GMMHMM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gaussian Mixture Model Hidden Markov Models for Speech Recognition \n",
    "\n",
    "Problem 1: Sampling from a GMMHMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gmmhmm as GH\n",
    "import MFCC\n",
    "from scipy.io.wavfile import read as wread\n",
    "import glob\n",
    "import pickle\n",
    "\n",
    "def sample_gmmhmm(gmmhmm, n_sim):\n",
    " \"\"\"\n",
    " Simulate sampling from a GMMHMM.\n",
    " [A, weights, means, covars, pi]\n",
    " Returns\n",
    " -------\n",
    " states : ndarray of shape (n_sim,)\n",
    " The sequence of states\n",
    " obs : ndarray of shape (n_sim, K)\n",
    " The generated observations (column vectors of length K)\n",
    " \"\"\"\n",
    "\n",
    " state_dist = gmmhmm[-1]\n",
    " A = gmmhmm[0]\n",
    " weights = gmmhmm[1]\n",
    " means, covars = gmmhmm[2], gmmhmm[3]\n",
    " K = means[0,0].size\n",
    " \n",
    " states = np.zeros(n_sim, dtype = int)\n",
    " obs = np.zeros((n_sim, K))\n",
    " for i in xrange(n_sim):\n",
    "  s = np.random.multinomial(1,state_dist)[0]\n",
    "  states[i] = s\n",
    "  component = np.random.multinomial(1, weights[s, :])[0]\n",
    "  mu, sig = means[s, component,:], covars[s, component, :, :]\n",
    "  obs[i,:] =  np.random.multivariate_normal(mu, sig)\n",
    "#  print \"state \", states[i], obs[i]\n",
    "  state_dist = A.dot(state_dist)\n",
    " return states, obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load the wav files and extract cepler coefficients with the below function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load():\n",
    " names = [\"Mathematics\", \"Biology\", \"PoliticalScience\", \"Statistics\", \"Psychology\"]\n",
    " sampledict = {}\n",
    " for name in names:\n",
    "  sampledict[name] = []\n",
    "  for fname in glob.glob(\"Samples/\"+name+\" *\"):\n",
    "   w = wread(fname)\n",
    "   sampledict[name].append(MFCC.extract(w[1])[:30])\n",
    " return names, sampledict "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've loaded the data, we can train the model with the handy function below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialize(n):\n",
    " T = np.random.random((n,n))\n",
    " pi = np.random.random(n)\n",
    " pi /= np.sum(pi)\n",
    " T /= np.sum(T, axis = 1).reshape((n,1))\n",
    " return pi, T\n",
    "\n",
    "def load_and_train():\n",
    " names, sampledict = load()\n",
    " best_models = {}\n",
    " for name in names:\n",
    "  bestprob = -np.inf\n",
    "  bestmodel = None\n",
    "  #Random Restarts\n",
    "  for i in xrange(10):\n",
    "   startprob, transmat = initialize(5)\n",
    "   model = GH.GMMHMM(n_components=5, n_mix=3, transmat=transmat, startprob=startprob,  cvtype='diag')\n",
    "   # these values for covars_prior and var should work well for this problem\n",
    "   model.covars_prior = 0.01\n",
    "   model.fit(sampledict[name][:20], init_params='mc', var=0.1)\n",
    "   print \"Trained Again on \"+name+\", new prob: \", model.logprob\n",
    "   if model.logprob > bestprob:\n",
    "     bestprob = model.logprob\n",
    "     bestmodel = model\n",
    "     print \"New Best Prob for \"+name+\" \"+str(bestprob)\n",
    "  best_models[name] = bestmodel\n",
    " #save\n",
    " f = open(\"gmmmodels\",\"wb\")\n",
    " pickle.dump(best_models, f)\n",
    " f.close()\n",
    " return best_models, names, sampledict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the above code trains in only 2 minutes, as we were smart and used only 30 cepler coefficients, we validate the accuracy of our model on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trained Again on Mathematics, new prob:  -4040.77268791\n",
      "New Best Prob for Mathematics -4040.77268791\n",
      "Trained Again on Mathematics, new prob:  -3953.42508\n",
      "New Best Prob for Mathematics -3953.42508\n",
      "Trained Again on Mathematics, new prob:  -3971.93788922\n",
      "Trained Again on Mathematics, new prob:  -3899.3927969\n",
      "New Best Prob for Mathematics -3899.3927969\n",
      "Trained Again on Mathematics, new prob:  -4134.07959978\n",
      "Trained Again on Mathematics, new prob:  -4333.75254349\n",
      "Trained Again on Mathematics, new prob:  -3882.54045267\n",
      "New Best Prob for Mathematics -3882.54045267\n",
      "Trained Again on Mathematics, new prob:  -4025.89108343\n",
      "Trained Again on Mathematics, new prob:  -4317.11607219\n",
      "Trained Again on Mathematics, new prob:  -4319.64135\n",
      "Trained Again on Biology, new prob:  -5004.84692867\n",
      "New Best Prob for Biology -5004.84692867\n",
      "Trained Again on Biology, new prob:  -4524.3939161\n",
      "New Best Prob for Biology -4524.3939161\n",
      "Trained Again on Biology, new prob:  -4462.23374134\n",
      "New Best Prob for Biology -4462.23374134\n",
      "Trained Again on Biology, new prob:  -4586.08358652\n",
      "Trained Again on Biology, new prob:  -4575.51388269\n",
      "Trained Again on Biology, new prob:  -4332.69896562\n",
      "New Best Prob for Biology -4332.69896562\n",
      "Trained Again on Biology, new prob:  -4466.2697196\n",
      "Trained Again on Biology, new prob:  -4316.7011324\n",
      "New Best Prob for Biology -4316.7011324\n",
      "Trained Again on Biology, new prob:  -4373.073409\n",
      "Trained Again on Biology, new prob:  -4612.29253681\n",
      "Trained Again on PoliticalScience, new prob:  -1932.77714177\n",
      "New Best Prob for PoliticalScience -1932.77714177\n",
      "Trained Again on PoliticalScience, new prob:  -2302.76964794\n",
      "Trained Again on PoliticalScience, new prob:  -1863.18990294\n",
      "New Best Prob for PoliticalScience -1863.18990294\n",
      "Trained Again on PoliticalScience, new prob:  -2072.03368078\n",
      "Trained Again on PoliticalScience, new prob:  -2064.30919072\n",
      "Trained Again on PoliticalScience, new prob:  -1834.77201534\n",
      "New Best Prob for PoliticalScience -1834.77201534\n",
      "Trained Again on PoliticalScience, new prob:  -2041.67312553\n",
      "Trained Again on PoliticalScience, new prob:  -1952.32455679\n",
      "Trained Again on PoliticalScience, new prob:  -2070.38968429\n",
      "Trained Again on PoliticalScience, new prob:  -2379.71130876\n",
      "Trained Again on Statistics, new prob:  -2220.71896965\n",
      "New Best Prob for Statistics -2220.71896965\n",
      "Trained Again on Statistics, new prob:  -3037.51085026\n",
      "Trained Again on Statistics, new prob:  -2639.1350379\n",
      "Trained Again on Statistics, new prob:  -2486.83141677\n",
      "Trained Again on Statistics, new prob:  -3157.27740082\n",
      "Trained Again on Statistics, new prob:  -2980.16167903\n",
      "Trained Again on Statistics, new prob:  -2771.57870867\n",
      "Trained Again on Statistics, new prob:  -2980.30008321\n",
      "Trained Again on Statistics, new prob:  -3207.82616883\n",
      "Trained Again on Statistics, new prob:  -2815.31401567\n",
      "Trained Again on Psychology, new prob:  -3690.74488437\n",
      "New Best Prob for Psychology -3690.74488437\n",
      "Trained Again on Psychology, new prob:  -3681.01682609\n",
      "New Best Prob for Psychology -3681.01682609\n",
      "Trained Again on Psychology, new prob:  -3631.53617711\n",
      "New Best Prob for Psychology -3631.53617711\n",
      "Trained Again on Psychology, new prob:  -4022.31114729\n",
      "Trained Again on Psychology, new prob:  -3610.41759163\n",
      "New Best Prob for Psychology -3610.41759163\n",
      "Trained Again on Psychology, new prob:  -3699.57592073\n",
      "Trained Again on Psychology, new prob:  -3776.32335579\n",
      "Trained Again on Psychology, new prob:  -3722.16285512\n",
      "Trained Again on Psychology, new prob:  -4046.02667289\n",
      "Trained Again on Psychology, new prob:  -3682.6092499\n",
      "Accuracy Breakdown:  {'Mathematics': 100.0, 'Biology': 60.0, 'Statistics': 100.0, 'Psychology': 100.0, 'PoliticalScience': 100.0}\n",
      "Overall Accuracy:  92.0\n"
     ]
    }
   ],
   "source": [
    "def test():\n",
    " models, names, sampledict  = load_and_train()\n",
    " accuracies = {}\n",
    " for name in names:\n",
    "   tot = len(sampledict[name]) - 20\n",
    "   cor = 0.\n",
    "   for sample in sampledict[name][20:]:\n",
    "     mscore = -np.inf\n",
    "     bname = None\n",
    "     for cand_name in names:\n",
    "      score =  models[cand_name].score(sample)\n",
    "      if score > mscore:\n",
    "       mscore = score\n",
    "       bname = cand_name\n",
    "     if bname == name:\n",
    "      cor += 1.\n",
    "   accuracies[name] = 100*cor/tot\n",
    " return accuracies\n",
    "adict = test()\n",
    "print \"Accuracy Breakdown: \", adict\n",
    "print \"Overall Accuracy: \", sum([adict[name] for name in adict])/len(adict.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be noted that accuracy is highly dependant on the initial conditions. On a different run, I obtained the following output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Trained Again on Mathematics, new prob:  -3912.2283613\n",
      "New Best Prob for Mathematics -3912.2283613\n",
      "Trained Again on Mathematics, new prob:  -4088.19268306\n",
      "Trained Again on Mathematics, new prob:  -3984.41664154\n",
      "Trained Again on Mathematics, new prob:  -4024.96627592\n",
      "Trained Again on Mathematics, new prob:  -4030.07805858\n",
      "Trained Again on Mathematics, new prob:  -4085.71020813\n",
      "Trained Again on Mathematics, new prob:  -4169.75890684\n",
      "Trained Again on Mathematics, new prob:  -4057.68004774\n",
      "Trained Again on Mathematics, new prob:  -3956.42304341\n",
      "Trained Again on Mathematics, new prob:  -4049.61447941\n",
      "Trained Again on Biology, new prob:  -4478.17131295\n",
      "New Best Prob for Biology -4478.17131295\n",
      "Trained Again on Biology, new prob:  -4297.7317647\n",
      "New Best Prob for Biology -4297.7317647\n",
      "Trained Again on Biology, new prob:  -4540.24990046\n",
      "Trained Again on Biology, new prob:  -4155.51881087\n",
      "New Best Prob for Biology -4155.51881087\n",
      "Trained Again on Biology, new prob:  -4277.78063657\n",
      "Trained Again on Biology, new prob:  -4923.82994236\n",
      "Trained Again on Biology, new prob:  -4417.30835921\n",
      "Trained Again on Biology, new prob:  -4827.63211316\n",
      "Trained Again on Biology, new prob:  -4500.40941922\n",
      "Trained Again on Biology, new prob:  -4384.06583096\n",
      "Trained Again on PoliticalScience, new prob:  -2313.91853051\n",
      "New Best Prob for PoliticalScience -2313.91853051\n",
      "Trained Again on PoliticalScience, new prob:  -2241.76953245\n",
      "New Best Prob for PoliticalScience -2241.76953245\n",
      "Trained Again on PoliticalScience, new prob:  -2164.98729171\n",
      "New Best Prob for PoliticalScience -2164.98729171\n",
      "Trained Again on PoliticalScience, new prob:  -2218.73028128\n",
      "Trained Again on PoliticalScience, new prob:  -2131.45507306\n",
      "New Best Prob for PoliticalScience -2131.45507306\n",
      "Trained Again on PoliticalScience, new prob:  -1803.70656584\n",
      "New Best Prob for PoliticalScience -1803.70656584\n",
      "Trained Again on PoliticalScience, new prob:  -2021.76269025\n",
      "Trained Again on PoliticalScience, new prob:  -2212.87686714\n",
      "Trained Again on PoliticalScience, new prob:  -1787.27665936\n",
      "New Best Prob for PoliticalScience -1787.27665936\n",
      "Trained Again on PoliticalScience, new prob:  -2413.09640232\n",
      "Trained Again on Statistics, new prob:  -3130.06366036\n",
      "New Best Prob for Statistics -3130.06366036\n",
      "Trained Again on Statistics, new prob:  -2695.19321107\n",
      "New Best Prob for Statistics -2695.19321107\n",
      "Trained Again on Statistics, new prob:  -2710.00080068\n",
      "Trained Again on Statistics, new prob:  -2343.90802172\n",
      "New Best Prob for Statistics -2343.90802172\n",
      "Trained Again on Statistics, new prob:  -2571.58609146\n",
      "Trained Again on Statistics, new prob:  -3041.35933206\n",
      "Trained Again on Statistics, new prob:  -3104.50978636\n",
      "Trained Again on Statistics, new prob:  -2590.50602515\n",
      "Trained Again on Statistics, new prob:  -2879.63760985\n",
      "Trained Again on Statistics, new prob:  -2977.88081599\n",
      "Trained Again on Psychology, new prob:  -3861.90855544\n",
      "New Best Prob for Psychology -3861.90855544\n",
      "Trained Again on Psychology, new prob:  -3546.42568755\n",
      "New Best Prob for Psychology -3546.42568755\n",
      "Trained Again on Psychology, new prob:  -3994.22072117\n",
      "Trained Again on Psychology, new prob:  -3545.0881218\n",
      "New Best Prob for Psychology -3545.0881218\n",
      "Trained Again on Psychology, new prob:  -3602.94127203\n",
      "Trained Again on Psychology, new prob:  -3716.33163344\n",
      "Trained Again on Psychology, new prob:  -3560.04022452\n",
      "Trained Again on Psychology, new prob:  -3577.94841488\n",
      "Trained Again on Psychology, new prob:  -3669.19155851\n",
      "Trained Again on Psychology, new prob:  -3657.24364314\n",
      "Accuracy Breakdown:  {'Mathematics': 100.0, 'Biology': 90.0, 'Statistics': 100.0, 'Psychology': 100.0, 'PoliticalScience': 100.0}\n",
      "Overall Accuracy:  98.0\n"
     ]
    }
   ],
   "source": [
    "print \"\"\"\n",
    "Trained Again on Mathematics, new prob:  -3912.2283613\n",
    "New Best Prob for Mathematics -3912.2283613\n",
    "Trained Again on Mathematics, new prob:  -4088.19268306\n",
    "Trained Again on Mathematics, new prob:  -3984.41664154\n",
    "Trained Again on Mathematics, new prob:  -4024.96627592\n",
    "Trained Again on Mathematics, new prob:  -4030.07805858\n",
    "Trained Again on Mathematics, new prob:  -4085.71020813\n",
    "Trained Again on Mathematics, new prob:  -4169.75890684\n",
    "Trained Again on Mathematics, new prob:  -4057.68004774\n",
    "Trained Again on Mathematics, new prob:  -3956.42304341\n",
    "Trained Again on Mathematics, new prob:  -4049.61447941\n",
    "Trained Again on Biology, new prob:  -4478.17131295\n",
    "New Best Prob for Biology -4478.17131295\n",
    "Trained Again on Biology, new prob:  -4297.7317647\n",
    "New Best Prob for Biology -4297.7317647\n",
    "Trained Again on Biology, new prob:  -4540.24990046\n",
    "Trained Again on Biology, new prob:  -4155.51881087\n",
    "New Best Prob for Biology -4155.51881087\n",
    "Trained Again on Biology, new prob:  -4277.78063657\n",
    "Trained Again on Biology, new prob:  -4923.82994236\n",
    "Trained Again on Biology, new prob:  -4417.30835921\n",
    "Trained Again on Biology, new prob:  -4827.63211316\n",
    "Trained Again on Biology, new prob:  -4500.40941922\n",
    "Trained Again on Biology, new prob:  -4384.06583096\n",
    "Trained Again on PoliticalScience, new prob:  -2313.91853051\n",
    "New Best Prob for PoliticalScience -2313.91853051\n",
    "Trained Again on PoliticalScience, new prob:  -2241.76953245\n",
    "New Best Prob for PoliticalScience -2241.76953245\n",
    "Trained Again on PoliticalScience, new prob:  -2164.98729171\n",
    "New Best Prob for PoliticalScience -2164.98729171\n",
    "Trained Again on PoliticalScience, new prob:  -2218.73028128\n",
    "Trained Again on PoliticalScience, new prob:  -2131.45507306\n",
    "New Best Prob for PoliticalScience -2131.45507306\n",
    "Trained Again on PoliticalScience, new prob:  -1803.70656584\n",
    "New Best Prob for PoliticalScience -1803.70656584\n",
    "Trained Again on PoliticalScience, new prob:  -2021.76269025\n",
    "Trained Again on PoliticalScience, new prob:  -2212.87686714\n",
    "Trained Again on PoliticalScience, new prob:  -1787.27665936\n",
    "New Best Prob for PoliticalScience -1787.27665936\n",
    "Trained Again on PoliticalScience, new prob:  -2413.09640232\n",
    "Trained Again on Statistics, new prob:  -3130.06366036\n",
    "New Best Prob for Statistics -3130.06366036\n",
    "Trained Again on Statistics, new prob:  -2695.19321107\n",
    "New Best Prob for Statistics -2695.19321107\n",
    "Trained Again on Statistics, new prob:  -2710.00080068\n",
    "Trained Again on Statistics, new prob:  -2343.90802172\n",
    "New Best Prob for Statistics -2343.90802172\n",
    "Trained Again on Statistics, new prob:  -2571.58609146\n",
    "Trained Again on Statistics, new prob:  -3041.35933206\n",
    "Trained Again on Statistics, new prob:  -3104.50978636\n",
    "Trained Again on Statistics, new prob:  -2590.50602515\n",
    "Trained Again on Statistics, new prob:  -2879.63760985\n",
    "Trained Again on Statistics, new prob:  -2977.88081599\n",
    "Trained Again on Psychology, new prob:  -3861.90855544\n",
    "New Best Prob for Psychology -3861.90855544\n",
    "Trained Again on Psychology, new prob:  -3546.42568755\n",
    "New Best Prob for Psychology -3546.42568755\n",
    "Trained Again on Psychology, new prob:  -3994.22072117\n",
    "Trained Again on Psychology, new prob:  -3545.0881218\n",
    "New Best Prob for Psychology -3545.0881218\n",
    "Trained Again on Psychology, new prob:  -3602.94127203\n",
    "Trained Again on Psychology, new prob:  -3716.33163344\n",
    "Trained Again on Psychology, new prob:  -3560.04022452\n",
    "Trained Again on Psychology, new prob:  -3577.94841488\n",
    "Trained Again on Psychology, new prob:  -3669.19155851\n",
    "Trained Again on Psychology, new prob:  -3657.24364314\n",
    "Accuracy Breakdown:  {'Mathematics': 100.0, 'Biology': 90.0, 'Statistics': 100.0, 'Psychology': 100.0, 'PoliticalScience': 100.0}\n",
    "Overall Accuracy:  98.0\"\"\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code ran for 2 minutes, got 98% accuracy. YEEEHAW!!!"
   ]
  }
 ],
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