Module 3 updated

Module 2/Linear Regression.ipynb

@@ -115,6 +115,7 @@
     "theta = np.zeros((2,1))\n",
     "theta = np.matrix(theta)\n",
     "X = np.matrix(X)\n",
+    "y=y_init\n",
     "X[0:5]"
    ]
   },

Module 3/.ipynb_checkpoints/Logistic Regression-checkpoint.ipynb

@@ -0,0 +1,299 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Logistic Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.datasets import make_classification\n",
+    "\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Generate Dummy Classification Data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dataset = make_classification(n_classes=2, n_samples=100, n_features=2, random_state=42, n_informative=2, n_redundant=0, n_repeated=0, n_clusters_per_class=1)\n",
+    "X_init = dataset[0]\n",
+    "y_init = dataset[1]\n",
+    "theta_0 = np.zeroes(X.shape[1])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Plotting the data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "matrix([[ 1.        ,  1.22831184, -0.75717844],\n",
+       "        [ 1.        ,  0.69840909, -1.38029525],\n",
+       "        [ 1.        ,  2.54881729,  2.50225822],\n",
+       "        [ 1.        ,  0.57357881, -1.35297943],\n",
+       "        [ 1.        ,  0.58590018, -1.33745666]])"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X_0 = X_init[:,0]\n",
+    "X_1 = X_init[:,1]\n",
+    "\n",
+    "X = np.concatenate((np.ones((100,1)), X_init), axis=1)\n",
+    "theta = np.zeros((3,1))\n",
+    "theta = np.matrix(theta)\n",
+    "X = np.matrix(X)\n",
+    "X[0:5]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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6XcRubKKkzfcc1MzsqffIEivPyqdOzKh/aUHu0kvTM3MB+IZdk2r0jjJJd1y3hp9NLEru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\nkDMEdgDIGQI7AOQMgR0Acub/AVi6d15h3KnEAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1204f89b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(x=X_0, y=X_1)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Defining the sigmoid function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def sigmoid(z):\n",
+    "    g = np.matrix(np.zeros(np.matrix(z).shape))\n",
+    "    \n",
+    "    # ====================== YOUR CODE HERE ======================\n",
+    "    # Instructions: Compute the sigmoid of each value of z (z can be a matrix,\n",
+    "    #              vector or scalar).\n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    # =============================================================\n",
+    "    return g"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Evalutating sigmoid(0) should give you exactly 0.5"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0.]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(sigmoid(0))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Computing the cost J(θ)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def costFunction(theta, X, y):\n",
+    "    m = len(y)\n",
+    "    J = 0;\n",
+    "    grad = np.zeros(theta.shape)\n",
+    "    \n",
+    "    # ====================== YOUR CODE HERE ======================\n",
+    "    # Instructions: Compute the cost of a particular choice of theta.\n",
+    "    #           You should set J to the cost.\n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    # =============================================================\n",
+    "    return J"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Computing the Gradient"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def costFunction(theta, X, y):\n",
+    "    m = len(y)\n",
+    "    J = 0;\n",
+    "    grad = np.zeros(theta.shape)\n",
+    "     \n",
+    "    # ====================== YOUR CODE HERE ======================\n",
+    "    # Instructions: Compute the partial derivatives and set grad to the partial\n",
+    "    #           derivatives of the cost w.r.t. each parameter in theta\n",
+    "    # \n",
+    "    # Note: grad should have the same dimensions as theta\n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    \n",
+    "    # =============================================================\n",
+    "    return grad.flatten()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Learning parameters using Scipy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "from scipy.optimize import minimize\n",
+    "res = minimize(costFunction, theta_0, args=(X,y), method=None, jac=gradient, options={'maxiter':1000})\n",
+    "res"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Plotting the decision boundary"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "plt.scatter(40, 75, c='r',label='(40, 75)')\n",
+    "plotData(X[1:,:], 'x1', 'x2', 'yes', 'no')\n",
+    "x1_min, x1_max = X[:,1].min(), X[:,1].max(),\n",
+    "x2_min, x2_max = X[:,2].min(), X[:,2].max(),\n",
+    "xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))\n",
+    "h = sigmoid(np.c_[np.ones((xx1.ravel().shape[0],1)), xx1.ravel(), xx2.ravel()].dot(res.x))\n",
+    "h = h.reshape(xx1.shape)\n",
+    "plt.contour(xx1, xx2, h, [0.5], linewidths=1, colors='g');"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.6.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}