3 - Directed probabilistic graphical models

Abstract

This chapter formally introduces the directed probabilistic graphical models, i.e., Bayesian Networks (BNs). It first provides a definition of BNs, their important properties, and the types of BNs. It then discusses various BN inference methods, including both exact inference and approximate inference methods, for both posterior probability and MAP inferences. This chapter continues to discuss various learning methods to learn both the parameters and structures of BNs under both complete and incomplete training data. Finally, the chapter introduces dynamic Bayesian Networks, Hidden Markov models, and their associated learning and inference methods. This chapter ends with a discussion of the hierarchical Bayesian Networks, including both hierarchical Bayes models and the hierarchical deep models.