{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In the following, please experiment with various parameters and try different datasets, by generating different (X,y) values (with different parameters)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "\n",
    "from matplotlib import pylab as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11a376d90>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QheDeHTFG4q1DZ+MLRc7MZSmbNsPRAAf7u7ZcK75d3SHem8o2rFQE4De0jv1u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\nB1cx+wSxfYnPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1182da350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check the help for 'datasets.make_classification' function\n",
    "# NOTE: we let the labels to be 0/1: SKLEARN would use the required internal\n",
    "# representation.\n",
    "X, y = datasets.make_classification(1000, n_features=2, \n",
    "                                    n_informative=2, n_redundant=0, \n",
    "                                    n_clusters_per_class=1)\n",
    "                                    \n",
    "plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Paired)     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. LDA\n",
    "In the following, the linear models will contain .coeff_ and .intercept_ attributes that you can check and use to plot the decision surface (plane).\n",
    "\n",
    "Go to http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html for the details of the class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train a model on the first 500 points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis(n_components=None, priors=None, shrinkage=None,\n",
       "              solver='svd', store_covariance=False, tol=0.0001)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LDA()\n",
    "model.fit(X[0:500,:], y[0:500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict on some new data points (last 500 from X) and count the mismatched predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.035999999999999997"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yp = model.predict(X[500:1001,:])\n",
    "sum(yp != y[500:1001]) / 500.0  # note that we divide to a float, to avoid integer division!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transform the data into the maximum separating space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aabe710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xt = model.transform(X)\n",
    "_ = plt.hist([X[y==0,0], Xt[y==1,0]], bins=30, color=['blue','red'])     # just put the result in a dummy varibale '_'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also obtain estimates of the posterior probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUuP+B4lM7b4MyYXiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a9f2150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prb = model.predict_proba(X)\n",
    "_ = plt.hist([prb[y==0,0], prb[y==1,0]], bins=30, color=['blue','red'])     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how the class label is chosen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = model.decision_function(X)    # returns h(x)=<w,x>+w0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TODO:\n",
    "- plot the transformed data separately for training data and testing data.\n",
    "- check how the sign (use numpy.sign()) of df is mapped onto class labels\n",
    "- generate a higher dimensional dataset (n_features=5) - call it differently - and study: \n",
    "    * the optimal subspace (plot different pairs of coordinates)\n",
    "    * select to have more redundant or linearly dependent features and see how the LD subspace changes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Logistic regression\n",
    "\n",
    "Check the documentation: http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html\n",
    "\n",
    "Train and classify:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "model = LogisticRegression(C=1000)  # large values imply less penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X[0:500,:], y[0:500])\n",
    "yp = model.predict(X[500:1001,:])\n",
    "sum(yp != y[500:1001])/ 500.0            # compare with LDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b307d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check the fitted posterior probabilities:\n",
    "prb = model.predict_proba(X)\n",
    "_ = plt.hist([prb[y==0,0], prb[y==1,0]], bins=30, color=['blue','red'])     \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TODO:\n",
    "- Check what .transform() method does\n",
    "- Generate a higher dimensional space, with some correlation structure\n",
    "between variables and see how the subspace generated by .transform() changes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Linear SVM\n",
    "\n",
    "Check the documentation: http://scikit-learn.org/stable/modules/generated/sklearn.svm.LinearSVC.html\n",
    "\n",
    "Train and classify:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "model = LinearSVC()\n",
    "\n",
    "model.fit(X[0:500,:], y[0:500])\n",
    "yp = model.predict(X[500:1001,:])\n",
    "sum(yp != y[500:1001])/ 500.0            # compare with LDA and logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TODO\n",
    "- Use model.decision_function(X) * y to get the margins\n",
    "- Plot the margin density (histogram); change C (e.g. 0.1, 10, 1000) and see how the margin distribution changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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  "language_info": {
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    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
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   "pygments_lexer": "ipython2",
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