Kneser-Ney Smoothing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import defaultdict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_datasets = ['gutenberg']\n",
    "test_datasets  = ['gutenberg']\n",
    "prefix = '_'.join(train_datasets) + '-' + '_'.join(test_datasets)\n",
    "\n",
    "word_to_id = np.load('%s_word_to_id.npy' % prefix).item()\n",
    "id_to_word = np.load('%s_id_to_word.npy' % prefix).item()\n",
    "n_grams = np.load('%s_n_grams.npy' % prefix).item()\n",
    "train_sentences = np.load('%s_train.npy' % prefix)\n",
    "valid_sentences = np.load('%s_valid.npy' % prefix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Store conditional counts\n",
    "conditional_n_grams = dict()\n",
    "\n",
    "for n in range(1,2+1):\n",
    "    conditional_n_grams[n] = defaultdict(dict)\n",
    "    \n",
    "    for n_gram, count in n_grams[n].iteritems():\n",
    "        conditional_n_grams[n][n_gram[:-1]][n_gram[-1]] = count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Store continuation counts\n",
    "continuations = dict()\n",
    "\n",
    "for n in range(1,2+1):\n",
    "    continuations[n] = defaultdict(set)\n",
    "    \n",
    "    for n_gram, count in n_grams[n].iteritems():        \n",
    "        if count > 0:\n",
    "            continuations[n][n_gram[1:]].add(n_gram[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "continuation_prob = np.zeros((len(word_to_id) + 1,))\n",
    "denominator = sum([len(x) for x in continuations[n].values()])\n",
    "\n",
    "for i in range(len(word_to_id) + 1):\n",
    "    continuation_prob[i] = float(len(continuations[2][(i,)])) / denominator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_distribution(context, d=0.75):\n",
    "    n = len(context) + 1\n",
    "    assert n == 2\n",
    "    \n",
    "    # create probability distribution by copying continuation probability\n",
    "    counts = np.array(continuation_prob)\n",
    "    \n",
    "    # premultiply with lambda_\n",
    "    lambda_ = float(d)/n_grams[n-1][context] * len(conditional_n_grams[n][context])\n",
    "    counts *= lambda_\n",
    "    \n",
    "    for i in conditional_n_grams[n][context]:\n",
    "        bigram_score = float(max(conditional_n_grams[n][context][i] - d, 0))/n_grams[n-1][context]\n",
    "        counts[i] += bigram_score\n",
    "        \n",
    "    return counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probability(context, next_word):\n",
    "    probabilities = get_distribution(context)\n",
    "    return probabilities[next_word]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_perplexity(sentence):\n",
    "    running_prob = 0\n",
    "\n",
    "    for pos in range(1, len(sentence)):\n",
    "        query_n = 1\n",
    "        if query_n == 0:\n",
    "            context = tuple()\n",
    "        else:\n",
    "            context = tuple(map(lambda x: word_to_id[x] if x in word_to_id else 0, sentence[:pos][-1 * query_n:]))\n",
    "        next_word = word_to_id[sentence[pos]] if sentence[pos] in word_to_id else 0\n",
    "\n",
    "        running_prob += np.log(get_probability(context, next_word))\n",
    "        #print running_prob\n",
    "\n",
    "    return np.exp(-running_prob/len(sentence))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9856"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(valid_sentences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "1980 123.281377737 159.476603103\n",
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      "2012 321.124331163 159.601157515\n",
      "2013 352.782338712 159.697076672\n",
      "2014 206.944027281 159.72052429\n",
      "2015 473.907780419 159.876371143\n",
      "2016 22.3132157944 159.808169281\n",
      "2017 220.166857375 159.838079434\n",
      "2018 87.5869060975 159.802293811\n",
      "2019 208.772334881 159.826536405\n",
      "2020 168.529105893 159.830842476\n",
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    {
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     "output_type": "stream",
     "text": [
      "2060 112.30608533 160.107146579\n",
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      "9628 1566.09150857 204.443497728\n",
      "9629 80.9107207045 204.430669817\n",
      "9630 83.2959402208 204.418092231\n",
      "9631 96.9687936472 204.406936781\n",
      "9632 833.461546774 204.472238827\n",
      "9633 22.6493327989 204.453365783\n",
      "9634 87.9690882532 204.441276081\n",
      "9635 195.68156716 204.440367021\n",
      "9636 85.0614177196 204.427979457\n",
      "9637 210.254738045 204.428584018\n",
      "9638 392.121851622 204.448056294\n",
      "9639 73.8898630586 204.434512913\n",
      "9640 137.890132439 204.427610685\n",
      "9641 461.113772716 204.454232357\n",
      "9642 74.3829073135 204.440743679\n",
      "9643 132.865409261 204.433321931\n",
      "9644 154.817130049 204.428177691\n",
      "9645 164.087622431 204.423995589\n",
      "9646 64.3800250113 204.409478748\n",
      "9647 470.765367544 204.437086116\n",
      "9648 66.2959740879 204.422769491\n",
      "9649 241.247425359 204.426585518\n",
      "9650 45.1566155457 204.410082568\n",
      "9651 373.335021027 204.427584116\n",
      "9652 96.0439805444 204.416356145\n",
      "9653 500.949643961 204.447072251\n",
      "9654 52.0459733712 204.431287569\n",
      "9655 969.994402124 204.510571239\n",
      "9656 646.359470871 204.5563255\n",
      "9657 43.0900266711 204.539607101\n",
      "9658 23.5278286398 204.520866882\n",
      "9659 135.508548336 204.513722749\n",
      "9660 29.6312490625 204.495620847\n",
      "9661 647.360999458 204.541456635\n",
      "9662 44.7370087705 204.524918867\n",
      "9663 172.715185562 204.521627297\n",
      "9664 80.2592435121 204.508770351\n",
      "9665 109.48270535 204.498939391\n",
      "9666 40.328797571 204.481956858\n",
      "9667 110.038781377 204.472188222\n",
      "9668 306.385230999 204.482728406\n",
      "9669 268.746208397 204.489374061\n",
      "9670 211.511253243 204.490100137\n",
      "9671 612.43223984 204.532277777\n",
      "9672 84.7637332806 204.51989604\n",
      "9673 49.2836099212 204.503849287\n",
      "9674 344.652485916 204.518334934\n",
      "9675 32.4132675423 204.500548135\n",
      "9676 422.114815073 204.523035917\n",
      "9677 56.6948267335 204.507761252\n",
      "9678 1092.53543916 204.599509127\n",
      "9679 48.2828268031 204.583360709\n",
      "9680 164.454347856 204.579215578\n",
      "9681 529.211407847 204.612745034\n",
      "9682 43.5232567634 204.596108714\n",
      "9683 464.908365229 204.622989368\n",
      "9684 47.8313853828 204.606800251\n",
      "9685 1932.3735493 204.785177987\n",
      "9686 56.1220537966 204.769831324\n",
      "9687 54.8094192695 204.754352338\n",
      "9688 312.460139991 204.765468634\n",
      "9689 296.110916076 204.774895408\n",
      "9690 622.372180822 204.817986656\n",
      "9691 264.572871507 204.824152039\n",
      "9692 142.873487207 204.81776076\n",
      "9693 42.5732800685 204.801024172\n",
      "9694 1236.63092587 204.907453249\n",
      "9695 52.3725573819 204.891721515\n",
      "9696 293.07120794 204.900814996\n",
      "9697 87.5547413677 204.888714968\n",
      "9698 108.902385652 204.87881845\n",
      "9699 76.8910085557 204.86562383\n",
      "9700 107.970369286 204.855635658\n",
      "9701 321.51690757 204.867660114\n",
      "9702 38.5073296842 204.850514868\n",
      "9703 26.5584830866 204.832141822\n",
      "9704 697.290055226 204.882884523\n",
      "9705 219.482134098 204.88438867\n",
      "9706 181.391188026 204.881968437\n",
      "9707 144.055739298 204.875702859\n",
      "9708 334.99724535 204.889105016\n",
      "9709 167.540417375 204.885258602\n",
      "9710 103.503082695 204.87481867\n",
      "9711 343.678809281 204.889110679\n",
      "9712 276.854709153 204.896519883\n",
      "9713 58.4112148674 204.88144007\n",
      "9714 287.721851323 204.889967132\n",
      "9715 390.042466246 204.909023585\n",
      "9716 65.4979264609 204.894676452\n",
      "9717 87.0385709339 204.882548843\n",
      "9718 154.43880675 204.877358623\n",
      "9719 272.481525653 204.884313785\n",
      "9720 128.372436315 204.876443002\n",
      "9721 77.76948652 204.863368845\n",
      "9722 48.5168992621 204.84728878\n",
      "9723 47.4390670185 204.83110118\n",
      "9724 106.088618256 204.820947711\n",
      "9725 363.611442612 204.837274104\n",
      "9726 32.7850330592 204.819585995\n",
      "9727 308.852450088 204.830280162\n",
      "9728 121.601203729 204.821725421\n",
      "9729 254.165737348 204.826796748\n",
      "9730 993.552071572 204.907849597\n",
      "9731 1073.93443095 204.997145382\n",
      "9732 68.1228298708 204.983082471\n",
      "9733 526.044568927 205.016065981\n",
      "9734 105.173081164 205.005809897\n",
      "9735 70.4332221003 204.991987733\n",
      "9736 26.0834446025 204.97361364\n",
      "9737 159.20310243 204.968913443\n",
      "9738 88.8817900633 204.956993624\n",
      "9739 261.17057856 204.962765039\n",
      "9740 541.298206642 204.997292854\n",
      "9741 263.964479424 205.003345737\n",
      "9742 307.534794774 205.013869338\n",
      "9743 88.7748771093 205.001940049\n",
      "9744 31.8940244458 204.984176281\n",
      "9745 47.7956587118 204.968047765\n",
      "9746 153.85976593 204.962804277\n",
      "9747 55.8118523508 204.947503605\n",
      "9748 223.495632504 204.949406172\n",
      "9749 251.724491548 204.954203617\n",
      "9750 831.347658114 205.018442511\n",
      "9751 157.873499567 205.013608124\n",
      "9752 35.1616868685 204.996192772\n",
      "9753 406.558018365 205.016857302\n",
      "9754 211.404268766 205.017512086\n",
      "9755 71.8990523741 205.003867307\n",
      "9756 102.367222458 204.993348024\n",
      "9757 35.8988285419 204.976019215\n",
      "9758 47.5649962171 204.959889384\n",
      "9759 27.0048671008 204.941656287\n",
      "9760 125.409366417 204.933508322\n",
      "9761 167.586613473 204.92968258\n",
      "9762 444.823067644 204.954254267\n",
      "9763 61.8589387182 204.939598868\n",
      "9764 39.3537332321 204.92264179\n",
      "9765 59.7203953973 204.907773651\n",
      "9766 187.348049426 204.905975789\n",
      "9767 120.108267191 204.897294614\n",
      "9768 19.9472625845 204.878362274\n",
      "9769 381.962856492 204.896487606\n",
      "9770 15.1940526271 204.877072763\n",
      "9771 320.594585788 204.888914506\n",
      "9772 463.210174766 204.915346641\n",
      "9773 131.671324005 204.90785288\n",
      "9774 131.432783256 204.900336249\n",
      "9775 131.624231111 204.892840739\n",
      "9776 862.444752791 204.960095716\n",
      "9777 268.95911929 204.966640922\n",
      "9778 144.680076669 204.960476021\n",
      "9779 54.6876881602 204.945110706\n",
      "9780 79.4937281275 204.932284677\n",
      "9781 23.3396044359 204.913720715\n",
      "9782 15.1940526271 204.894327925\n",
      "9783 73.743877489 204.880923341\n",
      "9784 102.364950526 204.870446491\n",
      "9785 271.92217697 204.877298293\n",
      "9786 553.473233427 204.912916555\n",
      "9787 105.197841502 204.902729073\n",
      "9788 163.832888294 204.898533564\n",
      "9789 607.759299353 204.939683795\n",
      "9790 15.3469544944 204.920319815\n",
      "9791 1275.73205634 205.029675589\n",
      "9792 1226.83362847 205.134015827\n",
      "9793 197.117780401 205.133197343\n",
      "9794 321.862550777 205.145114581\n",
      "9795 55.4400742138 205.129832319\n",
      "9796 307.576564392 205.140289268\n",
      "9797 90.1726912593 205.128555486\n",
      "9798 755.919537992 205.184764383\n",
      "9799 103.958750753 205.174435198\n",
      "9800 257.832677531 205.17980794\n",
      "9801 142.26613694 205.173389488\n",
      "9802 61.6788354852 205.158751667\n",
      "9803 265.279505598 205.164883935\n",
      "9804 367.506572574 205.181440966\n",
      "9805 119.018458872 205.172654205\n",
      "9806 1122.75340992 205.266218063\n",
      "9807 326.129225979 205.278540963\n",
      "9808 196.891259869 205.277685903\n",
      "9809 90.0758654276 205.265942598\n",
      "9810 1371.55754571 205.384818514\n",
      "9811 300.75884278 205.394538655\n",
      "9812 126.390927766 205.386487742\n",
      "9813 110.858225085 205.37685576\n",
      "9814 314.377396254 205.387961266\n",
      "9815 86.1815062477 205.375817169\n",
      "9816 120.224050839 205.36714326\n",
      "9817 224.526123402 205.369094674\n",
      "9818 372.051683197 205.38607019\n",
      "9819 47.8647008995 205.370029317\n",
      "9820 18.7379809184 205.351025952\n",
      "9821 94.5692405879 205.339747008\n",
      "9822 188.917250299 205.338075167\n",
      "9823 133.065898142 205.330718471\n",
      "9824 120.337362592 205.322067748\n",
      "9825 1348.94762291 205.43845545\n",
      "9826 225.03788039 205.440449896\n",
      "9827 84.2872242853 205.428122543\n",
      "9828 43.0410397192 205.411601322\n",
      "9829 1215.57609454 205.51436475\n",
      "9830 111.654434064 205.504817406\n",
      "9831 16.528473912 205.485596867\n",
      "9832 68.6566407588 205.471681586\n",
      "9833 60.4142992683 205.456930988\n",
      "9834 126.447864136 205.448897529\n",
      "9835 439.572670301 205.472700271\n",
      "9836 209.192781254 205.473078444\n",
      "9837 63.2454524703 205.458621478\n",
      "9838 106.86935678 205.448601226\n",
      "9839 322.743238975 205.460521413\n",
      "9840 121.759811505 205.452016107\n",
      "9841 672.117037634 205.499431777\n",
      "9842 184.095266722 205.49725722\n",
      "9843 50.2555953748 205.481487039\n",
      "9844 47.546893086 205.465444927\n",
      "9845 1620.16939975 205.609128042\n",
      "9846 206.236765765 205.609191781\n",
      "9847 15.1940526271 205.589856369\n",
      "9848 145.512384395 205.583756514\n",
      "9849 62.1114486696 205.569190797\n",
      "9850 147.47037753 205.56329304\n",
      "9851 38.0389061489 205.54628894\n",
      "9852 49.797393105 205.530481684\n",
      "9853 208.433824209 205.53077632\n",
      "9854 98.4117235085 205.519906807\n",
      "9855 92.3329546561 205.508422741\n"
     ]
    }
   ],
   "source": [
    "ppls = []\n",
    "\n",
    "for i, sentence in enumerate(valid_sentences):\n",
    "    temp = compute_perplexity(sentence)\n",
    "    ppls += [temp]\n",
    "    print i, temp, np.mean(ppls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "205.50842274089328"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(ppls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_from_distrib(context):\n",
    "    n = len(context) + 1\n",
    "    \n",
    "    # normalize to construct distribution\n",
    "    probabilities = get_distribution(context)\n",
    "    print context, sum(probabilities)\n",
    "    choice = np.random.choice(len(word_to_id) + 1, p=probabilities)\n",
    "    \n",
    "    return choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7332,) 1.0\n",
      "(22598,) 1.0\n",
      "(7999,) 1.0\n",
      "(318,) 1.0\n",
      "(4402,) 1.0\n",
      "(11050,) 1.0\n",
      "(559,) 1.0\n",
      "(15944,) 1.0\n",
      "(11853,) 1.0\n"
     ]
    }
   ],
   "source": [
    "tokens = [word_to_id['@@start@@'],]\n",
    "\n",
    "while True:\n",
    "    try:\n",
    "        while len(tokens) < 10:\n",
    "            try:\n",
    "                tokens.append(sample_from_distrib((tokens[-2],tokens[-1],)))\n",
    "            except:\n",
    "                try:\n",
    "                    tokens.append(sample_from_distrib((tokens[-1],)))\n",
    "                except KeyError:\n",
    "                    tokens.append(sample_from_distrib(tuple()))\n",
    "\n",
    "            if id_to_word[tokens[-1]] == '@@end@@':\n",
    "                break\n",
    "    except KeyError:\n",
    "        continue\n",
    "    else:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "@@start@@\n",
      "@@number@@\n",
      "they\n",
      "had\n",
      "reached\n",
      "but\n",
      "one\n",
      "side\n",
      "of\n",
      "death\n"
     ]
    }
   ],
   "source": [
    "for id_ in tokens:\n",
    "    print id_to_word[id_]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
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