Assignment2_Exercise1_Multivariate Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assignment2.Exercise1: Multivariate Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt('GPUbenchmark.csv' ,delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18, 7)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X =  data[:,0:6]\n",
    "y = data[:,6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question. Normalizing X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(X):\n",
    "    means = X.mean(axis=0)\n",
    "    stds = X.std(axis=0)\n",
    "    \n",
    "    def normal_(x):\n",
    "        return (x - means) / stds\n",
    "    \n",
    "    return normal_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "func_normal=normalize(X)\n",
    "normalX = func_normal(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 6)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(normalX.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question2. Plot X vs y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1080 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20, 15))\n",
    "for c in range(normalX.shape[1]):\n",
    "    plt.subplot(2,3, c+1)\n",
    "    plt.plot(normalX[:, c], y, 'o', alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question3. Compute beta using the normal equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Vectorization \n",
    "#Extending Xe\n",
    "Xe = np.c_[np.ones((normalX.shape[0],1)),normalX]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Normaal Equation: beta\n",
    "beta = np.linalg.inv(Xe.T.dot(Xe)).dot(Xe.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([65.18888889, 18.05577085, -5.3521726 , 13.04504442,  4.19572708,\n",
       "       10.04004069,  1.26250957])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "110.80403513783277"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test = np.array([2432, 1607, 1683, 8, 8, 256])\n",
    "normal_test = func_normal(test)\n",
    "normal_test_e = np.insert(normal_test,0,1)\n",
    "\n",
    "\n",
    "predicted = np.sum(normal_test_e.dot(beta))\n",
    "predicted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question4. cost J(beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.396444360915678"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cost function J\n",
    "j = np.dot(Xe,beta)-y\n",
    "J = (j.T.dot(j))/X.shape[0]\n",
    "\n",
    "J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question5.Gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta,N, rate):\n",
    "\n",
    "    for i in range(N):\n",
    "        prediction = np.dot(X, theta)  \n",
    "        error = prediction - y\n",
    "        cost = 1/(X.shape[0]) * np.dot(error.T, error) \n",
    "        theta = theta - (rate * np.dot(X.T, error))\n",
    "\n",
    "\n",
    "    print(cost)\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.39644436092588\n"
     ]
    }
   ],
   "source": [
    "init_theta = np.zeros(Xe.shape[1])\n",
    "\n",
    "theta = gradient_descent(Xe, y, theta=init_theta, N=1000000, rate=0.0001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question5(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "α =0.0001 , N = 90960 \n"
     ]
    }
   ],
   "source": [
    "cost_normalEq = J\n",
    "\n",
    "theta =  init_theta\n",
    "rate=0.0001\n",
    "i=1\n",
    "\n",
    "while True:\n",
    "    prediction = np.dot(Xe, theta)  \n",
    "    error = prediction - y\n",
    "    cost = 1/(Xe.shape[0]) * np.dot(error.T, error) \n",
    "    theta = theta - (rate * np.dot(Xe.T, error)) \n",
    "    if cost <= 1.01*cost_normalEq:\n",
    "        break\n",
    "    else :\n",
    "        i +=1\n",
    "        continue\n",
    "\n",
    "print(\"α ={} , N = {} \".format(rate,i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exe1.Question5(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "111.79502694112682"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predicted = np.sum(normal_test_e.dot(theta))\n",
    "predicted"
   ]
  }
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