Bayesian Networks, 2nd Edition

6

Theory and Algorithms for Bayesian Networks

In this chapter we will provide the theoretical foundations underpinning the classes of BNs we explored in the previous chapters. In particular, we will introduce the formal definition of a BN and its fundamental properties. We will then show how these properties provide a rigorous foundation for BN learning and inference.

6.1 Conditional Independence and Graphical Separation

BNs are a class of graphical models, which allow an intuitive representation of the probabilistic structure of multivariate data using graphs. We introduced them in Chapter 1 as the combination of:

• A set of random variables $X=\{X_1,X_2,\dots ,X_p\}$ describing the quantities of interest. The multivariate probability distribution ...