linear-regression-demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression - Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# imports\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "source": [
    "#### Import the data\n",
    "Here, we're using a dataset with two features representing how cool Toms are across the world are based on how many backgrounds effects they used."
   ],
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   }
  },
  {
   "source": [
    "# get data from CSV (dataset)\n",
    "points = genfromtxt('data.csv', delimiter=',')\n",
    "\n",
    "# extract columns (select features)\n",
    "x = array(points[:,0])\n",
    "y = array(points[:,1])\n",
    "\n",
    "# plot the dataset\n",
    "plt.scatter(x,y)\n",
    "plt.xlabel('Backgrounds Toms Used')\n",
    "plt.ylabel('How Cool A Tom Is')\n",
    "plt.title('Dataset Plot')\n",
    "plt.show()"
   ],
   "cell_type": "code",
   "metadata": {
    "collapsed": false
   },
   "execution_count": 60,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining the hyperparamters.\n",
    "Hyperparamters lets us control speed and complexity "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# hyperparamters\n",
    "learning_rate = 0.000001 # step closer to better b and m values\n",
    "# y = mx + b\n",
    "initial_b = 0 # starting y intercept\n",
    "initial_m = 0 # starting slope value\n",
    "num_iterations = 1000 # number of iternations to improve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Sum of squares: it is a measure of the discrepancy between the data and an estimation model\n",
    "# https://en.wikipedia.org/wiki/Residual_sum_of_squares\n",
    "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": 63,
   "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": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Optimized b: 0.029472081221699396\nOptimized m: 1.4689072254569766\nMinimized cost: 112.89968139674588\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": 65,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "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": [
    "#### Plot line of best fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent converges to local minimum after 5 iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
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     }
    }
   ],
   "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('Backgrounds Toms Used')\n",
    "plt.ylabel('How Cool A Tom Is')\n",
    "plt.title('Line of best fit')\n",
    "plt.show()"
   ]
  }
 ],
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