LogisticRegression_simple_py3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Logistic Regression Using numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 20, 30, 40, 50, 60, 70]\n",
      "[0, 0, 0, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "x=[10, 20, 30, 40, 50, 60, 70]\n",
    "y=[0, 0, 0, 1, 1, 1, 1]\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.0, 10.0], [1.0, 20.0], [1.0, 30.0], [1.0, 40.0], [1.0, 50.0], [1.0, 60.0], [1.0, 70.0]]\n"
     ]
    }
   ],
   "source": [
    "xx=[ [1.0, float(ix) ] for ix in x]\n",
    "print(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 2)\n",
      "<class 'numpy.ndarray'>\n",
      "[[ 1. 10.]\n",
      " [ 1. 20.]\n",
      " [ 1. 30.]\n",
      " [ 1. 40.]\n",
      " [ 1. 50.]\n",
      " [ 1. 60.]\n",
      " [ 1. 70.]]\n",
      "[0 0 0 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "X=np.array(xx)\n",
    "y=np.array(y)\n",
    "print(X.shape)\n",
    "print ( type(X))\n",
    "print(X)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 2)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "print(X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "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": [
    "plt.scatter(x, y, color = 'red') \n",
    "plt.title('x vs y')\n",
    "plt.xlabel('x data')\n",
    "plt.ylabel('y data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "    \n",
    "def linRG(x, theta):\n",
    "    return np.dot(theta, x.T)\n",
    "\n",
    "def predict(X, theta):\n",
    "  z = linRG(X, theta)\n",
    "  return sigmoid(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(x, h, y):\n",
    "    '''\n",
    "    #     return (1 / n) * np.dot(x.T, h - y)\n",
    "    #compute partial derivative for  all( each time ith X (i.e. x1) in each row ) column. to find all thetas gradient. then average.\n",
    "    #for i=0, X=all rows ith column. this gives a column matrix. where (h-y) is a row matrix.\n",
    "    '''\n",
    "    n = x.shape[0]\n",
    "    return (1 / n) * np.dot( (h - y), X)\n",
    "\n",
    "def gradient_man(x, h, y):\n",
    "    '''compute manually. worked!\n",
    "    '''\n",
    "    gds=[]\n",
    "    for icol in range( x.shape[1] ):\n",
    "#         gd=np.dot( (h-y), x[:,icol])\n",
    "#         print('gd=',gd)\n",
    "        gd=0\n",
    "        for irow in range(x.shape[0]):\n",
    "            gd+=(h[irow]-y[irow]) *x[irow][icol]\n",
    "        gda=gd/x.shape[0]\n",
    "        gds.append(gda)\n",
    "    \n",
    "    return gds\n",
    "\n",
    "def loss(h, y):\n",
    "    return (- y * np.log(h) - (1 - y ) * np.log(1 - h) ).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 21.  41.  61.  81. 101. 121. 141.]\n",
      "[1. 1. 1. 1. 1. 1. 1.]\n",
      "[0.42857143 8.57142857]\n"
     ]
    }
   ],
   "source": [
    "#Testing Gradient Function\n",
    "theta = np.array([1,2])\n",
    "z = linRG(X, theta)\n",
    "print(z)\n",
    "h=sigmoid(z) \n",
    "print(h)\n",
    "\n",
    "gd=gradient(X, h, y)\n",
    "print(gd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0.]\n"
     ]
    }
   ],
   "source": [
    "# weights initialization\n",
    "theta = np.zeros(2)\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training started\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Python37\\lib\\site-packages\\ipykernel_launcher.py:26: RuntimeWarning: divide by zero encountered in log\n",
      "C:\\Python37\\lib\\site-packages\\ipykernel_launcher.py:26: RuntimeWarning: invalid value encountered in multiply\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training completed\n"
     ]
    }
   ],
   "source": [
    "epoch=90000\n",
    "# epoch=40\n",
    "lr=0.1\n",
    "# lr=0.01\n",
    "cost_history=[]\n",
    "\n",
    "print('training started')\n",
    "for i in range(epoch):\n",
    "    h=predict(X, theta) \n",
    "    cost=loss(h,y)\n",
    "    gd=gradient(X, h, y)\n",
    "#     gd2=gradient_man(X,h,y)\n",
    "    theta = theta-lr * gd\n",
    "    \n",
    "    cost_history.append(cost)\n",
    "    \n",
    "#     if i % 10000 == 0:\n",
    "#         print(\"iter: \"+str(i) + \" cost: \"+str(cost))\n",
    "\n",
    "print('training completed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-29.28835743   0.84097994]\n"
     ]
    }
   ],
   "source": [
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. 10.]\n",
      " [ 1. 20.]\n",
      " [ 1. 30.]\n",
      " [ 1. 40.]\n",
      " [ 1. 50.]\n",
      " [ 1. 60.]\n",
      " [ 1. 70.]]\n",
      "1.0\n",
      "[1. 1. 1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "print(X)\n",
    "print(X[0,0])\n",
    "print(X[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8.56165004e-10 3.84490213e-06 1.69738945e-02 9.87268217e-01\n",
      " 9.99997128e-01 9.99999999e-01 1.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "pd=predict(X, theta)\n",
    "print(pd) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "# for ipd in pd:\n",
    "# #     print( ipd.round()  )\n",
    "#     if ipd > 0.5:\n",
    "#         print(1)\n",
    "#     else:\n",
    "#         print(0)\n",
    "prd=[ 1 if ipd>0.5 else 0 for ipd in pd]\n",
    "print(prd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(predicted_labels, actual_labels):\n",
    "    diff = predicted_labels - actual_labels\n",
    "    return 1.0 - (float(np.count_nonzero(diff)) / len(diff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(prd, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.737493292839326e-08 0.0\n"
     ]
    }
   ],
   "source": [
    "#Prediction for new data.\n",
    "nx=np.array((1, 15))\n",
    "fp=predict(nx, theta)\n",
    "print(fp , fp.round())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6931471805599453, nan, 2.4424634306924244, 17.718350615552108, nan, nan, nan, 0.6135692171075535, nan, 0.5677908066351388]\n"
     ]
    }
   ],
   "source": [
    "print(cost_history[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "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": [
    "# npt=90000\n",
    "npt=epoch\n",
    "plt.plot(cost_history)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix \n",
    "from sklearn.metrics import classification_report "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 0]\n",
      " [0 4]]\n"
     ]
    }
   ],
   "source": [
    "results = confusion_matrix(y, prd) \n",
    "print(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00         3\n",
      "           1       1.00      1.00      1.00         4\n",
      "\n",
      "   micro avg       1.00      1.00      1.00         7\n",
      "   macro avg       1.00      1.00      1.00         7\n",
      "weighted avg       1.00      1.00      1.00         7\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print( classification_report(y, prd) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression Algorithm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#Training\n",
    "\n",
    "epoch=50000\n",
    "\n",
    "lr=0.1\n",
    "\n",
    "theta=np.array([0, 0])\n",
    "\n",
    "for i in range(epoch):\n",
    "\n",
    "\tz=linearRegression(X, theta)\n",
    "    \n",
    "\tpredict=sigmoid(z)\n",
    "    \n",
    "\tgd=gradient(predict, y, X)\n",
    "    \n",
    "\ttheta=theta- lr*gd\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#You can now print the theta\n",
    "\n",
    "#Prediction on Training data with the traind theta values.\n",
    "\n",
    "z=linearRegression(X, theta)\n",
    "\n",
    "pd=sigmoid(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculating decision boundary line.\n",
    "yy=[]\n",
    "for i in x:\n",
    "    cy=theta[0]+theta[1]*i\n",
    "#     cy=sigmoid(cy)\n",
    "    if cy>2:\n",
    "        cy=2\n",
    "    elif cy<-2:\n",
    "        cy=-2\n",
    "    yy.append(cy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "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": [
    "plt.scatter(x,y)  \n",
    "# plt.plot(px, sigmoid(np.array(py)) )  \n",
    "plt.plot(x,yy)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Expreriment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_thd(th, pd):\n",
    "    prd=[ 1 if ipd>th else 0 for ipd in pd]\n",
    "    return prd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.metrics import roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 0, 1, 1, 1, 1]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y\n",
    "prd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 0, 1, 1, 1, 1]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_thd(0.3, pd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 0, 1, 1, 1, 1]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_thd(0.9, pd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
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