Linear Regression From Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c33de807-3f38-4b78-b474-48f45c674e20",
   "metadata": {},
   "source": [
    "# What on earth is this Linear Regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f0a1fc6-ff76-4e0f-b563-4d5af6d8d007",
   "metadata": {},
   "source": [
    "Linear Regression predicts continuous target when there is a direct relationship between the target variable and one or multiple predictors. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14506547",
   "metadata": {},
   "source": [
    "First things first, we import the required libraries. Here, Linear Regression has been implemented from scratch and no external libraries like `tensorflow`, `sklearn` or `pytorch` have been employed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c1ace64a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd                                 # for csv file I/O, data preprocessing etc.\n",
    "import matplotlib.pyplot as plt                     # for data visualization   \n",
    "import matplotlib as mpl                       \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2148e2ac",
   "metadata": {},
   "source": [
    "Having imported the libraries, we load the *comma seperated values* file into a `pandas` DataFrame. We can also use NumPy's `loadtxt()` for reading a csv file. Refer [this](https://numpy.org/doc/stable/reference/generated/numpy.loadtxt.html) to check the usage guide.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "516f6a93",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Features</th>\n",
       "      <th>Targets</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-10.000000</td>\n",
       "      <td>-12.494938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-9.959920</td>\n",
       "      <td>-16.144029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-9.919840</td>\n",
       "      <td>-16.175059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-9.879760</td>\n",
       "      <td>-23.393130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-9.839679</td>\n",
       "      <td>-12.531222</td>\n",
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      "text/plain": [
       "    Features    Targets\n",
       "0 -10.000000 -12.494938\n",
       "1  -9.959920 -16.144029\n",
       "2  -9.919840 -16.175059\n",
       "3  -9.879760 -23.393130\n",
       "4  -9.839679 -12.531222"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"data/numpydataset.csv\")      # load the csv file as a DataFrame\n",
    "data.head()                                     # displays the first 5 rows in the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "104a0c5e-560e-4353-b128-0ec11a7aa027",
   "metadata": {},
   "source": [
    "Well, how many observations does the dataset has? By using the `shape` property, we see that the dataset has 500 rows (observations) and 2 columns (variables)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "a85a36f2-6f92-441c-aa70-bcb31f7fc15a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 2)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d494e55-f78f-4ac5-b97f-e4c1da88ea97",
   "metadata": {},
   "source": [
    "We now [unpack](https://realpython.com/lessons/tuple-assignment-packing-unpacking/) the tuple obtained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "777becb3-3364-48f2-ad93-358871d29b40",
   "metadata": {},
   "outputs": [],
   "source": [
    "rows, cols = data.shape\n",
    "samples = rows          # number of samples, here 500"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "522a75f0-8f62-4c9b-ae92-801cdcd5c611",
   "metadata": {},
   "source": [
    "The number of rows corresponds to the total number of data samples. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd434bf8-3cb6-4073-93bc-bde8875ab105",
   "metadata": {},
   "source": [
    "# Mean Square Error"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae6fe76b",
   "metadata": {},
   "source": [
    "We define a method `MSE()` that will compute the loss incurred at each epoch. We aim to minimise the distance between the data and the line after each epoch. The higher the cost (or Error), the more the parameter values need to be changed in order to bring it down.</br>\n",
    "The Error function is represented as $$ E = \\frac{1}{n} \\sum_{i=0}^{n} (y_i - \\hat{y})^2 $$ where, </br> $ y_i $ is the actual value, </br> $ \\hat{y} $ is the predicted value, </br> $ n $ is the total number of data points or samples. </br>\n",
    "\n",
    "An *epoch* is a single iteration over a dataset of features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "239f4f20",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MSE(points, m, c):\n",
    "    \"\"\"Computes the Mean Square Error.\"\"\"\n",
    "    total_err = 0\n",
    "    \n",
    "    for i in range(samples):\n",
    "        x = points.Features.iloc[i]\n",
    "        y = points.Targets.iloc[i]\n",
    "        total_err += (y - (m * x + c)) ** 2\n",
    "    return total_err / samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aa757d5",
   "metadata": {},
   "source": [
    "We invoke the function to calculate the initial loss when `m=0` and `c=0`. We can resort to using `m` and `w` interchangeably because they both refer to the *weight* or the *slope* of a straight line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "76c4402b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "182.94204589695937"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE(data, m=0, c=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adc034bd-8729-4eaf-a6c7-aa6ccf44e64a",
   "metadata": {},
   "source": [
    "We get a loss of around `183`. As I wrote earlier, our aim in Linear Regression is to minimise this value. Hence, we perform the elegant [Gradient Descent](https://developer.ibm.com/learningpaths/learning-path-machine-learning-for-developers/learn-regression-algorithms/?mhsrc=ibmsearch_a&mhq=regression) Algorithm. Extensively used in Machine Learning, this process involves finding the **local minimum** of a function. The sole idea behind this algorithm is akin to that of a blind, old man trying to go down a hill.</br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaa1dfc9-5cfb-474a-a72b-c191a3ca4d4c",
   "metadata": {},
   "source": [
    "# Intuition Behind Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abceb545-541d-41a8-aaf6-a5667f646172",
   "metadata": {},
   "source": [
    "Let's consider a scenario where a blind man, equipped only with a blind cane, is standing at a hill's summit at some point. If we wishes to descent, he should take miniature steps towards the bottom of the hill lest he stumble. He will extensively use the local neighbourhood information to plan his next step carefully. He can stop when he is very close to the bottom of the hill. This bottom, is analogous to the **global minimizers** of any function. If he feels a flat surface or a small valley with his cane, he might deduce that he reached the bottom, when in fact he didn't. Such a flat surface is analogous to stationary points of a function, that are definitely not the **global minimizers**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddb6f7ef-0a4c-472a-9156-5f235ebdae0c",
   "metadata": {},
   "source": [
    "# So What Is Gradient Descent?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2d14f69-b4b6-4ae1-99bb-82f7a8815331",
   "metadata": {},
   "source": [
    "Similarly, the basic storyline of Gradient Descent is to\n",
    "* start at some point (also known as the initialization),\n",
    "* somehow move down slowly (with small step-size) using the local neighborhood\n",
    "information towards the minimizer/stationary point,\n",
    "* and when very close to or at the minimizer/stationary point, we stop.\n",
    "\n",
    "Mathematically, provided a certain learning rate $ \\gamma $, take iterative steps (slowly) in the direction of $ -\\nabla{E} $ (negative gradient) in order to minimise the error rate. Each iteration of gradient descent updates the `m` and the `c` (collectively denoted by $\\theta$) according to,</br>\n",
    "$$ \\theta^{t+1} = \\theta^{t} - \\gamma \\frac{\\partial{E}(X, \\theta)}{\\partial{\\theta}} $$ where $ \\theta^t $ denotes the weights (slope) and the bias (intercept) at iteration $t$.\n",
    "<!-- MORE EXPLANATION SHOULD BE PROVIDED --></br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "99e9d5b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(m_new, c_new, points, step_size):\n",
    "    \"\"\"The Gradient Descent Algorithm that updates both slope \n",
    "    and the intercept to minimise the Mean Square Error obtained\n",
    "    at each epoch.\"\"\"\n",
    "    \n",
    "    m_gradient = 0\n",
    "    c_gradient = 0\n",
    "    \n",
    "    for i in range(samples):      \n",
    "        x = points.iloc[i].Features  # Pandas index-based selection\n",
    "        y = points.iloc[i].Targets   \n",
    "        \n",
    "       # obtaining the gradient w.r.t both m and c\n",
    "        m_gradient += -(2/samples) * x * (y - (m_new * x + c_new))\n",
    "        c_gradient += -(2/samples) * (y - (m_new * x + c_new))\n",
    "        \n",
    "    # updating m and b\n",
    "    m = m_new - step_size * m_gradient\n",
    "    c = c_new - step_size * c_gradient\n",
    "    return m, c\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a682dcf",
   "metadata": {},
   "source": [
    "Let's recapitulate. The process is simple; start with $m=0$ and $c=0$ and obtain new pairs of `m` and `c` at each epoch. Tentatively, we choose the step_size to be `0.001` and it can be readjusted if required.</br>It's now the time for action!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "4109a79c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, m: 0.136583491906185, c:0.010312358814106729, Loss: 164.80508456949966\n",
      "Epoch 2, m: 0.26402492243027265, c:0.02060409291058524, Loss: 149.00149960714555\n",
      "Epoch 3, m: 0.3829362050996419, c:0.030875243538870792, Loss: 135.22943429119366\n",
      "Epoch 4, m: 0.4938882957025642, c:0.041125851865899773, Loss: 123.2260882044345\n",
      "Epoch 5, m: 0.5974139337480966, c:0.05135595897627469, Loss: 112.76266383116663\n",
      "Epoch 6, m: 0.694010200429459, c:0.06156560587242887, Loss: 103.63996700446971\n",
      "Epoch 7, m: 0.7841409053730308, c:0.07175483347479074, Loss: 95.68457660100785\n",
      "Epoch 8, m: 0.8682388136330048, c:0.08192368262194788, Loss: 88.74550982980166\n",
      "Epoch 9, m: 0.946707723624676, c:0.0920721940708107, Loss: 82.69131899125425\n",
      "Epoch 10, m: 1.019924405973618, c:0.10220040849677581, Loss: 77.40756387953367\n",
      "Epoch 11, m: 1.0882404125901861, c:0.11230836649388898, Loss: 72.7946112247259\n",
      "Epoch 12, m: 1.1519837646556652, c:0.12239610857500792, Loss: 68.7657188598652\n",
      "Epoch 13, m: 1.211460527624978, c:0.1324636751719646, Loss: 65.24536777297835\n",
      "Epoch 14, m: 1.2669562808083688, c:0.1425111066357274, Loss: 62.167809970895924\n",
      "Epoch 15, m: 1.318737488588302, c:0.15253844323656268, Loss: 59.47580423146678\n",
      "Epoch 16, m: 1.3670527798555105, c:0.16254572516419627, Loss: 57.11951543374669\n",
      "Epoch 17, m: 1.412134141807439, c:0.1725329925279746, Loss: 55.05555630120099\n",
      "Epoch 18, m: 1.454198033841142, c:0.18250028535702537, Loss: 53.24615313144453\n",
      "Epoch 19, m: 1.4934464268890222, c:0.19244764360041805, Loss: 51.65841947019917\n",
      "Epoch 20, m: 1.5300677731878056, c:0.20237510712732393, Loss: 50.26372376282575\n",
      "Epoch 21, m: 1.5642379111371314, c:0.212282715727176, Loss: 49.03713882389988\n",
      "Epoch 22, m: 1.5961209095924542, c:0.22217050910982838, Loss: 47.95696253858989\n",
      "Epoch 23, m: 1.6258698556461584, c:0.23203852690571544, Loss: 47.00430057932759\n",
      "Epoch 24, m: 1.6536275896794341, c:0.24188680866601073, Loss: 46.16270311376038\n",
      "Epoch 25, m: 1.6795273912142903, c:0.2517153938627854, Loss: 45.417848518184684\n",
      "Epoch 26, m: 1.7036936188588374, c:0.2615243218891666, Loss: 44.75726801453284\n",
      "Epoch 27, m: 1.726242307418559, c:0.271313632059495, Loss: 44.17010593591504\n",
      "Epoch 28, m: 1.747281725040616, c:0.2810833636094827, Loss: 43.64691101082227\n",
      "Epoch 29, m: 1.766912893066327, c:0.2908335556963705, Loss: 43.17945465256069\n",
      "Epoch 30, m: 1.785230071087912, c:0.30056424739908444, Loss: 42.76057275977557\n",
      "Epoch 31, m: 1.8023212095385133, c:0.310275477718393, Loss: 42.38402798602195\n",
      "Epoch 32, m: 1.8182683719886135, c:0.3199672855770629, Loss: 42.044389829940435\n",
      "Epoch 33, m: 1.8331481291765226, c:0.3296397098200155, Loss: 41.73693024027346\n",
      "Epoch 34, m: 1.8470319266648803, c:0.3392927892144822, Loss: 41.457532728294936\n",
      "Epoch 35, m: 1.8599864278884861, c:0.34892656245015996, Loss: 41.202613239959625\n",
      "Epoch 36, m: 1.872073834240612, c:0.35854106813936637, Loss: 40.96905126621261\n",
      "Epoch 37, m: 1.8833521837346998, c:0.36813634481719437, Loss: 40.754129866766554\n",
      "Epoch 38, m: 1.893875629675476, c:0.3777124309416667, Loss: 40.55548345405504\n",
      "Epoch 39, m: 1.9036947006775309, c:0.3872693648938901, Loss: 40.3710523332919\n",
      "Epoch 40, m: 1.912856543279849, c:0.39680718497820905, Loss: 40.19904312447905\n",
      "Epoch 41, m: 1.9214051483212105, c:0.40632592942235934, Loss: 40.037894305313465\n",
      "Epoch 42, m: 1.9293815621634107, c:0.4158256363776214, Loss: 39.88624621241111\n",
      "Epoch 43, m: 1.9368240837764936, c:0.4253063439189729, Loss: 39.74291492399708\n",
      "Epoch 44, m: 1.9437684486323081, c:0.43476809004524164, Loss: 39.60686952184921\n",
      "Epoch 45, m: 1.9502480002893565, c:0.4442109126792579, Loss: 39.47721229526082\n",
      "Epoch 46, m: 1.956293850492807, c:0.4536348496680061, Loss: 39.353161506362284\n",
      "Epoch 47, m: 1.9619350285583912, c:0.4630399387827768, Loss: 39.23403638539311\n",
      "Epoch 48, m: 1.9671986207574614, c:0.472426217719318, Loss: 39.119244067397304\n",
      "Epoch 49, m: 1.9721099003724656, c:0.48179372409798604, Loss: 39.00826821914452\n",
      "Epoch 50, m: 1.9766924490473072, c:0.49114249546389677, Loss: 38.900659137584604\n",
      "Epoch 51, m: 1.9809682700152556, c:0.5004725692870757, Loss: 38.79602512943569\n",
      "Epoch 52, m: 1.9849578937480747, c:0.5097839829626083, Loss: 38.694025006144344\n",
      "Epoch 53, m: 1.9886804765336472, c:0.5190767738107898, Loss: 38.594361549901606\n",
      "Epoch 54, m: 1.9921538924554156, c:0.5283509790772749, Loss: 38.49677582507268\n",
      "Epoch 55, m: 1.9953948192152862, c:0.5376066359332271, Loss: 38.40104222565477\n",
      "Epoch 56, m: 1.9984188182120712, c:0.5468437814754674, Loss: 38.30696416352856\n",
      "Epoch 57, m: 2.001240409259973, c:0.5560624527266232, Loss: 38.214370314595214\n",
      "Epoch 58, m: 2.0038731403058714, c:0.5652626866352767, Loss: 38.12311135061229\n",
      "Epoch 59, m: 2.00632965248016, c:0.5744445200761128, Loss: 38.033057093888054\n",
      "Epoch 60, m: 2.0086217407934845, c:0.5836079898500672, Loss: 37.94409404011957\n",
      "Epoch 61, m: 2.010760410770807, c:0.5927531326844738, Loss: 37.856123201742555\n",
      "Epoch 62, m: 2.0127559312947376, c:0.6018799852332116, Loss: 37.7690582303219\n",
      "Epoch 63, m: 2.014617883911856, c:0.610988584076852, Loss: 37.68282378187899\n",
      "Epoch 64, m: 2.0163552088387706, c:0.620078965722805, Loss: 37.59735409372298\n",
      "Epoch 65, m: 2.0179762478888135, c:0.6291511666054661, Loss: 37.51259174541928\n",
      "Epoch 66, m: 2.0194887845254867, c:0.6382052230863619, Loss: 37.42848658007096\n",
      "Epoch 67, m: 2.0209000812349758, c:0.6472411714542958, Loss: 37.34499476517036\n",
      "Epoch 68, m: 2.0222169143971764, c:0.6562590479254939, Loss: 37.262077974962104\n",
      "Epoch 69, m: 2.0234456068226687, c:0.6652588886437497, Loss: 37.1797026785953\n",
      "Epoch 70, m: 2.0245920581118653, c:0.6742407296805689, Loss: 37.097839520377676\n",
      "Epoch 71, m: 2.025661772982106, c:0.6832046070353145, Loss: 37.01646278021491\n",
      "Epoch 72, m: 2.026659887698707, c:0.6921505566353506, Loss: 36.93554990385882\n",
      "Epoch 73, m: 2.0275911947368823, c:0.7010786143361867, Loss: 36.855081093933755\n",
      "Epoch 74, m: 2.0284601657929433, c:0.709988815921621, Loss: 36.77503895387637\n",
      "Epoch 75, m: 2.029270973255272, c:0.7188811971038844, Loss: 36.6954081779427\n",
      "Epoch 76, m: 2.030027510238158, c:0.7277557935237834, Loss: 36.616175281321354\n",
      "Epoch 77, m: 2.0307334092746947, c:0.7366126407508425, Loss: 36.53732836516482\n",
      "Epoch 78, m: 2.031392059758485, c:0.7454517742834476, Loss: 36.458856912020046\n",
      "Epoch 79, m: 2.03200662421791, c:0.7542732295489873, Loss: 36.38075160772501\n",
      "Epoch 80, m: 2.0325800535010923, c:0.7630770419039961, Loss: 36.3030041863474\n",
      "Epoch 81, m: 2.0331151009444786, c:0.7718632466342948, Loss: 36.22560729518375\n",
      "Epoch 82, m: 2.033614335593057, c:0.780631878955133, Loss: 36.148554377223256\n",
      "Epoch 83, m: 2.034080154535699, c:0.7893829740113294, Loss: 36.07183956881718\n",
      "Epoch 84, m: 2.034514794414845, c:0.7981165668774135, Loss: 35.99545761058602\n",
      "Epoch 85, m: 2.034920342165808, c:0.8068326925577654, Loss: 35.91940376985135\n",
      "Epoch 86, m: 2.0352987450372475, c:0.8155313859867566, Loss: 35.843673773101905\n",
      "Epoch 87, m: 2.0356518199409392, c:0.8242126820288898, Loss: 35.76826374719523\n",
      "Epoch 88, m: 2.0359812621757265, c:0.8328766154789387, Loss: 35.693170168164606\n",
      "Epoch 89, m: 2.0362886535675444, c:0.8415232210620874, Loss: 35.618389816647195\n",
      "Epoch 90, m: 2.0365754700645993, c:0.8501525334340699, Loss: 35.543919739076856\n",
      "Epoch 91, m: 2.0368430888241758, c:0.8587645871813085, Loss: 35.469757213895946\n",
      "Epoch 92, m: 2.0370927948250954, c:0.8673594168210527, Loss: 35.39589972213603\n",
      "Epoch 93, m: 2.0373257870375765, c:0.8759370568015172, Loss: 35.322344921803\n",
      "Epoch 94, m: 2.037543184180124, c:0.884497541502021, Loss: 35.24909062557425\n",
      "Epoch 95, m: 2.0377460300910863, c:0.8930409052331236, Loss: 35.17613478137853\n",
      "Epoch 96, m: 2.0379352987406736, c:0.9015671822367641, Loss: 35.103475455486894\n",
      "Epoch 97, m: 2.038111898907503, c:0.9100764066863973, Loss: 35.03111081778845\n",
      "Epoch 98, m: 2.0382766785421236, c:0.9185686126871313, Loss: 34.95903912896949\n",
      "Epoch 99, m: 2.038430428838475, c:0.9270438342758638, Loss: 34.887258729348694\n",
      "Epoch 100, m: 2.038573888032826, c:0.9355021054214188, Loss: 34.815768029154874\n",
      "2.038573888032826 0.9355021054214188\n"
     ]
    }
   ],
   "source": [
    "m, c = 0, 0\n",
    "L = 0.001       # initial learning rate, can be adjusted later\n",
    "epochs = 100    # we iterate over the same dataset 100 times\n",
    "\n",
    "for epoch in range(1, epochs+1):\n",
    "    m, c = gradient_descent(m, c, data, L)\n",
    "    loss = MSE(data, m, c)\n",
    "    print(f\"Epoch {epoch}, m: {m}, c:{c}, Loss: {loss}\")\n",
    "#     if not(epoch % 10):\n",
    "#         print(f\"Epoch {epoch}, m: {m}, c:{c}\")\n",
    "print(m, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "258461ad-50b3-4a6d-806d-aa564b9c730f",
   "metadata": {},
   "source": [
    "Having obtained the final values for both `m` and `c`, we now perform visualization using `matplotlib`.</br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b250cefa-5b99-44c0-9e65-670d1548152e",
   "metadata": {},
   "source": [
    "# Data Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "8214be9c-bc25-4559-b1b4-f475ad2f483e",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('fivethirtyeight')  # setting the theme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "8298d39c-68e2-49e7-a80f-4d89e0cf39c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams['figure.figsize'] = (6, 4)    # setting the figure size\n",
    "mpl.rcParams['axes.labelsize'] = 10        # setting the label size\n",
    "mpl.rcParams['xtick.labelsize'] = 10       # setting the xtick's label size\n",
    "mpl.rcParams['ytick.labelsize'] = 10       # settingthe ytick's label size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "0ccd2003",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create just a figure and only one subplot\n",
    "fig, ax = plt.subplots(tight_layout=True)\n",
    "\n",
    "# scatter plot, actual values\n",
    "ax.scatter(data.Features, \n",
    "           data.Targets, \n",
    "           marker=\".\",\n",
    "           color=\"r\",\n",
    "           linewidths=1, \n",
    "           label=\"Points\")\n",
    "\n",
    "# line plot, predicted values\n",
    "ax.plot(data.Features, \n",
    "        [m * x + c for x in data.Features],  \n",
    "        \"g-\",\n",
    "        linewidth=2,\n",
    "        label=\"$ f(x) = mx+c $\")\n",
    "\n",
    "# legend\n",
    "ax.legend(loc=\"lower right\", \n",
    "          bbox_to_anchor=(.96, 0.0),\n",
    "          shadow=True,\n",
    "          fontsize=10)\n",
    "\n",
    "# labels\n",
    "ax.set_xlabel(\"Features\")\n",
    "ax.set_ylabel(\"Targets\")\n",
    "\n",
    "# display the final plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6feb9053-65c7-4be0-a59f-9dc3e67518af",
   "metadata": {},
   "source": [
    "We can clearly see the BAD line-fitting that followed."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9224a616",
   "metadata": {},
   "source": [
    "Let's check our final loss value. Is it way lesser than the initial value i.e. `183`?\n",
    "After 100 epochs, the final loss value is 35 (rounded up).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "6d038ad7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.815768029154874"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE(data, m, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d702dfe",
   "metadata": {},
   "source": [
    "An average loss of `35` indicates that our model is gradually getting better. We can tweak our model in order to reduce loss further.</br>\n",
    "Our learning rate is `0.001` which is microscopic. The algorithm will take a LOT of time to converge i.e. reach the minima value for the error function $E$. Increasing the epoch is a bad option because it will result in an unnecessary increase in computation resources. Let's try adjusting the **learning rate**. How about `0.01`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "99d8917d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, m: 1.3658349190618497, c:0.10312358814106728, Loss: 57.771463654789635\n",
      "Epoch 2, m: 1.817463699913964, c:0.20418470451931323, Loss: 43.18968867478232\n",
      "Epoch 3, m: 1.9667998699352043, c:0.3032245985699943, Loss: 40.73483420008382\n",
      "Epoch 4, m: 2.0161795654332098, c:0.4002836947396617, Loss: 39.63997666358201\n",
      "Epoch 5, m: 2.032507520858402, c:0.4954016089859357, Loss: 38.726544463098776\n",
      "Epoch 6, m: 2.0379065441953887, c:0.5886171649472842, Loss: 37.864380213169895\n",
      "Epoch 7, m: 2.0396917923929903, c:0.6799684097894059, Loss: 37.038008221408205\n",
      "Epoch 8, m: 2.0402821049232593, c:0.7694926297346849, Loss: 36.24454102698065\n",
      "Epoch 9, m: 2.040477298445292, c:0.8572263652810584, Loss: 35.48251486509766\n",
      "Epoch 10, m: 2.040541841393459, c:0.9432054261165045, Loss: 34.75066709662237\n",
      "Epoch 11, m: 2.040563183250068, c:1.0274649057352416, Loss: 34.04780073566182\n",
      "Epoch 12, m: 2.0405702401766015, c:1.110039195761604, Loss: 33.372767908386045\n",
      "Epoch 13, m: 2.0405725736292624, c:1.1909619999874392, Loss: 32.72446638389023\n",
      "Epoch 14, m: 2.0405733452118064, c:1.2702663481287577, Loss: 32.10183760007278\n",
      "Epoch 15, m: 2.0405736003443105, c:1.3479846093072496, Loss: 31.503864916128222\n",
      "Epoch 16, m: 2.040573684706762, c:1.4241485052621718, Loss: 30.92957195047156\n",
      "Epoch 17, m: 2.040573712602162, c:1.4987891232979957, Loss: 30.37802098625533\n",
      "Epoch 18, m: 2.0405737218260915, c:1.571936928973103, Loss: 29.848311440222062\n",
      "Epoch 19, m: 2.0405737248760887, c:1.6436217785347083, Loss: 29.339578392211763\n",
      "Epoch 20, m: 2.0405737258846046, c:1.7138729311050813, Loss: 28.850991172902614\n",
      "Epoch 21, m: 2.040573726218082, c:1.7827190606240468, Loss: 28.38175200747814\n",
      "Epoch 22, m: 2.0405737263283497, c:1.850188267552633, Loss: 27.931094713004455\n",
      "Epoch 23, m: 2.040573726364811, c:1.9163080903426477, Loss: 27.498283447391984\n",
      "Epoch 24, m: 2.0405737263768673, c:1.981105516676862, Loss: 27.082611507897692\n",
      "Epoch 25, m: 2.040573726380854, c:2.044606994484392, Loss: 26.683400177207456\n",
      "Epoch 26, m: 2.040573726382172, c:2.1068384427357714, Loss: 26.299997615212487\n",
      "Epoch 27, m: 2.040573726382608, c:2.1678252620221232, Loss: 25.931777794672534\n",
      "Epoch 28, m: 2.040573726382752, c:2.227592344922748, Loss: 25.57813947902598\n",
      "Epoch 29, m: 2.0405737263828, c:2.2861640861653605, Loss: 25.23850524067899\n",
      "Epoch 30, m: 2.040573726382816, c:2.3435643925831204, Loss: 24.91232051817058\n",
      "Epoch 31, m: 2.0405737263828208, c:2.399816692872525, Loss: 24.599052710673497\n",
      "Epoch 32, m: 2.0405737263828225, c:2.4549439471561416, Loss: 24.298190308353323\n",
      "Epoch 33, m: 2.040573726382823, c:2.508968656354086, Loss: 24.009242057164982\n",
      "Epoch 34, m: 2.0405737263828234, c:2.5619128713680714, Loss: 23.731736156723734\n",
      "Epoch 35, m: 2.0405737263828234, c:2.613798202081777, Loss: 23.465219489939948\n",
      "Epoch 36, m: 2.0405737263828234, c:2.664645826181209, Loss: 23.209256883160776\n",
      "Epoch 37, m: 2.0405737263828234, c:2.714476497798652, Loss: 22.96343039561006\n",
      "Epoch 38, m: 2.0405737263828234, c:2.7633105559837463, Loss: 22.727338636966394\n",
      "Epoch 39, m: 2.0405737263828234, c:2.8111679330051387, Loss: 22.500596111964978\n",
      "Epoch 40, m: 2.0405737263828234, c:2.858068162486103, Loss: 22.282832590953618\n",
      "Epoch 41, m: 2.0405737263828234, c:2.9040303873774485, Loss: 22.073692505374336\n",
      "Epoch 42, m: 2.0405737263828234, c:2.949073367770967, Loss: 21.872834367183987\n",
      "Epoch 43, m: 2.0405737263828234, c:2.993215488556615, Loss: 21.679930211265955\n",
      "Epoch 44, m: 2.0405737263828234, c:3.03647476692655, Loss: 21.494665059922315\n",
      "Epoch 45, m: 2.0405737263828234, c:3.078868859729086, Loss: 21.316736408571852\n",
      "Epoch 46, m: 2.0405737263828234, c:3.1204150706755716, Loss: 21.14585373181485\n",
      "Epoch 47, m: 2.0405737263828234, c:3.1611303574031275, Loss: 20.981738009057477\n",
      "Epoch 48, m: 2.0405737263828234, c:3.2010313383961324, Loss: 20.824121268921264\n",
      "Epoch 49, m: 2.0405737263828234, c:3.2401342997692772, Loss: 20.672746151694465\n",
      "Epoch 50, m: 2.040573726382823, c:3.278455201914959, Loss: 20.527365489109823\n",
      "Epoch 51, m: 2.0405737263828234, c:3.3160096860177273, Loss: 20.387741900763547\n",
      "Epoch 52, m: 2.0405737263828234, c:3.3528130804384397, Loss: 20.25364740651577\n",
      "Epoch 53, m: 2.0405737263828234, c:3.3888804069707383, Loss: 20.124863054240194\n",
      "Epoch 54, m: 2.0405737263828234, c:3.424226386972391, Loss: 20.001178562314763\n",
      "Epoch 55, m: 2.0405737263828234, c:3.4588654473740106, Loss: 19.882391976269535\n",
      "Epoch 56, m: 2.0405737263828234, c:3.4928117265675978, Loss: 19.76830933903175\n",
      "Epoch 57, m: 2.0405737263828234, c:3.526079080177313, Loss: 19.658744374228576\n",
      "Epoch 58, m: 2.0405737263828234, c:3.558681086714834, Loss: 19.55351818203159\n",
      "Epoch 59, m: 2.0405737263828234, c:3.5906310531216046, Loss: 19.452458947045578\n",
      "Epoch 60, m: 2.0405737263828234, c:3.6219420202002395, Loss: 19.35540165776508\n",
      "Epoch 61, m: 2.0405737263828234, c:3.652626767937302, Loss: 19.26218783714002\n",
      "Epoch 62, m: 2.0405737263828234, c:3.682697820719623, Loss: 19.17266528381176\n",
      "Epoch 63, m: 2.0405737263828234, c:3.7121674524462978, Loss: 19.08668782359528\n",
      "Epoch 64, m: 2.0405737263828234, c:3.741047691538439, Loss: 19.004115070803376\n",
      "Epoch 65, m: 2.0405737263828234, c:3.7693503258487375, Loss: 18.924812199022007\n",
      "Epoch 66, m: 2.0405737263828234, c:3.79708690747283, Loss: 18.848649720963216\n",
      "Epoch 67, m: 2.0405737263828234, c:3.8242687574644405, Loss: 18.775503277035558\n",
      "Epoch 68, m: 2.0405737263828234, c:3.850906970456219, Loss: 18.70525343228743\n",
      "Epoch 69, m: 2.0405737263828234, c:3.877012419188162, Loss: 18.63778548139131\n",
      "Epoch 70, m: 2.0405737263828234, c:3.9025957589454663, Loss: 18.57298926135068\n",
      "Epoch 71, m: 2.0405737263828234, c:3.9276674319076244, Loss: 18.510758971623645\n",
      "Epoch 72, m: 2.0405737263828234, c:3.952237671410539, Loss: 18.45099300136981\n",
      "Epoch 73, m: 2.0405737263828234, c:3.9763165061233954, Loss: 18.393593763538043\n",
      "Epoch 74, m: 2.0405737263828234, c:3.999913764141995, Loss: 18.338467535524412\n",
      "Epoch 75, m: 2.0405737263828234, c:4.023039077000222, Loss: 18.28552430614011\n",
      "Epoch 76, m: 2.0405737263828234, c:4.045701883601285, Loss: 18.234677628639417\n",
      "Epoch 77, m: 2.0405737263828234, c:4.067911434070326, Loss: 18.18584447956777\n",
      "Epoch 78, m: 2.0405737263828234, c:4.0896767935299865, Loss: 18.138945123199353\n",
      "Epoch 79, m: 2.0405737263828234, c:4.111006845800454, Loss: 18.093902981343124\n",
      "Epoch 80, m: 2.0405737263828234, c:4.131910297025512, Loss: 18.05064450830442\n",
      "Epoch 81, m: 2.0405737263828234, c:4.1523956792260694, Loss: 18.009099070798012\n",
      "Epoch 82, m: 2.0405737263828234, c:4.1724713537826155, Loss: 17.969198832616907\n",
      "Epoch 83, m: 2.0405737263828234, c:4.19214551484803, Loss: 17.93087864386771\n",
      "Epoch 84, m: 2.0405737263828234, c:4.211426192692136, Loss: 17.894075934593022\n",
      "Epoch 85, m: 2.0405737263828234, c:4.2303212569793605, Loss: 17.858730612605612\n",
      "Epoch 86, m: 2.0405737263828234, c:4.24883841998084, Loss: 17.82478496536891\n",
      "Epoch 87, m: 2.0405737263828234, c:4.266985239722291, Loss: 17.79218356576276\n",
      "Epoch 88, m: 2.0405737263828234, c:4.284769123068912, Loss: 17.76087318158103\n",
      "Epoch 89, m: 2.0405737263828234, c:4.302197328748601, Loss: 17.730802688612872\n",
      "Epoch 90, m: 2.0405737263828234, c:4.3192769703146965, Loss: 17.701922987166288\n",
      "Epoch 91, m: 2.0405737263828234, c:4.33601501904947, Loss: 17.67418692189696\n",
      "Epoch 92, m: 2.0405737263828234, c:4.352418306809548, Loss: 17.647549204812314\n",
      "Epoch 93, m: 2.0405737263828234, c:4.368493528814424, Loss: 17.62196634132419\n",
      "Epoch 94, m: 2.0405737263828234, c:4.384247246379203, Loss: 17.59739655923023\n",
      "Epoch 95, m: 2.0405737263828234, c:4.399685889592686, Loss: 17.573799740507177\n",
      "Epoch 96, m: 2.0405737263828234, c:4.414815759941899, Loss: 17.551137355805576\n",
      "Epoch 97, m: 2.0405737263828234, c:4.429643032884128, Loss: 17.52937240153813\n",
      "Epoch 98, m: 2.0405737263828234, c:4.444173760367512, Loss: 17.508469339459705\n",
      "Epoch 99, m: 2.0405737263828234, c:4.458413873301229, Loss: 17.488394038639566\n",
      "Epoch 100, m: 2.0405737263828234, c:4.472369183976271, Loss: 17.469113719731904\n",
      "2.0405737263828234 4.472369183976271\n"
     ]
    }
   ],
   "source": [
    "m, c = 0, 0\n",
    "L = 0.01   # new learning rate\n",
    "epochs = 100\n",
    "\n",
    "for epoch in range(1, epochs+1):\n",
    "    m, c = gradient_descent(m, c, data, L)\n",
    "    loss = MSE(data, m, c)\n",
    "    print(f\"Epoch {epoch}, m: {m}, c:{c}, Loss: {loss}\")\n",
    "#     if not(epoch % 10):\n",
    "#         print(f\"Epoch {epoch}, m: {m}, c:{c}\")\n",
    "print(m, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b586f2fd",
   "metadata": {},
   "source": [
    "Let's observe the new loss value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "28384f41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.469113719731904"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE(data, m, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0c1737a",
   "metadata": {},
   "source": [
    "Bingo! We were able to minimize the loss. Our **Gradient Descent** algorithm proved to be very efficient.\n",
    "Let's quickly perform 2-D visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "875078c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(tight_layout=True)\n",
    "\n",
    "ax.scatter(data.Features, \n",
    "           data.Targets, \n",
    "           color=\"r\",\n",
    "           marker=\".\", \n",
    "           linewidths=1, \n",
    "           label=\"Points\")\n",
    "\n",
    "ax.plot(data.Features, \n",
    "        [m * x + c for x in data.Features],   \n",
    "        'g-',\n",
    "        linewidth=2,\n",
    "        label=\"$ f(x) = mx+c $\")\n",
    "\n",
    "ax.legend(loc=\"lower right\", \n",
    "          bbox_to_anchor=(.96, 0.0),\n",
    "          shadow=True,\n",
    "          fontsize=10)\n",
    "ax.set_xlabel(\"Features\")\n",
    "ax.set_ylabel(\"Targets\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17355549-38e1-4f5e-a9a1-28ec8c01dffd",
   "metadata": {},
   "source": [
    "Much better!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}