linear-regression-demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression\n",
    "\n",
    "The goal of this project was to build a linear regression model from the ground up using numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "#imports\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Import the data\n",
    "Here, we're using a dataset with two columns containing the amount of hours studied and the test scores students achieved, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pHsRa4I2S7gTekDw3M7OKVDqTOiJuBG5MHv8YOKnK8piZ2S51akGYmVmNOECY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\nZmapHCDMzCyVA4SZmaX6/0N/eEipr4MtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116110438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = genfromtxt('data.csv', delimiter=',')\n",
    "\n",
    "#Extract columns\n",
    "x = array(points[:,0])\n",
    "y = array(points[:,1])\n",
    "\n",
    "#Plot the dataset\n",
    "plt.scatter(x,y)\n",
    "plt.xlabel('Hours of study')\n",
    "plt.ylabel('Test scores')\n",
    "plt.title('Dataset')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining the hyperparamters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#hyperparamters\n",
    "learning_rate = 0.0001\n",
    "initial_b = 0\n",
    "initial_m = 0\n",
    "num_iterations = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_cost(b, m, points):\n",
    "    total_cost = 0\n",
    "    N = float(len(points))\n",
    "    \n",
    "    #Compute sum of squared errors\n",
    "    for i in range(0, len(points)):\n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        total_cost += (y - (m * x + b)) ** 2\n",
    "        \n",
    "    #Return average of squared error\n",
    "    return total_cost/N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define Gradient Descent functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):\n",
    "    b = starting_b\n",
    "    m = starting_m\n",
    "    cost_graph = []\n",
    "\n",
    "    #For every iteration, optimize b, m and compute its cost\n",
    "    for i in range(num_iterations):\n",
    "        cost_graph.append(compute_cost(b, m, points))\n",
    "        b, m = step_gradient(b, m, array(points), learning_rate)\n",
    "\n",
    "    return [b, m, cost_graph]\n",
    "\n",
    "def step_gradient(b_current, m_current, points, learning_rate):\n",
    "    m_gradient = 0\n",
    "    b_gradient = 0\n",
    "    N = float(len(points))\n",
    "\n",
    "    #Calculate Gradient\n",
    "    for i in range(0, len(points)):\n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        m_gradient += - (2/N) * x * (y - (m_current * x + b_current))\n",
    "        b_gradient += - (2/N) * (y - (m_current * x + b_current))\n",
    "    \n",
    "    #Update current m and b\n",
    "    m_updated = m_current - learning_rate * m_gradient\n",
    "    b_updated = b_current - learning_rate * b_gradient\n",
    "\n",
    "    #Return updated parameters\n",
    "    return b_updated, m_updated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Run gradient_descent_runner() to get optimized parameters b and m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized b: 0.0296393478747\n",
      "Optimized m: 1.47741737555\n",
      "Minimized cost: 112.655851815\n"
     ]
    }
   ],
   "source": [
    "b, m, cost_graph = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)\n",
    "\n",
    "#Print optimized parameters\n",
    "print ('Optimized b:', b)\n",
    "print ('Optimized m:', m)\n",
    "\n",
    "#Print error with optimized parameters\n",
    "print ('Minimized cost:', compute_cost(b, m, points))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting the cost per iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jjKNb+J25LcyZ1ph2qWY2DJ+2cnikavOObu5/dj2/fGY99z7TsfuKrdZpjfmj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\nlyNmB4sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe24198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost_graph)\n",
    "plt.xlabel('No. of iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost per iteration')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent converges to local minimum after 5 iterations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot line of best fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11946af98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot dataset\n",
    "plt.scatter(x, y)\n",
    "#Predict y values\n",
    "pred = m * x + b\n",
    "#Plot predictions as line of best fit\n",
    "plt.plot(x, pred, c='r')\n",
    "plt.xlabel('Hours of study')\n",
    "plt.ylabel('Test scores')\n",
    "plt.title('Line of best fit')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}