LogisticRegression_simple_py3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression Using numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 35,
   "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": 36,
   "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"
     ]
    }
   ],
   "source": [
    "X=np.array(xx)\n",
    "y=np.array(y)\n",
    "print(X.shape)\n",
    "print ( type(X))\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 2)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "print(X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 15,
   "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": 16,
   "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": 40,
   "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": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0.]\n",
      "[ 1. 10.] [ 1. 10.]\n"
     ]
    }
   ],
   "source": [
    "print(theta) \n",
    "print(X[0], X[0].T)  #Same because transposing 1D array is still 1D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training started\n",
      "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": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-13.47594347   0.38992892]\n"
     ]
    }
   ],
   "source": [
    "print(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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": 24,
   "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": 25,
   "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": 44,
   "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(prd, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix \n",
    "from sklearn.metrics import classification_report "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": 28,
   "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2)\n"
     ]
    }
   ],
   "source": [
    "nx=np.array([[1 ,55]])\n",
    "print(nx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.99965449] 1.0\n"
     ]
    }
   ],
   "source": [
    "fp=predict(nx, theta)\n",
    "print(fp , fp[0].round())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.004277120964536875, 0.004277117287301942, 0.004277113610073303, 0.004277109932850914, 0.0042771062556347895, 0.004277102578424993, 0.004277098901221446, 0.004277095224024226, 0.00427709154683324, 0.004277087869648487]\n"
     ]
    }
   ],
   "source": [
    "print(cost_history[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}