LogisticRegression_Line.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from sklearn.linear_model import LogisticRegression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original X.shape: (2000, 1)\n",
      "X.shape after adding the labels: (2000, 2)\n",
      "y.shape for the labels: (2000, 1)\n"
     ]
    }
   ],
   "source": [
    "xstart=0\n",
    "xstop = 50\n",
    "Npoints = 1000\n",
    "x = np.linspace(xstart,xstop,Npoints).reshape(Npoints,1)\n",
    "# mTrue = np.random.randn(1)\n",
    "# cTrue = np.random.randn(1)\n",
    "mTrue = 2.5\n",
    "cTrue = 1.5\n",
    "\n",
    "yTrue = mTrue*x+cTrue\n",
    "noiseAmp = 10\n",
    "bias = -20\n",
    "yNoisyUpper = yTrue+noiseAmp*np.random.random(Npoints).reshape(Npoints,1)+bias\n",
    "yNoisyLower = yTrue-noiseAmp*np.random.random(Npoints).reshape(Npoints,1)-bias\n",
    "yNoisy = np.concatenate((yNoisyLower,yNoisyUpper),axis=0)\n",
    "plt.scatter(x,yNoisyUpper,label='Class 1')\n",
    "plt.scatter(x,yNoisyLower,label='Class 0')\n",
    "\n",
    "plt.plot(x,yTrue,'r-',label='Decision boundary')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('True f(x,y)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "X = np.concatenate((x,x),axis=0)\n",
    "print(f\"Original X.shape: {X.shape}\")\n",
    "X = np.concatenate((X,yNoisy),axis=1)\n",
    "print(f\"X.shape after adding the labels: {X.shape}\")\n",
    "y = np.concatenate((np.zeros((Npoints,1)),np.ones((Npoints,1))),axis=0)\n",
    "print(f\"y.shape for the labels: {y.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def sigma(z):\n",
    "    '''Computes the sigmoid for a numpy array z\n",
    "    '''\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def computeGradient(x,y,z):\n",
    "    '''Computes the gradient for the cross entropy loss function. x,y are (n,) numPy arrays, signifying the 2 features.\n",
    "       z =  theta0+theta1x+theta2y is an (n,) numPy array. Returns the (3,) gradient at the current iteration.\n",
    "    '''\n",
    "    n = x.shape[0]\n",
    "    sigma_z = sigma(z)\n",
    "#     print(f\"sigma_z: {sigma_z}\")\n",
    "#     print(f\"sigma_z.shape: {sigma_z.shape}\")\n",
    "#     estimation_error = (y/sigma_z)-((1-y)/(1-sigma_z))\n",
    "    estimation_error = sigma_z-y\n",
    "    term1 = sum(sigma_z*(1-sigma_z)*estimation_error)\n",
    "    term2 = sum(x*sigma_z*(1-sigma_z)*estimation_error)\n",
    "    term3 = sum(y*sigma_z*(1-sigma_z)*estimation_error)\n",
    "    return (np.array([term1,term2,term3]))/n\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def GradientDescent(X,y,start,step_size,tolerance,Niter):    \n",
    "    ''' Will perform gradient descent on X (nx2), using target y (nx1) \n",
    "    '''    \n",
    "    gradNorm = 10000\n",
    "    i = 0\n",
    "    current_theta_estimate = start\n",
    "    norms = []\n",
    "    n = X.shape[0]            \n",
    "    while i<Niter and gradNorm > tolerance:        \n",
    "        z_estimate = current_theta_estimate[0]+current_theta_estimate[1]*X[:,0] + current_theta_estimate[2]*X[:,1]\n",
    "#         print(f\"z_estimate.shape = {z_estimate.shape}\")\n",
    "#         print(f\"z_estimate = {z_estimate}\")\n",
    "        grad = computeGradient(X[:,0],X[:,1],z_estimate)\n",
    "#         print(f\"grad = {grad}\")\n",
    "        gradNorm = np.linalg.norm(grad)\n",
    "        norms.append(gradNorm)        \n",
    "        current_theta_estimate = current_theta_estimate - step_size*grad\n",
    "        i+=1\n",
    "    plt.plot(np.array(list(range(1,i+1))),norms)\n",
    "    plt.xlabel('Iterations')\n",
    "    plt.ylabel('||gradient||')\n",
    "    plt.grid(True)\n",
    "    plt.title(\"Convergence of gradient descent\")\n",
    "    print(f\"Started at location {start}\")\n",
    "    print(f\"Finished with {i} iterations\")\n",
    "    print(f\"Finished with gradient norm = {gradNorm}\")\n",
    "    print(f\"Finished at location {current_theta_estimate}\")\n",
    "    return current_theta_estimate\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def VanillaLogisticRegression(X,y):    \n",
    "    '''Assumes that the input matrix is an nx2 numPy array with n observations and y is an nx1 target vector \n",
    "    '''\n",
    "    n = X.shape[0]\n",
    "    theta_estimate_start = np.random.rand(3)\n",
    "    theta_estimate_start = np.array([-cTrue,mTrue,1])\n",
    "    learning_rate = 1e-6\n",
    "    err_tolerance = 1e-6\n",
    "    MaxIter = 1000\n",
    "    estimated_coeff = GradientDescent(X,y,theta_estimate_start,learning_rate,err_tolerance,MaxIter)\n",
    "    return estimated_coeff\n",
    "\n",
    "    \n",
    "    \n",
    "    \n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Started at location [-1.5  2.5  1. ]\n",
      "Finished with 1000 iterations\n",
      "Finished with gradient norm = 0.006429355181319465\n",
      "Finished at location [-1.50000143  2.49999781  1.00000587]\n",
      "theta estimated [ theta0,theta1, theta2]: [-1.50000143  2.49999781  1.00000587]\n",
      "Slope estimated : 2.499983124637193\n",
      "Original slope : 2.5\n",
      "Intercept estimated : 1.4999926149639653\n",
      "Original intercept : 1.5\n",
      "[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]\n",
      "Sum error: 392.0\n",
      "Error probability : 0.196\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=y.reshape(2000,)\n",
    "theta_est = VanillaLogisticRegression(X,y)\n",
    "print(f\"theta estimated [ theta0,theta1, theta2]: {theta_est}\")\n",
    "m_est  = theta_est[1]/theta_est[2]\n",
    "c_est = -theta_est[0]/theta_est[2]\n",
    "y_decision_boundary = m_est*X[:,0] -c_est\n",
    "print(f\"Slope estimated : {m_est}\")\n",
    "print(f\"Original slope : {mTrue}\")\n",
    "print(f\"Intercept estimated : {c_est}\")\n",
    "print(f\"Original intercept : {cTrue}\")\n",
    "y_pred_algo = list(map(lambda q: 0 if q<0 else 1,X[:,1]-y_decision_boundary))\n",
    "print(y_pred_algo[Npoints-5:Npoints+6])\n",
    "sumErr = sum(abs(y_pred_algo-y))\n",
    "print(f\"Sum error: {sumErr}\")\n",
    "errRate = sumErr/(2*Npoints)\n",
    "print(f\"Error probability : {errRate}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "logReg = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\saurmisr\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='warn', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logReg.fit(X,y)\n",
    "# print(X.shape)\n",
    "# print(y.shape)\n",
    "# X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
    "#     Training vector, where n_samples is the number of samples and\n",
    "#     n_features is the number of features.\n",
    "\n",
    "# y : array-like, shape (n_samples,)\n",
    "#     Target vector relative to X. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions change at this point!\n",
      "[0. 0. 0. 1. 1. 1.]\n",
      "Prediction Probabilities change at this point!\n",
      "[[9.99995938e-01 4.06237420e-06]\n",
      " [9.99929469e-01 7.05314677e-05]\n",
      " [9.99996094e-01 3.90593689e-06]\n",
      " [1.24086584e-06 9.99998759e-01]\n",
      " [9.60709027e-05 9.99903929e-01]\n",
      " [5.86315523e-06 9.99994137e-01]]\n",
      "Estimated Coefficients:[theta0,theta1,theta2] : \n",
      "[[-0.0928818  -1.66790126  0.65827048]]\n",
      "Slope estimated : 2.533762828759853\n",
      "Original slope : 2.5\n",
      "Intercept estimated : 0.14109975758143\n",
      "Original intercept : 1.5\n"
     ]
    }
   ],
   "source": [
    "y_pred = logReg.predict(X)\n",
    "y_pred = logReg.predict(X)\n",
    "prob_pred = logReg.predict_proba(X)\n",
    "print(\"Predictions change at this point!\")\n",
    "print(y_pred[Npoints-3:Npoints+3])\n",
    "print(\"Prediction Probabilities change at this point!\")\n",
    "print(prob_pred[Npoints-3:Npoints+3,:])\n",
    "theta_est_skl = np.concatenate((np.array([logReg.intercept_]),logReg.coef_),axis=1)\n",
    "print(\"Estimated Coefficients:[theta0,theta1,theta2] : \")\n",
    "print(theta_est_skl)\n",
    "m_est_skl  = -theta_est_skl[0,1]/theta_est_skl[0,2]\n",
    "c_est_skl = -theta_est_skl[0,0]/theta_est_skl[0,2]\n",
    "print(f\"Slope estimated : {m_est_skl}\")\n",
    "print(f\"Original slope : {mTrue}\")\n",
    "print(f\"Intercept estimated : {c_est_skl}\")\n",
    "print(f\"Original intercept : {cTrue}\")\n",
    "y_decision_boundary_est = m_est_skl*x + c_est_skl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_decision_boundary = m_est*x + c_est\n",
    "plt.plot(x,yTrue,'b-',label='Original decision boundary')\n",
    "plt.plot(x,y_decision_boundary_est,'r-',label='Skl-Estimated decision boundary')\n",
    "plt.plot(x,y_decision_boundary,'k-',label='Estimated decision boundary')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Original vs Estimated Decision boundary')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}