ML_Algorithms_Linear_Regression.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Followb1ind1y/Machine_Learning_Algorithms_from_Scratch/blob/main/ML_Algorithms_Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IcQieWIdoRMA"
      },
      "source": [
        "# **Machine Learning Algorithms: Linear Regression**\n"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "2DwiyV5IpBPB"
      },
      "source": [
        "## **Linear Regression Basics**\n",
        "\n",
        "**Regression** is a method of modelling a target value based on independent predictors. This method is mostly used for forecasting and finding out **cause and effect relationship between variables**. Regression techniques mostly differ based on the number of independent variables and the type of relationship between the independent and dependent variables. Regression problems usually have one continuous and unbounded dependent variable. The inputs, however, can be continuous, discrete, or even categorical data.\n",
        "\n",
        "**Linear Regression** with multiple variables is also known as **“multivariate linear regression”**. The multivariable form of the hypothesis function accommodating these multiple features is as follows:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xsk4rUxgLfJz"
      },
      "source": [
        "$$\n",
        "\\begin{align*}&\\mathrm{Hypothesis}: h_{\\theta}(x) = \\theta_{0} + \\theta_{1}x_{1} + \\theta_{2}x_{2} + \\theta_{3}x_{3} + \\cdot\\cdot\\cdot + \\theta_{n}x_{n} \\\\&\\mathrm{Cost \\ Function}: J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}(h_{\\theta}(x^{(i)})-y^{(i)})^2 \\\\&\\mathrm{Goal}: \\min_{\\theta}J(\\theta) \\\\\\end{align*}\n",
        "$$"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "AVw1Ho3gFOAo"
      },
      "source": [
        "## **Gradient Descent for Linear Regression**\n",
        "\n",
        "Gradient descent is a generic optimization algorithm used in many machine learning algorithms. It iteratively tweaks the parameters of the model in order to minimize the cost function. We do this is by taking the **derivative** (the tangential line to a function) of our cost function. The slope of the tangent is the derivative at that point and it will give us a direction to move towards. We make steps down the cost function in the direction with the steepest descent. The size of each step is determined by the parameter **$\\alpha$**, which is called the **learning rate**. The **gradient descent algorithm** can be represented as:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uqlFMekFF19U"
      },
      "source": [
        "$$\\begin{align*}  \n",
        "&\\frac{\\partial J(\\theta)}{\\partial \\theta_{0}}= \\frac{1}{m}\\sum_{i=1}^{m}(h_{\\theta}(x^{(i)})-y^{(i)}) \\\\\n",
        "&\\frac{\\partial J(\\theta)}{\\partial \\theta_{j}}= \\frac{1}{m}\\sum_{i=1}^{m}(h_{\\theta}(x^{(i)})-y^{(i)})x_{j}^{(i)} \\\\\n",
        "\\end{align*}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wNOak6y8F6TK"
      },
      "source": [
        "$$\n",
        "\\begin{bmatrix}\n",
        "\\theta_{0} \\\\\n",
        "\\theta_{1} \\\\\n",
        "\\cdot\\cdot\\cdot \\\\\n",
        "\\theta_{n}\n",
        "\\end{bmatrix}\n",
        "= \n",
        "\\begin{bmatrix}\n",
        "\\theta_{0} \\\\\n",
        "\\theta_{1} \\\\\n",
        "\\cdot\\cdot\\cdot \\\\\n",
        "\\theta_{n}\n",
        "\\end{bmatrix} \n",
        "-\n",
        "\\alpha\n",
        "\\begin{bmatrix}\n",
        "\\frac{\\partial J(\\theta)}{\\partial \\theta_{0}} \\\\\n",
        "\\frac{\\partial J(\\theta)}{\\partial \\theta_{1}} \\\\\n",
        "\\cdot\\cdot\\cdot \\\\\n",
        "\\frac{\\partial J(\\theta)}{\\partial \\theta_{n}}\n",
        "\\end{bmatrix}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "laU-yNy6GBxG"
      },
      "source": [
        "$$\\begin{align*}  \n",
        "&repect\\ until \\ convergence\\{ \\\\\n",
        "&\\ \\ \\ \\ \\theta_{j} :=\\theta_{j} - \\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_{\\theta}(x^{(i)})-y^{(i)})x_{j}^{(i)}) \\ \\ \\ \\ for \\ j := 0 \\cdot\\cdot\\cdot n \\\\\n",
        "&\\} \\\\\n",
        "\\end{align*}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hr30u-4-GKBL"
      },
      "source": [
        "We should adjust our parameter $\\alpha$ to ensure that the gradient descent algorithm converges in a reasonable time. **If $\\alpha$ is too small**, gradient descent can be slow. **If $\\alpha$ is too large**, gradient descent can overshoot the minimum. It may fail to converge, or even diverge. Failure to converge or too much time to obtain the minimum value imply that our step size is wrong."
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "cqXBx2XaGctv"
      },
      "source": [
        "## **Evaluation Metrics for Linear Regression**\n",
        "\n",
        "We can use **Mean squared error(MSE)** and **Root mean squared error(RMSE)** to evaluate our model. The Mean Squared Error (MSE) of an estimator measures the average of error squares i.e. the average squared difference between the estimated values and true value. MSE is defined by:\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MWKqwIIjLkA8"
      },
      "source": [
        "$$ MSE = \\frac{1}{m}\\sum_{i=1}^{m}(h(x^{(i)})-y^{(i)})^2$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n4gby4zgLmIT"
      },
      "source": [
        "RMSE is the square root of the average of the sum of the squares of residuals. RMSE is defined by:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LnkROLxgLn8p"
      },
      "source": [
        "\n",
        "$$ RMSE = \\sqrt{\\frac{1}{m}\\sum_{i=1}^{m}(h(x^{(i)})-y^{(i)})^2}$$"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "TEzCa_vjo2rs"
      },
      "source": [
        "## **Dataset Initialization**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "AuGSGmD6niYS"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "Hs3J6bsFqkeT"
      },
      "outputs": [],
      "source": [
        "np.random.seed(10)\n",
        "x = np.random.rand(100, 1)\n",
        "y = 2 + 3 * x + np.random.rand(100, 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "3iQgwDa1rBzR",
        "outputId": "629b2058-68dd-48bf-d6e2-bf78e5938129"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Y')"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y)\n",
        "ax.set_title('Linear Regression Random Data')\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "tcxmp5cLrlqz"
      },
      "source": [
        "## **Implementing Linear Regression from scratch**\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "on7B7eRbrWeV"
      },
      "outputs": [],
      "source": [
        "class LinearRegressionUsingGD:\n",
        "    def __init__(self, learning_rate=0.05, n_iterations=1000):\n",
        "        self.learning_rate = learning_rate\n",
        "        self.n_iterations = n_iterations\n",
        "    \n",
        "    def MSE(self, x, y):\n",
        "        return np.square(np.subtract(x,y)).mean()\n",
        "    \n",
        "    def fit(self, x, y):\n",
        "        self.iters, self.losses = [], []\n",
        "        self.m = x.shape[0]\n",
        "        self.theta = np.zeros((x.shape[1]+1,1))\n",
        "        self.new_x = np.concatenate((np.ones((100,1)),x), axis=1)\n",
        "\n",
        "        for i in range(self.n_iterations):\n",
        "            y_pred = np.dot(self.new_x, self.theta) # h_{\\theta}(x)\n",
        "            residuals = y_pred - y # (h_{\\theta}(x) - y)\n",
        "            gradient_vector = np.dot(self.new_x.T, residuals) # x^{T}.(h_{\\theta}(x) - y)\n",
        "            self.theta -= (self.learning_rate / self.m) * gradient_vector\n",
        "            loss = np.sum((residuals ** 2)) / (2 * self.m) # cost function (1/2m).sum(h_{\\theta}(x) - y)^2)\n",
        "            self.iters.append(i)\n",
        "            self.losses.append(loss)\n",
        "\n",
        "        self.plot_curve()\n",
        "        print(\"Final MSE: {}\".format(self.MSE(self.predict(x),y)))\n",
        "        print(\"Slope:\", self.theta[1:])\n",
        "        print(\"Intercept:\", self.theta[:1])\n",
        "    \n",
        "    def predict(self, x):\n",
        "        return np.dot(self.new_x, self.theta)\n",
        "    \n",
        "    def plot_curve(self):\n",
        "        plt.title(\"Training Curve\")\n",
        "        plt.plot(self.iters, self.losses, label=\"Train\")\n",
        "        plt.xlabel(\"Iterations\")\n",
        "        plt.ylabel(\"Loss\")\n",
        "        plt.show()\n",
        "\n",
        "        print(\"Final Training Loss: {}\".format(self.losses[-1]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "id": "WAxyRsLzUXrP",
        "outputId": "e6292fe4-4dd1-4cc5-f586-1fd2c8ccec2c"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Final Training Loss: 0.03743135871093361\n",
            "Final MSE: 0.0748452010424157\n",
            "Slope: [[2.8674393]]\n",
            "Intercept: [[2.52497525]]\n"
          ]
        }
      ],
      "source": [
        "# Model initialization\n",
        "Linear_Regression_GD = LinearRegressionUsingGD(learning_rate=0.5, n_iterations=100)\n",
        "# Fit the data(train the model)\n",
        "Linear_Regression_GD.fit(x, y)\n",
        "# Predict\n",
        "y_pred = Linear_Regression_GD.predict(x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "dzCf3YKGUYhY",
        "outputId": "426239a2-c296-4885-f59f-9ce703e294db"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9c79169400>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y, label='Data Point')\n",
        "plt.plot(x, y_pred, color='red', label='Linear Regression')\n",
        "ax.set_title('Linear Regression Random Data')\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "plt.legend()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "-Nzxb6nDjJ1Z"
      },
      "source": [
        "## **Implementing Linear Regression from Scikit-learn**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "E_rjFO-yVzNt"
      },
      "outputs": [],
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import mean_squared_error"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TqcK-Q_sjS1h",
        "outputId": "dcbf0826-8470-4783-e26b-907a8821030c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Slope: [[2.92754349]]\n",
            "Intercept: [2.49392672]\n",
            "Mean squared error:  0.07456852793404223\n"
          ]
        }
      ],
      "source": [
        "# Model initialization\n",
        "regression_model = LinearRegression()\n",
        "# Fit the data(train the model)\n",
        "regression_model.fit(x, y)\n",
        "# Predict\n",
        "y_predicted = regression_model.predict(x)\n",
        "\n",
        "# model evaluation\n",
        "mse = mean_squared_error(y, y_predicted)\n",
        "\n",
        "# printing values\n",
        "print('Slope:' ,regression_model.coef_)\n",
        "print('Intercept:', regression_model.intercept_)\n",
        "print('Mean squared error: ', mse)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "C67GsoX7jaFN",
        "outputId": "0edfbd23-6935-44ca-c1d4-531f1ad82ac2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9c71613730>"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y, label='Data Point')\n",
        "plt.plot(x, y_predicted, color='red', label='Scikit-learn Linear Regression')\n",
        "ax.set_title('Linear Regression Random Data')\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "plt.legend()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## **Reference**\n",
        "\n",
        "* Agarwal, A. (2018, November 14). Linear regression using python. Medium. Retrieved January 23, 2023, from `https://towardsdatascience.com/linear-regression-using-python-b136c91bf0a2` "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8uiPYdvRkA3j",
        "outputId": "960f172b-20d0-454c-9bb9-dcddac459cb7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[NbConvertApp] Converting notebook ML_Algorithms_Linear_Regression.ipynb to html\n",
            "[NbConvertApp] Writing 363742 bytes to ML_Algorithms_Linear_Regression.html\n"
          ]
        },
        {
          "data": {
            "text/plain": []
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "%%shell\n",
        "jupyter nbconvert --to html ML_Algorithms_Linear_Regression.ipynb"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "authorship_tag": "ABX9TyNaKoEhqi5r19pECsFqM/Ka",
      "include_colab_link": true,
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.8.2 (default, Dec 21 2020, 15:06:04) \n[Clang 12.0.0 (clang-1200.0.32.29)]"
    },
    "vscode": {
      "interpreter": {
        "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}