Code-Example-016.1-LogisticRegression-without-lib.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression implementation without Scikit-learn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.stats import norm\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "from matplotlib import pyplot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib.cm as cm\n",
    "from random import sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating Some Example Data with 2 Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_feature = 2 # the number of features\n",
    "n_components = 2 # the number of clusters\n",
    "\n",
    "n = 1000 # the number of total samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.21895948,  -9.0632939 ],\n",
       "       [ -1.17379771,  -4.92688779],\n",
       "       [  0.79041678, -14.59641646],\n",
       "       ...,\n",
       "       [ -0.78260563, -21.50260563],\n",
       "       [ -3.21323086, -13.90436388],\n",
       "       [ -1.40482172,  -9.1035902 ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generate isotropic Gaussian blobs (data from mixture Gaussian distributions)\n",
    "X, y = make_blobs(n_samples=n, # the number of total samples\n",
    "                  centers=n_components, # the number of clusters\n",
    "                  n_features=n_feature, # the number of features\n",
    "                  cluster_std = [5] * n_components, # the std of each cluster\n",
    "                  random_state=2) # 2\n",
    "\n",
    "# X = np.hstack((np.ones((m, 1)), X))\n",
    "\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [ 2.21895948 -9.0632939 ] , y = 1\n",
      "x = [-1.17379771 -4.92688779] , y = 0\n",
      "x = [  0.79041678 -14.59641646] , y = 0\n",
      "x = [-0.98141459 -0.14837778] , y = 1\n",
      "x = [ 6.64249161 -1.88234499] , y = 1\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    print('x =', X[i, ], ', y =', y[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 0, 1, 0, 1, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Just to show you what is inside it. We print the first 10 elements of this numpy array. \n",
    "y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "# scatter plot, data points annotated by different colors\n",
    "df = pd.DataFrame(dict(feature_1=X[:,0], feature_2=X[:,1], label=y))\n",
    "\n",
    "\n",
    "cluster_name = set(y)\n",
    "colors = dict(zip(cluster_name, cm.rainbow(np.linspace(0, 1, len(cluster_name)))))\n",
    "fig, ax = pyplot.subplots()\n",
    "\n",
    "grouped = df.groupby('label')\n",
    "\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='feature_1', y='feature_2', label=key, color=colors[key].reshape(1,-1))\n",
    "    \n",
    "pyplot.title('Original 2D Data from {} Clusters'.format(n_components))\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Create Test/Train\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    To convert continuous value into a range of 0 to 1\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    z : Continuous value\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    Value in range between 0 to 1.\n",
    "    \"\"\"\n",
    "    g = 1 / (1 + np.exp(-z))\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(X, y, weights):\n",
    "    \"\"\"\n",
    "    Compute cost for logistic regression.\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "        Dimension (n x d)\n",
    "        n = number of training examples\n",
    "        d = number of features (including X_0 column of ones)\n",
    "    y : 1D array of labels/target value for each traing example. dimension(1 x n)\n",
    "\n",
    "    weights : 1D array of fitting parameters or weights. Dimension (1 x d)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    cost : The cost of using theta as the parameter for linear regression to fit the data points in X and y.\n",
    "    \"\"\"\n",
    "    n, d = X.shape\n",
    "    x_dot_weights = X.dot(weights)\n",
    "\n",
    "    cost = 1.0 / n * (-y.T.dot(np.log(sigmoid(x_dot_weights))) - (1 - y).T.dot(np.log(1 - sigmoid(x_dot_weights))))\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(X, y, weights):\n",
    "    \"\"\"\n",
    "    Compute gradient for logistic regression.\n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "    Dimension(m x n)\n",
    "        m = number of training examples\n",
    "        n = number of features (including X_0 column of ones)\n",
    "    y : 1D array of labels/target value for each traing example. dimension(1 x m)\n",
    "\n",
    "    weights : 1D array of fitting parameters or weights. Dimension (1 x n)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    grad: (numpy array)The gradient of the cost with respect to the parameters theta\n",
    "    \"\"\"\n",
    "    n, d = X.shape\n",
    "    x_dot_weights = X.dot(weights)\n",
    "\n",
    "    grad = (1.0 / n )* (sigmoid(x_dot_weights) - y).T.dot(X)\n",
    "\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6931471805599452\n",
      "[-0.67306356 -2.04334234]\n"
     ]
    }
   ],
   "source": [
    "weights = np.zeros(3)\n",
    "\n",
    "\n",
    "cost = cost_function(X_train, y_train, weights)\n",
    "grad = gradient(X_train, y_train, weights)\n",
    "\n",
    "print(cost)\n",
    "print(grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost is:  0.6931471805599452\n",
      "Cost is:  0.6511134846383863\n",
      "Cost is:  0.6229190405104337\n",
      "Cost is:  0.6036035082550789\n",
      "Cost is:  0.5900191803151973\n",
      "Cost is:  0.5802123005192352\n",
      "Cost is:  0.5729596806860497\n",
      "Cost is:  0.5674791245365727\n",
      "Cost is:  0.5632577662507976\n",
      "Cost is:  0.5599508128988057\n",
      "Cost is:  0.5573209544439478\n",
      "Cost is:  0.5552013119692716\n",
      "Cost is:  0.5534722323572873\n",
      "Cost is:  0.5520464066691345\n",
      "Cost is:  0.5508591097625557\n",
      "Cost is:  0.5498616639131213\n",
      "Cost is:  0.5490169768875469\n",
      "Cost is:  0.5482964423386212\n",
      "Cost is:  0.5476777519263867\n",
      "Cost is:  0.5471433283213929\n",
      "Cost is:  0.5466791878435845\n",
      "Cost is:  0.5462741047978773\n",
      "Cost is:  0.5459189905440346\n",
      "Cost is:  0.5456064273138438\n",
      "Cost is:  0.5453303148290212\n",
      "Cost is:  0.5450856000165374\n",
      "Cost is:  0.5448680685411954\n",
      "Cost is:  0.5446741827442848\n",
      "Cost is:  0.5445009547150678\n",
      "Cost is:  0.5443458461715964\n",
      "Cost is:  0.5442066889517527\n",
      "Cost is:  0.5440816214600913\n",
      "Cost is:  0.5439690375493144\n",
      "Cost is:  0.5438675451535706\n",
      "Cost is:  0.5437759326158412\n",
      "Cost is:  0.5436931411211442\n",
      "Cost is:  0.543618242002312\n",
      "Cost is:  0.5435504179553222\n",
      "Cost is:  0.5434889474080857\n",
      "Cost is:  0.5434331914459675\n",
      "Cost is:  0.5433825828207332\n",
      "Cost is:  0.5433366166656732\n",
      "Cost is:  0.5432948426148074\n",
      "Cost is:  0.5432568580831242\n",
      "Cost is:  0.5432223025114467\n",
      "Cost is:  0.5431908524164782\n",
      "Cost is:  0.5431622171160342\n",
      "Cost is:  0.5431361350230083\n",
      "Cost is:  0.5431123704205175\n",
      "Cost is:  0.5430907106459192\n",
      "Cost is:  0.5430709636237131\n",
      "Cost is:  0.5430529556973651\n",
      "Cost is:  0.5430365297182581\n",
      "Cost is:  0.5430215433566582\n",
      "Cost is:  0.5430078676050905\n",
      "Cost is:  0.5429953854490447\n",
      "Cost is:  0.5429839906836916\n",
      "Cost is:  0.542973586858408\n",
      "Cost is:  0.542964086333523\n",
      "Cost is:  0.5429554094358684\n",
      "Cost is:  0.5429474837015621\n",
      "Cost is:  0.5429402431959987\n",
      "Cost is:  0.5429336279023322\n",
      "Cost is:  0.5429275831708597\n",
      "Cost is:  0.5429220592226568\n",
      "Cost is:  0.5429170107016453\n",
      "Cost is:  0.5429123962699641\n",
      "Cost is:  0.5429081782421266\n",
      "Cost is:  0.5429043222539709\n",
      "Cost is:  0.542900796962862\n",
      "Cost is:  0.5428975737760048\n",
      "Cost is:  0.5428946266040695\n",
      "Cost is:  0.5428919316376376\n",
      "Cost is:  0.5428894671442426\n",
      "Cost is:  0.5428872132840112\n",
      "Cost is:  0.542885151942124\n",
      "Cost is:  0.5428832665764897\n",
      "Cost is:  0.5428815420792007\n",
      "Cost is:  0.54287996465047\n",
      "Cost is:  0.5428785216838873\n",
      "Cost is:  0.5428772016619454\n",
      "Cost is:  0.5428759940608846\n",
      "Cost is:  0.5428748892640024\n",
      "Cost is:  0.5428738784826549\n",
      "Cost is:  0.5428729536842463\n",
      "Cost is:  0.5428721075265764\n",
      "Cost is:  0.542871333297972\n",
      "Cost is:  0.5428706248626766\n",
      "Cost is:  0.5428699766110342\n",
      "Cost is:  0.5428693834140316\n",
      "Cost is:  0.5428688405818161\n",
      "Cost is:  0.5428683438258309\n",
      "Cost is:  0.5428678892242494\n",
      "Cost is:  0.5428674731904173\n",
      "Cost is:  0.5428670924440339\n",
      "Cost is:  0.5428667439848356\n",
      "Cost is:  0.5428664250685578\n",
      "Cost is:  0.5428661331849772\n",
      "Cost is:  0.5428658660378528\n",
      "Cost is:  0.5428656215265973\n"
     ]
    }
   ],
   "source": [
    "weights = np.zeros(3)\n",
    "\n",
    "\n",
    "# Now we optimize it using Gradient Descent. \n",
    "num_iterations = 100\n",
    "learnin_rate = 0.01\n",
    "\n",
    "cost_list = []\n",
    "\n",
    "\n",
    "# Implementation here is removed. \n",
    "\n",
    "# Your task to implement the GD here. \n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    \n",
    "    # \n",
    "    # Calculate the costs \n",
    "    ..... \n",
    "    \n",
    "    print(\"Cost is: \", cost)\n",
    "    # keep the costs for our visualization later \n",
    "    \n",
    "    cost_list.append(cost)\n",
    "    \n",
    "    # Calculate the gradients [CODE REMOVED]\n",
    "    ....\n",
    "    \n",
    "    # Use the gradient to update the weights [CODE REMOVED] \n",
    "    ....\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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.plot(np.arange(num_iterations), cost_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(weights, X):\n",
    "    \"\"\"\n",
    "    Predict the class between 0 and 1 using learned logistic regression parameters weights.\n",
    "    Using threshold value 0.5 to convert probability value to class value \n",
    "\n",
    "    I/P\n",
    "    ----------\n",
    "    X : 2D array where each row represent the training example and each column represent the feature ndarray. \n",
    "        Dimension(n x d)\n",
    "        n= number of training examples\n",
    "        d= number of features (including X_0 column of ones)\n",
    "\n",
    "    theta : 1D array of fitting parameters or weights. Dimension (1 x n)\n",
    "\n",
    "    O/P\n",
    "    -------\n",
    "    Class type based on threshold\n",
    "    \"\"\"\n",
    "    p = sigmoid(X.dot(weights)) >= 0.5\n",
    "    return p.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n",
       "       1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,\n",
       "       0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       0, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = predict(weights, X_test)\n",
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0,\n",
       "       1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0,\n",
       "       0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1,\n",
       "       1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,\n",
       "       1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1,\n",
       "       1, 1])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy is:  0.7\n"
     ]
    }
   ],
   "source": [
    "# Correct Predictions are the cases that are equal. \n",
    "\n",
    "correct = np.sum(predictions == y_test)\n",
    "\n",
    "\n",
    "print(\"Accuracy is: \", correct/y_test.size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}