah Goodman's original code is not currently available. However related implementations include\n",
    "\n",
    "- The [PCFG examples](https://github.com/probmods/webppl/tree/master/examples) provided in WebPPL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the setup block. I'm piggy-backing off of a lot of work from the Natural Language Toolkit.\n",
    "\n",
    "Also I'm setting the random seed so that this is reproducable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import nltk\n",
    "from nltk import Tree\n",
    "from nltk.tree import ImmutableProbabilisticTree, ProbabilisticTree\n",
    "from nltk.grammar import ProbabilisticProduction ,Nonterminal, PCFG\n",
    "import itertools\n",
    "import pandas as pd\n",
    "import time\n",
    "import scipy.stats as st\n",
    "import multiprocessing\n",
    "data_path = \"Data/Concepts/concepts_catalog.pickle\"\n",
    "cd = pd.read_pickle(data_path)\n",
    "%pylab inline\n",
    "random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The concepts come from a set based Jacob Feldman's (2000) study of 76 distinct concepts. The intesion is the formula for the concept and the extention is the set of examples that correspond to it. Each are accessed using `c_i` corresponding to the concept index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def intension(c_i=0,o=\" or \",a=\" and \",f=\"f\"):\n",
    "    d = cd[\"D\"][c_i]\n",
    "    p = cd[\"True Examples\"][c_i]\n",
    "    e_format = \"{0:0\"+str(d)+\"b}\"\n",
    "    r = [e_format.format(int(example)) for example in p]\n",
    "    if f:\n",
    "        r_new = []\n",
    "        for term in r:\n",
    "            r_new.append([f+str(i)+'='+term[i] for i in range(len(term))] + ['true'])\n",
    "    if a and o:\n",
    "        r_new = [(a).join(term) for term in r_new]\n",
    "        r_new += ['false']\n",
    "        r_new = (o).join(r_new)\n",
    "    return r_new\n",
    "def extension(c_i=0,f=\"f\"):\n",
    "    features = cd[\"Domain\"][c_i]\n",
    "    n_ex = prod(features)\n",
    "    true_ex = cd[\"True Examples\"][c_i]\n",
    "    examples = true_ex + cd[\"False Examples\"][c_i]\n",
    "    e_format = \"{0:0\"+str(len(features))+\"b}\"\n",
    "    extension = []\n",
    "    for example in examples:\n",
    "        e_string = e_format.format(int(example))\n",
    "        e = {f+str(i):e_string[i] for i in range(len(e_string))}\n",
    "        extension.append( (e, example in true_ex) )\n",
    "    return extension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f0=0 and f1=1 and f2=0 and f3=0 and true or f0=0 and f1=1 and f2=0 and f3=1 and true or f0=0 and f1=1 and f2=1 and f3=0 and true or f0=0 and f1=1 and f2=1 and f3=1 and true or f0=1 and f1=0 and f2=0 and f3=0 and true or f0=1 and f1=0 and f2=0 and f3=1 and true or f0=1 and f1=0 and f2=1 and f3=0 and true or f0=1 and f1=0 and f2=1 and f3=1 and true or f0=1 and f1=1 and f2=0 and f3=0 and true or f0=1 and f1=1 and f2=0 and f3=1 and true or f0=1 and f1=1 and f2=1 and f3=0 and true or f0=1 and f1=1 and f2=1 and f3=1 and true or false\n",
      "[({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '0'}, True), ({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '0'}, True), ({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '1'}, True), ({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '1'}, True), ({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '0'}, True), ({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '0'}, True), ({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '1'}, True), ({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '1'}, True), ({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '0'}, True), ({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '0'}, True), ({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '1'}, True), ({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '1'}, True), ({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '0'}, False), ({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '0'}, False), ({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '1'}, False), ({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '1'}, False)]\n"
     ]
    }
   ],
   "source": [
    "print(intension(57)) # print an unreduced intesions\n",
    "print(extension(57)) # print an extension (the examples in the concept)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function generates a Disjunctive Normal Form grammar based on an input concept. The input concept is used to determine the set of features to include, i.e. a two feature concept will only use $f_0$ and $f_1$ while a three feature concept will add $f_2$.\n",
    "\n",
    "While a slightly different notation is used from Goodman et al. (2008) it should be equivalent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grammar with 16 productions (start state = D)\n",
      "    D -> C 'or' D [0.5]\n",
      "    D -> 'false' [0.5]\n",
      "    C -> P 'and' C [0.5]\n",
      "    C -> 'true' [0.5]\n",
      "    P -> F0 [0.25]\n",
      "    F0 -> 'f0=0' [0.5]\n",
      "    F0 -> 'f0=1' [0.5]\n",
      "    P -> F1 [0.25]\n",
      "    F1 -> 'f1=0' [0.5]\n",
      "    F1 -> 'f1=1' [0.5]\n",
      "    P -> F2 [0.25]\n",
      "    F2 -> 'f2=0' [0.5]\n",
      "    F2 -> 'f2=1' [0.5]\n",
      "    P -> F3 [0.25]\n",
      "    F3 -> 'f3=0' [0.5]\n",
      "    F3 -> 'f3=1' [0.5]\n"
     ]
    }
   ],
   "source": [
    "def uniform_dnf(c_i):\n",
    "    # this is the basic-level DNF grammar.\n",
    "    base = nltk.PCFG.fromstring(\"\"\"\n",
    "    D -> C 'or' D [0.5] | 'false' [0.5]\n",
    "    C -> P 'and' C [0.5] | 'true' [0.5]\n",
    "    \"\"\")\n",
    "    domain = cd[\"Domain\"][c_i]\n",
    "    # add productions for features and feature values\n",
    "    new_productions = []\n",
    "    P = Nonterminal('P')\n",
    "    for i in range(len(domain)):\n",
    "        F_i = Nonterminal('F'+str(i))\n",
    "        new_productions.append(ProbabilisticProduction(P,[F_i],prob=1/len(domain)))\n",
    "        for j in range(domain[i]):\n",
    "            A_j = 'f'+str(i)+'='+str(j)\n",
    "            new_productions.append(ProbabilisticProduction(F_i,[A_j],prob=1/domain[i]))\n",
    "    return PCFG(base.start(), base.productions() + new_productions)\n",
    "print(uniform_dnf(40))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`pcfg_generate()` generates a PCFG parse based on `pcfg`. If passed a Tree with one or more nonterminal leaves, `pcfg_generate` will generate subtrees for each nonterminal leaf.\n",
    "\n",
    "**Important**: this function returns a `ProbabilisticTree` that differs from the NLTK class `ProbabilisticTree` in the meaning of the `.prob()` and `.logprob()` properties. Here, `.prob()` refers to the probability associated with the top-level parse, not the cumulative probability of the entire tree. The cumulative probability can be determined by `2**sum([st.logprob() for st in out.subtrees()])`. A helper function, `prob_tree()`,  has been added to do just that. This was done to simplify recalculation of cumulative probabilities for trimmed trees."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def pcfg_generate(pcfg, start=None):\n",
    "    \n",
    "    def sample_production(node):\n",
    "        productions = pcfg.productions(node)\n",
    "        dist = [p.prob() for p in productions]\n",
    "        choice = productions[random.choice(len(dist), 1, dist)[0]]\n",
    "        return ProbabilisticTree(node.symbol(), choice.rhs(), logprob=choice.logprob())\n",
    "    \n",
    "    if not start:\n",
    "        start = pcfg.start()\n",
    "        \n",
    "    if isinstance(start, Nonterminal):\n",
    "        tree = sample_production(start)\n",
    "    elif isinstance(start, Tree):\n",
    "        tree = start.copy(deep=True)\n",
    "    else:\n",
    "        raise TypeError(\"Expected a node, tree or None\")\n",
    "    \n",
    "    for tp in tree.treepositions('leaves'):\n",
    "        if isinstance(tree[tp],Nonterminal):\n",
    "            tree[tp] = pcfg_generate(pcfg,tree[tp])\n",
    "\n",
    "    return tree\n",
    "\n",
    "def prob_tree(tree, log=True):\n",
    "    lp = sum( st.logprob() for st in tree.subtrees() )\n",
    "    if log:\n",
    "        return lp/math.log2(math.e)\n",
    "    else:\n",
    "        return 2**(lp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`trim_tree()` selects a nonternminal node $n \\in T$ uniformly at random and removes all nodes below $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def trim_tree(tree):\n",
    "    if not isinstance(tree, Tree):\n",
    "        raise TypeError('tree must be a Tree!')\n",
    "    if any( [isinstance(leaf, Nonterminal) for leaf in tree.leaves()] ):\n",
    "        return tree\n",
    "    \n",
    "    # randomly sample candidate index (c_i) from candidate nonterminal nodes\n",
    "    candidates = [tp for tp in tree.treepositions() if \n",
    "                  tp not in set(tree.treepositions('leaves')) ]\n",
    "    c_i = candidates[random.choice(len(candidates))]\n",
    "    \n",
    "    if c_i == ():\n",
    "        return Nonterminal(tree.label())\n",
    "    \n",
    "    # deep copy new tree\n",
    "    tree_p = tree.copy(deep=True)\n",
    "    \n",
    "    tree_p[c_i] = Nonterminal(tree[c_i].label())\n",
    "    return tree_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# a few utility functions\n",
    "\n",
    "def m_beta(a, log=True):\n",
    "    lp = sum( [math.lgamma(a_i) for a_i in a] ) - math.lgamma(sum(a))\n",
    "    if log:\n",
    "        return lp\n",
    "    else:\n",
    "        return math.exp(lp) \n",
    "\n",
    "def to_dict(grammar):\n",
    "    p_dict = {}\n",
    "    for production in grammar.productions():\n",
    "        if production.lhs() not in p_dict:\n",
    "            p_dict[production.lhs()] = {}\n",
    "        if production.rhs() not in p_dict[production.lhs()]:\n",
    "            p_dict[production.lhs()][production.rhs()] = 1\n",
    "    return p_dict\n",
    "\n",
    "def rr_prior(formula, grammar, log=True):\n",
    "    use_count = {production.lhs():{} for production in grammar.productions()}\n",
    "    for production in grammar.productions():\n",
    "        use_count[production.lhs()][production.rhs()] = 1\n",
    "    for production in formula.productions():\n",
    "        use_count[production.lhs()][production.rhs()] += 1\n",
    "    lp = 0\n",
    "    for key in use_count:\n",
    "        c = list(use_count[key].values())\n",
    "        lp += m_beta( c ) - m_beta(ones_like(c))\n",
    "    if log:\n",
    "        return lp\n",
    "    else:\n",
    "        return math.exp(lp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Here's how things work.\n",
    "First we generate a grammar based on the target conecpt (this is so that the number of features in the grammar and concept match).\n",
    "We then build a parser specific to this grammar.\n",
    "The parsed formula is then passed to the 'rational rules prior' formula which gives the formula a probability.\n",
    "\n",
    "The next few cells compare probabilities for specific formulas first to explicit calculations and then to the results in Goodman et al.'s demo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula:  f0=0 and true or false\n",
      "rr prior:  0.0034722222222222246\n"
     ]
    }
   ],
   "source": [
    "test_i = 30\n",
    "test_grammar = uniform_dnf(test_i)\n",
    "test_parser = nltk.ViterbiParser(test_grammar)\n",
    "test_f = 'f0=0 and true or false'\n",
    "test_formula = test_parser.parse_one(test_f.split(' '))\n",
    "print('formula: ',test_f)\n",
    "print('rr prior: ', rr_prior(test_formula,test_grammar,log=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0034722222222222246"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = m_beta([2]) - m_beta([1])\n",
    "x += m_beta([2, 2]) - m_beta([1, 1])\n",
    "x += m_beta([2, 2]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1, 1, 1]) - m_beta([1, 1, 1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "math.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula:  f0=0 and f2=0 and true or f1=0 and f3=0 and true or false\n",
      "rr prior:  5.905139833711254e-08\n"
     ]
    }
   ],
   "source": [
    "test_f = 'f0=0 and f2=0 and true or f1=0 and f3=0 and true or false'\n",
    "test_formula = test_parser.parse_one(test_f.split(' '))\n",
    "print('formula: ',test_f)\n",
    "print('rr prior: ', rr_prior(test_formula,test_grammar,log=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.905139833711254e-08"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = m_beta([2]) - m_beta([1])\n",
    "x += m_beta([3, 2]) - m_beta([1, 1])\n",
    "x += m_beta([5, 3]) - m_beta([1, 1])\n",
    "x += m_beta([2, 2, 2, 2]) - m_beta([1, 1, 1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "math.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula:  f0=0 and f2=0 and true or f0=0 and f3=0 and true or false\n",
      "rr prior:  1.5747039556563356e-07\n"
     ]
    }
   ],
   "source": [
    "test_f = 'f0=0 and f2=0 and true or f0=0 and f3=0 and true or false'\n",
    "test_formula = test_parser.parse_one(test_f.split(' '))\n",
    "print('formula: ',test_f)\n",
    "print('rr prior: ', rr_prior(test_formula,test_grammar,log=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.574703955656333e-07"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = m_beta([2]) - m_beta([1])\n",
    "x += m_beta([3, 2]) - m_beta([1, 1])\n",
    "x += m_beta([5, 3]) - m_beta([1, 1])\n",
    "x += m_beta([3, 1, 2, 2]) - m_beta([1, 1, 1, 1])\n",
    "x += m_beta([3, 1]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "x += m_beta([2, 1]) - m_beta([1, 1])\n",
    "math.exp(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood, $P(E,l(E)|F_T,p_e)$, the is probability of a formula generating a set of labels that match a concept. $p_e$ is an optional parameter that allows outliers at a certain probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def evaluate_formula(formula,example):\n",
    "#     formula = ' '.join(formula.leaves())\n",
    "    terms = formula.split(' or ')\n",
    "    for term in terms:\n",
    "        t = term.split(' and ')\n",
    "        out = True\n",
    "        for literal in t:\n",
    "            if literal[2] == '=':\n",
    "                [var, val] = literal.split('=')\n",
    "                if example[var] != val:\n",
    "                    out = False\n",
    "                    break\n",
    "            elif 'false' in literal:\n",
    "                out = False\n",
    "                break\n",
    "            else:\n",
    "                continue\n",
    "                \n",
    "        if out == True:\n",
    "            break\n",
    "    return out\n",
    "\n",
    "def likelihood(concept,formula,b=1, log=True):\n",
    "    if isinstance(formula,Tree):\n",
    "        formula = ' '.join(formula.leaves())\n",
    "    n_t = 0\n",
    "    p_e = e**(-b)\n",
    "    for l_e in concept:\n",
    "        if evaluate_formula(formula,l_e[0])==l_e[1]:\n",
    "            n_t +=1\n",
    "    n_f = len(concept) - n_t\n",
    "    lp = n_f*math.log(p_e) + n_t*math.log(1 - p_e)\n",
    "    if log:\n",
    "        return lp\n",
    "    else:\n",
    "        return math.exp(lp)\n",
    "    \n",
    "def percent_correct(concept,formula,b=1, log=True):\n",
    "    if isinstance(formula,Tree):\n",
    "        formula = ' '.join(formula.leaves())\n",
    "    n_t = 0\n",
    "    p_e = e**(-b)\n",
    "    for l_e in concept:\n",
    "        if evaluate_formula(formula,l_e[0])==l_e[1]:\n",
    "            n_t +=1\n",
    "    n_f = len(concept) - n_t\n",
    "    p = (1-p_e)*n_t/len(concept) + p_e*n_f/len(concept)\n",
    "    if log:\n",
    "        return math.log(p)\n",
    "    else:\n",
    "        return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula:  f0=0 and f2=0 and true or f0=0 and f3=0 and true or false\n",
      "example:  {'f1': '0', 'f0': '0', 'f3': '0', 'f2': '1'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_example = {'f0':'0', 'f1':'0', 'f2':'1', 'f3':'0'}\n",
    "print('formula: ', test_f)\n",
    "print('example: ', test_example)\n",
    "evaluate_formula(test_f,test_example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula:  f0=0 and f2=0 and true or f0=0 and f3=0 and true or false\n",
      "example:  {'f1': '0', 'f0': '0', 'f3': '1', 'f2': '1'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_example = {'f0':'0', 'f1':'0', 'f2':'1', 'f3':'1'}\n",
    "print('formula: ', test_f)\n",
    "print('example: ', test_example)\n",
    "evaluate_formula(test_f,test_example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f0=0 and f1=1 and f2=0 and f3=0 and true or f0=0 and f1=1 and f2=0 and f3=1 and true or f0=0 and f1=1 and f2=1 and f3=0 and true or f0=0 and f1=1 and f2=1 and f3=1 and true or f0=1 and f1=0 and f2=0 and f3=0 and true or f0=1 and f1=0 and f2=0 and f3=1 and true or f0=1 and f1=0 and f2=1 and f3=0 and true or f0=1 and f1=0 and f2=1 and f3=1 and true or f0=1 and f1=1 and f2=0 and f3=0 and true or f0=1 and f1=1 and f2=0 and f3=1 and true or f0=1 and f1=1 and f2=1 and f3=0 and true or f0=1 and f1=1 and f2=1 and f3=1 and true or false\n",
      "({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '0'}, False) False\n",
      "({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '0'}, False) False\n",
      "({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '1'}, False) False\n",
      "({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '1'}, False) False\n"
     ]
    }
   ],
   "source": [
    "test_formula = intension(57)\n",
    "test_examples = extension(57)\n",
    "print(test_formula)\n",
    "for example in test_examples:\n",
    "    print(example, evaluate_formula(test_formula,example[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true or false\n",
      "({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '0', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '1', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '0'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '0', 'f2': '1'}, True) True\n",
      "({'f1': '1', 'f0': '1', 'f3': '1', 'f2': '1'}, True) True\n",
      "({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '0'}, False) True\n",
      "({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '0'}, False) True\n",
      "({'f1': '0', 'f0': '0', 'f3': '0', 'f2': '1'}, False) True\n",
      "({'f1': '0', 'f0': '0', 'f3': '1', 'f2': '1'}, False) True\n"
     ]
    }
   ],
   "source": [
    "test_formula = 'true or false'\n",
    "test_examples = extension(57)\n",
    "print(test_formula)\n",
    "for example in test_examples:\n",
    "    print(example, evaluate_formula(test_formula,example[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7487606239116668"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percent_correct(test_examples, test_formula, b=6, log=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**TODO**:\n",
    "\n",
    "- validate results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following sampling process estimates the complexity of different concepts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def pcfg_sample(c_i=0,b=1,num_samples=1000):\n",
    "    concept = extension(c_i)\n",
    "    dnf_grammar = uniform_dnf(c_i)\n",
    "    log = []\n",
    "    #initialize\n",
    "    tree = pcfg_generate(dnf_grammar)\n",
    "    l_denominator = likelihood(concept,tree,b) - prob_tree(tree) + rr_prior(tree,dnf_grammar) - math.log(len(tree.treepositions()))\n",
    "    \n",
    "    for i in range(num_samples):\n",
    "        not_new = True\n",
    "        while not_new:\n",
    "            tree_prime = pcfg_generate(dnf_grammar, trim_tree(tree))\n",
    "            if tree != tree_prime:\n",
    "                not_new = False\n",
    "        l_numerator = likelihood(concept,tree_prime,b) - prob_tree(tree_prime) + rr_prior(tree_prime,dnf_grammar) - math.log(len(tree_prime.treepositions()))\n",
    "        log.append(tree)\n",
    "        if random.random() < min(math.exp(l_numerator - l_denominator), 1):\n",
    "            tree = tree_prime.copy()\n",
    "            l_denominator = l_numerator\n",
    "    return log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def parallel_sample(c_i,b=1,num_samples=10000,blocks=8):\n",
    "    num_blocks = min(blocks, multiprocessing.cpu_count())\n",
    "    pool = multiprocessing.Pool()\n",
    "    block_samples = int(num_samples/num_blocks)\n",
    "    \n",
    "    tasks = [(c_i, b, block_samples) for i in range(num_blocks)]\n",
    "    results = pool.starmap(pcfg_sample,tasks)\n",
    "    \n",
    "    log = []\n",
    "    \n",
    "    for new in results:\n",
    "        log.extend(new)\n",
    "    \n",
    "    pool.terminate()\n",
    "    pool.join()\n",
    "    \n",
    "    return log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ceil(log10(99.1+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def sample_summary(log):\n",
    "    t = dict()\n",
    "    for tree in log:\n",
    "        key = ' '.join(tree.leaves())\n",
    "        try: t[key] +=1\n",
    "        except: t[key] = 1\n",
    "    print('accepted trees (>02%):')\n",
    "    sorted_t = sorted(t.items(), key=lambda x: -x[1])\n",
    "    for pair in sorted_t:\n",
    "        if pair[1] > num_samples*(1/50): \n",
    "            print('{0:>5}: {1}'.format(pair[1],pair[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35.940948 seconds have elapsed\n",
      "concept:  f0=0\n",
      "accepted trees (>02%):\n",
      " 5032: f0=0 and true or false\n",
      " 1244: f0=0 and f0=0 and true or false\n",
      "  216: f0=0 and f0=0 and f0=0 and true or false\n"
     ]
    }
   ],
   "source": [
    "c_i = 6\n",
    "b = 6\n",
    "num_samples=10000\n",
    "start = time.time()\n",
    "log = parallel_sample(c_i=c_i,b=b, num_samples=num_samples)\n",
    "elapsed = time.time()-start\n",
    "print(\"%f seconds have elapsed\" % elapsed)\n",
    "print('concept: ',cd[\"DNFconcept\"][c_i])\n",
    "sample_summary(log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.452952 seconds have elapsed\n",
      "concept:  f0=0 and f1=0\n",
      "accepted trees (>02%):\n",
      " 2796: f0=0 and f1=0 and true or false\n",
      " 1592: false\n",
      " 1120: f1=0 and f0=0 and true or false\n",
      "  452: f0=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and true or false\n",
      "  420: f0=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and f1=0 and true or false\n",
      "  336: f0=0 and f1=0 and f1=0 and true or false\n",
      "  336: f0=0 and f0=0 and f1=0 and true or false\n",
      "  324: f0=0 and f1=0 and f0=0 and true or false\n",
      "  280: f1=0 and f1=0 and f1=0 and f0=0 and f1=0 and f1=0 and f1=0 and f1=0 and true or false\n",
      "  224: f1=0 and f1=0 and f1=0 and f0=0 and f1=0 and true or false\n"
     ]
    }
   ],
   "source": [
    "c_i = 0\n",
    "b = 6\n",
    "num_samples=10000\n",
    "start = time.time()\n",
    "log = parallel_sample(c_i=c_i,b=b, num_samples=num_samples)\n",
    "elapsed = time.time()-start\n",
    "print(\"%f seconds have elapsed\" % elapsed)\n",
    "print('concept: ',cd[\"DNFconcept\"][c_i])\n",
    "sample_summary(log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.483607 seconds have elapsed\n",
      "concept:  f0=1 or f1=1\n",
      "accepted trees (>02%):\n",
      " 2252: f0=1 and true or f1=1 and true or false\n",
      "  480: f0=1 and true or f1=1 and f0=0 and true or false\n",
      "  300: f1=1 and true or f0=1 and true or false\n",
      "  220: f0=0 and f1=1 and f1=1 and true or f0=1 and true or false\n"
     ]
    }
   ],
   "source": [
    "c_i = 57\n",
    "b = 6\n",
    "num_samples=10000\n",
    "start = time.time()\n",
    "log = parallel_sample(c_i=c_i,b=b, num_samples=num_samples)\n",
    "elapsed = time.time()-start\n",
    "print(\"%f seconds have elapsed\" % elapsed)\n",
    "print('concept: ',cd[\"DNFconcept\"][c_i])\n",
    "sample_summary(log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([52, 57, 22, 75, 28, 26, 71, 54, 34,  7])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tc = numpy.random.choice(len(cd), 10, replace=False)\n",
    "tc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "figsize(20,15)\n",
    "\n",
    "def latexify(concept):\n",
    "    c = concept.split(' or ')\n",
    "    c = [term.split(' and ') for term in c]\n",
    "    c = [ [l[0] + '_' + l[1:] for l in term] for term in c]\n",
    "    c = [ '('+(' \\\\wedge ').join(term)+')' for term in c]\n",
    "    c = '$'+(' \\\\vee ').join(c)+'$'\n",
    "    return c\n",
    "\n",
    "def plot_regression(x,y,l=None):\n",
    "    slope, intercept, r_value, p_value, std_err = st.linregress(x,y)\n",
    "    x_fit = linspace(min(x), max(x), 100)\n",
    "    y_fit = slope*x_fit + intercept\n",
    "    scatter(x, y, marker='.', color='black')\n",
    "    plot(x_fit, y_fit)\n",
    "    title('$ r^2 = %.3f $' % r_value**2)\n",
    "    if l:\n",
    "        for i in range(len(l)):\n",
    "            text(x[i],y[i],l[i],fontsize=6,verticalalignment='center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "57\n",
      "64\n",
      "67\n",
      "75\n",
      "71\n",
      "54\n",
      "59\n",
      "38.281475 seconds have elapsed\n"
     ]
    }
   ],
   "source": [
    "b = 10\n",
    "num_samples=2000\n",
    "\n",
    "y = []\n",
    "start = time.time()\n",
    "test_concepts = [57, 64, 67, 75, 71, 54, 59]\n",
    "# test_concepts = range(len(cd))\n",
    "\n",
    "for c_i in test_concepts:\n",
    "    print(c_i)\n",
    "    log = parallel_sample(c_i=c_i, b=b, num_samples=num_samples)\n",
    "    y.append(mean([percent_correct(extension(c_i),step[0],b=b,log=False) for step in log]))\n",
    "\n",
    "elapsed = time.time()-start\n",
    "print(\"%f seconds have elapsed\" % elapsed)\n",
    "\n",
    "y0 = []\n",
    "l = []\n",
    "for i in range(len(test_concepts)):\n",
    "    y0.append(cd[\"Percent Correct\"][test_concepts[i]])\n",
    "    l.append(latexify(cd[\"DNFconcept\"][test_concepts[i]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10c763748>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OZNgauybZIclvyrJcXhRFsbooAwAAAKCOPPdc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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c5cc588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_regression(y,y0,l)\n",
    "from time import localtime, strftime\n",
    "suptitle(\"feldman PC vs predicted for $b = %.1f$\" % b, fontsize=12)\n",
    "xlabel(\"predicted percent correct\")\n",
    "ylabel(\"measured percent correct\")\n",
    "# savefig(\"images/test-concepts.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10c64c5f8>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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63ifJzLIsj2yrcAAAAACQJK+8kkyfXk2R/e53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\nZpOcW7ZFjHF1NoJJkiRJUn20ZEmyxeLQofD223DggfCLX8CgQbDffmm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RunXw2GMwdCjM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\nU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c719860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y0 = []\n",
    "l = []\n",
    "for i in range(len(test_concepts)):\n",
    "    y0.append(cd[\"Percent Correct\"][test_concepts[i]])\n",
    "    l.append(str(i) + \":\" + latexify(cd[\"DNFconcept\"][test_concepts[i]]))\n",
    "plot_regression(y,y0,l)\n",
    "from time import localtime, strftime\n",
    "suptitle(\"feldman PC vs predicted for $b = %.1f$\" % b, fontsize=12)\n",
    "xlabel(\"predicted percent correct\")\n",
    "ylabel(\"measured percent correct\")\n",
    "# c_time = strftime(\"%Y-%m-%d-%H-%M-%S\", localtime())\n",
    "# fig_path = 'output/2013-11-3-DNF-Sampler/' + c_time + '.pdf'\n",
    "# savefig(fig_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 completed. Avg time: 44.78246002197265 seconds\n",
      "10 completed. Avg time: 84.81611042022705 seconds\n",
      "15 completed. Avg time: 101.77172487576803 seconds\n",
      "20 completed. Avg time: 95.54808330535889 seconds\n",
      "25 completed. Avg time: 82.03994704246522 seconds\n",
      "30 completed. Avg time: 75.99392046928406 seconds\n",
      "35 completed. Avg time: 69.30150769097465 seconds\n",
      "40 completed. Avg time: 63.85999675393104 seconds\n",
      "45 completed. Avg time: 65.47094857957629 seconds\n",
      "50 completed. Avg time: 66.47603147983551 seconds\n",
      "55 completed. Avg time: 65.72619403925809 seconds\n",
      "60 completed. Avg time: 66.13979216814042 seconds\n",
      "65 completed. Avg time: 65.77441552602328 seconds\n",
      "70 completed. Avg time: 65.25243924345288 seconds\n",
      "75 completed. Avg time: 65.26656601587932 seconds\n"
     ]
    }
   ],
   "source": [
    "b = 6\n",
    "num_samples=10000\n",
    "\n",
    "samples = []\n",
    "data = []\n",
    "start = time.time()\n",
    "\n",
    "for c_i in range(len(cd)):\n",
    "    log = parallel_sample(c_i=c_i, b=b, num_samples=num_samples)\n",
    "    samples.append(log)\n",
    "    y = [percent_correct(extension(c_i),step[0],b=b,log=False) for step in log]\n",
    "    data.append(y)\n",
    "    \n",
    "    if (c_i+1) % 5 == 0:\n",
    "        print(\"{0} completed. Avg time: {1} seconds\".format(c_i+1,(time.time()-start)/(c_i+1) ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vfnfygAe0PR20QyABAAAAgBHX7/dSVXVWrhykqur0+722R2KJaJrky19OVq9O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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d194c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = []\n",
    "y = []\n",
    "y_ses = []\n",
    "for i in range(len(data)):\n",
    "    x.append(cd[\"Percent Correct\"][i] )\n",
    "    y.append(mean(data[i]))\n",
    "    y_ses.append( std(data[i])/( len(data[i])**2) )\n",
    "\n",
    "errorbar(x, y, yerr=y_ses, fmt='.', c='b')\n",
    "plot_regression(x,y)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}