Chapter 04 - Linear Methods for Classification.ipynb

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   "source": [
    "# Chapter 4 - Linear Methods for Classification"
   ]
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    "### Section 4.1\n",
    "\n",
    "* Linear method for classification -> decision boundaries are linear.\n",
    "* Discriminant methods model a discriminant function for each class and classify a point $x$ to the class with maximum discriminant value. A posterior probability function is also considered a discriminant method.\n",
    "* Linear methods are also those where we apply a monotonic linear transformation to the decision boundary, e.g. $logit(\\frac{p}{1-p})$.\n",
    "* Linear discriminant analysis (LDA) and linear logistic regression result in log-odds or logit decision boundaries."
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    "### Section 4.2\n",
    "\n",
    "* Indicator response matrix - binary encoding of response target. Generalized to predicting more than 1 class.\n",
    "* You can linear regress on and indicator response matrix, just like in Chapter 3, fit to the regression for all classes simultaneously (multiple linear regression).\n",
    "* Classify to the class with the largest fitted prediction.\n",
    "* The sum of predicted values (across classes) should equal 1, as long as there is an intercept.\n",
    "* When K (# of classes) >= 3 we run into problems because we have a single linear decision boundary to separate the classes. At least one class will be bisected by the decision boundary.\n",
    "* A polynomial boundary of degree up to K-1 may be needed to create an accurate boundary around K classes."
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     "text": [
      "Target names:\n",
      "['setosa' 'versicolor' 'virginica']\n",
      "Feature names:\n",
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n"
     ]
    }
   ],
   "source": [
    "import pandas\n",
    "from sklearn import datasets\n",
    "\n",
    "# Load the iris classification data\n",
    "iris = datasets.load_iris()\n",
    "print('Target names:')\n",
    "print(iris.target_names)\n",
    "Y = iris.target\n",
    "print('Feature names:')\n",
    "print(iris.feature_names)\n",
    "X = iris.data"
   ]
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Code source: Gaël Varoquaux\n",
    "# Modified for documentation by Jaques Grobler\n",
    "# License: BSD 3 clause\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn import datasets\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# Import iris data\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:, :2]  # we only take the first two features.\n",
    "Y = iris.target\n",
    "\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "\n",
    "plt.figure(2, figsize=(8, 6))\n",
    "plt.clf()\n",
    "\n",
    "# Plot the training points\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.jet)\n",
    "plt.xlabel('Sepal length')\n",
    "plt.ylabel('Sepal width')\n",
    "\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "# To getter a better understanding of interaction of the dimensions\n",
    "# plot the first three PCA dimensions\n",
    "fig = plt.figure(1, figsize=(8, 6))\n",
    "ax = Axes3D(fig, elev=-150, azim=110)\n",
    "X_reduced = PCA(n_components=3).fit_transform(iris.data)\n",
    "ax.scatter(X_reduced[:, 0], X_reduced[:, 1], X_reduced[:, 2], c=Y,\n",
    "           cmap=plt.cm.jet)\n",
    "\n",
    "ax.set_title(\"First three PCA directions\")\n",
    "ax.set_xlabel(\"1st eigenvector\")\n",
    "ax.w_xaxis.set_ticklabels([])\n",
    "ax.set_ylabel(\"2nd eigenvector\")\n",
    "ax.w_yaxis.set_ticklabels([])\n",
    "ax.set_zlabel(\"3rd eigenvector\")\n",
    "ax.w_zaxis.set_ticklabels([])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.33, random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 1, 1, 1, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 1, 1, 0, 2,\n",
       "       2, 2, 2, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0,\n",
       "       2, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1,\n",
       "       0, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 2, 0, 1, 2, 2, 1, 1, 2, 0,\n",
       "       2, 0, 0, 1, 0, 2, 2, 2, 1, 0, 2, 0])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 0],\n",
       "       [0, 0, 1],\n",
       "       [0, 1, 0],\n",
       "       [0, 1, 0],\n",
       "       [0, 1, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [0, 1, 0],\n",
       "       [1, 0, 0],\n",
       "       [0, 0, 1]], dtype=uint8)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an indicator response matrix\n",
    "y_train_encoded = pandas.get_dummies(y_train).values\n",
    "y_test_encoded = pandas.get_dummies(y_test).values\n",
    "y_train_encoded[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lr.fit(X_train, y_train_encoded)\n",
    "lr_train_predict = lr.predict(X_train)\n",
    "lr_test_predict = lr.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.10880129,  0.88877386,  0.22002743],\n",
       "       [-0.04610103, -0.07946781,  1.12556884],\n",
       "       [ 0.15881846,  0.72114187,  0.12003967],\n",
       "       [ 0.12393228,  0.37314439,  0.50292333],\n",
       "       [ 0.22147377,  0.2473549 ,  0.53117133],\n",
       "       [ 1.15769199, -0.05980603, -0.09788596],\n",
       "       [ 1.02293023,  0.02667591, -0.04960615],\n",
       "       [ 0.11791298,  0.39022958,  0.49185744],\n",
       "       [ 0.89800685,  0.23732071, -0.13532756],\n",
       "       [ 0.00412843,  0.21784477,  0.7780268 ],\n",
       "       [ 0.84750108,  0.24282143, -0.09032251],\n",
       "       [ 0.827394  ,  0.29785377, -0.12524778],\n",
       "       [-0.04265389,  0.40855253,  0.63410136],\n",
       "       [ 0.26210482,  0.61004612,  0.12784905],\n",
       "       [-0.1270868 ,  0.20631934,  0.92076747],\n",
       "       [ 1.0237325 ,  0.03353703, -0.05726953],\n",
       "       [-0.04422878,  0.29053247,  0.75369631],\n",
       "       [ 0.78637759,  0.40105734, -0.18743493],\n",
       "       [ 0.1925983 ,  0.54136355,  0.26603815],\n",
       "       [-0.03720066,  0.45922499,  0.57797567],\n",
       "       [ 0.88653431,  0.20373344, -0.09026776],\n",
       "       [-0.11254579,  0.14877331,  0.96377248],\n",
       "       [ 0.07703713, -0.04498053,  0.9679434 ],\n",
       "       [-0.02944297,  0.30550533,  0.72393764],\n",
       "       [-0.23121367,  0.41695168,  0.81426199],\n",
       "       [ 0.01410738,  0.46058539,  0.52530723],\n",
       "       [ 0.91975669,  0.08961289, -0.00936958],\n",
       "       [ 0.24926395,  0.6373554 ,  0.11338065],\n",
       "       [-0.23361374,  0.66530279,  0.56831094],\n",
       "       [ 0.18150442,  0.42993847,  0.38855711],\n",
       "       [ 0.82603427,  0.35665042, -0.18268469],\n",
       "       [-0.16643271,  0.38358397,  0.78284873],\n",
       "       [ 0.21318826,  0.36243451,  0.42437724],\n",
       "       [ 0.20206474,  0.35530724,  0.44262802],\n",
       "       [ 1.00372964,  0.04251049, -0.04624014],\n",
       "       [ 1.02449841, -0.1242385 ,  0.09974009],\n",
       "       [ 0.96762431, -0.12811258,  0.16048827],\n",
       "       [ 0.15976989,  0.18748942,  0.65274069],\n",
       "       [-0.19465509,  0.56797587,  0.62667922],\n",
       "       [-0.07421248,  0.32779968,  0.74641279],\n",
       "       [ 0.18643842,  0.43987098,  0.37369059],\n",
       "       [ 0.9249355 ,  0.17206429, -0.09699978],\n",
       "       [ 1.04439704, -0.08715308,  0.04275604],\n",
       "       [ 0.95060863,  0.11954563, -0.07015426],\n",
       "       [-0.14531492,  0.24329498,  0.90201994],\n",
       "       [-0.094943  ,  0.38815096,  0.70679204],\n",
       "       [ 0.19224928,  0.51490355,  0.29284717],\n",
       "       [ 0.12671101,  0.7039469 ,  0.16934209],\n",
       "       [ 0.04792546,  0.17440935,  0.77766519],\n",
       "       [-0.03086868,  0.30396314,  0.72690554],\n",
       "       [ 0.02350783,  0.21419025,  0.76230192],\n",
       "       [-0.09446201,  0.53528862,  0.55917339],\n",
       "       [ 0.1863342 ,  0.48592987,  0.32773593],\n",
       "       [ 0.93658685,  0.2178316 , -0.15441845],\n",
       "       [ 0.91328415,  0.12629697, -0.03958111],\n",
       "       [ 0.13628167,  0.47183171,  0.39188662],\n",
       "       [ 0.80759959,  0.21470947, -0.02230906],\n",
       "       [ 1.05577396, -0.00960682, -0.04616713],\n",
       "       [ 0.04771702,  0.26652712,  0.68575587],\n",
       "       [ 0.17819786,  0.71748735,  0.10431479],\n",
       "       [ 1.00957013,  0.01324524, -0.02281538],\n",
       "       [ 0.95714717,  0.14320038, -0.10034754],\n",
       "       [ 0.98090311,  0.21513613, -0.19603924],\n",
       "       [ 0.21176926,  0.62982679,  0.15840395],\n",
       "       [ 0.8840233 ,  0.22920897, -0.11323227],\n",
       "       [ 0.21910334,  0.39140819,  0.38948847],\n",
       "       [ 0.82547681,  0.42230819, -0.24778499],\n",
       "       [ 0.09561427,  0.60149528,  0.30289045],\n",
       "       [-0.17068398,  0.81672833,  0.35395566],\n",
       "       [ 0.81392968,  0.33048198, -0.14441167],\n",
       "       [ 0.16188022,  0.36107411,  0.47704567],\n",
       "       [ 0.14692231,  0.60285567,  0.25022202],\n",
       "       [ 0.01919916, -0.07209556,  1.0528964 ],\n",
       "       [ 0.77990504,  0.43774142, -0.21764646],\n",
       "       [ 0.06072809,  0.25349779,  0.68577412],\n",
       "       [ 0.86541653,  0.34402244, -0.20943896],\n",
       "       [ 0.14681809,  0.64891455,  0.20426736],\n",
       "       [ 0.05198933,  0.38817628,  0.55983439],\n",
       "       [-0.20797695,  0.44814748,  0.75982947],\n",
       "       [-0.02591937, -0.07626121,  1.10218058],\n",
       "       [ 1.20017236, -0.26786513,  0.06769277],\n",
       "       [ 0.05264243,  0.93555097,  0.0118066 ],\n",
       "       [-0.29091144,  0.57672977,  0.71418167],\n",
       "       [-0.16664975,  0.47780163,  0.68884812],\n",
       "       [ 0.24819397,  0.27421624,  0.47758979],\n",
       "       [ 0.07599007,  0.53263092,  0.39137901],\n",
       "       [-0.12881847, -0.04510317,  1.17392165],\n",
       "       [ 1.07472975, -0.09796029,  0.02323054],\n",
       "       [-0.0353858 ,  0.1097951 ,  0.9255907 ],\n",
       "       [ 0.96361971,  0.1065163 , -0.07013601],\n",
       "       [ 0.97015824,  0.13017105, -0.10032929],\n",
       "       [ 0.12389404,  0.4795421 ,  0.39656386],\n",
       "       [ 0.77462201,  0.40134891, -0.17597092],\n",
       "       [-0.090424  ,  0.31128464,  0.77913936],\n",
       "       [-0.05254393,  0.5099099 ,  0.54263403],\n",
       "       [-0.16771785,  0.50061956,  0.66709829],\n",
       "       [ 0.27786499,  0.37512568,  0.34700932],\n",
       "       [ 1.21384512, -0.39261111,  0.17876598],\n",
       "       [-0.02916854,  0.27372639,  0.75544215],\n",
       "       [ 0.84558389,  0.36727584, -0.21285973]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_train_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "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.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Probabilities should sum to 1.\n",
    "lr_train_predict.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Pick index with best score (= class with best score in this case)\n",
    "lr_train_classified = [pandas.Series(x).idxmax() for x in lr_train_predict]\n",
    "lr_test_classified = [pandas.Series(x).idxmax() for x in lr_test_predict]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 1, 2, 2, 0, 0, 2, 0, 2]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_train_classified[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score, precision_score, recall_score\n",
    "\n",
    "def summarize_apr(y_true, y_predicted, tag):\n",
    "    print('''\n",
    "        {tag}\n",
    "        ----------------------------------\n",
    "        Accuracy: {accuracy}\n",
    "        Precision: {precision}\n",
    "        Recall: {recall}\n",
    "    '''.format(tag=tag,\n",
    "                accuracy=round(accuracy_score(y_true, y_predicted), 4),\n",
    "                precision=round(precision_score(y_true, y_predicted, average='macro'), 4),\n",
    "                recall=round(recall_score(y_true, y_predicted, average='macro'), 4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        Linear Regression Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.88\n",
      "        Precision: 0.8916\n",
      "        Recall: 0.8729\n",
      "    \n",
      "\n",
      "        Linear Regression Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.76\n",
      "        Precision: 0.8061\n",
      "        Recall: 0.7815\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "summarize_apr(y_train, lr_train_classified, 'Linear Regression Train')\n",
    "summarize_apr(y_test, lr_test_classified, 'Linear Regression Test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Section 4.3\n",
    "* For proper classification, we are really looking to find the posterior probabilities $P(G|X=x)$.\n",
    "* By decomposing the above posterior probability with Bayes theorem, it is clear that being able to estimate $P(X|G=g)$ is sufficient. Many techniques are based on estimating this density (linear/quadratic discriminant analysis, Gaussian mixtures, nonparametric density estimates, Naive Bayes).\n",
    "\n",
    "**LDA**\n",
    "* LDA assumes each class density follows a multivariate Gaussian with a common covariance matrix for each class k. The log odds ratio is used to compare class probabilities.\n",
    "* \"Odds ratio for a success rate of $p$ is defined as $\\frac{p}{1-p}$. A nice feature of this ratio is the plain English explanation you can do with it in a betting scenario. As an example, assume p=0.8. Your odds ratio is $\\frac{0.80}{1-0.8}=\\frac{0.80}{0.20}=4$. So you could say you are four times more likely to win than lose, or vice versa. Lots of horse race betting (and their pay off) also works in the same way.\"\n",
    "* Odds ratio in our context is used to say: Given X, probability that the observation belongs to class $k$ is $m$ times more likely than the probability that observation belongs to class $l$.\n",
    "* A linear hyperplane will become the boundary between any 2 given classes.\n",
    "* If we do not assume homogeneous covariance matrices, we get quadratic discriminant analysis.\n",
    "* Not robust to gross outliers (see pg. 128).\n",
    "\n",
    "**Regularized QDA**\n",
    "* We can regularize QDA by shrinking the disparate covariances of QDA towards the common covariance of LDA.\n",
    "\n",
    "**Reduced Rank LDA**\n",
    "* Sphering is a linear process which applied to each point leads to random variables with mean 0 and the identity matrix as covariance matrix, meaning that they are uncorrelated and all have variance 1.\n",
    "* Assuming we have sphered our data, only the projection of $X^*$ onto $\\mu_{1}^{*} - \\mu_{2}^{*}$ is needed. That is, project the data onto the distance between its centroids.  This projects the data into a subspace of rank $K-1$, which is significant reduction for large $p$. We lose no information in this projection.\n",
    "* Fisher's method give us this optimal projection, so that the centroids are as spread out as possible.\n",
    "* Amounts to the regression of an indicator matrix followed by an eigen-decomposition of $\\hat{Y}^TY$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        LDA Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.99\n",
      "        Precision: 0.9905\n",
      "        Recall: 0.9892\n",
      "    \n",
      "\n",
      "        LDA Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.98\n",
      "        Precision: 0.9804\n",
      "        Recall: 0.9825\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "# First lets try LDA\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "lda = LinearDiscriminantAnalysis(solver='svd', shrinkage=None, priors=None, n_components=None, \n",
    "                                 store_covariance=False, tol=0.0001)\n",
    "\n",
    "lda.fit(X_train, y_train)\n",
    "lda_train_classified = lda.predict(X_train)\n",
    "lda_test_classified = lda.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, lda_train_classified, 'LDA Train')\n",
    "summarize_apr(y_test, lda_test_classified, 'LDA Test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        LDA Regularization Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.97\n",
      "        Precision: 0.9698\n",
      "        Recall: 0.9687\n",
      "    \n",
      "\n",
      "        LDA Regularization Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.98\n",
      "        Precision: 0.9804\n",
      "        Recall: 0.9825\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "# Now let's use it with regularization\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "lda = LinearDiscriminantAnalysis(solver='eigen', shrinkage='auto', priors=None, n_components=None, \n",
    "                                 store_covariance=False, tol=0.0001)\n",
    "\n",
    "lda.fit(X_train, y_train)\n",
    "lda_train_classified = lda.predict(X_train)\n",
    "lda_test_classified = lda.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, lda_train_classified, 'LDA Regularization Train')\n",
    "summarize_apr(y_test, lda_test_classified, 'LDA Regularization Test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        QDA Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.98\n",
      "        Precision: 0.9794\n",
      "        Recall: 0.9794\n",
      "    \n",
      "\n",
      "        QDA Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.98\n",
      "        Precision: 0.9804\n",
      "        Recall: 0.9825\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "# Now let's use QDA\n",
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n",
    "qda = QuadraticDiscriminantAnalysis(priors=None, reg_param=0.0, tol=0.0001)\n",
    "\n",
    "qda.fit(X_train, y_train)\n",
    "qda_train_classified = qda.predict(X_train)\n",
    "qda_test_classified = qda.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, qda_train_classified, 'QDA Train')\n",
    "summarize_apr(y_test, qda_test_classified, 'QDA Test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        QDA Regularization Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.95\n",
      "        Precision: 0.9485\n",
      "        Recall: 0.9491\n",
      "    \n",
      "\n",
      "        QDA Regularization Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.98\n",
      "        Precision: 0.9804\n",
      "        Recall: 0.9825\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "# Now let's use QDA with regularziation\n",
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n",
    "qda = QuadraticDiscriminantAnalysis(priors=None, reg_param=0.50, tol=0.0001)\n",
    "\n",
    "qda.fit(X_train, y_train)\n",
    "qda_train_classified = qda.predict(X_train)\n",
    "qda_test_classified = qda.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, qda_train_classified, 'QDA Regularization Train')\n",
    "summarize_apr(y_test, qda_test_classified, 'QDA Regularization Test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Section 4.4 (Logistic regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "* Model posterior probabilities of the K classes via linear functions in x, while at the same time ensuring they sum to one and predictions remain in [0, 1].\n",
    "\n",
    "\n",
    "* Model specified in terms of $K-1$ log-odds or logit transformations.\n",
    "\n",
    "$log\\frac{Pr(G=1|X=x)}{Pr(G=K|X=x)}=\\beta_{10} + \\beta_{1}^{T}x$\n",
    "\n",
    "$log\\frac{Pr(G=2|X=x)}{Pr(G=K|X=x)}=\\beta_{20} + \\beta_{2}^{T}x$\n",
    "\n",
    "...\n",
    "\n",
    "$log\\frac{Pr(G=K-1|X=x)}{Pr(G=K|X=x)}=\\beta_{(K-1)0} + \\beta_{K-1}^{T}x$\n",
    "\n",
    "* Method is invariant to the choice of denominator.\n",
    "\n",
    "* When K=2 the method simplifies greatly since there is only 1 linear function.\n",
    "\n",
    "* Models are usually fit via MLE. The systems of MLE equations to solve are non-linear in $\\beta$ so we use something like the Newton-Rhapson method.\n",
    "\n",
    "* There is a connection between logistic regression and weighted least squares fit. This provides a convenient algorithm and some other inferential tools.\n",
    "\n",
    "* L1 regularization (lasso) can be applied to the logistic regression model.\n",
    "\n",
    "* Generally thought as a safer, more robust bet than using LDA, since it relies on fewer assumptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        Logistic Regression Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.95\n",
      "        Precision: 0.9573\n",
      "        Recall: 0.9462\n",
      "    \n",
      "\n",
      "        Logistic Regression Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.86\n",
      "        Precision: 0.8986\n",
      "        Recall: 0.8772\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "logr = LogisticRegression(penalty='l2', dual=False, tol=0.0001, C=1.0, fit_intercept=True, \n",
    "                          intercept_scaling=1, class_weight=None, random_state=None, solver='liblinear', \n",
    "                          max_iter=100, multi_class='ovr', verbose=0, warm_start=False, n_jobs=1)\n",
    "\n",
    "logr.fit(X_train, y_train)\n",
    "logr_train_classified = logr.predict(X_train)\n",
    "logr_test_classified = logr.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, logr_train_classified, 'Logistic Regression Train')\n",
    "summarize_apr(y_test, logr_test_classified, 'Logistic Regression Test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Section 4.5 (Separating Hyperplanes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "* Methods that construct decision boundaries to explicitly separate the data into classes as well as possible.\n",
    "* Form the basis for SVM (support vector machines).\n",
    "* Rosenblatt's perceptron - tries to find a separating hyperplane by minimizing the distances of misclassified points to the decision boundary. Forms the foundation behind neural networks. Number of problems with this algorithm - non-unique solution that depends on starting values. Can require a large number of steps. Does not converge with inseparable data.\n",
    "* Optimal separating hyperplanes separate the two classes and maximizes the distance to the closest point from either class. This provides a unique solution and leads to better classification performance on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        Perceptron Regression Train\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.42\n",
      "        Precision: 0.7828\n",
      "        Recall: 0.4389\n",
      "    \n",
      "\n",
      "        Perceptron Regression Test\n",
      "        ----------------------------------\n",
      "        Accuracy: 0.46\n",
      "        Precision: 0.8043\n",
      "        Recall: 0.4208\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Perceptron\n",
    "perceptron = Perceptron(penalty=None, alpha=0.0001, fit_intercept=True, shuffle=True, \n",
    "                        verbose=0, eta0=1.0, n_jobs=1, random_state=0, class_weight=None, warm_start=False)\n",
    "\n",
    "perceptron.fit(X_train, y_train)\n",
    "perceptron_train_classified = perceptron.predict(X_train)\n",
    "perceptron_test_classified = perceptron.predict(X_test)\n",
    "\n",
    "summarize_apr(y_train, perceptron_train_classified, 'Perceptron Regression Train')\n",
    "summarize_apr(y_test, perceptron_test_classified, 'Perceptron Regression Test')"
   ]
  }
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