Machine Learning II.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "rcParams['figure.figsize'] = (10, 4) #wide graphs by default\n",
      "from __future__ import print_function\n",
      "from __future__ import division\n",
      "\n",
      "# A lot of code below borrowed from the scikits learn docs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://peekaboo-vision.blogspot.com/2013/01/machine-learning-cheat-sheet-for-scikit.html\n",
      "\n",
      "![http://1.bp.blogspot.com/-ME24ePzpzIM/UQLWTwurfXI/AAAAAAAAANw/W3EETIroA80/s1600/drop_shadows_background.png](http://1.bp.blogspot.com/-ME24ePzpzIM/UQLWTwurfXI/AAAAAAAAANw/W3EETIroA80/s1600/drop_shadows_background.png)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import load_iris\n",
      "data = load_iris()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Desicion Trees"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://scikit-learn.org/stable/modules/tree.html"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import tree"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf = tree.DecisionTreeClassifier()\n",
      "clf.fit(data.data, data.target)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "DecisionTreeClassifier(compute_importances=None, criterion='gini',\n",
        "            max_depth=None, max_features=None, max_leaf_nodes=None,\n",
        "            min_density=None, min_samples_leaf=1, min_samples_split=2,\n",
        "            random_state=None, splitter='best')"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf.predict(data.data[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([0])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf.predict(data.data[10])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([0])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf.predict(data.data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image #needed to render in notebook\n",
      "import StringIO, pydot  #needed to convert dot format to png\n",
      "\n",
      "dot_data = StringIO.StringIO() \n",
      "tree.export_graphviz(clf, out_file=dot_data) \n",
      "graph = pydot.graph_from_dot_data(dot_data.getvalue())\n",
      "Image(graph.create_png())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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Wao+Li4ORkRGGDBmiaVOpVFoxgwYNwrNnz3Dx4kVNW0ExrFOnTozRY0yB7OxsxMbGwsPD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\n",
       "prompt_number": 8,
       "text": [
        "<IPython.core.display.Image at 0x7ff03e35ba90>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Cross-validation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://scikit-learn.org/stable/modules/classes.html#module-sklearn.cross_validation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.naive_bayes import GaussianNB\n",
      "\n",
      "clf2 = GaussianNB()\n",
      "\n",
      "clf2.fit(data.data, data.target)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "GaussianNB()"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import cross_validation"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kf = cross_validation.KFold(len(data.data), n_folds=10)\n",
      "len(kf)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "10"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pc_folds = []\n",
      "for train_index, test_index in kf:\n",
      "    clf2 = GaussianNB()\n",
      "    clf2.fit(data.data[train_index], data.target[train_index])\n",
      "    predictions = clf2.predict(data.data[test_index])\n",
      "    pc_right = sum(predictions == data.target[test_index])/float(len(test_index))\n",
      "    pc_folds.append(pc_right)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pc_folds"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[1.0,\n",
        " 1.0,\n",
        " 1.0,\n",
        " 0.93333333333333335,\n",
        " 0.93333333333333335,\n",
        " 0.8666666666666667,\n",
        " 1.0,\n",
        " 0.8666666666666667,\n",
        " 0.8666666666666667,\n",
        " 1.0]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mean(pc_folds)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.94666666666666688"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "min(pc_folds)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "0.8666666666666667"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Metrics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import metrics"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predictions = clf2.predict(data.data)\n",
      "predictions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "metrics.accuracy_score(data.target, predictions)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "0.96666666666666667"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(metrics.classification_report(data.target, predictions))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "             precision    recall  f1-score   support\n",
        "\n",
        "          0       1.00      1.00      1.00        50\n",
        "          1       0.94      0.96      0.95        50\n",
        "          2       0.96      0.94      0.95        50\n",
        "\n",
        "avg / total       0.97      0.97      0.97       150\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "metrics.confusion_matrix(data.target, predictions)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([[50,  0,  0],\n",
        "       [ 0, 48,  2],\n",
        "       [ 0,  3, 47]])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "confmat = metrics.confusion_matrix(data.target, predictions)\n",
      "imshow(confmat,interpolation='nearest', cmap=cm.gray_r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.image.AxesImage at 0x7ff03c61fa50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAAEACAYAAACtefPrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNAttMXtGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff03df320d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "confmat = metrics.confusion_matrix(data.target, predictions)\n",
      "\n",
      "imshow(confmat.max() - confmat,interpolation='nearest', cmap=cm.gray)\n",
      "\n",
      "for rownum, row in enumerate(confmat):\n",
      "    for colnum, val in enumerate(row):\n",
      "        text(colnum, rownum, str(val/sum(data.target == rownum).astype(float)), fontsize=24, color='black' if val < confmat.max()/2 else 'white', ha='center', va='center' )\n",
      "        \n",
      "xticks(arange(len(data.target_names)), data.target_names)\n",
      "yticks(arange(len(data.target_names)), data.target_names);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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itZxrXmRkpE/1rlq1itLSUizL4r777qsyv1GjRkycONF+7l5vdHS0PT1x4kRCQ0O57bbb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\nCCGEEEIIIYQQtfX/Adp9aS0t4vyFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff03df4d410>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://media.aau.dk/null_space_pursuits/2012/01/frustrations-with-music-genre.html"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Dimensionality reduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/dimensionality_reduction/projection/principal_component_analysis.ipynb\n",
      "\n",
      "http://gael-varoquaux.info/science/ica_vs_pca.html\n",
      "\n",
      "From: http://nbviewer.ipython.org/github/temporaer/tutorial_ml_gkbionics/blob/master/1%20-%20PCA.ipynb"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Cov = array([[2.9, -2.2], [-2.2, 6.5]])\n",
      "X = random.multivariate_normal([1,2], Cov, size=200)\n",
      "figure(figsize=(4,4))\n",
      "scatter(X[:,0], X[:,1])\n",
      "axis('equal') # equal scaling on both axis;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WQCiB52k0utNsdnfyvZjsaJcsv8BZs2blu1/27NnDmjWb0MenJOvXb8EDBw7c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\nIP8HJCke+SQXyZ4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff03df3f590>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "http://en.wikipedia.org/wiki/Multivariate_normal_distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(cov(X,rowvar=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 2.33164768 -1.78245345]\n",
        " [-1.78245345  5.34877268]]\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.decomposition import PCA\n",
      "pca = PCA()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X_pca = pca.fit_transform(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pca.components_, pca.mean_"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "(array([[-0.42069867,  0.90720043],\n",
        "        [-0.90720043, -0.42069867]]), array([ 1.27415321,  1.85932007]))"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "figure(figsize=(4,4))\n",
      "scatter(X_pca[:,0], X_pca[:,1])\n",
      "# axis('equal');\n",
      "axis('equal') # equal scaling on both axis;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FokWf49lnX0BwcCloNN+pRydBkn5AhQohuervnj1/ICnpOSi3kAdiYnpj164/Mx1XqVII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\nmZmZmZmZmZmZmdl/9QWzfXR1fBBm8gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff03df903d0>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "var(X_pca[:,0]), var(X_pca[:,1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "(6.1444781813112739, 1.4975400813297965)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Hidden Markov Models"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "notes = [\"A\", \"B\", \"C\", \"D\"]\n",
      "\n",
      "markov_model = [ [ 0.5,  0.3, 0.2, 0],\n",
      "                [0.2, 0.1, 0.6, 0.1],\n",
      "                [0.1, 0, 0.2, 0.7],\n",
      "                [0, 0, 0.9, 0.1] ]\n",
      "state = random.randint(0, 4)\n",
      "print(state)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "throw = random.random()\n",
      "print(throw)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.919680708341\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "probabilities = markov_model[state]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cumsum(probabilities)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([ 0.1,  0.1,  0.3,  1. ])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cumsum(probabilities) > throw"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([False, False, False,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "argmax(cumsum(probabilities) > throw)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "3"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "state = argmax(cumsum(probabilities) > throw)\n",
      "print(state)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "throw = random.random()\n",
      "state = argmax(cumsum(probabilities) > throw)\n",
      "probabilities = markov_model[state]\n",
      "print(state)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "throw = random.random()\n",
      "state = argmax(cumsum(probabilities) > throw)\n",
      "probabilities = markov_model[state]\n",
      "print(state)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def markov(matrix, state, num_iter=10):\n",
      "    out = [state]\n",
      "    probabilities = markov_model[state]\n",
      "    for i in range(num_iter):\n",
      "        throw = random.random()\n",
      "        state = argmax(cumsum(probabilities) > throw)\n",
      "        probabilities = markov_model[state]\n",
      "        out.append(state)\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "markov(markov_model, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "[0, 1, 2, 3, 2, 0, 0, 0, 0, 0, 0]"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "markov_model"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "[[0.5, 0.3, 0.2, 0],\n",
        " [0.2, 0.1, 0.6, 0.1],\n",
        " [0.1, 0, 0.2, 0.7],\n",
        " [0, 0, 0.9, 0.1]]"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "markov(markov_model, 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "[3, 2, 3, 2, 0, 1, 2, 3, 2, 3, 2]"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hidden Markov Models have a \"hidden\" internal state which determines the output"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "possible_outputs = ['M', 'N', 'O']\n",
      "output_probabilites = [ [ 0.1, 0.9, 0],\n",
      "                       [0.8, 0.1, 0.1],\n",
      "                       [0.1, 0, 0.9],\n",
      "                       [0.2, 0.3, 0.5]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "states = markov(markov_model, 3)\n",
      "for state in states:\n",
      "    throw = random.random()\n",
      "    out_index = argmax(cumsum(output_probabilites[state]) > throw)\n",
      "    print(possible_outputs[out_index])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "N\n",
        "M\n",
        "O\n",
        "O\n",
        "O\n",
        "M\n",
        "N\n",
        "M\n",
        "N\n",
        "M\n",
        "O\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def genHMM(markov_model, initial_state, possible_outputs, output_probabilites, num_iter=10):\n",
      "    out = []\n",
      "    states = markov(markov_model, initial_state)\n",
      "    for state in states:\n",
      "        throw = random.random()\n",
      "        out_index = argmax(cumsum(output_probabilites[state]) > throw)\n",
      "        out.append(possible_outputs[out_index])\n",
      "    return out, states"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "genHMM(markov_model, 3, possible_outputs, output_probabilites)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "(['N', 'O', 'N', 'O', 'N', 'O', 'M', 'N', 'O', 'M', 'O'],\n",
        " [3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2])"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By Andr\u00e9s Cabrera mantaraya36@gmail.com\n",
      "\n",
      "For course MAT 201A at UCSB\n",
      "\n",
      "This ipython notebook is licensed under the CC-BY-NC-SA license: http://creativecommons.org/licenses/by-nc-sa/4.0/\n",
      "\n",
      "![http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}