presession/Linear-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jXG99obpc6th"
   },
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ng1TXRuSdDmE"
   },
   "source": [
    "So far we have seen what Machine Learning is and why we use machine learning\n",
    "\n",
    "We also have seen the difference between supervised and unsupervised learning\n",
    "\n",
    "While talking about supervised learning we have defined regression to be a part of it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AJPo1o0ldU9N"
   },
   "source": [
    "#### So get ready to finally learn your first Machine Learning Algorithm - Linear Regression!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "opHojCYbdYqC"
   },
   "source": [
    "Let's first start by importing some relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bE6pSKj3mJE7"
   },
   "outputs": [],
   "source": [
    "import pandas as pd                   # This is the library which is used for operations which have to be done on any data\n",
    "import numpy as np                    # This is the library we will be using for linear algebra\n",
    "import matplotlib.pyplot as plt       # This is the library we use for plotting graphs and make visualisations\n",
    "%matplotlib inline\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "eGPkfSxNd2c0"
   },
   "source": [
    "Now that we have finished importing libraries let's read our data into a DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iI-29vnowuiO"
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"data.csv\")        # Reads a CSV file into a DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 988,
     "status": "ok",
     "timestamp": 1588870711556,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "NKDEwgbXGT8l",
    "outputId": "d0abdeee-7df3-4cdf-d478-791c9646e67b"
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>feature</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.848383</td>\n",
       "      <td>34.465973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.294726</td>\n",
       "      <td>2.751125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.001241</td>\n",
       "      <td>5.097244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.186086</td>\n",
       "      <td>23.181563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.851089</td>\n",
       "      <td>20.401837</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    feature     target\n",
       "0  0.848383  34.465973\n",
       "1 -0.294726   2.751125\n",
       "2  1.001241   5.097244\n",
       "3  0.186086  23.181563\n",
       "4 -0.851089  20.401837"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(5)                           # Gives us the first 5 elements of the DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hqQrw1TLeOXp"
   },
   "source": [
    "So we have finished the first step of this whole process\n",
    "\n",
    "Our data is ready\n",
    "\n",
    "Let's explore this data a little more"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 978,
     "status": "ok",
     "timestamp": 1588870713943,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "qHy9STwownMB",
    "outputId": "0d0f92d4-550d-4667-d819-958b7acdbc64"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = data['feature'].values\n",
    "y = data['target'].values\n",
    "\n",
    "#Lets Visualise the dataset\n",
    "plt.scatter(x,y)                        # the scatter function makes a scatter plot of the data that is passed to it\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yL1g-MIye_3h"
   },
   "source": [
    "We can see that the Feature is Linearly increasing with the Target\n",
    "\n",
    "So it is safe to assume that the trend followed here is of the form y = ax + b where y is the Target, x is the Feature and a and b are parameters(slope and intercept)\n",
    "\n",
    "The model needs to finally learn what will be the best choice for a and b so that we can represent the points accurately\n",
    "\n",
    "Get ready to dive into the algorithm!!\n",
    "\n",
    "Take as much time as you need to understand this, you can contact any group admin for doubts or post your doubts in the link on the github repository for doubt clarification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jSwzNId7w-Df"
   },
   "outputs": [],
   "source": [
    "'''Usually the data is split into batches and trained over\n",
    "But since the dataset is very small, we shall use the whole data as one batch'''\n",
    "\n",
    "'''If its not split into batches and is trained on each data point one by one, the cost function\n",
    "would fluctuate a lot and would converge very slowly as each data point is completely new to it\n",
    "whereas a batch would give a better over all idea'''\n",
    "\n",
    "'''Usually we dont take the entire dataset as a batch as datasets are quite large and there\n",
    "will be memory issues'''\n",
    "\n",
    "#Defining the model parameters\n",
    "num_iters = 400 #The number of times you want to train over the dataset\n",
    "lr=0.01 #Learning rate\n",
    "a = 0.0  #Initial value of slope\n",
    "b = 0.0  #Initial value of bias\n",
    "\n",
    "#for plotting\n",
    "cost_vals = []\n",
    "\n",
    "for i in range(num_iters):\n",
    "  #make a prediction first\n",
    "  #note that y_pred is a vector of predictions\n",
    "  y_pred = a*x+b\n",
    "\n",
    "  #find the error and cost. The mean squared error cost function is used\n",
    "  error = y_pred-y\n",
    "  cost = 0.5*np.mean(error**2)\n",
    "  \n",
    "  '''Now we shall compute the partial derivatives of the cost with\n",
    "  respect to a and b\n",
    "  Since y_pred and y are vectors, your partial derivative will also be a vector of \n",
    "  partial derivatives for each input\n",
    "  So we shall find the mean partial derivative and update with this mean value\n",
    "  Look at the uploaded image for the formula\n",
    "  '''\n",
    "  a_derivative = np.mean((y_pred-y)*x) #y_pred-y * x does a element wise multiplication \n",
    "  b_derivative = np.mean(y_pred-y)\n",
    "\n",
    "  #Now to update the values of a and b, in other words, perform gradient descent\n",
    "  a = a - lr*a_derivative\n",
    "  b = b - lr*b_derivative\n",
    "\n",
    "  cost_vals.append(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2580,
     "status": "ok",
     "timestamp": 1588870721609,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "DrR6XlE-C3H8",
    "outputId": "1aa6ae50-ebac-4cac-d380-1d210023d971"
   },
   "source": [
    "<img src=\"images/lin-reg.jpeg\" width=\"500\" height=\"500\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 938,
     "status": "ok",
     "timestamp": 1588870723922,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "roDqo3X7z_Rh",
    "outputId": "f6125579-dfc0-49c8-b5f8-6c0df84d9d26"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Lets see how the cost changes with number of iters\n",
    "x_axis = np.arange(0,len(cost_vals),1)\n",
    "plt.plot(x_axis,cost_vals)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1350,
     "status": "ok",
     "timestamp": 1588870725140,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "8UNAc0O70cQU",
    "outputId": "48b69cb7-e887-4f88-dd7f-d1ecca3ce14c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7effa04b0588>]"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Lets now plot the line to see how well it has fit the data\n",
    "plt.figure()\n",
    "plt.scatter(x,y)\n",
    "linex = np.arange(-3,3,1)\n",
    "liney = a*linex + b\n",
    "plt.plot(linex,liney)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1046,
     "status": "ok",
     "timestamp": 1588870725563,
     "user": {
      "displayName": "Aditya Das me19b194",
      "photoUrl": "",
      "userId": "09366802235048220900"
     },
     "user_tz": -330
    },
    "id": "ATaQgVz9Bbuq",
    "outputId": "667a4323-6ce8-4583-dd49-5257a09a70cd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  28.331297201934877\n",
      "b =  1.8689084353409613\n"
     ]
    }
   ],
   "source": [
    "#Lets see what values it has learnt \n",
    "print(\"a = \",a)\n",
    "print(\"b = \",b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_ayZaK-HIi7X"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "Linear-Regression.ipynb",
   "provenance": []
  },
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}