machine-learning/regression/univariate-linear-regression-implementation-with-batch-gradient-descent-from-scratch.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Univariate Linear Regression Implementation with Batch Gradient Descent from Scratch",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyN+/4d6QAay3jU1Vj4ZVRfG"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UejnaSULteQb"
      },
      "source": [
        "# **Univariate Linear Regression Implementation with Batch Gradient Descent from Scratch**\n",
        "*By Carlos Santiago Bañón*\n",
        "\n",
        "* **Year:** 2020\n",
        "* **Technologies:** Python, NumPy, Matplotlib\n",
        "* **Area(s):** Machine Learning, Regression\n",
        "* **Keywords:** `batch-gradient-descent`, `gradient-descent`, `linear-regression`, `machine-learning`, `regression`\n",
        "* **Description:** This notebook presents an implementation of univariate linear regression with batch gradient descent from scratch."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qo7fXeWTt7KA"
      },
      "source": [
        "## 1. Import Statements\n",
        "---"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1-lY_A_oRfr9"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DdQ4c2aNuRIA"
      },
      "source": [
        "## 2. Random Data Generation\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TSAosfUGuWQ2"
      },
      "source": [
        "To better visualize the data we are working with, we will be generating random data based on the specific linear function $f(x) = 2x + 3$. Doing so will allow us to better visualize the regression line after we train our model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WWqllHo4Qsw0"
      },
      "source": [
        "def f(X):\n",
        "  return (2 * X) + 3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xEq-p4PEuuBa"
      },
      "source": [
        "# Generate 100 training examples.\n",
        "m = 100\n",
        "X = np.random.rand(m, 1)\n",
        "y = f(X) + np.random.rand(m, 1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KPUk697wrMV3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "3f019d7e-5ab0-4da8-f062-d8695ba9b26f"
      },
      "source": [
        "# Plot the random data.\n",
        "plt.scatter(X, y)\n",
        "plt.title('Random Data for Linear Regression')\n",
        "plt.xlabel(r'$X$')\n",
        "plt.ylabel(r'$y$')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zw3GhUwUvqRj"
      },
      "source": [
        "## 3. Batch Gradient Descent\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3gBfeYr6vumD"
      },
      "source": [
        "Once we have our data ready, we must define the optimization algorithm we will be using in our linear regression model.\n",
        "\n",
        "Here, we will employ **Batch Gradient Descent**, which will help us minimize the parameters in our hypothesis function for linear regression."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aQRJKCXrwPNj"
      },
      "source": [
        "Therefore, we begin by defining the **Mean Squared Error (MSE)** cost function, which will be our cost function for batch gradient descent algorithm:\n",
        "\n",
        "$J(\\theta_0, \\theta_1) = \\frac{1}{2m} \\sum_{i = 1}^{m}(h_\\theta(x^{(i)})-y^{(i)})^2$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9iuSEP1aX7UX"
      },
      "source": [
        "def cost_function(X, y, theta):\n",
        "  \"\"\"\n",
        "  Compute the mean squared error cost function.\n",
        "\n",
        "  :X: the features.\n",
        "  :y: the labels.\n",
        "  :theta: the weights.\n",
        "  \"\"\"\n",
        "  \n",
        "  m = len(y)\n",
        "\n",
        "  # Calculate the hypothesis.\n",
        "  h = np.dot(X, theta)\n",
        "\n",
        "  # Calculate the squared error.\n",
        "  squared_error = (h - y) ** 2\n",
        "\n",
        "  # Sum all the squared errors and multiply by the reciprocal.\n",
        "  J = (1 / 2 * m) * np.dot(np.ones(m), squared_error)\n",
        "\n",
        "  return J"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OV2_DR4Kw-2X"
      },
      "source": [
        "Now, we're ready to formally define our batch gradient descent algorithm. Here, we employ the following instruction repeatedly for a certain number of iterations until our cost function is minimized:\n",
        "\n",
        "$\\theta_j := \\theta_j - \\alpha\\frac{\\partial}{\\partial\\theta_j}J(\\theta_0, \\theta_1)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zocRPluqYnr_"
      },
      "source": [
        "def batch_gradient_descent(X, y, theta, alpha, iterations):\n",
        "  \"\"\"\n",
        "  Minimize the cost using batch gradient descent.\n",
        "\n",
        "  :X: the features.\n",
        "  :y: the labels.\n",
        "  :theta: the weights.\n",
        "  :alpha: the learning rate.\n",
        "  :iterations: the number of iterations.\n",
        "  \"\"\"\n",
        "\n",
        "  m = len(y)\n",
        "  J_history = np.zeros((iterations, 1));\n",
        "\n",
        "  for i in range(iterations):\n",
        "\n",
        "    # Calculate the hypothesis.\n",
        "    h = np.dot(X, theta)\n",
        "\n",
        "    # Calculate the loss.\n",
        "    loss = h - y\n",
        "\n",
        "    # Calculate the gradient.\n",
        "    gradient = np.dot(X.T, loss) / m\n",
        "\n",
        "    # Adjust theta accordingly.\n",
        "    theta = theta - alpha * gradient\n",
        "\n",
        "    J_history[i] = cost_function(X, y, theta)\n",
        "  \n",
        "  # Plot the cost function.\n",
        "  plt.title('Cost Function')\n",
        "  plt.xlabel('Iterations')\n",
        "  plt.ylabel(r'$J(\\theta)$')\n",
        "  x = np.linspace(0, iterations, iterations)\n",
        "  plt.plot(x, J_history)\n",
        "  plt.show()\n",
        "\n",
        "  return theta"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ok4tD588y7Yc"
      },
      "source": [
        "## 4. Linear Regression\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x7LF7yLMx6IF"
      },
      "source": [
        "Once our minimization algorithm is defined, we can proceed to build our linear regression model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bfHTvMO1VBUb"
      },
      "source": [
        "def linear_regression(X, y):\n",
        "  \"\"\"\n",
        "  Perform linear regression and return the weights.\n",
        "\n",
        "  :X: the features.\n",
        "  :y: the labels.\n",
        "  \"\"\"\n",
        "  \n",
        "  # Set up our initial values.\n",
        "  alpha = 0.01\n",
        "  iterations = 500\n",
        "  theta = np.zeros((2, 1))\n",
        "\n",
        "  # Add an extra column of ones for vectorization.\n",
        "  X_train = np.append(np.ones((m, 1)), X, axis = 1)\n",
        "\n",
        "  # Calculate the cost.\n",
        "  J = cost_function(X_train, y, theta)\n",
        "\n",
        "  # Use batch gradient descent to minimize the cost.\n",
        "  theta = batch_gradient_descent(X_train, y, theta, alpha, iterations)\n",
        "\n",
        "  return theta"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ThKWOe3zyvRU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "outputId": "c6912624-b216-4d41-91e8-2d223b8d5c40"
      },
      "source": [
        "theta = linear_regression(X, y)\n",
        "\n",
        "print(\"Theta:\", theta)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Theta: [[3.537885  ]\n",
            " [1.95170603]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Y5R8FmOz-0G"
      },
      "source": [
        "Finally, once we have the values for $\\theta$ that minimize our cost function $J(\\theta)$, we can produce a final plot for our model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gQHUdo_JwREM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "226945ff-9f66-4aed-b386-d6b27d8afd91"
      },
      "source": [
        "# Plot the prediction line with the original data.\n",
        "plt.scatter(X, y)\n",
        "plt.title('Linear Regression')\n",
        "plt.xlabel(r'$X$')\n",
        "plt.ylabel(r'$y$')\n",
        "x = np.linspace(0, 1, 1000)\n",
        "plt.plot(x, x * theta[1] + theta[0], '-r')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}