Maximum A Posteriori (MAP) and Regularization with Priors

Maximum a posteriori (MAP)

Before moving to more complex multivariate models, this is a good opportunity to discuss regularization within a Bayesian framework again. Maximum likelihood estimation is the workhorse of probabilistic supervised learning, though it is useful to put this into an even wider context of probabilistic modeling. In the probabilistic sense, choosing parameter values, given the data, should be based on a model of the parameters themselves, as shown below: