Linear Regression & Extended Gradient Descent in Machine Learning Using Python (MLUP-101) Module 06 Part 01, Session 10

In this tutorial, we will be learning about Linear Regression and Extended Gradient Descent in Machine Learning using Python. This tutorial is part of the MLUP-101 course (Machine Learning Using Python – 101) and specifically covers Module 6, Part 1 – Session 10.

Linear Regression is a popular technique used in regression analysis to model the relationship between a dependent variable and one or more independent variables. It is one of the simplest machine learning algorithms and is a great starting point for beginners in the field of machine learning.

Extended Gradient Descent is an optimization algorithm used to find the minimum of a function. It is particularly useful in training machine learning models, including linear regression models.

In this tutorial, we will walk through the process of implementing linear regression and extended gradient descent from scratch in Python. We will be using the numpy library for mathematical operations and matplotlib for visualization.

Let’s get started by importing the necessary libraries:

import numpy as np
import matplotlib.pyplot as plt

Next, let’s generate some sample data for our linear regression model. We will use the following equation to generate our data:

np.random.seed(0)
X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)

Now, let’s visualize our data using a scatter plot:

plt.scatter(X, y)
plt.xlabel('X')
plt.ylabel('y')
plt.title('Sample Data for Linear Regression')
plt.show()

Next, we will implement the gradient descent algorithm to train our linear regression model. The formula for updating the parameters in gradient descent is as follows:

def gradient_descent(X, y, alpha=0.01, iterations=100):
    m = X.shape[0]
    theta = np.random.randn(2, 1)
    X_b = np.c_[np.ones((m, 1)), X]

    for i in range(iterations):
        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)
        theta = theta - alpha * gradients

    return theta

Now, let’s train our linear regression model using the gradient descent algorithm:

theta = gradient_descent(X, y)
print('Parameters of the Linear Regression Model: ', theta)

Finally, let’s visualize our linear regression model along with the sample data:

plt.scatter(X, y)
plt.plot(X, theta[0] + theta[1]*X, 'r')
plt.xlabel('X')
plt.ylabel('y')
plt.title('Linear Regression Model')
plt.show()

Congratulations! You have successfully implemented Linear Regression and Extended Gradient Descent in Python. This tutorial covered the basics of linear regression and gradient descent, which are essential concepts in machine learning. Feel free to experiment with different datasets and hyperparameters to further your understanding of these concepts. Thank you for following along with this tutorial!