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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Exercise: Linear Regression with Numpy\n",
      "\n",
      "** Perdicting Gallons per Mileage on the AUTO Dataset **\n",
      "\n",
      "\n",
      "by \n",
      "\n",
      "[__Michael Granitzer__ (michael.granitzer@uni-passau.de)]( http://www.mendeley.com/profiles/michael-granitzer/)\n",
      "\n",
      "\n",
      "__License__\n",
      "\n",
      "This work is licensded under a [Creative Commons Attribution 3.0 Unported License](http://creativecommons.org/licenses/by/3.0/)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Introduction\n",
      "\n",
      "The goal of this exercise is to implement linear regression through minimization of the Residual Sum of Sqaures (RSS) on the [UCI AUTO Dataset](http://archive.ics.uci.edu/ml/datasets/Auto+MPG).\n",
      "\n",
      "We will cover\n",
      " \n",
      " * Numpy usage: Load data, slice data, concatenate data\n",
      " * Calculate a linear model given a subset of the AUTO Dataset\n",
      " * Plot data and linear model for low dimensional variables and\n",
      " * Evaluate the goodness of fit\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Setting up IPython Notebook\n",
      "The code below simply sets up ipython notebook and displays graphs inline (e.g. as HTML)\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Preparation and Preprocessing\n",
      "\n",
      "We will \n",
      "\n",
      " * Load the data\n",
      " * Clean the data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Download and import the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#shell scripts for downloading the data and placing it in a corresponding directory\n",
      "!mkdir AUTO \n",
      "!curl -o AUTO/data \"http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data\"\n",
      "!curl -o AUTO/description \"http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.names\"\n",
      "#download the description and display it here.\n",
      "!cat AUTO/description"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mkdir: AUTO: File exists\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\r\n",
        "                                 Dload  Upload   Total   Spent    Left  Speed\r\n",
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:--  0:00:01 --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "  8 30286    8  2621    0     0   1130      0  0:00:26  0:00:02  0:00:24  1130"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "100 30286  100 30286    0     0  10424      0  0:00:02  0:00:02 --:--:-- 10421\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\r\n",
        "                                 Dload  Upload   Total   Spent    Left  Speed\r\n",
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "100  1660  100  1660    0     0   3780      0 --:--:-- --:--:-- --:--:--  3781\r",
        "100  1660  100  1660    0     0   3778      0 --:--:-- --:--:-- --:--:--  3772\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1. Title: Auto-Mpg Data\r\n",
        "\r\n",
        "2. Sources:\r\n",
        "   (a) Origin:  This dataset was taken from the StatLib library which is\r\n",
        "                maintained at Carnegie Mellon University. The dataset was \r\n",
        "                used in the 1983 American Statistical Association Exposition.\r\n",
        "   (c) Date: July 7, 1993\r\n",
        "\r\n",
        "3. Past Usage:\r\n",
        "    -  See 2b (above)\r\n",
        "    -  Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning.\r\n",
        "       In Proceedings on the Tenth International Conference of Machine \r\n",
        "       Learning, 236-243, University of Massachusetts, Amherst. Morgan\r\n",
        "       Kaufmann.\r\n",
        "\r\n",
        "4. Relevant Information:\r\n",
        "\r\n",
        "   This dataset is a slightly modified version of the dataset provided in\r\n",
        "   the StatLib library.  In line with the use by Ross Quinlan (1993) in\r\n",
        "   predicting the attribute \"mpg\", 8 of the original instances were removed \r\n",
        "   because they had unknown values for the \"mpg\" attribute.  The original \r\n",
        "   dataset is available in the file \"auto-mpg.data-original\".\r\n",
        "\r\n",
        "   \"The data concerns city-cycle fuel consumption in miles per gallon,\r\n",
        "    to be predicted in terms of 3 multivalued discrete and 5 continuous\r\n",
        "    attributes.\" (Quinlan, 1993)\r\n",
        "\r\n",
        "5. Number of Instances: 398\r\n",
        "\r\n",
        "6. Number of Attributes: 9 including the class attribute\r\n",
        "\r\n",
        "7. Attribute Information:\r\n",
        "\r\n",
        "    1. mpg:           continuous\r\n",
        "    2. cylinders:     multi-valued discrete\r\n",
        "    3. displacement:  continuous\r\n",
        "    4. horsepower:    continuous\r\n",
        "    5. weight:        continuous\r\n",
        "    6. acceleration:  continuous\r\n",
        "    7. model year:    multi-valued discrete\r\n",
        "    8. origin:        multi-valued discrete\r\n",
        "    9. car name:      string (unique for each instance)\r\n",
        "\r\n",
        "8. Missing Attribute Values:  horsepower has 6 missing values\r\n",
        "\r\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import numpy now and load the data set into a numpy array\n",
      "import numpy as np\n",
      "auto = np.loadtxt(\"./AUTO/data\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "could not convert string to float: \"chevrolet",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-29-c5f2c0598e56>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#import numpy now and load the data set into a numpy array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mauto\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloadtxt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"./AUTO/data\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/lib/npyio.pyc\u001b[0m in \u001b[0;36mloadtxt\u001b[0;34m(fname, dtype, comments, delimiter, converters, skiprows, usecols, unpack, ndmin)\u001b[0m\n\u001b[1;32m    825\u001b[0m                 \u001b[0mvals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mvals\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0musecols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    826\u001b[0m             \u001b[0;31m# Convert each value according to its column and store\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 827\u001b[0;31m             \u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mconv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mconv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconverters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    828\u001b[0m             \u001b[0;31m# Then pack it according to the dtype's nesting\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    829\u001b[0m             \u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpack_items\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpacking\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mValueError\u001b[0m: could not convert string to float: \"chevrolet"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An error occured, since parts of the data contain no numbers. Lets investigate"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#look at the first few examples.\n",
      "!cat AUTO/data|grep \"?\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Clean the Data\n",
      "\n",
      "We see, that the lost column is a string. We can not handle strings and hence have to exclude the cloumn. Moreover, some rows have a `?` indicating missing values. we to take care of these too."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#load the data, but exclude the last column \n",
      "#note that some rows have a '?' for missing values\n",
      "#so we need to use the genfromtxt function, which allows proper handling\n",
      "auto = np.genfromtxt(\"./AUTO/data\",usecols=(0,1,2,3,4,5,6,7),missing_values='?')\n",
      "#store the feature names for latter use\n",
      "feature = ['mpg','cylinders','displacement','horsepower','weight','acceleration', \n",
      "           'model year', 'origin']\n",
      "auto.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "auto"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#missing values are displayed as nan. lets take a look which columns there are\n",
      "np.any(np.isnan(auto),axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#lets take a look which rows are affected \n",
      "auto_nan_rows = np.any(np.isnan(auto),axis=1)\n",
      "auto[auto_nan_rows,]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#lets remove nans \n",
      "auto_wo_nan = auto[~auto_nan_rows,]\n",
      "print 'removed %d items'%(auto.shape[0]-auto_wo_nan.shape[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Analysing the data set \n",
      "\n",
      "Before applying data mining methods on an unknown data set, one should try to get some statistical description of the data set. A good method therefore is the [boxplot](http://en.wikipedia.org/wiki/Box_plot)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = figure()\n",
      "ax1 = fig.add_subplot(1,1,1)\n",
      "ax1.boxplot(auto_wo_nan[:,0:2],vert=False)\n",
      "ax1.set_title(\"AUTO Data\")\n",
      "ax1.set_yticklabels(feature[0:2])\n",
      "fig.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107461c50>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Implementing the linear model\n",
      "\n",
      "Using Numpy this becomes pretty easy. We just have to implement the function \n",
      "\n",
      "$$w=(X^TX)^{-1}X^Ty$$\n",
      "\n",
      "(see [lecture slides, ML:II-45](http://www.uni-weimar.de/medien/webis/teaching/lecturenotes/machine-learning/unit-en-regression.pdf))\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.linalg as la\n",
      "def linreg(X,y,bias=True):\n",
      "    \"\"\"\n",
      "    X: data matrix n rows, d columns\n",
      "    Y: target values n rows, 1 column\n",
      "    bias: if true, a bias term is included at the end of the weight vector\n",
      "    return: parameter vector w\n",
      "    \"\"\"\n",
      "    if bias:\n",
      "        X = np.concatenate((X,-np.ones((X.shape[0],1))), axis=1)\n",
      "    w = np.dot(np.dot(la.inv(np.dot(X.T,X)),X.T),y) #that is the model\n",
      "    out = np.dot(X,w) # that is the models output \n",
      "    rss = np.sum((out-y)**2) #that is the residual sum of squares\n",
      "    return (w,out,rss) #we pass back the vector, the output and the rss error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### The Pseudoinverse\n",
      "\n",
      "$(X^TX)^{-1}X^T$ defines the so called pseudo-inverse (more specificall the [Moore-Penrose Matrix Inverse](http://mathworld.wolfram.com/Moore-PenroseMatrixInverse.html), but why do we need that strange thing?\n",
      "\n",
      "First of all, recall from you Linear Algebra class that the inverse only exists for squared matrices. This is not the case in our example. So a way to approximate the inverse for non-squared matrices is to use the above pseudo-inverse. But why?\n",
      "\n",
      "We will get to this by an example. Consider that you have a one dimensional set of data points $X$. Lets say you want to predict the miles-per-gallon based on the weight of the car, that is $mpg = w_1*carweight+w_0$. So how many data points do you need for deriving the exact $w_1$ and $w_0$?\n",
      "\n",
      "The answer is **2**. Given **2** data points you can uniquely find both parameters. Recall again from linear algebra that $mpg = w_1*carweight+w_0$. forms a linear equation system with two parameters. Given a system of linear equations, we have three possibilities:\n",
      "\n",
      "  * **Determined: The number of equations (= the number of data points in our case) is the same as the number of parameters. **\n",
      "  \n",
      "  In this case, if there exists a unique solution we can find it by solving the linear equation system.\n",
      "  \n",
      "  * **Underdetermined: You have less data points (= lower number of equations) than parameters**\n",
      "  \n",
      "  If we have lets say 1 data point in our example above, than we can find an infinite amount of different solutions. The system of linear equations is **underdetermined**. This does not happen often in data mining, so we ignore the case. The data mining solution to this would be in getting more data or reducing the model.\n",
      "\n",
      "  * **Overdetermined: You have more data points than parameters**\n",
      "  \n",
      "  If you have more data points than parameters, say 3, than you will have an **overdetermined** set of linear equations. That is what we often have in data analysis. So drilling further down we can distinguish between two cases again:\n",
      "     \n",
      "     1. There is one exact solution, satisfying all data points\n",
      "     \n",
      "     Like for example $mpg = 5*carweight+2$. We can generate an infinite amount of data points, where the vector space for those data points is spanned by two basis vectors. In practice we are given the data and do not know the exact model. So it is unlikely that a linear model is the correct model. Moreover, while the linear model might be the correct model, measurements could be noisy. For example, measuring the weight of a car might not be perfectly exact to the last point beyond the comma. So it is unlikely, that we can find an exact solution.\n",
      "     \n",
      "     This case is in principal the same as the determined case. We can find a unique solution.\n",
      "     \n",
      "     2. There is no unique solution, i.e. not all data points can be predicted by the model\n",
      "     \n",
      "     This is the case we will see below. The model can not explain all the data, only parts of it. Our goal here is to find \"the best solution\", where best has to be specified. That brings me back to the pseudoinverse above. The pseudoinverse provides the solution with the minimum variance, i.e. squared difference. A different choice of the pseudoinverse yields a different \"best\" solution. This is the case solved by the `linreg` function (and of course it also finds the unique solution, if it exists)\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#the determined case, note that the data is one dimensional, because the last dimension is only the bias term\n",
      "w=np.array([2, 0.5]).T\n",
      "x=np.array([[3,1], [7,1]])\n",
      "y=np.dot(x,w)\n",
      "plot (x[:,0],y,'g.') #plot the data points\n",
      "plot ([1,8],np.dot([[1,1],[8,1]],w),'r') #plot the line\n",
      "title(\"two points determine the solution uniquely\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114206750>"
       ]
      }
     ],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#the underdetermined case, note that the data is one dimensional, because the last dimension is only the bias term\n",
      "w1=np.array([2, 0.5]).T #one correct solution\n",
      "w2=np.array([-0.5, 8]).T #the second correct solution. in fact, infinit correct solutions exists\n",
      "x=np.array([[3,1]])\n",
      "y=np.dot(x,w1)\n",
      "plot (x[:,0],y,'g.') #plot the data points\n",
      "plot ([1,8],np.dot([[1,1],[8,1]],w1),'r') #plot solution w1\n",
      "plot ([1,8],np.dot([[1,1],[8,1]],w2),'b') #plot solution w2. it also goes through the data point x\n",
      "title(\"two points determine the solution uniquely\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114162bd0>"
       ]
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#the overdetermined case, with a unique solution\n",
      "w1=np.array([2, 0.5]).T #one correct solution\n",
      "x=np.array([[3,1],[5,1],[7,1],[8,1]])\n",
      "y=np.dot(x,w1)\n",
      "plot (x[:,0],y,'g.') #plot the data points\n",
      "plot ([1,8],np.dot([[1,1],[8,1]],w1),'r') #plot solution w1\n",
      "title(\"two points determine the solution uniquely\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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W8T4iG8ClElvVNN6Xl8d4H5GN4Izb1giBzS+MxPitR5AX6oEBOVlwDe5t6aqI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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113feb450>"
       ]
      }
     ],
     "prompt_number": 165
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### A first test\n",
      "\n",
      "Now lets test it on a small example. We want to predict miles-per-gallon (first feature) by cylinders und displacement (second and third feature)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "feature\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "['mpg',\n",
        " 'cylinders',\n",
        " 'displacement',\n",
        " 'horsepower',\n",
        " 'weight',\n",
        " 'acceleration',\n",
        " 'model year',\n",
        " 'origin']"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X=auto_wo_nan[:,1:3]\n",
      "y=auto_wo_nan[:,0]\n",
      "(w,out,rss) = linreg(X,y)\n",
      "print rss\n",
      "print w"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "8342.56636579\n",
        "[ -0.57634772  -0.0511185  -36.53770683]\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Works. But was does the RSS mean? In principal, it is the (squared) deviation of the linear model from the data, the discrpeancy of the data from the model. Other names are sum of squared errors of prediction (SSE).It is an unscaled (i.e. depending on the number of data points considerd) measure ofdispersion (also called vairability). \n",
      "\n",
      "The RSS can be seen as a statistical variable measuring the deviation per data point. In order to get an **estimator of deviation per data point**, we can simply calculate the average RSS per data point. This is also known as the Mean  Squared Error (or MSE). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mse = rss/(y.shape[0])\n",
      "sqrt(mse)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 113,
       "text": [
        "4.613247994156219"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A intuitive interpretation of the Root-Mean-Square-Error $rmse=\\sqrt{mse}$,  although not theoretical sound, is that on average we are \u00b1 4.6 miles-per-gallon wrong with our model. The square root scales the error down to the unit of the attribute and hence allows propert interpretation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Predicting on single variables\n",
      "\n",
      "Now lets analye the AUTO data set and how good our regression is. We will first estimate a linear model from all single variables, plot the data plus the model and finally plot the MSE as summary"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_feat = auto_wo_nan.shape[1]\n",
      "rmses =[]\n",
      "\n",
      "for i in xrange(1,n_feat):\n",
      "    X=auto_wo_nan[:,i:i+1] #i+1 is needed so that X stays a matrix\n",
      "    y=auto_wo_nan[:,0]\n",
      "    (w,out,rss) = linreg(X,y)\n",
      "    rmse = sqrt(rss/(y.shape[0]))\n",
      "    plot(X,y,'g.')\n",
      "    plot(X,out,'r')\n",
      "    title('miles-per-galon vs. '+ feature[i] + ' (rmse='+str(rmse)+')')\n",
      "    show()\n",
      "    rmses.append(rmse)\n",
      "# now plot MSE curve   \n",
      "ind = np.arange(len(rmses))\n",
      "width = 0.3\n",
      "bar(ind,rmses,width, label= 'Root Mean Square Errors',)\n",
      "xticks(ind+width/2., feature)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6RKFQQKFQ8I/XrFmjtmaj0b1NPv30U5iamuL999/nn0tOTkZAQABu3LghPDn1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1138469d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZhRnia6cOTjg566TW+pzh0bbg95NhbEypNza1jAocpdX0AnCGR1uD30+GsRFH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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113e7d590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nmJACOT77OELcQ3DuuXN47/B7LW7j3lQ5OPXCmOXjitJ2QLPVi3p+XZXnbqqN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\nqDPGmBX5f3MTPZZDEuySAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114001610>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QCASynVuBk1UVkiApZ0dnZE/NRhA/SCtTiLTTtq1j2/tZKN38MOCBAVgTv4aU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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113c1acd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kCCIiIhAWFoY333wTgHxT5eDgYERGRiIyMhJHjhwR3VhCP5YakWWWZGq0e3be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\nh/ezygAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113fd68d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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e6FoMBNRBkefn56Nnz57w9fWFt7c3Fi1aBECzqLKbmxv8/Pzg5+eHkydP6j5i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\nFDlBEISRQ4qcIAjCyCFFThAEYeT8f8PA0gXQtoTfAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113fd1150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ohy2SvTJ7QueMdmRr6oYtMpmTvTF7Qt9zbg+mfznd3NUQmYzT55K9skiXi8TJ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1136fcd50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p0zB48GB4enpi1qxZ8Pf3R69evVpaBgDA09MTv/3tbzFq1CgYDAb1QNDMmTNR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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1138961d0>"
       ]
      }
     ],
     "prompt_number": 134
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Predicting on all variables\n",
      "\n",
      "Extension to all variables is easy. We go from a 1D vector to a nD Matrix. Numpy handles the matrix calculation for us, so we just have to change the data. Since visualisation is not feasible, we have to rely on the MSE calculation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X=auto_wo_nan[:,1:8]\n",
      "y=auto_wo_nan[:,0]\n",
      "(w,out,rss) = linreg(X,y)\n",
      "rmse = sqrt(rss/(y.shape[0]))\n",
      "print \"MSE for all features is %f\"%(rmse)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MSE for all features is 3.293551\n"
       ]
      }
     ],
     "prompt_number": 338
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Linear Regression for learning Classifications \n",
      "\n",
      "Now lets investigate the use of Linear Regression for classification. Therefore, we will introdued a new attribute called `greeness`. The attribute should reflect environmental impact of a car.\n",
      "\n",
      "Afterwards, we will modify the linear regression algorithm to make such predictions.\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the greeness attriute. usually this should be given in the data set\n",
      "#1 means a car as low environmental impact, -1 is for high impact\n",
      "green_mask = auto_wo_nan[:,0]>=25 #we need that later\n",
      "greeness = (green_mask)*2-1 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "greeness"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "array([-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,\n",
        "       -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,\n",
        "       -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,\n",
        "       -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,\n",
        "       -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,\n",
        "        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,\n",
        "        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,\n",
        "        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,\n",
        "       -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,\n",
        "        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,\n",
        "        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,\n",
        "        1,  1,  1,  1,  1,  1,  1,  1,  1, -1,  1,  1,  1,  1,  1,  1,  1,\n",
        "        1])"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we simply use greeness as the dependent variable for our regression problem, i.e. the value we want to predict. For illustrative purpose, we only take the two variables which allows us to plot the examples in 2D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#select examples and plot in 2D\n",
      "X=auto_wo_nan[:,(4,5)]\n",
      "y=greeness\n",
      "plot (X[green_mask,0],X[green_mask,1],'g.') #all green carse are plotted, yes you guess right, GREEN\n",
      "plot (X[~green_mask,0],X[~green_mask,1],'r.') #all others are red\n",
      "xlabel(feature[4])\n",
      "ylabel(feature[5])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ejOPHj1v/bmpqwuDBwZOvz9tQU1d5/C15h77p/sar9jxSWmqOpy8qMu8I5o1N+6P6b5gK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\nt3l5eWhvb5dSBI/QBi+C8BM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YNm0akpKSEBkZaf3cVlFYfs/KysKgQYOg0+nIIU2oBkrZ\nTRBecu7cOdx88824cuUK5s2bh9WrV2Pu3LmBFosguEIrB4LwkrKyMmRnZyMjIwO33norKQYiKKGV\nA0EQBOEErRwIgiAIJ0g5EARBEE6QciAIgiCcIOVAEARBOEHKgSAIgnCClANBEAThxP8DPY6MoJqy\nx1kAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114cd2b90>"
       ]
      }
     ],
     "prompt_number": 406
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#now calculate the regression\n",
      "\n",
      "(w,out,rss) = linreg(X,y)\n",
      "green_predicted = out>0  #so that is based on the model we learned\n",
      "#lets plot it for analysis reasons\n",
      "plot (X[green_predicted,0],X[green_predicted,1],'g.') #all green carse are plotted, yes you guess right, GREEN\n",
      "plot (X[~green_predicted,0],X[~green_predicted,1],'r.') #all others are red\n",
      "xlabel(feature[4])\n",
      "ylabel(feature[5])\n",
      "#lets also plot w in the feature space. Note that 0=X*w is the line of separation\n",
      "#hence, 0=w1*weight+w2*acceleration-w0 ==> acceleration=-w1/w2*weight+w0/w2\n",
      "f = lambda weight:-w[0]/w[1]*weight+w[2]/w[1] #line function for separating positive from negative ones\n",
      "plot([2720,2850],[f(2720),f(2850)],'b')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ye2avpP5FA94cgFN1p3Cj/YbtWGTXSGzM3Yjcv+Z26l/krIeTcAEXKpCuwV0d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\nyoEwHppaDkZ37RhdPi1wNQc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       "text": [
        "<matplotlib.figure.Figure at 0x114ccd490>"
       ]
      }
     ],
     "prompt_number": 341
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Decision Boundary\n",
      "\n",
      "As we can see, there seems to be linear line as boundary of deciding between green cars and non-green ones (visualised as blue line). This is called the **decision boundary**. In general, the decision boundary is the separating function/hypothesis between two or more classes. In our case, it is a linear function determined by our model that $X*w^T\\geq 0$ are green cars. Hence, the decision boundary is given as: \n",
      "\n",
      "$$0=Xw^T$$\n",
      "\n",
      "For the case with 2 attributes, we can be rephrased the decision boundary in a line equation for plotting as follows: \n",
      "\n",
      "$$0=w_1*x_0+w_2*x_1-w_0 \\Rightarrow y=x_1=-\\frac{w_1}{w_2}*x_0+\\frac{w_0}{w_2}$$\n",
      "\n",
      "and we can draw the separating line between green and non green cars as done above. Moreover, we can compare on the original data what part of the classification is correct and which one is incorrect.\n",
      "\n",
      "\n",
      "Recall also, that if two vectors $a$ and $b$ are orthogonal to each other, their dot product is zero, e.g. $a\\cdot b=0$. Hence, the parameter vector $w$ is orthogonal to all examples $x$ on the decision boundary. \n",
      "\n",
      "The following figure shows the decision boundary (in blue) and the pependricular vector (in black). Since the attributes of the auto data set are of very different scale, we rescale the data first (Otherwise the figure would be hard to interpret)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#now calculate the regression\n",
      "X_scaled = (X-np.min(X,axis=0))/(np.max(X,axis=0)-np.min(X,axis=0))\n",
      "(w,out,rss) = linreg(X_scaled,y)\n",
      "#now plot the ORIGINAL DATA\n",
      "plot (X_scaled[green_mask,0],X_scaled[green_mask,1],'g.') #all green carse are plotted, yes you guess right, GREEN\n",
      "plot (X_scaled[~green_mask,0],X_scaled[~green_mask,1],'r.') #all others are red\n",
      "xlabel(feature[4])\n",
      "ylabel(feature[5])\n",
      "# and plot the found w\n",
      "k1,d1 = -w[0]/w[1],w[2]/w[1]\n",
      "f = lambda weight:k1*weight+d1 #line function for separating positive from negative ones\n",
      "plot([0.325,0.345],[f(0.325),f(0.345)],'b')\n",
      "k2=-1.0/k1\n",
      "f2 = lambda weight:k2*weight+f(0.344)-k2*(0.344) #perpendicular line through point 0.32,f(0.32)\n",
      "print [0.325,0.342],[f2(0.325),f2(0.342)]\n",
      "plot([0.1,0.346],[f2(0.1),f2(0.346)],'k')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0.325, 0.342] [0.86658102948130777, 0.86617068812434339]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PPmP33Xcfi4iIYMuXL2d33XUXO3jwoCQtJBUBYopGikP5kd2PiHPe2u2sY3EW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\nDFC4KqEYvmzwublc0ENmJhf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       "text": [
        "<matplotlib.figure.Figure at 0x114c45810>"
       ]
      }
     ],
     "prompt_number": 360
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now lets do it with two other attributes: acceleration and horsepower"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#select examples and plot in 2D\n",
      "X=auto_wo_nan[:,(5,3)]\n",
      "y=greeness\n",
      "#now calculate the regression\n",
      "(w,out,rss) = linreg(X,y)\n",
      "#now plot the ORIGINAL DATA\n",
      "plot (X[green_mask,0],X[green_mask,1],'g.') #all green carse are plotted, yes you guess right, GREEN\n",
      "plot (X[~green_mask,0],X[~green_mask,1],'r.') #all others are red\n",
      "xlabel(feature[5])\n",
      "ylabel(feature[3])\n",
      "# and plot the found w\n",
      "k1,d1 = -w[0]/w[1],w[2]/w[1]\n",
      "f = lambda weight:k1*weight+d1 #line function for separating positive from negative ones\n",
      "mi,ma = min(X[:,0]),max(X[:,0])\n",
      "plot([mi,ma],[f(mi),f(ma)],'b')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2JlChJJwa8k2MvxAzgE8MLy/hOB4ewnHEXDdjg9Rs1XDMvZOYBkvvnWa3rqmp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\n3gCqpMCcP8ix0myEhon+rGb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       "text": [
        "<matplotlib.figure.Figure at 0x114cc7110>"
       ]
      }
     ],
     "prompt_number": 335
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Evaluating the classification accuracy\n",
      "\n",
      "We can also estimate the fraction of examples wrongly classified by calculating\n",
      "\n",
      "$$ n_{correct}=\\frac{n + \\sum y \\odot (sgn(X\\cdot w^T))}{2} $$\n",
      "\n",
      "where $\\odot$ is the Hadamard (or element-wise) product and $sgn$ is the signum function. Note that for $y=\\{-1,1\\}$ $\\sum y \\odot sgn(X\\cdot w^T)$ corresponds to the number of correctly classified examples minus the number of incorrectly classified examples (i.e. $n_{correct}-n_{incorrect}$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = y*np.sign(out)\n",
      "print \"correct: %d\"%(np.sum(result==1)),\"wrong: %d\"%(np.sum(result==-1))\n",
      "#or as a one liner using the hadamad product\n",
      "n_correct = (y.shape[0]+ np.sum(result))/2\n",
      "n = len(result)\n",
      "print \"Traininging accuracy: %d (%f) \"%(n_correct,100*n_correct/n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "correct: 337 wrong: 55\n",
        "Traininging accuracy: 337 (85.969388) \n"
       ]
      }
     ],
     "prompt_number": 379
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, this is only the error on the training set, which does not provide a lot of insights on the generalization performance of the model. For example, if the model would be more complex (i.e. fiting a polynomial with more parameter) we can increase the accuracy on the training data easily. By just storing that data points we could achieve an accuracy of 100%. \n",
      "\n",
      "In order to test the generalization performance, i.e. how good a model predicts unseen examples, we have to use some examples for testing. Examples, that are not used in the training process. This is what we do next"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Random Splitting and Cross Validation\n",
      "\n",
      "One simple approach on generating training and test data is to make a random split. This is done next."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X=auto_wo_nan\n",
      "y=greeness\n",
      "#prepare test training split\n",
      "idx =  np.random.permutation(np.arange(X.shape[0])) # create a array with indices 1..N and perumtatet it\n",
      "X_train = X[idx[0:(len(idx)*0.8)],:]  # take the first 80% as training data. \n",
      "y_train = y[idx[0:(len(idx)*0.8)]]  # take the first 80% as training data. \n",
      "X_test  = X[idx[len(idx)*0.8:len(idx)],:]  # take the last 20% as test data. \n",
      "y_test  = y[idx[len(idx)*0.8:len(idx)]]  # take the last 20% as test data. \n",
      "#now train it\n",
      "(w,out,rss) = linreg(X_train,y_train,bias=False) #bias is false to avaoid adding clutter code to concatenate matrices\n",
      "result = y_train*np.sign(out)\n",
      "n_correct = (y_train.shape[0]+ np.sum(result))/2\n",
      "n = len(result)\n",
      "print \"Traininging accuracy: %d (%f) \"%(n_correct,100*n_correct/n)\n",
      "#and test it\n",
      "result = y_test * np.sign(np.dot(X_test,w))\n",
      "n_correct = (y_test.shape[0]+ np.sum(result))/2\n",
      "n = len(result)\n",
      "print \"Testing accuracy: %d (%f) \"%(n_correct,100*n_correct/n)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Traininging accuracy: 302 (96.485623) \n",
        "Testing accuracy: 75 (94.936709) \n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since we rely on random splitting, there is a chance to get a very bad/very good split. Hence, random splitting has to be conducted several times in a row and the results have to be averaged in order to obtain a reliable estiamtor. A better way is to do cross-validation, which will be covered in another tutorial."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}