logistic-regression/Logistic Regression.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Introduction to Logistic Regression"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Scott Hendrickson  (2014-03-20)\n",
      "\n",
      "Classification: \n",
      "\n",
      "* Learn classification of vectors from labeled training data\n",
      "* Vectors of N dimensions\n",
      "* Labels: {0,1}\n",
      "* Generalize to predict class of new vectors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pandas as pd \n",
      "from ggplot import *\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simple 1-D Example"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dat_1d = {\"x\"    :[2, 2, 1, 0.25, -0.4, -1, -2, -2, 1], \n",
      "       \"label\":[0, 0, 0,    0,    1,  1,  1,  1, 1]}\n",
      "df_1d = pd.DataFrame.from_dict(data = dat_1d)\n",
      "df_1d"
     ],
     "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>label</th>\n",
        "      <th>x</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "      <td> 2.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0</td>\n",
        "      <td> 2.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0</td>\n",
        "      <td> 0.25</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1</td>\n",
        "      <td>-0.40</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> 1</td>\n",
        "      <td>-1.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td> 1</td>\n",
        "      <td>-2.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td> 1</td>\n",
        "      <td>-2.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1.00</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>9 rows \u00d7 2 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "   label     x\n",
        "0      0  2.00\n",
        "1      0  2.00\n",
        "2      0  1.00\n",
        "3      0  0.25\n",
        "4      1 -0.40\n",
        "5      1 -1.00\n",
        "6      1 -2.00\n",
        "7      1 -2.00\n",
        "8      1  1.00\n",
        "\n",
        "[9 rows x 2 columns]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_1d[\"label_fact\"] = pd.Categorical.from_array([str(x) for x in df_1d.label])\n",
      "ggplot(aes(x=\"x\",y=\"label\", color=\"label_fact\"), data=df_1d) + geom_point()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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HLF26NP3ntWvX6vTTT9fkyZMl6aiRKEktLS1KJBJDGzwHfr/f1fn6JZNJV+ek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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d0ec510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<ggplot: (287567401)>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Sigmoid Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Properties of function of distance from boundary:\n",
      "\n",
      "* Continuous\n",
      "* Domain of all reals\n",
      "* Range [0,1]\n",
      "* Convex function (differentiable, $\\frac{d s(x)}{dx} > 0 \\text{ } \\forall \\text{ } x$\n",
      "\n",
      "$f(x) = \\frac{1}{1 + \\exp(-z)}$\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sigmoid(x):\n",
      "    # vector in, vector out\n",
      "    return 1./(1. + np.exp(-x))\n",
      "\n",
      "# Let's see it\n",
      "d_sig = pd.DataFrame.from_dict({\"x\": np.linspace(-8,8,30), \n",
      "                                \"y\": sigmoid(np.linspace(-8,8,30))})\n",
      "ggplot(aes(x=\"x\", y=\"y\"), data = d_sig) + geom_line(color=\"orange\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1Jz8u39J5uK1bt+rGG2/U1q1bFQ6H9YlPfEJ/8zd/o2nTSnuKqLOzU5lMpqR/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\nF17QE088oS9+8YuKRCKm47jaE088odd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       "text": [
        "<matplotlib.figure.Figure at 0x11237e290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<ggplot: (287556145)>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Model predicts $l(x) = [0,1]$ based on sigmoid.  Calculate argument to sigmoid from input data, e.g.:\n",
      "\n",
      "For 1-D input vectors:\n",
      "\n",
      "   $z = \\beta_0 + \\beta_1 x$\n",
      "\n",
      "Or 2-D input vectors:\n",
      "\n",
      "   $z = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2$\n",
      "\n",
      "$\\ldots$\n",
      "\n",
      "Model prediction in 1-D:\n",
      "\n",
      "$y(x) = sigmoid(\\beta_0 + \\beta_1 x) = \\frac{1}{1 + \\exp(-(\\beta_0 + \\beta_1 x))}$\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Cost Function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "\n",
      "Need a cost function for which optimization will give the boundary N-dim plane defined by $[\\beta_0, \\beta_1, \\ldots ]$.\n",
      "\n",
      "###Least Squares?\n",
      "\n",
      "$Cost = \\frac{1}{m} \\sum{\\frac{1}{2}(l(x) - y(x))^2}$\n",
      "\n",
      "This is the cost if the model prediction is $y(x)$ and the actual outcome is $l(x)$. With the sigmoid, this funciton is not convex, so local minima are challenging.\n",
      "\n",
      "Why is this a problem?\n",
      "\n",
      "Lots of local minima mean gradient descent may not find the global optimum. We would like a convex function so if you run gradient descent and converge to the global minimum.\n",
      "\n",
      "###Logistic Regression Cost Function\n",
      "For model y(x):\n",
      "    \n",
      "$C = -[1-l(x)]\\ln[l(x)-y(x)] - l(x) \\ln[y(x)] $\n",
      "\n",
      "$C = -[\\text{cost for label 0}] - [\\text{cost for label 1}]$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cost(label_arr, model_arr):\n",
      "    # inputs are nb.array([])\n",
      "    # sum over training set\n",
      "    c = -(1. - label_arr)*np.log(1. - model_arr) - label_arr*np.log(model_arr)\n",
      "    return np.sum(c)/len(c)\n",
      "print \"Model  ~ Label: {:.4}\".format(cost(np.array([0,0,0,1,1,1]), np.array([0.1,0.2,0.05,0.99,0.98,0.99])))\n",
      "print \"Model !~ Label: {:.4}\".format(cost(np.array([0,0,0,1,1,1]), np.array([0.99,0.98,0.99,0.1,0.2,0.05])))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Model  ~ Label: 0.07002\n",
        "Model !~ Label: 3.338\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def model_1d(model_vec, df):\n",
      "    # Calculate model output\n",
      "    z = model_vec[0] + model_vec[1] * df.x\n",
      "    return sigmoid(z)\n",
      "    \n",
      "def model_cost(model_vec, df, model):\n",
      "    # model_vec is python vector\n",
      "    # df is data frame with column x and column label\n",
      "    # model is a functionto calculate model output\n",
      "    return cost(df.label, model(model_vec, df))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import minimize as mini\n",
      "res_1d = mini(model_cost, x0=[0.1,0.1], args=(df_1d, model_1d)) \n",
      "print (res_1d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   status: 0\n",
        "  success: True\n",
        "     njev: 13\n",
        "     nfev: 52\n",
        " hess_inv: array([[ 14.24001119,  -8.10781827],\n",
        "       [ -8.10781827,  14.28838055]])\n",
        "      fun: 0.3234494073359467\n",
        "        x: array([ 0.92795283, -1.97511698])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([  3.44961882e-06,   4.65661287e-06])\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_pred_1d = pd.DataFrame.from_dict({\"x\": np.linspace(-3,3,99)})\n",
      "df_pred_1d[\"y\"] = model_1d(res_1d.x, df_pred_1d)\n",
      "df_pred_1d.head()"
     ],
     "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>x</th>\n",
        "      <th>y</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>-3.000000</td>\n",
        "      <td> 0.998945</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>-2.938776</td>\n",
        "      <td> 0.998810</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>-2.877551</td>\n",
        "      <td> 0.998657</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>-2.816327</td>\n",
        "      <td> 0.998485</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>-2.755102</td>\n",
        "      <td> 0.998290</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 2 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "          x         y\n",
        "0 -3.000000  0.998945\n",
        "1 -2.938776  0.998810\n",
        "2 -2.877551  0.998657\n",
        "3 -2.816327  0.998485\n",
        "4 -2.755102  0.998290\n",
        "\n",
        "[5 rows x 2 columns]"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ggplot(aes(x=\"x\",y=\"label\", color=\"label_fact\"), data=df_1d) + \\\n",
      "  geom_point() + \\\n",
      "  geom_line(aes(x=\"x\", y=\"y\"), color=\"green\", data=df_pred_1d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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H+vHIj6ajAIBtUPwAGFE1vKrGnTdOT6x5wnQUALANih8AY8a0HKMNhzbom33f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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112f7a710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<ggplot: (282128693)>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example - 2D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dat_2d = {   \"x1\":[-1.0, 0.3, 2.05, 0.95,  2,-1.1,-2.4,-0.9,-2.1], \n",
      "             \"x2\":[ 2.0, 0.6,  2.1,  2.1, -1,-1  ,-1.8,  -2, 0.0], \n",
      "       \"label\":[0,0,0,0,0,1,1,1,1]}\n",
      "df_2d = pd.DataFrame.from_dict(data = dat_2d)\n",
      "df_2d[\"label_fact\"] = pd.Categorical.from_array([str(x) for x in df_2d.label])\n",
      "df_2d"
     ],
     "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>label</th>\n",
        "      <th>x1</th>\n",
        "      <th>x2</th>\n",
        "      <th>label_fact</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "      <td>-1.00</td>\n",
        "      <td> 2.0</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0</td>\n",
        "      <td> 0.30</td>\n",
        "      <td> 0.6</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "      <td> 2.05</td>\n",
        "      <td> 2.1</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0</td>\n",
        "      <td> 0.95</td>\n",
        "      <td> 2.1</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 0</td>\n",
        "      <td> 2.00</td>\n",
        "      <td>-1.0</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> 1</td>\n",
        "      <td>-1.10</td>\n",
        "      <td>-1.0</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td> 1</td>\n",
        "      <td>-2.40</td>\n",
        "      <td>-1.8</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td> 1</td>\n",
        "      <td>-0.90</td>\n",
        "      <td>-2.0</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
        "      <td> 1</td>\n",
        "      <td>-2.10</td>\n",
        "      <td> 0.0</td>\n",
        "      <td> 1</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>9 rows \u00d7 4 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "   label    x1   x2 label_fact\n",
        "0      0 -1.00  2.0          0\n",
        "1      0  0.30  0.6          0\n",
        "2      0  2.05  2.1          0\n",
        "3      0  0.95  2.1          0\n",
        "4      0  2.00 -1.0          0\n",
        "5      1 -1.10 -1.0          1\n",
        "6      1 -2.40 -1.8          1\n",
        "7      1 -0.90 -2.0          1\n",
        "8      1 -2.10  0.0          1\n",
        "\n",
        "[9 rows x 4 columns]"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ggplot(aes(x=\"x1\",y=\"x2\", color=\"label_fact\"), data=df_2d) + geom_point()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qMh2jRwqYDtBZeXl5qq2tVTweNx2lXfn5+WpoaDAdo13BYFBFRUWqr6+nxzTQ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\nAAv8f2ySsQnxYv90AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c76cf10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<ggplot: (287556169)>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def model_2d(model_vec, df):\n",
      "    z = model_vec[0] + model_vec[1] * df.x1 + model_vec[2] * df.x2\n",
      "    return sigmoid(z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res_2d = mini(model_cost, x0=[1,1,0.5], args=(df_2d, model_2d)) \n",
      "print (res_2d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   status: 0\n",
        "  success: True\n",
        "     njev: 19\n",
        "     nfev: 95\n",
        " hess_inv: array([[ 26585.66512643,  35936.64997437,  28285.71275239],\n",
        "       [ 35936.64997437,  48579.4332378 ,  38236.01146309],\n",
        "       [ 28285.71275239,  38236.01146309,  30096.51214756]])\n",
        "      fun: 4.171345112083083e-06\n",
        "        x: array([-5.27977744, -8.66641472, -7.1442268 ])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([  1.12009656e-06,   1.18361356e-07,   5.67908933e-06])\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# z = 0 defines a line\n",
      "x1 = np.linspace(-3,3,27)\n",
      "x2 = -(res_2d.x[0] + x1*res_2d.x[1])/res_2d.x[2]\n",
      "df_pred_2d = pd.DataFrame.from_dict({ \"x1\": x1, \n",
      "                                      \"x2\": x2  })\n",
      "df_pred_2d[\"y\"] = model_2d(res_2d.x, df_pred_2d)\n",
      "df_pred_2d.head()"
     ],
     "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>-3.000000</td>\n",
        "      <td> 2.900169</td>\n",
        "      <td> 0.5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>-2.769231</td>\n",
        "      <td> 2.620231</td>\n",
        "      <td> 0.5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>-2.538462</td>\n",
        "      <td> 2.340293</td>\n",
        "      <td> 0.5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>-2.307692</td>\n",
        "      <td> 2.060355</td>\n",
        "      <td> 0.5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>-2.076923</td>\n",
        "      <td> 1.780417</td>\n",
        "      <td> 0.5</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 3 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "         x1        x2    y\n",
        "0 -3.000000  2.900169  0.5\n",
        "1 -2.769231  2.620231  0.5\n",
        "2 -2.538462  2.340293  0.5\n",
        "3 -2.307692  2.060355  0.5\n",
        "4 -2.076923  1.780417  0.5\n",
        "\n",
        "[5 rows x 3 columns]"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ggplot(aes(x=\"x1\", y=\"x2\"),data=df_pred_2d) + geom_line() + geom_point(aes(x=\"x1\",y=\"x2\", color=\"label_fact\"), data=df_2d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PPqrPPvvMdCRUQ1xcnFwul/bu3auHHnqIfyCB/9K+fXvFxsYe/jg6Olrt27c3mMishISE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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d0ec050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<ggplot: (287531813)>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import norm\n",
      "# Make some data\n",
      "npts = 65\n",
      "x1 = np.concatenate((norm.rvs(loc=2, scale=1.5,   size=npts),  norm.rvs(loc=-2, scale=1.5, size=npts)))\n",
      "x2 = np.concatenate((norm.rvs(loc=2, scale=1.5, size=npts),  norm.rvs(loc=-1, scale=1.5,   size=npts)))\n",
      "lab = [0]*npts + [1]*npts\n",
      "# Plots and fits\n",
      "dat_gaus = {  \"x1\": x1, \n",
      "              \"x2\": x2 , \n",
      "           \"label\": lab }\n",
      "df_2d_gaus = pd.DataFrame.from_dict(data = dat_gaus)\n",
      "df_2d_gaus[\"label_fact\"] = pd.Categorical.from_array([str(x) for x in df_2d_gaus.label])\n",
      "# Fit\n",
      "res_2d_gaus = mini(model_cost, x0=[0.1,1.2,0.5], args=(df_2d_gaus, model_2d))\n",
      "# z = 0 defines a line\n",
      "x1 = np.linspace(-4, 4, 27)\n",
      "x2 = -(res_2d_gaus.x[0] + x1*res_2d_gaus.x[1])/res_2d_gaus.x[2]\n",
      "print res_2d_gaus\n",
      "df_2d_gaus_pred = pd.DataFrame.from_dict({\"x1\": x1, \"x2\": x2})\n",
      "df_2d_gaus_pred[\"y\"] = model_2d(res_2d_gaus.x, df_2d_gaus)\n",
      "ggplot(aes(x=\"x1\", y=\"x2\"), data=df_2d_gaus_pred) + \\\n",
      "     geom_line(color=\"red\") + \\\n",
      "     geom_point(aes(x=\"x1\",y=\"x2\", color=\"label_fact\"), data=df_2d_gaus)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   status: 0\n",
        "  success: True\n",
        "     njev: 25\n",
        "     nfev: 125\n",
        " hess_inv: array([[  62.21889931,  -38.26727073,  -24.90246783],\n",
        "       [ -38.26727073,  136.80563705,   59.50383824],\n",
        "       [ -24.90246783,   59.50383824,   68.78974595]])\n",
        "      fun: 0.060892790277256276\n",
        "        x: array([ 1.06422726, -2.93912367, -2.09587989])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([  2.24681571e-06,  -3.12458724e-07,   1.49244443e-06])\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xfv31V1555RVOnjwJFNxou0aNGjzwwAMmJ/MPOmIlIj4nZcIEAr/4gsB168yO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\nMhxKosKyKH3wQdKff56UZctMpxGppxsNRCR55ZwAJ8/H3vUmpHeEVqe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       "text": [
        "<matplotlib.figure.Figure at 0x1123ea110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "<ggplot: (287566385)>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def model_quad(model_vec, df):\n",
      "    # quadratic\n",
      "    z = model_vec[0] + model_vec[1]*df.x2 + model_vec[2]*df.x1*df.x1 + model_vec[3]*df.x1\n",
      "    return sigmoid(z)\n",
      "# Make some data\n",
      "npts = 100\n",
      "x1 = np.concatenate((norm.rvs(loc=-3,scale=1, size=npts), \n",
      "                     norm.rvs(loc=0, scale=1, size=npts),\n",
      "                     norm.rvs(loc=0, scale=1, size=npts),\n",
      "                     norm.rvs(loc=3, scale=1, size=npts)))\n",
      "x2 = np.concatenate((norm.rvs(loc=4, scale=6, size=npts), \n",
      "                     norm.rvs(loc=-5, scale=2, size=npts),\n",
      "                     norm.rvs(loc=6, scale=2, size=npts),\n",
      "                     norm.rvs(loc=4, scale=6, size=npts)))\n",
      "lab = [0]*npts + [1]*npts + [0]*npts + [0]*npts\n",
      "# Plots and fits\n",
      "dat_quad = {    \"x1\": x1, \n",
      "                \"x2\": x2, \n",
      "             \"label\": lab }\n",
      "df_quad = pd.DataFrame.from_dict(data = dat_quad)\n",
      "df_quad[\"label_fact\"] = pd.Categorical.from_array([str(x) for x in df_quad.label])\n",
      "# Fit\n",
      "res_quad = mini(model_cost, x0=[0.5, 1.2, -1, 2], args=(df_quad, model_quad))\n",
      "print res_quad\n",
      "# z = 0 defines a line\n",
      "x1 = np.linspace(-3,3,21)\n",
      "x2 = -(res_quad.x[0] + res_quad.x[3]*x1 + res_quad.x[2]*x1*x1)/res_quad.x[1]\n",
      "df_quad_pred = pd.DataFrame.from_dict({\"x1\": x1, \"x2\": x2})\n",
      "df_quad_pred[\"y\"] = model_2d(res_quad.x, df_quad)\n",
      "ggplot(aes(x=\"x1\", y=\"x2\"), data=df_quad_pred) + \\\n",
      "     geom_line(color=\"red\") + \\\n",
      "     geom_point(aes(x=\"x1\",y=\"x2\", color=\"label_fact\"), data=df_quad)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   status: 0\n",
        "  success: True\n",
        "     njev: 33\n",
        "     nfev: 198\n",
        " hess_inv: array([[ 81.81109734,   0.46931549, -19.57898876,   3.00398338],\n",
        "       [  0.46931549,   4.06837566,   5.65185489,  -2.85425827],\n",
        "       [-19.57898876,   5.65185489,  18.31695346,  -9.71437105],\n",
        "       [  3.00398338,  -2.85425827,  -9.71437105,  28.75195032]])\n",
        "      fun: 0.08494712883483503\n",
        "        x: array([ 0.41457294, -0.78381036, -1.17937652,  0.32299065])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([ -3.28756869e-07,  -1.57207251e-06,  -4.22820449e-07,\n",
        "        -4.17232513e-07])\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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69OmsXLky/W9EiByiZs2a1KxZ862v2bRpE9u3b8fGxobRo0fj5uaWrPh5vVhz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\nhBBCiBCQpEsIIYQQIgQk6RJCCCGECAFJu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       "text": [
        "<matplotlib.figure.Figure at 0x112387690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "<ggplot: (287541013)>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##EndNotes:\n",
      "\n",
      "Followup ideas that are important to success with machine learning:\n",
      "\n",
      "* Split data into training set and test set, hold out test set and measure error in both sets during training to estimate point where generalization breaks down due to over-fitting!  This may mean you don't use a canned optimizer as I did in these demos.\n",
      "* Dimensionlity: As you get more dimensions in your input vector, it is harder to fill the space with data $Volume \\propto d^{N_d}$.  This means addition another dimension requires lots more data!\n",
      "* Regularization helps limit complexity of model. Add a term like $C = \\ldots + \\sum{\\beta_i}^2$ to penalize having many large model parameters $\\beta$ in the model.\n",
      "* Don't use this code, us scikits-learn!\n",
      "* Look at Baysian approach that gives you distributions of separating surfaces.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}