2. Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression // Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "#plt.style.use(r'C:\\Users\\Will\\.matplotlib\\stylelib\\test.mplstyle')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1.0 / (1.0 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x25aba350908>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i7GE9uPikPowZnENKsnZIiyQilYQclJKKaj7N38H7K7cx84stbCyuIMng5P5d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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25aba18fef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z = np.arange(-7, 7, 0.1)\n",
    "phi_z = sigmoid(z)\n",
    "\n",
    "plt.plot(z,phi_z)\n",
    "plt.axvline(0.0,color='k')\n",
    "#plt.axhspan(0.0, 1.0, facecolor='1.0', alpha=1.0, ls='dotted')\n",
    "plt.axhline(y=0.5, ls='dotted', color='k')\n",
    "plt.yticks([0.0,0.5,1.0])\n",
    "plt.ylim(-0.1,1.1)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('$\\phi (z)$')\n",
    "plt.title('Sigmoid Function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This sigmoid function takes real number values as input and transforms them to values in the range [0,1], with an intercept at $\\phi (z)$ = 0.5\n",
    "\n",
    "Notice that the intercept at $\\phi (z)$ = 0.5 occurs at z = 0\n",
    "\n",
    "$\\phi (0)$ = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticRegression(object):\n",
    "    \n",
    "    def __init__(self, eta=0.01, n_epochs=10, _shuffle=True, printing=False):\n",
    "        \n",
    "        \"\"\"Initializes Logistic Regression\"\"\"\n",
    "        self.eta = eta  #Initialize learning rate\n",
    "        self.n_epochs = n_epochs #Initialize number of epochs\n",
    "        self.shuffle = _shuffle #Initialize shuffle\n",
    "        self.printing = printing #Initialize printing options\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "    \n",
    "        \"\"\"Fit training data.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : {array-like}, shape = [n_samples, n_features]\n",
    "          :Training vectors, where n_samples is the number of samples and n_features is the number of features.\n",
    "        \n",
    "        y : array-like, shape = [n_samples]\n",
    "          :Target values\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        self : object\n",
    "        \"\"\"\n",
    "        \n",
    "        self.w_ = np.zeros(1 + X.shape[1])  #initialize the weights ('w_') to zero\n",
    "        self.cost_ = []  #for storing cost of each epoch\n",
    "        self.score_ = [] #for storing score of each epoch\n",
    "        \n",
    "        #For each epoch...\n",
    "        for i in range(1,n_epochs+1):\n",
    "            \n",
    "            sample_cost = [] #for storing cost of sample instance\n",
    "            \n",
    "            #SGD performs better when the training data is shuffled\n",
    "            if self._shuffle:\n",
    "                X, y = self._shuffle(X, y)            \n",
    "            \n",
    "            #For each sample instance xi...    Stochastic Gradient Descent runs model/updates weights for every sample instance xi\n",
    "            for xi, yi in zip(X,y):\n",
    "                \n",
    "                #Compute output and error for xi\n",
    "                output = self.net_input(xi) #Output is net input of xi and w_\n",
    "                errors = (yi - output) #Error is the difference between actual class yi and predicted class of xi (w.T * x)  #NOTE ORDER?\n",
    "\n",
    "                #Compute cost of sample xi\n",
    "                cost = self.log_likelihood(output,yi)  #Objective cost function J(x):  \n",
    "                sample_cost.append(cost)#append sample cost to sample_cost\n",
    "                \n",
    "                #Update weights with Gradient Descent\n",
    "                gradient = self.gradient(xi,errors) #Calculate gradient vector; vector of partial derivative of J(w) with respect to each weight\n",
    "                self.w_[1:] += self.eta * gradient #Update feature weights\n",
    "                self.w_[0] += self.eta * errors.sum() #Update model bias\n",
    "\n",
    "            #Calculate average cost of epoch\n",
    "            avg_cost = sum(sample_cost)/len(sample_cost)\n",
    "            self.cost_.append(avg_cost)\n",
    "            \n",
    "            #Score model after epoch\n",
    "            score = self.score(X, y)\n",
    "            self.score_.append(score) #record epoch score\n",
    "\n",
    "            #If printing=True, print results for each epoch\n",
    "            if self.printing:\n",
    "                print ('Epoch', i, score, self.w_, cost)\n",
    "\n",
    "        return self\n",
    "    \n",
    "    def net_input(self, X):\n",
    "        \"\"\"Calculate net input\"\"\"\n",
    "        return np.dot(X, self.w_[1:]) + self.w_[0] #Dot product of the training set and fitted weights, plus fitted weight-zero\n",
    "    \n",
    "    def sigmoid(self,z):\n",
    "        \"\"\"Transforms z to real number between 0 and 1\"\"\"\n",
    "        return 1.0 / (1.0 + np.exp(-self.net_input(z)))\n",
    "                      \n",
    "    def log_likelihood(self, X,y):\n",
    "        \"\"\"Compute log likelihood\"\"\"\n",
    "        ll = -1 * np.sum( y * np.log(self.sigmoid(X)) + (1 - y) * np.log(1 - self.sigmoid(X)))\n",
    "        return ll\n",
    "        \n",
    "    def gradient(self, X, errors):\n",
    "        \"\"\"Compute the gradient vector; vector of partial derivative of J(w) with respect to each weight\"\"\"\n",
    "        return X.T.dot(errors)\n",
    "    \n",
    "    def activation(self, X):\n",
    "        \"\"\"Compute sigmoid activation\"\"\"\n",
    "        return self.sigmoid(X)\n",
    "    \n",
    "    def predict(self, X):\n",
    "        \"\"\"Return class label after unit step\"\"\"\n",
    "        return np.where(self.activation(X) >= 0.5, 1, -1)\n",
    "        \n",
    "    def score(self, X, y):\n",
    "        \"\"\"Score the model --> Actual vs Predicted Classes\"\"\"\n",
    "        predicts = self.predict(X)\n",
    "        results = np.equal(predicts,y)\n",
    "        correct = np.sum(results)\n",
    "        score = float(correct) / float(len(results))\n",
    "        return score\n",
    "    \n",
    "    def _shuffle(self,X,y):\n",
    "        \"Shuffles the data\"\n",
    "        r = np.random.permutation(len(y))\n",
    "        return X[r], y[r]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load and Preview the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Import Iris dataset\n",
    "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', header=None)\n",
    "\n",
    "#Reduce dataset to two classes: Iris-setosa and Iris-versicolor\n",
    "data = df[(df[4] == 'Iris-setosa') |(df[4] == 'Iris-versicolor')]\n",
    "\n",
    "#Reduce dataset to two features and one target: sepal/petal length measurements and species\n",
    "data = data[[0,2,4]]\n",
    "\n",
    "#Define feature set\n",
    "X = data[[0,2]].values\n",
    "\n",
    "#Define target set\n",
    "y = data[4].values\n",
    "\n",
    "#Replace species name with numerical variable\n",
    "y = np.where(y == 'Iris-setosa',-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 0.52 [-0.01154337 -0.01980153  0.09801381] 1.38972033717\n",
      "Epoch 2 0.74 [-0.02379138 -0.04767158  0.17997591] 1.38551583222\n",
      "Epoch 3 0.99 [-0.03759955 -0.08823542  0.24473251] 1.26380754334\n",
      "Epoch 4 1.0 [-0.04984479 -0.12465637  0.30166146] 1.40429900462\n",
      "Epoch 5 1.0 [-0.06242479 -0.16581158  0.34831144] 1.41502765648\n",
      "Epoch 6 1.0 [-0.07027361 -0.18294883  0.40099319] 1.06860420175\n",
      "Epoch 7 1.0 [-0.07908207 -0.2081294   0.44302046] 1.43286475256\n",
      "Epoch 8 1.0 [-0.08700602 -0.2308108   0.4799043 ] 0.965160309803\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 8\n",
    "\n",
    "LR = LogisticRegression(n_epochs=n_epochs, eta=0.001, printing=True).fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x25aba72bf98>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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toH+DVYjkUuvWrZk+fXrYYYiIiEgJMbPfwo5B9qW/wURERCq2gv4NpmFxIiIi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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25aba18f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2,figsize=(20,7))\n",
    "fig.suptitle('Logistic Regression // Stochastic Gradient Descent\\neta=0.001', fontsize=18)\n",
    "\n",
    "ax1.plot(range(1, len(LR.score_) + 1), LR.score_)\n",
    "ax1.set_xlabel('Epochs', fontsize=15)\n",
    "ax1.set_ylabel('Accuracy', fontsize=15)\n",
    "\n",
    "ax2.plot(range(1, len(LR.cost_) + 1), LR.cost_)\n",
    "ax2.set_xlabel('Epochs', fontsize=15)\n",
    "ax2.set_ylabel('Log-Likelihood Cost', fontsize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}