Efficient Inference in General Hybrid Bayesian Networks for Classification

This chapter develops a hybrid propagation algorithm for general Bayesian networks with mixed discrete and continuous variables. It reviews the Pearl's message passing formulae, and discusses the message representation and manipulation for continuous variable and how to propagate messages between continuous variables with nonlinear functional relationship. The chapter describes the methods of network partition and message integration by introducing the concept of interface nodes. It shows how message passing could be done separately and finally integrated together via the channel of interface nodes. For complicated network segment such as the one with nonlinear and/or non‐Gaussian variables, one provide options to use loopy‐type message passing algorithm. Another recently developed method termed direct message passing (DMP) can propagate messages between different types of variables directly. The chapter focuses on developing a unified message passing algorithm for general hybrid networks popularly used in classification problems.