Implementing Linear Regression Using Gradient Descent Method

Gradient descent is a widely used optimization algorithm in machine learning, particularly suitable for problems like linear regression. Implementing gradient descent for linear regression in MATLAB helps understand the algorithm's core concepts and its practical applications in machine learning.

The core principle of gradient descent involves iteratively adjusting model parameters (such as weights and biases in linear regression) to minimize the loss function (e.g., mean squared error). During each iteration, the algorithm updates parameters along the gradient direction of the loss function at the current parameter values, gradually approaching the optimal solution. Key implementation aspects include defining learning rates and convergence criteria.

MATLAB implementation typically follows these steps: First, define the hypothesis function (e.g., linear function h_θ(x) = θ₀ + θ₁x). Second, compute the loss function using mean squared error: J(θ) = (1/2m)∑(h_θ(x⁽ⁱ⁾)-y⁽ⁱ⁾)². Third, calculate gradients using partial derivatives ∂J/∂θⱼ and update parameters through θⱼ := θⱼ - α(∂J/∂θⱼ). This process repeats until convergence or reaching preset iterations.

Gradient descent's advantages include simplicity and ease of implementation, but requires careful learning rate selection. Excessive learning rates may prevent convergence, while insufficient rates slow convergence speed. MATLAB's matrix computation capabilities make gradient descent implementation highly efficient, especially for large-scale dataset training through vectorized operations.

For beginners, implementing linear regression with gradient descent in MATLAB serves as excellent introductory practice. It not only helps understand fundamental optimization concepts but also builds foundation for learning more complex machine learning models. Key MATLAB functions involved might include matrix operations, loop structures, and convergence plotting functions.