Logistic Regression from scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seed = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dataset = pd.read_csv('Social_Network_Ads.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>User ID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>EstimatedSalary</th>\n",
       "      <th>Purchased</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15624510</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>19000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15810944</td>\n",
       "      <td>Male</td>\n",
       "      <td>35</td>\n",
       "      <td>20000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>15668575</td>\n",
       "      <td>Female</td>\n",
       "      <td>26</td>\n",
       "      <td>43000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15603246</td>\n",
       "      <td>Female</td>\n",
       "      <td>27</td>\n",
       "      <td>57000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>15804002</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>76000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    User ID  Gender  Age  EstimatedSalary  Purchased\n",
       "0  15624510    Male   19            19000          0\n",
       "1  15810944    Male   35            20000          0\n",
       "2  15668575  Female   26            43000          0\n",
       "3  15603246  Female   27            57000          0\n",
       "4  15804002    Male   19            76000          0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 400 entries, 0 to 399\n",
      "Data columns (total 5 columns):\n",
      "User ID            400 non-null int64\n",
      "Gender             400 non-null object\n",
      "Age                400 non-null int64\n",
      "EstimatedSalary    400 non-null int64\n",
      "Purchased          400 non-null int64\n",
      "dtypes: int64(4), object(1)\n",
      "memory usage: 15.7+ KB\n"
     ]
    }
   ],
   "source": [
    "dataset.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    257\n",
       "1    143\n",
       "Name: Purchased, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset['Purchased'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Prepocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = dataset.iloc[:, [2, 3]].values\n",
    "Y = dataset.iloc[:, 4].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = Y.reshape(400,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(400, 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gp/anaconda3/lib/python3.6/site-packages/sklearn/cross_validation.py:41: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.25, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gp/anaconda3/lib/python3.6/site-packages/sklearn/utils/validation.py:475: DataConversionWarning: Data with input dtype int64 was converted to float64 by StandardScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()\n",
    "X_train = sc.fit_transform(X_train)\n",
    "X_test = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(300, 2)\n",
      "(100, 2)\n",
      "(300, 1)\n",
      "(100, 1)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    z -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(z)\n",
    "    \"\"\"\n",
    "\n",
    "    s = 1/(1+np.exp(-z))\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_with_zeros(dim):\n",
    "    \"\"\"\n",
    "    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.\n",
    "    \n",
    "    Argument:\n",
    "    dim -- size of the w vector we want (or number of parameters in this case)\n",
    "    \n",
    "    Returns:\n",
    "    w -- initialized vector of shape (dim, 1)\n",
    "    b -- initialized scalar (corresponds to the bias)\n",
    "    \"\"\"\n",
    "    w = np.zeros((dim,1)) * 0.01\n",
    "    b = 0\n",
    "\n",
    "    assert(w.shape == (dim, 1))\n",
    "    assert(isinstance(b, float) or isinstance(b, int))\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forward and Backward propagation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def propagate(w, b, X, Y):\n",
    "    \"\"\"\n",
    "    Implements the cost function and its gradients\n",
    "\n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (dim, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (number of examples, 2)\n",
    "    Y -- true \"label\" vector (0 or 1) of size (number of examples, 1)\n",
    "\n",
    "    Return:\n",
    "    cost -- negative log-likelihood cost for logistic regression\n",
    "    dw -- gradient of the loss with respect to w, thus same shape as w\n",
    "    db -- gradient of the loss with respect to b, thus same shape as b\n",
    "    \"\"\"\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    \n",
    "    # FORWARD PROPAGATION (FROM X TO COST)\n",
    "    A = sigmoid(np.dot(X, w) + b)               \n",
    "    loss = - (Y * np.log(A) + (1-Y)* np.log(1-A))\n",
    "    cost =  np.sum(loss) / m                           \n",
    " \n",
    "    # BACKWARD PROPAGATION (TO FIND GRAD)\n",
    "    dw = np.dot(X.T, (A-Y)) / m\n",
    "    db = np.sum(A - Y) / m\n",
    "\n",
    "    assert(dw.shape == w.shape)\n",
    "    assert(db.dtype == float)\n",
    "    cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return grads, cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):\n",
    "    \"\"\"\n",
    "    This function optimizes w and b by running a gradient descent algorithm\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (2, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of shape (number of examples, 2)\n",
    "    Y -- true \"label\" vector (0 or 1) of size (number of examples, 1)\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    learning_rate -- learning rate of the gradient descent update rule\n",
    "    print_cost -- True to print the loss every 100 steps\n",
    "    \n",
    "    Returns:\n",
    "    params -- dictionary containing the weights w and bias b\n",
    "    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function\n",
    "    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.\n",
    "    \"\"\"\n",
    "    \n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        \n",
    "        \n",
    "        # Cost and gradient calculation\n",
    "        grads, cost = propagate(w, b, X, Y)\n",
    "        \n",
    "        # Retrieve derivatives from grads\n",
    "        dw = grads[\"dw\"]\n",
    "        db = grads[\"db\"]\n",
    "        \n",
    "        # update rule\n",
    "        w = w - learning_rate * dw\n",
    "        \n",
    "        # Record the costs\n",
    "        if i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "        \n",
    "        # Print the cost every 100 training iterations\n",
    "        if print_cost and i % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "    \n",
    "    params = {\"w\": w,\n",
    "              \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return params, grads, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict(w, b, X):\n",
    "    '''\n",
    "    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (2, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (number of examples, 2)\n",
    "    \n",
    "    Returns:\n",
    "    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X\n",
    "    '''\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    Y_prediction = np.zeros((m,1))\n",
    "    w = w.reshape(X.shape[1], 1)\n",
    "    \n",
    "    # Compute vector \"A\" predicting the probabilities of a test point\n",
    "    A = sigmoid(np.dot(X, w) + b)\n",
    "    \n",
    "    for i in range(A.shape[0]):\n",
    "        \n",
    "        # Convert probabilities A[0,i] to actual predictions p[0,i]\n",
    "        if A[i][0] > 0.5:\n",
    "            Y_prediction[i][0]=1\n",
    "        else:\n",
    "            Y_prediction[i][0]=0\n",
    "        pass\n",
    "    \n",
    "    assert(Y_prediction.shape == (m, 1))\n",
    "    \n",
    "    return Y_prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):\n",
    "\n",
    "    # initialize parameters with zeros\n",
    "    w, b = initialize_with_zeros(X_train.shape[1])\n",
    "\n",
    "    # Gradient descent\n",
    "    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)\n",
    "    \n",
    "    # Retrieve parameters w and b from dictionary \"parameters\"\n",
    "    w = parameters[\"w\"]\n",
    "    b = parameters[\"b\"]\n",
    "    \n",
    "    # Predict test/train set examples \n",
    "    Y_prediction_test = predict(w, b, X_test)\n",
    "    Y_prediction_train = predict(w, b, X_train)\n",
    "\n",
    "    # Print train/test Errors\n",
    "    print(\"train accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))\n",
    "    print(\"test accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))\n",
    "\n",
    "    \n",
    "    d = {\"costs\": costs,\n",
    "         \"Y_prediction_test\": Y_prediction_test, \n",
    "         \"Y_prediction_train\" : Y_prediction_train, \n",
    "         \"w\" : w, \n",
    "         \"b\" : b,\n",
    "         \"learning_rate\" : learning_rate,\n",
    "         \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693147\n",
      "Cost after iteration 100: 0.682202\n",
      "Cost after iteration 200: 0.671855\n",
      "Cost after iteration 300: 0.662072\n",
      "Cost after iteration 400: 0.652820\n",
      "Cost after iteration 500: 0.644067\n",
      "Cost after iteration 600: 0.635784\n",
      "Cost after iteration 700: 0.627942\n",
      "Cost after iteration 800: 0.620514\n",
      "Cost after iteration 900: 0.613474\n",
      "Cost after iteration 1000: 0.606799\n",
      "Cost after iteration 1100: 0.600466\n",
      "Cost after iteration 1200: 0.594454\n",
      "Cost after iteration 1300: 0.588743\n",
      "Cost after iteration 1400: 0.583315\n",
      "Cost after iteration 1500: 0.578151\n",
      "Cost after iteration 1600: 0.573237\n",
      "Cost after iteration 1700: 0.568558\n",
      "Cost after iteration 1800: 0.564098\n",
      "Cost after iteration 1900: 0.559845\n",
      "train accuracy: 82.0 %\n",
      "test accuracy: 85.0 %\n"
     ]
    }
   ],
   "source": [
    "d = model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.001, print_cost = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z5BSgsBApQEkJcdx1/hl8fl9XUupV5pGPFtHj+anMWbc994VFYkhhIRIDdaqU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1096f5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "costs = np.squeeze(d['costs'])\n",
    "plt.plot(costs)\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (per hundreds)')\n",
    "plt.title(\"Learning rate =\" + str(d[\"learning_rate\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "learning rate is: 1\n",
      "train accuracy: 81.0 %\n",
      "test accuracy: 84.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.1\n",
      "train accuracy: 81.0 %\n",
      "test accuracy: 84.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.01\n",
      "train accuracy: 81.0 %\n",
      "test accuracy: 84.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.001\n",
      "train accuracy: 81.33333333333333 %\n",
      "test accuracy: 85.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.0001\n",
      "train accuracy: 81.33333333333333 %\n",
      "test accuracy: 85.0 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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zZoo2baJo40byFi4iZ66n9eFwYO3XF1vfvtj79cPapw/GkJBAfgWBH6coV0oZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b43def0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rates = [1, 0.1, 0.01, 0.001, 0.0001]\n",
    "models = {}\n",
    "for i in learning_rates:\n",
    "    print (\"learning rate is: \" + str(i))\n",
    "    models[str(i)] = model(X_train, Y_train, X_test, Y_test, num_iterations = 1500, learning_rate = i, print_cost = False)\n",
    "    print ('\\n' + \"-------------------------------------------------------\" + '\\n')\n",
    "\n",
    "for i in learning_rates:\n",
    "    plt.plot(np.squeeze(models[str(i)][\"costs\"]), label= str(models[str(i)][\"learning_rate\"]))\n",
    "\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (hundreds)')\n",
    "\n",
    "legend = plt.legend(loc='upper center', shadow=True)\n",
    "frame = legend.get_frame()\n",
    "frame.set_facecolor('0.90')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": 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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}