
4
Theory and Algorithms for Bayesian Networks
In this chapter we will provide the theoretical foundations underpinning the
classes of BNs we explored in Chapter 1 (discrete BNs), Chapter 2 (GBNs)
and Chapter 3 (hybrid BNs). In particular, we will introduce the formal defi-
nition of a BN and its fundamental properties. We will then show how these
properties are at the base of BN learning and inference.
4.1 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 have intro-
duced them in Chapter 1 as the combination ...