How does Naïve Bayes relate to maximum likelihood estimation (MLE) and maximum a posteriori (MAP) estimation?

Naïve Bayes parameters are typically estimated using MLE, while MAP incorporates prior distributions for regularization.

In Naïve Bayes, likelihood parameters like P(x|C) are estimated using Maximum Likelihood Estimation (MLE), which uses observed frequency counts. MAP estimation extends MLE by incorporating priors over parameters, effectively regularizing estimates. This is particularly useful in sparse data scenarios where MLE may overfit rare events. Laplace smoothing can be interpreted as a MAP estimator with a Dirichlet prior.