2. Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/DeepLearning/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Deep Learning From Scratch</h1>\n",
    "<h1>Linear Regression</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.10.9\n",
      "IPython version      : 8.10.0\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 22.5.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 03a6cf9c5faed1d6e551b54357ff497cfa569fb9\n",
      "\n",
      "watermark : 2.4.2\n",
      "numpy     : 1.23.5\n",
      "matplotlib: 3.7.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -i -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('d4sci.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array(np.loadtxt(\"data/Anscombe1.dat\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10.    8.04]\n",
      " [ 8.    6.95]\n",
      " [13.    7.58]\n",
      " [ 9.    8.81]\n",
      " [11.    8.33]\n",
      " [14.    9.96]\n",
      " [ 6.    7.24]\n",
      " [ 4.    4.26]\n",
      " [12.   10.84]\n",
      " [ 7.    4.82]\n",
      " [ 5.    5.68]]\n"
     ]
    }
   ],
   "source": [
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[:, 0].reshape(-1, 1)\n",
    "y = data[:, 1].reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.],\n",
       "       [ 8.],\n",
       "       [13.],\n",
       "       [ 9.],\n",
       "       [11.],\n",
       "       [14.],\n",
       "       [ 6.],\n",
       "       [ 4.],\n",
       "       [12.],\n",
       "       [ 7.],\n",
       "       [ 5.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.04],\n",
       "       [ 6.95],\n",
       "       [ 7.58],\n",
       "       [ 8.81],\n",
       "       [ 8.33],\n",
       "       [ 9.96],\n",
       "       [ 7.24],\n",
       "       [ 4.26],\n",
       "       [10.84],\n",
       "       [ 4.82],\n",
       "       [ 5.68]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7a61853cd0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, '.', markersize=30, label='points')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get matrix dimensions and add the bias column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "M, N = X.shape\n",
    "X = np.concatenate((np.ones((M, 1)), X), axis=1) # Add x0 for the bias/intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. 10.]\n",
      " [ 1.  8.]\n",
      " [ 1. 13.]\n",
      " [ 1.  9.]\n",
      " [ 1. 11.]\n",
      " [ 1. 14.]\n",
      " [ 1.  6.]\n",
      " [ 1.  4.]\n",
      " [ 1. 12.]\n",
      " [ 1.  7.]\n",
      " [ 1.  5.]]\n"
     ]
    }
   ],
   "source": [
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the training parameters and initialize the weight matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01 # Step size\n",
    "epsilon = 0.12 # Maximum initial value\n",
    "\n",
    "# Initial random weights chosen uniformly between +/- epsilon\n",
    "weights = 2*np.random.rand(N+1, 1)*epsilon - epsilon\n",
    "count = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Procedure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 1.016062079312162 0.0008512756515690612 [0.33714331 0.76377468]\n",
      "200 0.93964903716122 0.0006846917399059294 [0.61186691 0.73657169]\n",
      "300 0.8781890639016857 0.0005507061993756945 [0.85824858 0.71217509]\n",
      "400 0.8287560324880023 0.00044293993976429746 [1.07921223 0.69029538]\n",
      "500 0.7889964220432137 0.00035626217838202745 [1.27738012 0.67067289]\n",
      "600 0.7570172660515031 0.00028654616202139493 [1.45510397 0.65307476]\n",
      "700 0.7312960276766381 0.000230472691044592 [1.6144929  0.63729215]\n",
      "800 0.7106081113442585 0.00018537209133373533 [1.75743843 0.62313775]\n",
      "900 0.6939685593935335 0.0001490971103323968 [1.88563696 0.6104436 ]\n",
      "1000 0.6805851579589711 0.0001199206857389612 [2.00060986 0.59905904]\n",
      "1100 0.6698207194398905 9.645371956512605e-05 [2.10372155 0.58884897]\n",
      "1200 0.6611627458150501 7.757894278814792e-05 [2.1961957  0.57969222]\n",
      "1300 0.6541990284641138 6.239772184157832e-05 [2.27912973 0.57148013]\n",
      "1400 0.6485980227963886 5.018727442207549e-05 [2.35350785 0.56411525]\n",
      "1500 0.6440930633172868 4.036625760617252e-05 [2.42021274 0.55751016]\n",
      "1600 0.6404696676072462 3.2467089952525896e-05 [2.480036   0.55158649]\n",
      "1700 0.6375553247519008 2.6113689812090612e-05 [2.53368759 0.54627394]\n",
      "1800 0.635211282047714 2.1003569971256297e-05 [2.58180419 0.54150946]\n",
      "1900 0.6333259389457611 1.6893436152520813e-05 [2.62495684 0.5372365 ]\n",
      "2000 0.6318095337174205 1.3587603698961281e-05 [2.66365763 0.53340437]\n",
      "2100 0.630589869872598 1.0928680975075267e-05 [2.69836584 0.52996758]\n",
      "2200 0.6296088788640166 8.790075903153394e-06 [2.72949338 0.52688534]\n",
      "2300 0.6288198554269419 7.069968879114263e-06 [2.75740964 0.52412109]\n",
      "2400 0.6281852339280631 5.686465111121031e-06 [2.7824459  0.52164201]\n",
      "2500 0.6276747998548587 4.573695587373194e-06 [2.8048993  0.51941869]\n",
      "2600 0.6272642512939481 3.6786810283517823e-06 [2.82503629 0.51742473]\n",
      "2700 0.6269340419099861 2.9588095340482568e-06 [2.84309584 0.51563648]\n",
      "2800 0.6266684503390045 2.379807814256729e-06 [2.85929227 0.51403272]\n",
      "2900 0.6264548316897401 1.914109430956046e-06 [2.87381779 0.51259441]\n",
      "3000 0.6262830155167157 1.53954234927145e-06 [2.88684479 0.51130448]\n",
      "3100 0.6261448216023993 1.2382733231008913e-06 [2.89852785 0.51014763]\n",
      "3199 0.6260346664535367 9.981300822525796e-07 [2.9089064  0.50911996]\n"
     ]
    }
   ],
   "source": [
    "oldJ = 0\n",
    "err = 1\n",
    "\n",
    "Js = []\n",
    "\n",
    "while err > 1e-6:\n",
    "    Hs = np.dot(X, weights)\n",
    "    deltas = alpha/M*np.dot(X.T, (Hs-y))\n",
    "\n",
    "    count += 1\n",
    "    weights -= deltas\n",
    "\n",
    "    J = np.sum(np.power(Hs-y, 2.))/(2*M)\n",
    "    Js.append(J)\n",
    "    err = np.abs(oldJ-J)\n",
    "    oldJ = J\n",
    "    \n",
    "    if count % 100 == 0:\n",
    "        print(count, J, err, weights.flatten())\n",
    "\n",
    "print(count, J, err, weights.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Error')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.semilogy(Js)\n",
    "ax.set_xlabel('Epoch')\n",
    "ax.set_ylabel('Error')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.9089064 , 0.50911996])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7a61965c00>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X.T[1], y, '.', markersize=30, label='points')\n",
    "plt.plot(X.T[1], np.dot(X, weights.flatten()), '-',\\\n",
    "         label='y = %2.2f + %2.2f x' % tuple(weights.flatten()))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "     <img src=\"https://raw.githubusercontent.com/DataForScience/DeepLearning/master/data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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