Logistic Regression.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import optimize\n",
      "import pandas as pd\n",
      "import seaborn as sns\n",
      "from ggplot import *\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Loading the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load training data\n",
      "data = pd.read_csv('ex2data2.txt',header=None, names = ('x1','x2','y'))\n",
      "data.info()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'pandas.core.frame.DataFrame'>\n",
        "Int64Index: 118 entries, 0 to 117\n",
        "Data columns (total 3 columns):\n",
        "x1    118 non-null float64\n",
        "x2    118 non-null float64\n",
        "y     118 non-null int64\n",
        "dtypes: float64(2), int64(1)\n",
        "memory usage: 3.7 KB\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Columns 1 & 2 are the training data, 3 is the label set."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.head(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>x1</th>\n",
        "      <th>x2</th>\n",
        "      <th>y</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0.051267</td>\n",
        "      <td> 0.69956</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>-0.092742</td>\n",
        "      <td> 0.68494</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "         x1       x2  y\n",
        "0  0.051267  0.69956  1\n",
        "1 -0.092742  0.68494  1"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the df values into numpy arrays\n",
      "X = data.ix[:,0:2].values\n",
      "y = data.ix[:,2].values\n",
      "y = y[:, None]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Visualizing the data\n",
      "On almost every release Pandas adds more and more helpful plot methods that help you avoid specifying your plot in matplot directly. These functions are very handy for exploration. I still find myself reaching for ggplot though, perhaps it's because I started in R years ago, or maybe it's because I subscribed to some of the concepts in Wilkinson's [The Grammar of Graphics]( http://www.amazon.com/The-Grammar-Graphics-Statistics-Computing/dp/0387245448). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.plot(kind='scatter', x=0, y=1, c = 2, s=40, title='Microchip Test 1 & 2',\n",
      "          figsize=None, legend= True)\n",
      "# pd.scatter_matrix(data, alpha=0.2, figsize=(6, 6), diagonal='kde')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x9a7f590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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i4eHBoEFDjMaf+/R5is2btwE6UlP1eHiUpFu3XnmuT48evfj770ij4aDMcwRg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\nUVHlm3/haNnZ2XzzTTxeXt507dq90gN+bm4uR48exmg0Eh4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nn5gmoKRgutE+Om/SXbVT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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9a7fc10>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here's another quick plot with the excellent seaborn package. The syntax is arbitrary across the various plot types unlike ggplot, but it's constantly improving."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sns.lmplot('x1', 'x2', hue='y', data=data, fit_reg=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<seaborn.axisgrid.FacetGrid at 0x7a4a270>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RKNARZuMAxUXXEwAgFIECABCKQAEACEWgAACEIlAAAEIx6wnImDzl3UI2ECiA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\nINT/B3HcSsLr272LAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9f96630>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One more take with ggplot. If anyone reading this knows a smarter way of adjusting the plot size please let me know."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ggplot(data ,aes(x='x1', y='x2', color='y')) +\\\n",
      "    geom_point(alpha=.7, size = 30) +\\\n",
      "    theme_matplotlib(rc={\"figure.figsize\": \"5, 5\"})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TQFLL9W7KaW8sRk8Q0BOGiPwM+ONVSGIyn2lCsKtM/8aelBzMZPDzO9MiKfkq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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x95b2b10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<ggplot: (10010983)>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we stated before we'll use logistic regression for binary classification. This means we'll be taking a continuous range of input and convert it to either 0 or 1 based on it's range:<br>\n",
      "\n",
      "$h_\\theta(x)$ = our Logistic Regression function.<br>\n",
      "If the output of $h_\\theta(x)\\geq .5$, then 1<br>\n",
      "If the output of $h_\\theta(x)\\lt .5$, then 0<br>\n",
      "\n",
      "Recall that we'll have a vector of coefficients $\\theta$ that we chose to get us as close to y (our labels) as possible, that is to say choose $\\theta_0$, $\\theta_1$, $\\theta_2$ (assuming we only have three coefficients) that minimize the sum of the squared differences (squared error).\n",
      "\n",
      "![caption](http://kldavenport.com/wp-content/uploads/2014/11/logisitic_regression_blog2.png \"Matrix Examples\")\n",
      "\n",
      "\n",
      "<br>\n",
      "So it's a clean linear algebra process of: **Prediction = Data * Parameters**\n",
      "\n",
      "\n",
      "\n",
      "Now we'll take our data and process it through the sigmoid function:\n",
      "$$h_\\theta(x) = g(\\theta^Tx): g(z) = \\frac{1}{1+e^{-z}}$$\n",
      "\n",
      "The logistic regression cost function including regularization (last term) is:\n",
      "\n",
      "$$J(\\theta) = \\frac{1}{m}\\sum\\limits_{i=1}^{m} [-y^{(i)}log(h_\\theta(x^{(i)})-(1 - y^{(i)})log(1 - h_\\theta(x^{(i)}))]+\\frac{\\lambda}{2m}\\sum\\limits_{j=1}^{n}\\theta^2_j$$\n",
      "\n",
      "The gradient of the cost including regularization is:\n",
      "\n",
      "$$\\frac{\\partial{J(\\theta)}}{\\partial{\\theta_j}} = \\frac{1}{m}\\sum\\limits_{i=1}^{m} (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)}     \\qquad \\qquad \\qquad   for \\,\\, j=0 $$\n",
      "\n",
      "$$\\frac{\\partial{J(\\theta)}}{\\partial{\\theta_j}} = (\\frac{1}{m}\\sum\\limits_{i=1}^{m} (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j    \\qquad    for \\,\\, j \\geq 1 $$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Feature Engineering:\n",
      "We can tell from the two-dimensional plots above that we have non-linearly separable data. We might want to start with seeing what kind of boundaries we can train using interactions between the two variables in our feature space. Since we're using logistic regression we'll need to manually construct these new features. This is not the case with more advanced non-linear methods such as SVMs with a Gaussian or polynomial kernel as the various interactions between the input variables are inherently captured by the structure of the model.\n",
      "\n",
      "Remember that depending on the scale of the new features we create (f.g. X1, X2, X1^2, X2^2, X1\\*X2, X1\\*X2^2), we might need to scale down variables to speed up convergence of the gradient descent. Logistic Regression, like SVMs can also suffer poor performance if some input variables have a larger range of values compared to others. Normalization is used to address this: http://scikit-learn.org/stable/modules/classes.html#module-sklearn.preprocessing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def new_features(X1, X2, degree=18):\n",
      "    \"\"\"\n",
      "    Returns a m x n matrix of the original inputs along with new columns based on their exponents and combinations.\n",
      "    Args:\n",
      "        x1, x2: 2D arrays (floats) with identical shapes\n",
      "        highest_poly_degree: int to specify the max polynomial\n",
      "    \"\"\"    \n",
      "    num_features = (degree + 1) * (degree + 2) / 2\n",
      "    out = np.empty(shape=(X1.shape[0], num_features), dtype=float)\n",
      "    k = 0\n",
      "    for i in xrange(0, degree + 1):\n",
      "        for j in xrange(i + 1):\n",
      "            new_feature_values = X1**(i - j) * X2**j\n",
      "            out[:, k] = new_feature_values[:, 0]\n",
      "            k += 1\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = new_features(X[:, 0][:, None], X[:, 1][:, None])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$g(z) = \\frac{1}{1+e^{-z}}$ expressed as:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sigmoid(z):\n",
      "    \"\"\"\n",
      "    Return Sigmoid of z\n",
      "    Args:\n",
      "        Z : array or scalar\n",
      "    \"\"\"\n",
      "    return 1.0 / (1.0 + np.exp(-z))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Usually we'd want to use a package function. Notice above that we are using numpy's exp and not the math library's exp. There is a common performance hit in Python code of accidentally bouncing back and forth between NumPy and standard functions which are not optimized for the contiguous C arrays of NumPy. \n",
      "\n",
      "Below we are using SciPy's expit over scipy.stats.logistic.cdf because it is the source operator and not a wrapper function with extra parameters like logistic.cdf. Note the 4x speedup between our manual and SciPy function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.special import expit"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit \n",
      "\n",
      "expit(X[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000 loops, best of 3: 15.4 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "sigmoid(X[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000 loops, best of 3: 8.94 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$g(\\theta^Tx)$ expressed as:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def h_of_theta(theta, X):\n",
      "    transposed_theta = theta[:, None]\n",
      "    return sigmoid(X.dot(transposed_theta))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$J(\\theta) = \\frac{1}{m}\\sum\\limits_{i=1}^{m} [-y^{(i)}log(h_\\theta(x^{(i)})-(1 - y^{(i)})log(1 - h_\\theta(x^{(i)}))]+\\frac{\\lambda}{2m}\\sum\\limits_{j=1}^{n}\\theta^2_j$ <br>\n",
      "\n",
      "Recall that the $\\frac{\\lambda}{2m}\\sum\\limits_{j=1}^{n}\\theta^2_j$ at the end of the line above is the regularization term.<br>\n",
      "expressed as:\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cost_function_reg(theta, X, y, lamda):\n",
      "    \"\"\"\n",
      "    Return cost of given theta for logistic regression\n",
      "    Args:\n",
      "        theta is a 1D numpy array \n",
      "        X is a m x n numpy array w/ the first column being an intercept of 1\n",
      "        y is a m x 1 numpy array, it is the label set for each obs in X\n",
      "        lambda : float is regularization parameter\n",
      "    \"\"\"\n",
      "    m = len(y) * 1.0\n",
      "    h_theta = h_of_theta(theta, X)\n",
      "\n",
      "\n",
      "    tol = .00000000000000000000001  \n",
      "    h_theta[h_theta < tol] = tol  # values close to zero are set to tol\n",
      "    h_theta[(h_theta < 1 + tol) & (h_theta > 1 - tol)] = 1 - tol  # values close to 1 get set to 1 - tol\n",
      "\n",
      "    regularization_term = (float(lamda)/2) * theta**2\n",
      "    cost_vector = y * np.log(h_theta) + (-y + 1) * np.log(-h_theta + 1)\n",
      "\n",
      "    J = -sum(cost_vector)/m + sum(regularization_term[1:])/m\n",
      "\n",
      "    return J[0]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "$\\frac{\\partial{J(\\theta)}}{\\partial{\\theta_j}} = \\frac{1}{m}\\sum\\limits_{i=1}^{m} (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)}     \\qquad \\qquad \\qquad   for \\,\\, j=0 $\n",
      "\n",
      "$\\frac{\\partial{J(\\theta)}}{\\partial{\\theta_j}} = (\\frac{1}{m}\\sum\\limits_{i=1}^{m} (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j    \\qquad    for \\,\\, j \\geq 1 $ expressed as:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gradient(theta, X, y, lamda):\n",
      "    \"\"\"\n",
      "    Return gradient of theta \n",
      "    Args:\n",
      "        theta is a 1D numpy array \n",
      "        X is a m x n numpy array w/ the first column being an intercept of 1\n",
      "        y is a m x 1 numpy array, it is the label set for each obs in X\n",
      "        lambda : float is regularization parameter\n",
      "    \"\"\"\n",
      "    m = len(y)\n",
      "    h_theta = h_of_theta(theta, X)\n",
      "    derivative_regularization_term = float(lamda) * theta/m\n",
      "    grad = (h_theta - y).T.dot(X)/m + derivative_regularization_term.T\n",
      "    grad[0][0] -= derivative_regularization_term[0]  \n",
      "    \n",
      "    return np.ndarray.flatten(grad)  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's see what we have so far and test one iteration of regularized logistic regression at initial theta."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m, n = X.shape\n",
      "initial_theta = np.zeros(n)\n",
      "lambda2 = 1\n",
      "\n",
      "cost = cost_function_reg(initial_theta, X, y, lambda2)\n",
      "grad = gradient(initial_theta, X, y, lambda2)\n",
      "\n",
      "print 'Training set size:', X.shape\n",
      "print ''\n",
      "print 'Cost at initial theta of zeros:', cost\n",
      "print '\\nGradient at initial theta (zeros):\\n'\n",
      "print grad"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Training set size: (118, 190)\n",
        "\n",
        "Cost at initial theta of zeros: 0.69314718056\n",
        "\n",
        "Gradient at initial theta (zeros):\n",
        "\n",
        "[  8.47457627e-03   1.87880932e-02   7.77711864e-05   5.03446395e-02\n",
        "   1.15013308e-02   3.76648474e-02   1.83559872e-02   7.32393391e-03\n",
        "   8.19244468e-03   2.34764889e-02   3.93486234e-02   2.23923907e-03\n",
        "   1.28600503e-02   3.09593720e-03   3.93028171e-02   1.99707467e-02\n",
        "   4.32983232e-03   3.38643902e-03   5.83822078e-03   4.47629067e-03\n",
        "   3.10079849e-02   3.10312442e-02   1.09740238e-03   6.31570797e-03\n",
        "   4.08503006e-04   7.26504316e-03   1.37646175e-03   3.87936363e-02\n",
        "   1.99427086e-02   2.74239681e-03   2.32500787e-03   2.21859968e-03\n",
        "   1.37054473e-03   4.59059364e-03   2.44887343e-03   3.45775396e-02\n",
        "   2.58470812e-02   9.24073316e-04   3.56449986e-03   2.36431492e-04\n",
        "   2.73345994e-03   1.41372690e-04   5.06220460e-03   7.44299593e-04\n",
        "   3.91158180e-02   1.94460178e-02   2.03971305e-03   1.67313910e-03\n",
        "   9.57374855e-04   8.28510751e-04   1.45754709e-03   5.55440822e-04\n",
        "   3.80878101e-03   1.42922173e-03   3.74400380e-02   2.27382094e-02\n",
        "   1.00011095e-03   2.22706585e-03   1.51733578e-04   1.25745954e-03\n",
        "   1.48580695e-04   1.57570852e-03   3.59508725e-06   3.99563605e-03\n",
        "   5.22308844e-04   4.06790884e-02   1.90410565e-02   1.75081954e-03\n",
        "   1.23641700e-03   4.69990556e-04   5.27414397e-04   5.55662823e-04\n",
        "   3.40580487e-04   1.05188919e-03   1.97028168e-04   3.35794866e-03\n",
        "   9.67859736e-04   4.06730521e-02   2.10163086e-02   1.15032574e-03\n",
        "   1.49782866e-03   1.02669187e-04   6.64345919e-04   1.09951984e-04\n",
        "   6.18955072e-04   7.43336884e-05   1.07123799e-03  -6.55122093e-05\n",
        "   3.44743950e-03   5.15509782e-04   4.35307118e-02   1.89437400e-02\n",
        "   1.66248899e-03   9.41574445e-04   2.61308468e-04   3.41532634e-04\n",
        "   2.43492082e-04   2.14664106e-04   3.63362793e-04   1.41628227e-04\n",
        "   8.21956083e-04   3.56919486e-05   3.11923871e-03   8.32085947e-04\n",
        "   4.47399893e-02   2.02778726e-02   1.31985563e-03   1.06764143e-03\n",
        "   7.86844535e-05   3.87047105e-04   6.94079048e-05   2.85477158e-04\n",
        "   6.90699995e-05   3.69582263e-04   2.39341381e-05   8.16074446e-04\n",
        "  -9.08769094e-05   3.17917837e-03   6.45964381e-04   4.77107504e-02\n",
        "   1.92318272e-02   1.68027441e-03   7.40076535e-04   1.63801867e-04\n",
        "   2.27678507e-04   1.19804339e-04   1.31380821e-04   1.46616000e-04\n",
        "   9.85447536e-05   2.59049209e-04   4.94761874e-05   6.85844461e-04\n",
        "  -3.01668071e-05   3.02344543e-03   9.01454727e-04   4.99273765e-02\n",
        "   2.02879133e-02   1.49547626e-03   8.00908230e-04   6.71510752e-05\n",
        "   2.41544808e-04   4.36257990e-05   1.48661051e-04   4.47256584e-05\n",
        "   1.50975684e-04   3.97448551e-05   2.53079620e-04  -7.50732189e-06\n",
        "   6.74686175e-04  -8.71168306e-05   3.08384121e-03   8.78361332e-04\n",
        "   5.33211342e-02   1.99316045e-02   1.76219133e-03   6.01669008e-04\n",
        "   1.14605446e-04   1.56266718e-04   6.51050016e-05   8.16103375e-05\n",
        "   6.70731769e-05   5.97739840e-05   9.62532096e-05   4.76882683e-05\n",
        "   1.98939294e-04   2.73386602e-06   6.02466949e-04  -4.37233090e-05\n",
        "   3.03428354e-03   1.11286804e-03   5.64868812e-02   2.09115586e-02\n",
        "   1.67875987e-03   6.31032018e-04   6.09263266e-05   1.58379301e-04\n",
        "   2.87976108e-05   8.46763041e-05   2.69063871e-05   7.05747985e-05\n",
        "   2.76208043e-05   9.30497298e-05   2.08125233e-05   1.91484135e-04\n",
        "  -2.66222573e-05   5.92085411e-04  -6.18760518e-05   3.11056877e-03\n",
        "   1.19614065e-03   6.05363861e-02]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Finding the optimal theta    \n",
      "[scipy.optimize](http://docs.scipy.org/doc/scipy-0.14.0/reference/optimize.html) contains SciPy's the optimization and root finding methods. In this instance we'll use fmin_bfgs to minimize our function using the BFGS algorithm. I'm no math PhD, but what we're doing with BFGS is approximating Newton's method, which is an iterative method applied to the derivative (slope) of a function to find zeros. As you can see we're digging just a little deeper than simply calling `fit, predict, score, transform` in sci-kit learn."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set options then run fmin_bfgs to obtain optimal theta (BFGS: quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno)\n",
      "\n",
      "initial_theta = np.zeros(n)\n",
      "lambda2 = 1\n",
      "myargs = (X, y, lambda2)\n",
      "opts = {'full_output': True, 'maxiter': 400}\n",
      "\n",
      "optimal_theta, cost, grad_at_min, inv_hessian_matrix,\\\n",
      "fun_calls, grad_calls, warn_flags = optimize.fmin_bfgs(cost_function_reg,\n",
      "                                initial_theta,\n",
      "                                args=myargs,\n",
      "                                fprime=gradient,\n",
      "                                **opts)\n",
      "\n",
      "print '\\nCost at theta found by fmin_bfgs:', cost\n",
      "print '\\noptimal theta:'\n",
      "print optimal_theta"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.518005\n",
        "         Iterations: 53\n",
        "         Function evaluations: 54\n",
        "         Gradient evaluations: 54\n",
        "\n",
        "Cost at theta found by fmin_bfgs: 0.518004571479\n",
        "\n",
        "optimal theta:\n",
        "[  1.23754420e+00   6.48852298e-01   1.16024020e+00  -1.89123994e+00\n",
        "  -9.12464294e-01  -1.36430785e+00   2.71970488e-01  -3.83457368e-01\n",
        "  -3.90662110e-01  -4.67405933e-03  -1.27271558e+00  -4.47942003e-02\n",
        "  -6.38674615e-01  -2.84056447e-01  -9.77153625e-01  -6.71236327e-02\n",
        "  -2.03895831e-01  -4.92696079e-02  -2.80220143e-01  -3.18509589e-01\n",
        "  -1.90206455e-01  -8.53376200e-01   3.54135607e-02  -2.95652986e-01\n",
        "   1.57572686e-02  -3.28933437e-01  -1.59278605e-01  -6.33230843e-01\n",
        "  -1.86892825e-01  -9.05868930e-02  -4.11336684e-02  -1.15366588e-01\n",
        "  -3.29768284e-02  -1.67770897e-01  -2.18100233e-01  -1.92024440e-01\n",
        "  -5.91401423e-01   4.26489595e-02  -1.53339472e-01   1.48781180e-02\n",
        "  -1.29818756e-01   1.45513951e-02  -1.85151104e-01  -1.10302809e-01\n",
        "  -4.09184876e-01  -2.10798012e-01  -3.83781435e-02  -3.56563679e-02\n",
        "  -4.52388677e-02  -1.79052300e-02  -6.42803048e-02  -1.26147039e-02\n",
        "  -1.03059025e-01  -1.50823023e-01  -1.58987034e-01  -4.21700386e-01\n",
        "   3.56090129e-02  -8.81273236e-02   1.00993005e-02  -5.70046727e-02\n",
        "   6.77354787e-03  -6.74706153e-02   1.29992453e-02  -1.11051973e-01\n",
        "  -8.49978342e-02  -2.68540418e-01  -1.97483190e-01  -1.53100034e-02\n",
        "  -2.86980653e-02  -1.82102569e-02  -1.24613779e-02  -2.38394851e-02\n",
        "  -6.06708518e-03  -3.82505586e-02  -1.83802437e-03  -6.67938687e-02\n",
        "  -1.08829077e-01  -1.24659979e-01  -3.07994299e-01   2.64518548e-02\n",
        "  -5.43497372e-02   6.98245550e-03  -2.83201915e-02   2.70787618e-03\n",
        "  -2.63466178e-02   4.77447913e-03  -3.91407704e-02   1.15527187e-02\n",
        "  -7.03368547e-02  -6.95210270e-02  -1.80344325e-01  -1.72048911e-01\n",
        "  -5.47521748e-03  -2.22987308e-02  -7.42943729e-03  -8.63887952e-03\n",
        "  -9.40591713e-03  -4.43180361e-03  -1.34148622e-02  -9.67176972e-04\n",
        "  -2.47119423e-02   3.29403161e-03  -4.56210773e-02  -8.24677278e-02\n",
        "  -9.65024056e-02  -2.29738561e-01   1.85258430e-02  -3.51384800e-02\n",
        "   4.72018650e-03  -1.55240497e-02   1.39740046e-03  -1.16594849e-02\n",
        "   1.19124992e-03  -1.39390152e-02   4.04370544e-03  -2.48939966e-02\n",
        "   1.02538005e-02  -4.68081953e-02  -5.88899271e-02  -1.24749463e-01\n",
        "  -1.45018258e-01  -1.57983611e-03  -1.70054838e-02  -3.00853930e-03\n",
        "  -6.03454679e-03  -3.92911834e-03  -2.97920489e-03  -5.09736970e-03\n",
        "  -1.44167844e-03  -8.17883038e-03   1.19043015e-03  -1.72968829e-02\n",
        "   5.57315818e-03  -3.25819703e-02  -6.53895286e-02  -7.54226296e-02\n",
        "  -1.74675103e-01   1.24708298e-02  -2.34829663e-02   3.09012293e-03\n",
        "  -9.13436500e-03   8.32318133e-04  -5.79083688e-03   3.02843716e-04\n",
        "  -5.56306821e-03   8.61010725e-04  -8.24973064e-03   3.59331400e-03\n",
        "  -1.71670381e-02   9.16688590e-03  -3.25860722e-02  -5.09721099e-02\n",
        "  -8.97362022e-02  -1.20459959e-01  -2.89275954e-04  -1.28352587e-02\n",
        "  -1.19226730e-03  -4.25477335e-03  -1.70859972e-03  -1.97800444e-03\n",
        "  -2.11997893e-03  -1.08853262e-03  -2.92730568e-03  -2.59745631e-04\n",
        "  -5.44639861e-03   2.07485981e-03  -1.29560727e-02   6.45691527e-03\n",
        "  -2.41585899e-02  -5.38016666e-02  -6.06616032e-02  -1.35177857e-01\n",
        "   8.09303963e-03  -1.60925202e-02   1.96166533e-03  -5.65049524e-03\n",
        "   5.08251909e-04  -3.14658375e-03   8.74458163e-05  -2.51640732e-03\n",
        "   1.13335145e-04  -2.99446682e-03   7.59845640e-04  -5.39858507e-03\n",
        "   3.24857528e-03  -1.26821829e-02   8.28121984e-03  -2.36434947e-02\n",
        "  -4.46954927e-02  -6.80711101e-02]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We've found a set of theta that allows us to get the cost down to ~0.52 from the ~0.69 we saw above in our initial thetas of zero. \n",
      "\n",
      "Let's reuse one of our plotting methods earlier (in this case seaborn) in this notebook and draw the decision boundry over it. Thanks to [github user Nonnormalizable](https://github.com/Nonnormalizable/NgMachineLearningPython/blob/master/ex2/helperFunctions.py) for the boundry code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_decision_boundary(theta, X, y):\n",
      "    # Simple seaborn scatterplot\n",
      "    sns.lmplot('x1','x2',hue='y',data=data,fit_reg=False,size = 6,aspect= 1.5,palette='Dark2',legend=False)\n",
      "    \n",
      "    z = np.zeros([50, 50])\n",
      "    uu = np.linspace(-1.0, 1.5, 50)\n",
      "    vv = np.linspace(-1.0, 1.5, 50)\n",
      "    for i, u in enumerate(uu):\n",
      "        for j, v in enumerate(vv):\n",
      "            z[i, j] = np.dot(new_features(np.array([[u]]), np.array([[v]])), theta)[0]\n",
      "    plt.contour(uu, vv, z.T, [0], colors='dodgerblue')\n",
      "    plt.axis([-.8, 1.2, -.8, 1.2])\n",
      "    plt.xticks(np.arange(-.8, 1.3, .2))\n",
      "    plt.yticks(np.arange(-.8, 1.3, .2))\n",
      "    plt.xlabel('Microchip Test 1')\n",
      "    plt.ylabel('Microchip Test 2')\n",
      "    plt.legend(('y=1', 'y=0'), loc='upper right', numpoints=1)\n",
      "    plt.title('Decision boundary for lambda = ' + str(lambda2), fontsize=13)\n",
      "    # plt.savefig('temp.png', transparent=True,orientation='landscape', pad_inches=0.4)\n",
      "\n",
      "\n",
      "plot_decision_boundary(optimal_theta, X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tlILPgR5nYwfc+WqI378WoiXsMK4iypWz2jhzbDhr/vBrYEh+0cCQ7AteWsOw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\nMUNcxgyJcmEiMXRd2NrksCVaxrI32ljd6Gf1Hh+LNgVZtOnQc0sCLuM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0e6mrgIfw1hh3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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x795ca90>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's compute the accuracy on the training set:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict(theta, X):\n",
      "    h_theta = h_of_theta(theta, X)\n",
      "    return np.round(h_theta)\n",
      "p = predict(optimal_theta, X)\n",
      "print '\\nTraining Accuracy: ', np.mean((p == y) * 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Training Accuracy:  83.0508474576\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's see what happens with a smaller lambda value:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "initial_theta = np.zeros(n)\n",
      "lambda2 = .0001\n",
      "myargs = (X, y, lambda2)\n",
      "opts = {'full_output': True, 'maxiter': 400}\n",
      "\n",
      "optimal_theta2, cost, grad_at_min, inv_hessian_matrix,\\\n",
      "fun_calls, grad_calls, warn_flags = optimize.fmin_bfgs(cost_function_reg,\n",
      "                                initial_theta,\n",
      "                                args=myargs,\n",
      "                                fprime=gradient,\n",
      "                                **opts)\n",
      "\n",
      "print '\\nCost at theta found by fmin_bfgs:', cost\n",
      "\n",
      "plot_decision_boundary(optimal_theta2, X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.263489\n",
        "         Iterations: 341\n",
        "         Function evaluations: 342\n",
        "         Gradient evaluations: 342\n",
        "\n",
        "Cost at theta found by fmin_bfgs: 0.263489151661\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FFkKIeCVBoIhpjemCG9HRpENyiE93uAi2wiyYYcCEvCD/OrOUgrwAy751Me29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\niIiUICWBIiIiIiXo/wE1deKzqlUmVAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9e00b30>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's look at what happens with a larger value for lambda:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "initial_theta = np.zeros(n)\n",
      "lambda2 = 10\n",
      "myargs = (X, y, lambda2)\n",
      "opts = {'full_output': True, 'maxiter': 400}\n",
      "\n",
      "optimal_theta3, cost, grad_at_min, inv_hessian_matrix,\\\n",
      "fun_calls, grad_calls, warn_flags = optimize.fmin_bfgs(cost_function_reg,\n",
      "                                initial_theta,\n",
      "                                args=myargs,\n",
      "                                fprime=gradient,\n",
      "                                **opts)\n",
      "\n",
      "print '\\nCost at theta found by fmin_bfgs:', cost\n",
      "\n",
      "plot_decision_boundary(optimal_theta3, X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.630696\n",
        "         Iterations: 21\n",
        "         Function evaluations: 22\n",
        "         Gradient evaluations: 22\n",
        "\n",
        "Cost at theta found by fmin_bfgs: 0.630695565717\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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domCnZtHAkMKigSH5Fbz0x+HF9hCP7Yrw+C4vMEwuuRd2XI5rcjhuai8nN3nd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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x795c050>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![sci-kit learn logo](http://kldavenport.com/scikit-learn-logo.png)\n",
      "\n",
      "###Regularized Logistic Regression with scikit-learn\n",
      "What we did above was more verbose than necessary, but could have been much worse without NumPy. Below we'll work on the same problem from beginning to end with substantially less lines of code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import optimize\n",
      "import pandas as pd\n",
      "import seaborn as sns\n",
      "from ggplot import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Loading data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('ex2data2.txt',header=None, names = ('x1','x2','y'))\n",
      "data.info()\n",
      "# Get the df values into numpy arrays\n",
      "X = data.ix[:,0:2].values\n",
      "y = data.ix[:,2].values\n",
      "y = y # Note we left it as a standard 1d array this time\n",
      "\n",
      "# No need to manually create the first zero coefficient\n",
      "# X = np.hstack((np.zeros(shape=(X.shape[0],1)),X))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'pandas.core.frame.DataFrame'>\n",
        "Int64Index: 118 entries, 0 to 117\n",
        "Data columns (total 3 columns):\n",
        "x1    118 non-null float64\n",
        "x2    118 non-null float64\n",
        "y     118 non-null int64\n",
        "dtypes: float64(2), int64(1)\n",
        "memory usage: 3.7 KB\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Fitting and scoring the Regularized Logistic Regression model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.linear_model import LogisticRegression\n",
      "from sklearn.cross_validation import train_test_split\n",
      "from sklearn import metrics\n",
      "from sklearn.cross_validation import cross_val_score\n",
      "\n",
      "model = LogisticRegression(tol = .00000000000000000000001)\n",
      "model = model.fit(X, y)\n",
      "\n",
      "# check the accuracy on the training set\n",
      "model.score(X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "0.5423728813559322"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "54% accuracy is pretty poor performance, let's check out what percentage of chips were labeled \"1\" (passed the test) below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "0.49152542372881358"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "49% means that we could have acheived similar performance just by guessing all ones or zeros for our label set. Hold on though, we forgot our feature engineering step. Let's use the `new_features` function we defined above to create many new features in X that might capture the non-linear relationship between variables x1 and x1."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'X shape before:', X.shape\n",
      "X = new_features(X[:, 0][:, None], X[:, 1][:, None])\n",
      "print 'X shape after:', X.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "X shape before: (118, 2)\n",
        "X shape after: (118, 190)\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try fitting and scoring the model again:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = LogisticRegression(tol = .00000000000000000000001)\n",
      "model = model.fit(X, y)\n",
      "model.score(X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "0.83050847457627119"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "83% is a marked improvement. Now we can move forward with more standard ML scoring methods. Up to this point we've been using the same set of data to train and score our data. Let's create a train and test set using scikit's handy `train_test_split` function.\n",
      "\n",
      "**Cross Validation Approach**\n",
      "1. Use the training set\n",
      "2. Split it into training/test sets\n",
      "3. Build a model on the train set\n",
      "4. Evaluate on the test set\n",
      "5. Repeat and average the estimated errors\n",
      "\n",
      "**Used to**\n",
      "1. Choose variables to include in a model\n",
      "2. Choose the type of prediction function to use\n",
      "3. Choose the parameters in the prediction function\n",
      "4. Compare different predictors\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0)\n",
      "model2 = LogisticRegression(tol = .00000000000000000000001 )\n",
      "model2.fit(X_train, y_train)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
        "          intercept_scaling=1, penalty='l2', random_state=None, tol=1e-23)"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predicted = model2.predict(X_test)\n",
      "print metrics.accuracy_score(y_test, predicted)\n",
      "print metrics.roc_auc_score(y_test, predicted)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.861111111111\n",
        "0.865325077399\n"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can even try a 10-fold cross-validation to observe how the accuracy changes. \n",
      "\n",
      "#### K-fold CV considerations\n",
      "- Larger k = less bias and more variance\n",
      "- Smaller k = more bias, less variance\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scores = cross_val_score(LogisticRegression(), X, y, scoring='accuracy', cv=10)\n",
      "print scores\n",
      "print scores.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.66666667  0.75        0.91666667  0.25        0.66666667  0.66666667\n",
        "  1.          0.66666667  0.72727273  0.81818182]\n",
        "0.712878787879\n"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We end up with an average score of 71%. Accuracy doesn't mean the same thing in all cases. Depending on your ML use case certain accuracy metrics might be more important that others. True negatives = Specificity and True Positives = Sensitivity. Much more on this: [here](http://en.wikipedia.org/wiki/Precision_and_recall)\n",
      "\n",
      "We don't go over more tuning in this post, but there are many opportunities to use scikit's built in grid and random search features to find an optimal tolerance level instead of our arbitrary `tol = .00000000000000000000001`. A quick google search will reveal that there is an incredible amount of work being done just in hyperparameter estimation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print metrics.confusion_matrix(y_test, predicted)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[15  4]\n",
        " [ 1 16]]\n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print metrics.classification_report(y_test, predicted)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "             precision    recall  f1-score   support\n",
        "\n",
        "          0       0.94      0.79      0.86        19\n",
        "          1       0.80      0.94      0.86        17\n",
        "\n",
        "avg / total       0.87      0.86      0.86        36\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}