Probabilistic Foundations for Machine Learning

Explain the difference between frequentist and Bayesian approaches to parameter estimation.

Derive Maximum Likelihood Estimation (MLE) for the parameters of a Gaussian distribution.

Apply Maximum A Posteriori (MAP) estimation to a linear regression problem.

Explain the concept of conjugate priors by deriving the posterior for a Beta-Binomial model.

Implement the training logic for a Gaussian Naive Bayes classifier from scratch.

Implement the prediction logic for a Gaussian Naive Bayes classifier from scratch.

Apply and evaluate a custom-built Naive Bayes classifier on a standard dataset.