Implementing Logistic Regression in MATLAB: Obtaining Final Regression Parameters Using Newton's Iteration Method

When implementing logistic regression in MATLAB, we can obtain the final regression parameters using the Newton iteration method. During the Newton iteration process, parameters are updated based on the gradient of the loss function, with iterations repeated until convergence is achieved. The key implementation involves calculating the Hessian matrix and gradient vector at each iteration step to update parameters using the Newton-Raphson update rule: θ_new = θ_old - H^(-1)∇J(θ), where H represents the Hessian matrix and ∇J(θ) is the gradient of the cost function. Additionally, we can further optimize model performance by adjusting hyperparameters such as the regularization parameter (lambda) and learning rate. The regularization term helps prevent overfitting by adding a penalty to the cost function, typically implemented as (lambda/2m)*sum(theta(2:end).^2) in the code. The algorithm typically includes convergence checks using tolerance thresholds or maximum iteration limits to ensure computational efficiency. In practice, MATLAB's matrix operations efficiently handle the necessary calculations for gradient descent and Hessian matrix computation. Key functions often involve implementing the sigmoid function (1./(1+exp(-z))), computing cost functions with regularization, and creating iteration loops with convergence conditions. Overall, logistic regression serves as a powerful classification algorithm that finds widespread applications across various domains, particularly in binary classification problems where probability estimates are required. The Newton method provides quadratic convergence near the optimum, making it particularly efficient for logistic regression optimization when the feature space is not excessively large.