parser.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install PYEVALB\n",
    "# !pip install unidecode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from nltk import Tree, grammar\n",
    "import random\n",
    "import queue\n",
    "import pickle as pkl\n",
    "from scipy.spatial import distance\n",
    "from PYEVALB import scorer\n",
    "from PYEVALB import parser\n",
    "from sklearn.metrics import precision_recall_fscore_support\n",
    "import unidecode\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('sequoia-corpus+fct.mrg_strict', 'r') as file:\n",
    "    data = file.read().splitlines()\n",
    "    \n",
    "file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ignore_functional_labels(string):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ----------------\n",
    "    Ignore functional labels in the non terminals of a rule, for example PP-MOD becomes PP\n",
    "    \n",
    "    Parameters\n",
    "    ----------------\n",
    "    string : String form of parse tree.\n",
    "    \n",
    "    Returns\n",
    "    ----------------\n",
    "    new string form of parse tree\n",
    "    \"\"\"\n",
    "    \n",
    "    l = string.split(' ')\n",
    "    for i in range(len(l)):\n",
    "        if l[i][0] == '(':\n",
    "            l[i] = l[i].split('-')[0]\n",
    "            \n",
    "    return ' '.join(l)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_nodes(rule):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Extract the non terminal and terminal nodes from a rule along with the status of the rule (either lexical 1, or not 0)\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    rule : nltk.grammar.Production object, the rule to consider.\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    3-tuple, tuple[0] : the lexical status.\n",
    "             tuple[1] : set containing the non terminal nodes.\n",
    "             tuple[2] : set containing the terminal nodes.\n",
    "    \"\"\"\n",
    "    if rule.is_lexical():\n",
    "        return True, set((rule._lhs,)), set((rule._rhs))\n",
    "    \n",
    "    else:\n",
    "        return False, set((rule._lhs,)).union(set(rule._rhs)), set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# random.seed(0)\n",
    "# random.shuffle(data)\n",
    "data, data_dev, data_test = data[:4*len(data)//5], data[4*len(data)//5:9*len(data)//10], data[9*len(data)//10:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "non_terminals = set()\n",
    "pos_tags = set()\n",
    "terminals = set()\n",
    "binaries = set()\n",
    "for string in data:\n",
    "    t = Tree.fromstring(ignore_functional_labels(string))\n",
    "    t.chomsky_normal_form()\n",
    "    rules = t.productions()\n",
    "    for rule in rules:\n",
    "        lexical, non_terminal_nodes, terminal_nodes = extract_nodes(rule)\n",
    "        if lexical:\n",
    "            non_terminals = non_terminals.union(non_terminal_nodes)\n",
    "            pos_tags = pos_tags.union(non_terminal_nodes)\n",
    "            terminals = terminals.union(terminal_nodes)\n",
    "            \n",
    "        else:\n",
    "            non_terminals = non_terminals.union(non_terminal_nodes)\n",
    "            if len(rule._rhs) == 2:\n",
    "                binaries.add(rule._rhs)\n",
    "\n",
    "# non_terminals = non_terminals.difference(pos_tags)\n",
    "start = rules[0]._lhs   # The start symbol\n",
    "sent = rules[0]._rhs[0] # The previous start symbol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of terminals : 8958\n",
      "Number of POS tags : 29\n",
      "Number of non terminals : 4335\n",
      "Number of binaries : 6120\n"
     ]
    }
   ],
   "source": [
    "print('Number of terminals : %d' %len(terminals))\n",
    "print('Number of POS tags : %d' %len(pos_tags))\n",
    "print('Number of non terminals : %d' %len(non_terminals))\n",
    "print('Number of binaries : %d' %len(binaries))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_symbol_non_terminal = dict((non_terminal._symbol, non_terminal) for non_terminal in non_terminals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_non_terminals_indices = {non_terminal : index for index, non_terminal in enumerate(non_terminals)}\n",
    "dict_indices_non_terminals = {index : non_terminal for non_terminal, index in dict_non_terminals_indices.items()}\n",
    "\n",
    "dict_pos_indices = {pos : index for index, pos in enumerate(pos_tags)}\n",
    "dict_indices_pos = {index : pos for pos, index in dict_pos_indices.items()}\n",
    "\n",
    "dict_terminals_indices = {terminal : index for index, terminal in enumerate(terminals)}\n",
    "dict_indices_terminals = {index : terminal for terminal, index in dict_terminals_indices.items()}\n",
    "\n",
    "dict_binaries_indices = {binary : index for index, binary in enumerate(binaries)}\n",
    "dict_indices_terminals = {index : binary for binary, index in dict_binaries_indices.items()}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCFG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def express_node(rule):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Express the nature of the rule and extract its left hand and right hand sides.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    rule : nltk.grammar.Production object, the rule to consider.\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    3-tuple, tuple[0] : String describing the rule {'lexical', 'start_node', 'unary', 'binary'}\n",
    "             tuple[1] : nltk.grammar.Production, the left hand side of the rule.\n",
    "             tuple[2] : nltk.grammar.Production, the right hand side of the rule.\n",
    "    \"\"\"\n",
    "    if rule.is_lexical():\n",
    "        return 'lexical', rule._lhs, rule._rhs[0]\n",
    "    \n",
    "    else:\n",
    "        lhs, rhs = rule._lhs, rule._rhs\n",
    "        if rhs[0] == sent:\n",
    "            return 'start_node', lhs, rhs[0]\n",
    "        \n",
    "        elif len(rhs) == 1:\n",
    "            return 'unary', lhs, rhs[0]\n",
    "        \n",
    "#         elif len(rhs) == 1 and rhs[0] == sent:\n",
    "#             return 'start_node -> sent', lhs, rhs[0]\n",
    "        \n",
    "        elif len(rhs) == 2:\n",
    "            return 'binary', lhs, rhs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pcfg(data):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ----------------\n",
    "    Create PCFG model from the data, i.e compute the probability of each rule (conditiona probabilities) statistically from the data\n",
    "    \n",
    "    Parameters\n",
    "    ----------------\n",
    "    data : List of strings representing parse trees.\n",
    "    \n",
    "    Returns\n",
    "    ----------------\n",
    "    dict_pcfg   : Dictionnary with three keys {'lexical', 'unary', 'binary'}\n",
    "                 - dict_pcfg['lexical']  : dictionnary of lexicons.\n",
    "                                           - keys   : POS tags; \n",
    "                                           - values : dictionnary of probabilities p(terminal|POS_tag)\n",
    "                                                     - keys   : terminals.\n",
    "                                                     - values : p(terminal|POS_tag)\n",
    "                 - dict_pcfg['unary']    : dictionnary of unary laws.\n",
    "                                           - keys   : non terminals; \n",
    "                                           - values : dictionnary of probabilities p(node|non_terminal), node here can be\n",
    "                                                      either a POS tag or a non terminal.\n",
    "                                                     - keys   : non terminals.\n",
    "                                                     - values : p(node|non_terminal)\n",
    "                                                                          \n",
    "                 - dict_pcfg['binary']   : dictionnary of binary laws.\n",
    "                                           - keys   : non terminals; \n",
    "                                           - values : dictionnary of probabilities p(node|non_terminal), node here is binary\n",
    "                                                      containing POS tags or non terminals.\n",
    "                                                     - keys   : non terminals.\n",
    "                                                     - values : p(node|non_terminal)\n",
    "                                                                        \n",
    "    dict_probas : Dictionnary rearranging the elements of dict_pcfg in a way that simplifies the use of the probabilities \n",
    "                  in the CYK algorithm, keys in {'lexical', 'unary', 'binary'}                  \n",
    "                  dictionnary of probabilities.\n",
    "                            - keys   : unary nodes (POS tags or non terminals).\n",
    "                            - values : probabilities p(node|unary_node)\n",
    "    \"\"\"\n",
    "    \n",
    "    # Initalize dictionnaries dict_lexicons, dict_unaries, dict_binaries that we put in dict_pcfg\n",
    "    dict_lexicons, dict_unaries, dict_binaries = {}, {start : {sent : 1.}}, {} # Notice that we already put the rule of the start node in\n",
    "                                                                              # Chomsky normal form\n",
    "    dict_pcfg = {'lexical' : dict_lexicons, 'unary' : dict_unaries, 'binary' : dict_binaries}\n",
    "    \n",
    "    # Loop over the data\n",
    "    for string in data:\n",
    "        t = Tree.fromstring(ignore_functional_labels(string)) # Ignore the functional labels (see the doc of ignore_functional_labels)\n",
    "        t.chomsky_normal_form()  # Convert the tree to Chomsky normal form\n",
    "        rules = t.productions()  # Get the rules\n",
    "        for rule in rules:       # We start by counting the rules in data\n",
    "            nature, lhs, rhs = express_node(rule)\n",
    "            if nature in ['lexical', 'unary', 'binary']:\n",
    "                if lhs in dict_pcfg[nature]:\n",
    "                    if rhs in dict_pcfg[nature][lhs]:\n",
    "                        dict_pcfg[nature][lhs][rhs] += 1\n",
    "\n",
    "                    else:\n",
    "                        dict_pcfg[nature][lhs][rhs] = 1\n",
    "\n",
    "                else:\n",
    "                    dict_pcfg[nature][lhs] = {rhs : 1}\n",
    "\n",
    "            elif nature == 'start_node':\n",
    "                continue\n",
    "                \n",
    "    dict_normalized = {}\n",
    "    for nature in dict_pcfg:\n",
    "        for lhs in dict_pcfg[nature]:\n",
    "            if lhs in dict_normalized:\n",
    "                dict_normalized[lhs] += sum(dict_pcfg[nature][lhs].values())\n",
    "                \n",
    "            else:\n",
    "                dict_normalized[lhs] = sum(dict_pcfg[nature][lhs].values())\n",
    "                \n",
    "    for nature in dict_pcfg:\n",
    "        for lhs in dict_pcfg[nature]:\n",
    "            dict_pcfg[nature][lhs] = dict((key, value/dict_normalized[lhs]) for key, value in dict_pcfg[nature][lhs].items())\n",
    "\n",
    "    dict_probas = {'lexical' : {}, 'unary' : {}, 'binary' : {}} # Initialize dict_probas\n",
    "    for nature in dict_pcfg:\n",
    "        for lhs in dict_pcfg[nature]:\n",
    "            for node in dict_pcfg[nature][lhs]:\n",
    "                if node in dict_probas[nature]:\n",
    "                    dict_probas[nature][node][lhs] = dict_pcfg[nature][lhs][node]\n",
    "\n",
    "                else:\n",
    "                    dict_probas[nature][node] = {lhs : dict_pcfg[nature][lhs][node]}\n",
    "                    \n",
    "    return dict_pcfg, dict_probas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_pcfg, dict_probas = pcfg(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CYK algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cyk(sentence):\n",
    "    \n",
    "    n = len(sentence) + 1\n",
    "    k = len(non_terminals)\n",
    "    scores = np.zeros((n, n, k))\n",
    "    back = [[[None for i in range(k)] for j in range(n)] for l in range(n)]\n",
    "    for i in range(0, n-1):\n",
    "        word = sentence[i]\n",
    "        for A in dict_probas['lexical'][word]:\n",
    "            scores[i, i+1, dict_non_terminals_indices[A]] = dict_probas['lexical'][word][A]\n",
    "                        \n",
    "        added = True\n",
    "        while added:\n",
    "            added = False\n",
    "            for B in dict_probas['unary']:\n",
    "                score_B = scores[i, i+1, dict_non_terminals_indices[B]]\n",
    "                if score_B > 0:\n",
    "                    for A in dict_probas['unary'][B]:\n",
    "                        prob = dict_probas['unary'][B][A]*score_B\n",
    "                        if prob > scores[i, i+1, dict_non_terminals_indices[A]]:\n",
    "                            scores[i, i+1, dict_non_terminals_indices[A]] = prob\n",
    "                            back[i][i+1][dict_non_terminals_indices[A]] = B\n",
    "                            added = True\n",
    "                                                        \n",
    "    for span in range(2, n):\n",
    "        for begin in range(0, n-span):\n",
    "            end = begin + span\n",
    "            for split in range(begin+1, end):\n",
    "                for B, C in dict_probas['binary']:\n",
    "                    score_B, score_C = scores[begin, split, dict_non_terminals_indices[B]], scores[split, end, dict_non_terminals_indices[C]]\n",
    "                    if score_B*score_C > 0:\n",
    "                        for A in dict_probas['binary'][(B, C)]:\n",
    "                            prob = score_B*score_C*dict_probas['binary'][(B, C)][A]\n",
    "                            if prob > scores[begin, end, dict_non_terminals_indices[A]]:\n",
    "                                scores[begin, end, dict_non_terminals_indices[A]] = prob\n",
    "                                back[begin][end][dict_non_terminals_indices[A]] = (split, B, C)\n",
    "                                \n",
    "            added = True\n",
    "            while added:\n",
    "                added = False\n",
    "                for B in dict_probas['unary']:\n",
    "                    score_B = scores[begin, end, dict_non_terminals_indices[B]]\n",
    "                    if score_B > 0:\n",
    "                        for A in dict_probas['unary'][B]:\n",
    "                            prob = prob = dict_probas['unary'][B][A]*score_B\n",
    "                            if prob > scores[begin, end, dict_non_terminals_indices[A]]:\n",
    "                                scores[begin, end, dict_non_terminals_indices[A]] = prob\n",
    "                                back[begin][end][dict_non_terminals_indices[A]] = B\n",
    "                                added = True\n",
    "                                \n",
    "                                \n",
    "    return scores, back"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6148"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dict_probas['unary']) + len(dict_probas['binary'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Backtrack : Build parse tree from CYK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_parentheses(back_track):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Build the parse tree from tha back_track return of CYK algorithm as a string with parentheses. Then if we want to get the parse\n",
    "    in a tree form, we can simply use function Tree.from_string of nltk package.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    back_track : 3D matrix in the form of list of lists, of \"shape\" (n, n, r).\n",
    "                 - n : the length of the sentence we want to parse.\n",
    "                 - r : the number of non terminal nodes in our grammar.\n",
    "                 \n",
    "    Returns\n",
    "    ---------------\n",
    "    String, the string form with parentheses of the parse tree.\n",
    "    \"\"\"\n",
    "    \n",
    "    string = '('\n",
    "    q = queue.LifoQueue()\n",
    "    begin = 0\n",
    "    end = len(back_track[0]) - 1\n",
    "    q.put((None, sent, 'start', 1, [begin, end]))\n",
    "\n",
    "    while not q.empty():\n",
    "        split, symbol, status, depth, border = q.get()   # border is begin for left and end for right\n",
    "        string += ' (' + symbol._symbol\n",
    "\n",
    "        if status == 'left':\n",
    "            border = [border[0], split]\n",
    "            children = back[border[0]][border[1]][dict_non_terminals_indices[symbol]]\n",
    "\n",
    "        elif status == 'right':\n",
    "            border = [split, border[1]]\n",
    "            children = back[border[0]][border[1]][dict_non_terminals_indices[symbol]]\n",
    "\n",
    "        elif status == 'start':\n",
    "            children = back[border[0]][border[1]][dict_non_terminals_indices[symbol]]\n",
    "\n",
    "        if children is not None:\n",
    "            if isinstance(children, grammar.Nonterminal):\n",
    "                node = (split, children, status, depth+1, border)\n",
    "                q.put(node)\n",
    "\n",
    "            elif len(children) == 3:\n",
    "                split, l_child, r_child = children\n",
    "                l_node, r_node = (split, l_child, 'left', 0, border), (split, r_child, 'right', depth+1, border)\n",
    "                q.put(r_node)\n",
    "                q.put(l_node)\n",
    "\n",
    "        else:\n",
    "            depth += 1\n",
    "            word = sentence[border[0]:border[1]][0]\n",
    "            string += ' ' + word + ')'*depth\n",
    "            \n",
    "    return string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Tree('', [Tree('SENT', [Tree('NP', [Tree('DET', ['Une']), Tree('NP|<NC-COORD>', [Tree('NC', ['heure']), Tree('COORD', [Tree('CC', ['et']), Tree('NP', [Tree('DET', ['vingt']), Tree('NC', ['minutes'])])])])]), Tree('SENT|<PONCT-VN-NP-PONCT>', [Tree('PONCT', [',']), Tree('SENT|<VN-NP-PONCT>', [Tree('VN', [Tree('CLS', [\"c'\"]), Tree('V', ['est'])]), Tree('SENT|<NP-PONCT>', [Tree('NP', [Tree('DET', ['le']), Tree('NP|<NC-Srel>', [Tree('NC', ['temps']), Tree('Srel', [Tree('NP', [Tree('PROREL', [\"qu'\"])]), Tree('Srel|<VN-PP-PONCT-VPinf>', [Tree('VN', [Tree('CLS', ['il']), Tree('VN|<V-VPP>', [Tree('V', ['aura']), Tree('VPP', ['fallu'])])]), Tree('Srel|<PP-PONCT-VPinf>', [Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('NPP', ['Thierry']), Tree('NP|<NPP-PONCT-NP>', [Tree('NPP', ['Guerry']), Tree('NP|<PONCT-NP>', [Tree('PONCT', [',']), Tree('NP', [Tree('NC', ['chauffeur-routier']), Tree('PP', [Tree('P', ['chez']), Tree('NP', [Tree('NPP', ['Caillaud']), Tree('NP|<PONCT-NP>', [Tree('PONCT', [',']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NP|<NC-PP-VPpart>', [Tree('NC', ['entreprise']), Tree('NP|<PP-VPpart>', [Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['charpente'])])]), Tree('VPpart', [Tree('VPP', ['chargée']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['pose']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['toiture']), Tree('PP', [Tree('P+D', ['des']), Tree('NP', [Tree('NC', ['cours']), Tree('NP|<PP-AP>', [Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('NC', ['tennis'])])]), Tree('AP', [Tree('ADJ', ['couverts'])])])])])])])])])])])])])])])])])])])])])])]), Tree('Srel|<PONCT-VPinf>', [Tree('PONCT', [',']), Tree('VPinf', [Tree('P', ['pour']), Tree('VPinf|<VN-PP-PONCT-PP>', [Tree('VN', [Tree('VINF', ['pénétrer'])]), Tree('VPinf|<PP-PONCT-PP>', [Tree('PP', [Tree('P', ['dans']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NP|<NC-PP>', [Tree('NC', ['enceinte']), Tree('PP', [Tree('P+D', ['du']), Tree('NP', [Tree('NC', ['complexe']), Tree('NP|<AP-PP>', [Tree('AP', [Tree('ADJ', ['sportif'])]), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['commune'])])])])])])])])]), Tree('VPinf|<PONCT-PP>', [Tree('PONCT', [',']), Tree('PP', [Tree('P', ['avec']), Tree('NP', [Tree('DET', ['son']), Tree('NP|<NC-PONCT-Srel>', [Tree('NC', ['semi-remorque']), Tree('NP|<PONCT-Srel>', [Tree('PONCT', [',']), Tree('Srel', [Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('PROREL', ['lequel'])])]), Tree('Srel|<VN-NP>', [Tree('VN', [Tree('V', ['étaient']), Tree('VPP', ['chargées'])]), Tree('NP', [Tree('DET', ['quatorze']), Tree('NP|<NC-PP>', [Tree('NC', ['tonnes']), Tree('PP', [Tree('P', [\"d'\"]), Tree('NP', [Tree('NC', ['éléments']), Tree('NP|<PP-PP-PONCT-VPpart>', [Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['bois'])])]), Tree('NP|<PP-PONCT-VPpart>', [Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['trente']), Tree('NP|<NC-PP>', [Tree('NC', ['mètres']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('ADJ', ['long'])])])])])]), Tree('NP|<PONCT-VPpart>', [Tree('PONCT', [',']), Tree('VPpart', [Tree('VPP', ['destinés']), Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['couverture']), Tree('PP', [Tree('P+D', ['du']), Tree('NP', [Tree('NC', ['bâtiment']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['construction']), Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('DET', ['le']), Tree('NC', ['stade'])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])]), Tree('PONCT', ['.'])])])])])])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = Tree.fromstring(ignore_functional_labels(data[97]))\n",
    "t.chomsky_normal_form()\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "83"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sentence = t.leaves()\n",
    "len(sentence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2643.805163383484\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "start_time = time()\n",
    "scores, back = cyk(sentence)\n",
    "print(time() - start_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Tree('', [Tree('SENT', [Tree('NP', [Tree('DET', ['Une']), Tree('NC', ['heure']), Tree('COORD', [Tree('CC', ['et']), Tree('NP', [Tree('DET', ['vingt']), Tree('NC', ['minutes'])])])]), Tree('PONCT', [',']), Tree('VN', [Tree('CLS', [\"c'\"]), Tree('V', ['est'])]), Tree('NP', [Tree('DET', ['le']), Tree('NC', ['temps']), Tree('Srel', [Tree('NP', [Tree('PROREL', [\"qu'\"])]), Tree('VN', [Tree('CLS', ['il']), Tree('V', ['aura']), Tree('VPP', ['fallu'])]), Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('NPP', ['Thierry']), Tree('NPP', ['Guerry']), Tree('PONCT', [',']), Tree('NP', [Tree('NC', ['chauffeur-routier']), Tree('PP', [Tree('P', ['chez']), Tree('NP', [Tree('NPP', ['Caillaud']), Tree('PONCT', [',']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NC', ['entreprise']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['charpente'])])]), Tree('VPpart', [Tree('VPP', ['chargée']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['pose']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['toiture']), Tree('PP', [Tree('P', [Tree('D', ['des'])]), Tree('NP', [Tree('NC', ['cours']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('NC', ['tennis'])])]), Tree('AP', [Tree('ADJ', ['couverts'])])])])])])])])])])])])])])]), Tree('PONCT', [',']), Tree('VPinf', [Tree('P', ['pour']), Tree('VN', [Tree('VINF', ['pénétrer'])]), Tree('PP', [Tree('P', ['dans']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NC', ['enceinte']), Tree('PP', [Tree('P', [Tree('D', ['du'])]), Tree('NP', [Tree('NC', ['complexe']), Tree('AP', [Tree('ADJ', ['sportif'])]), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['commune'])])])])])])]), Tree('PONCT', [',']), Tree('PP', [Tree('P', ['avec']), Tree('NP', [Tree('DET', ['son']), Tree('NC', ['semi-remorque']), Tree('PONCT', [',']), Tree('Srel', [Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('PROREL', ['lequel'])])]), Tree('VN', [Tree('V', ['étaient']), Tree('VPP', ['chargées'])]), Tree('NP', [Tree('DET', ['quatorze']), Tree('NC', ['tonnes']), Tree('PP', [Tree('P', [\"d'\"]), Tree('NP', [Tree('NC', ['éléments']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['bois'])])]), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['trente']), Tree('NC', ['mètres']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('ADJ', ['long'])])])])]), Tree('PONCT', [',']), Tree('VPpart', [Tree('VPP', ['destinés']), Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['couverture']), Tree('PP', [Tree('P', [Tree('D', ['du'])]), Tree('NP', [Tree('NC', ['bâtiment']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['construction']), Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('DET', ['le']), Tree('NC', ['stade'])])])])])])])])])])])])])])])])])])]), Tree('PONCT', ['.'])])])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.un_chomsky_normal_form()\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Tree('', [Tree('SENT', [Tree('NP', [Tree('DET', ['Une']), Tree('NP|<NC-COORD-PP>', [Tree('NC', ['heure']), Tree('NP|<COORD-PP>', [Tree('COORD', [Tree('CC', ['et']), Tree('COORD|<NP-Sint-VPinf>', [Tree('NP', [Tree('DET', ['vingt']), Tree('NC', ['minutes'])]), Tree('COORD|<Sint-VPinf>', [Tree('Sint', [Tree('PONCT', [',']), Tree('Sint|<VN-NP-PP-PONCT>', [Tree('VN', [Tree('CLS', [\"c'\"]), Tree('V', ['est'])]), Tree('Sint|<NP-PP-PONCT>', [Tree('NP', [Tree('DET', ['le']), Tree('NP|<NC-Srel>', [Tree('NC', ['temps']), Tree('Srel', [Tree('NP', [Tree('PROREL', [\"qu'\"])]), Tree('Srel|<VN-PP>', [Tree('VN', [Tree('CLS', ['il']), Tree('VN|<V-VPP>', [Tree('V', ['aura']), Tree('VPP', ['fallu'])])]), Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('NPP', ['Thierry']), Tree('NP|<NPP-PONCT-NP-PONCT-NP>', [Tree('NPP', ['Guerry']), Tree('NP|<PONCT-NP-PONCT-NP>', [Tree('PONCT', [',']), Tree('NP|<NP-PONCT-NP>', [Tree('NP', [Tree('NC', ['chauffeur-routier']), Tree('PP', [Tree('P', ['chez']), Tree('NP', [Tree('NPP', ['Caillaud'])])])]), Tree('NP|<PONCT-NP>', [Tree('PONCT', [',']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NP|<NC-PP>', [Tree('NC', ['entreprise']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['charpente']), Tree('VPpart', [Tree('VPP', ['chargée']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['pose']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['toiture']), Tree('PP', [Tree('P+D', ['des']), Tree('NP', [Tree('NC', ['cours'])])])])])])])])])])])])])])])])])])])])])])])]), Tree('Sint|<PP-PONCT>', [Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('NC', ['tennis']), Tree('AP', [Tree('ADJ', ['couverts'])])])]), Tree('PONCT', [','])])])])]), Tree('VPinf', [Tree('P', ['pour']), Tree('VPinf|<VN-PP-PONCT-PP-PONCT>', [Tree('VN', [Tree('VINF', ['pénétrer'])]), Tree('VPinf|<PP-PONCT-PP-PONCT>', [Tree('PP', [Tree('P', ['dans']), Tree('NP', [Tree('DET', [\"l'\"]), Tree('NP|<NC-PP>', [Tree('NC', ['enceinte']), Tree('PP', [Tree('P+D', ['du']), Tree('NP', [Tree('NC', ['complexe']), Tree('NP|<AP-PP>', [Tree('AP', [Tree('ADJ', ['sportif'])]), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['la']), Tree('NC', ['commune'])])])])])])])])]), Tree('VPinf|<PONCT-PP-PONCT>', [Tree('PONCT', [',']), Tree('VPinf|<PP-PONCT>', [Tree('PP', [Tree('P', ['avec']), Tree('NP', [Tree('DET', ['son']), Tree('NC', ['semi-remorque'])])]), Tree('PONCT', [','])])])])])])])])]), Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('PROREL', ['lequel'])])])])])]), Tree('SENT|<VN-NP-PP-PONCT-VPpart-PONCT>', [Tree('VN', [Tree('V', ['étaient']), Tree('VPP', ['chargées'])]), Tree('SENT|<NP-PP-PONCT-VPpart-PONCT>', [Tree('NP', [Tree('DET', ['quatorze']), Tree('NP|<NC-PP>', [Tree('NC', ['tonnes']), Tree('PP', [Tree('P', [\"d'\"]), Tree('NP', [Tree('NC', ['éléments'])])])])]), Tree('SENT|<PP-PONCT-VPpart-PONCT>', [Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['bois']), Tree('PP', [Tree('P', ['de']), Tree('NP', [Tree('DET', ['trente']), Tree('NP|<NC-PP>', [Tree('NC', ['mètres']), Tree('PP', [Tree('P', ['de']), Tree('AP', [Tree('ADJ', ['long'])])])])])])])]), Tree('SENT|<PONCT-VPpart-PONCT>', [Tree('PONCT', [',']), Tree('SENT|<VPpart-PONCT>', [Tree('VPpart', [Tree('VPP', ['destinés']), Tree('PP', [Tree('P', ['à']), Tree('NP', [Tree('DET', ['la']), Tree('NP|<NC-PP>', [Tree('NC', ['couverture']), Tree('PP', [Tree('P+D', ['du']), Tree('NP', [Tree('NC', ['bâtiment']), Tree('PP', [Tree('P', ['en']), Tree('NP', [Tree('NC', ['construction']), Tree('PP', [Tree('P', ['sur']), Tree('NP', [Tree('DET', ['le']), Tree('NC', ['stade'])])])])])])])])])])]), Tree('PONCT', ['.'])])])])])])])])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_test = Tree.fromstring(build_parentheses(back))\n",
    "# t_test.chomsky_normal_form()\n",
    "t_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\" \".join(str(t).split()) == \" \".join(str(t_test).split())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def score(true_parse, proposed_parse):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    -----------------\n",
    "    Evaluate a proposed parse given the true one, this function prints recall and precision of the whole parse and on POS tags only also.\n",
    "    \n",
    "    Parameters\n",
    "    -----------------\n",
    "    true_parse, proposed_parse : Bracketed strings, the true and proposed parse trees.\n",
    "    \n",
    "    Returns\n",
    "    -----------------\n",
    "    \"\"\"\n",
    "    \n",
    "    true_parse = true_parse[2:-1]\n",
    "    proposed_parse= proposed_parse[2:-1]\n",
    "    \n",
    "    gold_tree = parser.create_from_bracket_string(true_parse)\n",
    "    test_tree = parser.create_from_bracket_string(proposed_parse)\n",
    "    \n",
    "    # Compute recall and precision for POS tags\n",
    "    y_true = np.array(gold_tree.poss)\n",
    "    y_pred = np.array(test_tree.poss)\n",
    "\n",
    "    y_pred = (y_true == y_pred).astype(int)\n",
    "    y_true = np.ones(len(y_true)).astype(int)\n",
    "\n",
    "    (POS_precision, POS_recall, POS_f_score, beta) = precision_recall_fscore_support(y_true,y_pred, labels=[1])\n",
    "    \n",
    "    # Compute recall and precision for the whole parse\n",
    "    thescorer = scorer.Scorer() \n",
    "    result = thescorer.score_trees(gold_tree, test_tree)\n",
    "    \n",
    "    print('Parse recall : {:.2f}%'.format(result.recall*100))\n",
    "    print('Parse precision : {:.2f}%'.format(result.prec*100), end=\"\\n\\n\")\n",
    "    \n",
    "    print('POS recall : {:.2f}%'.format(POS_recall[0]*100))\n",
    "    print('POS precision : {:.2f}%'.format(POS_precision[0]*100))\n",
    "\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parse recall : 50.79%\n",
      "Parse precision : 50.79%\n",
      "\n",
      "POS recall : 100.00%\n",
      "POS precision : 100.00%\n"
     ]
    }
   ],
   "source": [
    "score(\" \".join(str(t).split()), \" \".join(str(t_test).split()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OOV module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Embedding similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "words, embeddings = pkl.load(open('polyglot-fr.pkl', 'rb'), encoding = 'latin')\n",
    "dict_words_embeddings = dict((word, embedding) for word, embedding in zip(words, embeddings))\n",
    "del words, embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.0, 'joue'),\n",
       " (0.16718369722366333, 'joua'),\n",
       " (0.21939945220947266, 'donne'),\n",
       " (0.22649264335632324, 'passe'),\n",
       " (0.2468007206916809, 'travaille'),\n",
       " (0.26890885829925537, 'tient'),\n",
       " (0.27211642265319824, 'occupe'),\n",
       " (0.2790296673774719, 'offre'),\n",
       " (0.2938283681869507, 'remporte'),\n",
       " (0.3001372814178467, 'ouvre')]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_original = 'joue'\n",
    "scores = []\n",
    "for word in dict_words_embeddings:\n",
    "    scores.append((distance.cosine(dict_words_embeddings[word_original], dict_words_embeddings[word]), word))\n",
    "    \n",
    "sorted(scores)[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formal similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def levenshtein(s1, s2):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Computes the Levenshtein distance between two strings.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    s1, s2 : The two strings we want to compare.\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    Float, the Levenshtein distance between s1 and s2\n",
    "    \"\"\"\n",
    "    \n",
    "    s1, s2 = unidecode.unidecode(s1.lower()), unidecode.unidecode(s2.lower())\n",
    "    n1, n2 = len(s1), len(s2)\n",
    "    lev = np.zeros((n1 + 1, n2 + 1))\n",
    "    for i in range(n1 + 1):\n",
    "        lev[i, 0] = i\n",
    "        \n",
    "    for j in range(n2 + 1):\n",
    "        lev[0, j] = j\n",
    "        \n",
    "    for i in range(1, n1 + 1):\n",
    "        for j in range(1, n2 + 1):\n",
    "            if s1[i-1] == s2[j-1]:\n",
    "                lev[i, j] = min(lev[i-1, j] + 1, lev[i, j-1] + 1, lev[i-1, j-1])\n",
    "                \n",
    "            else:\n",
    "                lev[i, j] = min(lev[i-1, j] + 1, lev[i, j-1] + 1, lev[i-1, j-1] + 1)\n",
    "                \n",
    "    return lev[n1, n2]\n",
    "\n",
    "def damerau_levenshtein(s1, s2):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Computes the Damerau-Levenshtein distance between two strings.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    s1, s2 : The two strings we want to compare.\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    Float, the Damerau-Levenshtein distance between s1 and s2\n",
    "    \"\"\"\n",
    "    \n",
    "#     s1, s2 = unidecode.unidecode(s1.lower()), unidecode.unidecode(s2.lower())\n",
    "    s1, s2 = s1.lower(), s2.lower()\n",
    "    n1, n2 = len(s1), len(s2)\n",
    "    alphabet = ['!', '\"', '#', '$', '%', '&', '(', ')', \"'\", '*', '+', \n",
    "                ',', '-', '.', '/', ':', ';', '<', '=', '>', '?', '@', \n",
    "                '[', ']', '^', '_', '`', '{', '|', '}', '~', ' ', '°',\n",
    "                'é', 'è', 'ë', 'ê', 'à', 'á', 'â', 'ä', 'ç', 'î', 'ï', \n",
    "                'ô', 'ó', 'ö', 'ù', 'û', 'ß', '©', '±', 'µ', '½'] + [str(i) for i in range(10)] + ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', \n",
    "                'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']\n",
    "    for char in s1 + s2:\n",
    "        if char not in alphabet:\n",
    "            return 10\n",
    "        \n",
    "    dict_alphabet_indices = {char:index for (index, char) in zip(range(len(alphabet)), alphabet)}\n",
    "    da, d = np.zeros(len(alphabet)).astype(np.int8), np.zeros((n1 + 2, n2 + 2)).astype(np.int8)\n",
    "    maxdist = n1 + n2\n",
    "    d[0, 0] = maxdist\n",
    "    for i in range(n1 + 1):\n",
    "        d[i+1, 0] = maxdist\n",
    "        d[i+1, 1] = i\n",
    "        \n",
    "    for j in range(n2 + 1):\n",
    "        d[0, j+1] = maxdist\n",
    "        d[1, j+1] = j\n",
    "        \n",
    "    for i in range(1, n1 + 1):\n",
    "        db = 0\n",
    "        for j in range(1, n2 + 1):\n",
    "            k = da[dict_alphabet_indices[s2[j-1]]]\n",
    "            l = db\n",
    "            if s1[i-1] == s2[j-1]:\n",
    "                cost = 0\n",
    "                db = j\n",
    "                \n",
    "            else:\n",
    "                cost = 1\n",
    "                \n",
    "            d[i+1, j+1] = min(d[i, j] + cost, d[i+1, j] + 1, \n",
    "                              d[i, j+1] + 1, d[k, l] + (i-k-1)+1+(j-l-1))\n",
    "            da[dict_alphabet_indices[s1[i-1]]] = i\n",
    "            \n",
    "    return d[-1, -1]\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Language model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unigram(data):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Compute a unigram model from the corpus data.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    data : List of bracketed strings\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    np.array of shape (#words_in_data,) containing the probabilities p(word).\n",
    "    \"\"\"\n",
    "  \n",
    "    probas = np.zeros(len(terminals))\n",
    "    for bracketed in data:\n",
    "        t = Tree.fromstring(bracketed)\n",
    "        for word in t.leaves():\n",
    "            probas[dict_terminals_indices[word]] += 1\n",
    "\n",
    "    return probas/probas.sum()\n",
    "\n",
    "def bigram(data):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Compute a bigram model from the corpus data.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    data : List of bracketed strings\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    np.array of shape (#words_in_data, #words_in_data) containing the probabilities p(word_current|word_previous).\n",
    "    \"\"\"\n",
    "  \n",
    "    probas = np.full((len(terminals), len(terminals)), 1e-50)\n",
    "    for bracketed in data:\n",
    "        t = Tree.fromstring(bracketed)\n",
    "        sentence = t.leaves()\n",
    "        if len(sentence) >= 2:\n",
    "            for i in range(1, len(sentence)):\n",
    "                index_1 = dict_terminals_indices[sentence[i - 1]] # The previous word in the sequene.\n",
    "                index_2 = dict_terminals_indices[sentence[i]] # The current word in the sequene.\n",
    "                probas[index_1, index_2] += 1\n",
    "\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "    return probas/((probas.sum(axis = 1).reshape(-1, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# t = Tree.fromstring(ignore_functional_labels(data[16]))\n",
    "# t.chomsky_normal_form()\n",
    "# t.leaves()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "probas_unigram, probas_bigram = unigram(data), bigram(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assigning OOV words to the training lexique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def closest_formal(s, terminals, thresh = 2, swap = True):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Get the terminals within a lower Damerau-Levenshtein (or Levenshtein) distance of thresh to the word s.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    s         : String, the oov word\n",
    "    terminals : Set of words we have in our corpus.\n",
    "    thresh    : Int, the threshold of Damerau-Levenshtein distance.\n",
    "    swap      : Boolean, True  : Use Damerau-Levenshtein distance.\n",
    "                         False : Use Levenshtein distance\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    Dictionnary of the closest words.\n",
    "        keys   : words in terminals.\n",
    "        values : distance(s, word)\n",
    "    \"\"\"\n",
    "    \n",
    "    if swap:\n",
    "        fun = lambda word : damerau_levenshtein(s, word)\n",
    "        \n",
    "    else:\n",
    "        fun = lambda word : levenshtein(s, word)\n",
    "        \n",
    "    return {word : score for word, score in zip(terminals, list(map(fun, terminals))) if score <= thresh}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_case = lambda s : s.lower()\n",
    "terminals_lower = set(map(lower_case, terminals))\n",
    "dict_terminals_lower_indices = {terminal.lower() : index for (terminal, index) in dict_terminals_indices.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "def closest_embedding(s, terminals, n_words = 10):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Get the terminals within a lower Damerau-Levenshtein (or Levenshtein) distance of thresh to the word s.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    s         : String, oov word\n",
    "    terminals : Set of words we have in our corpus.\n",
    "    n_words   : Int, number of closest words to s.\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    Dictionnary of the closest words.\n",
    "        keys   : words in terminals.\n",
    "        values : cosine_distance(s, word)\n",
    "    \"\"\"\n",
    "    \n",
    "    fun = lambda word : distance.cosine(dict_words_embeddings[s], dict_words_embeddings[word]) if word in dict_words_embeddings else 1.\n",
    "    return {score_word[1] : score_word[0] for score_word in sorted(zip(list(map(fun, terminals)), terminals))[:n_words]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mer': 0.0,\n",
       " 'terre': 0.22055935859680176,\n",
       " 'ville': 0.3071545362472534,\n",
       " 'pluie': 0.30734384059906006,\n",
       " 'forêt': 0.32614070177078247,\n",
       " 'nature': 0.3320302367210388,\n",
       " 'lumière': 0.3353707194328308,\n",
       " 'glace': 0.3402719497680664,\n",
       " 'neige': 0.3502733111381531,\n",
       " 'circulation': 0.352333128452301}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 'mer'\n",
    "closest_embedding(s, terminals_lower)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def choose_words(sentence, terminals, probas_unigram, probas_bigram, thresh = 2, swap = True, n_words = 10):\n",
    "    \n",
    "    \"\"\"\n",
    "    Description\n",
    "    ---------------\n",
    "    Given a word s of the sentence, start by checking if it is in the training lexique, if not then choose a similar word \n",
    "    from the lexique using the formal and embedding similarities and a bigram language model trained on the training corpus.\n",
    "    \n",
    "    Parameters\n",
    "    ---------------\n",
    "    sentence       : List of strings containing tokens of a sentence.\n",
    "    terminals      : Set of all words in the training corpus.\n",
    "    probas_unigram : 1D np.array of shape (len(terminals),), unigram model trained on the training corpus.\n",
    "    probas_bigram  : 2D np.array of shape (len(terminals), len(terminals)), bigram model trained on the training corpus.\n",
    "    thresh, swap,  : Parameters of closest_formal (see its doc).\n",
    "    n_words        : Parameters of closest_embedding (see its doc).\n",
    "    \n",
    "    Returns\n",
    "    ---------------\n",
    "    List of strings containing the closest words to the sentence from the training corpus.\n",
    "    \"\"\"\n",
    "    \n",
    "    log_proba = 0\n",
    "    for i in range(len(sentence)):\n",
    "        s = sentence[i]\n",
    "        if s in terminals:\n",
    "            log_proba += math.log(probas_unigram[dict_terminals_lower_indices[s]]) if i==0 else math.log(probas_bigram[dict_terminals_lower_indices[sentence[i-1]], dict_terminals_lower_indices[s]])\n",
    "            continue\n",
    "\n",
    "        else:\n",
    "            print(s + ' is oov')\n",
    "            words_formal = closest_formal(s, terminals, thresh, swap)\n",
    "            words_embedding = closest_embedding(s, terminals, n_words) if s in dict_words_embeddings else {}\n",
    "            words_proposed = set(words_formal.keys()) | set(words_embedding.keys()) # Set of the proposed words\n",
    "            if len(words_proposed) == 0:\n",
    "                print('word not found : Need to look for the closest words in the form among the polyglot words')\n",
    "                dict_closest = closest_formal(s, set(dict_words_embeddings.keys()), thresh=1)\n",
    "                if len(dict_closest) == 0:\n",
    "                    print(\"We didn't find matching words\")\n",
    "                    \n",
    "                    continue\n",
    "                    \n",
    "                else:\n",
    "                    words_proposed = set(closest_embedding(min(dict_closest, key = lambda word : dict_closest[word])[0], terminals, 1).keys())\n",
    "                    \n",
    "            if i == 0:\n",
    "                scores = []\n",
    "                for word in words_proposed:\n",
    "                    unigram = math.log(probas_unigram[dict_terminals_indices[word]])\n",
    "                    scores.append((unigram, word))\n",
    "                \n",
    "            else:\n",
    "                scores = []\n",
    "                for word in words_proposed:\n",
    "                    bigram = math.log(probas_bigram[dict_terminals_lower_indices[sentence[i-1]], dict_terminals_lower_indices[word]])\n",
    "                    score = log_proba + bigram\n",
    "                    scores.append((score, word))\n",
    "                \n",
    "            scores.sort(reverse = True)\n",
    "            sentence[i] = scores[0][1]\n",
    "            log_proba += scores[0][0]\n",
    "        \n",
    "    return sentence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alors , à qui profite le crime ?\n",
      "profite is oov\n",
      "crime is oov\n",
      "alors , à qui dispose le racisme ?\n"
     ]
    }
   ],
   "source": [
    "sentence = Tree.fromstring(data_test[np.random.randint(0, 309)]).leaves()\n",
    "sentence = [word.lower() for word in sentence]\n",
    "# sentence = \"guerre d' indochine\".split(' ')\n",
    "print(\" \".join(sentence))\n",
    "# print('\\n')\n",
    "print(\" \".join(choose_words(sentence, terminals_lower, probas_unigram, probas_bigram, thresh=2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sentence = \"rené mayer , président du conseil , y mit fin en 1953 en ramenant le taux des piastres à 10 francs , un cours plus réaliste , mais ce en violation des accords du 8 mars 1949 et des accords de pau de 1950 ; les états associés du cambodge , laos et viêtnam ne furent pas consultés .\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'alors , à qui dispose le racisme ?'"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\" \".join(sentence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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