Linear Regression Using Gradient Descent Algorithm

In the example presented in this document, we implement linear regression using the gradient descent method in MATLAB, which is a fundamental approach in machine learning. Gradient descent is an optimization algorithm that iteratively adjusts model parameters to minimize the loss function. For linear regression, we aim to find the best-fitting line that minimizes the discrepancy between predicted values and actual observations. The gradient descent algorithm helps us achieve this by calculating the gradient of the cost function with respect to the parameters and updating them in the opposite direction of the gradient. Key implementation aspects include: - Defining the hypothesis function: h_θ(x) = θ₀ + θ₁x - Calculating the cost function: J(θ) = (1/2m)∑(h_θ(xⁱ)-yⁱ)² - Implementing parameter updates: θⱼ := θⱼ - α(∂J(θ)/∂θⱼ) - Setting appropriate learning rate α and convergence criteria This method can be applied to various machine learning problems beyond linear regression. Therefore, mastering gradient descent is essential for machine learning practitioners. It serves as a powerful practical tool that enables better results in real-world problems through efficient parameter optimization and model training.