Modular Bayesian networks: reasoning, verification and model inaccuracies
Patrick de Oude · UvA-DARE (University of Amsterdam) · 2010
ReasoningIn this chapter we discuss design principles for modular Bayesian inference systems which can (i) cope with large quantities of heterogeneous information and (ii) can adapt to changing constellations of information sources on the fly.Locality of causal relations between variables in the problem domain facilitates decentralized modeling and inference.With the help of the theory of Bayesian networks and factor graphs we derive design and assembly rules to construct modular inference systems that support exact distributed inference without any centralized configuration and control.While the design rules guarantee that the local Bayesian network models correctly capture dependencies between all distributed variables, the assembly rules, on the other hand, guarantee that globally coherent message passing is supported.With the help of the assembly rules we can handle situations where the set of Bayesian network models does not correspond to hyper trees, while the internals of local inference models remain private.This is accomplished through targeted instantiations of variables with hard evidence.This chapter is organized as follows: in Section 3.1 and Section 3.2 we start with an introduction and related work, respectively.Next, in Section 3.3 a causal model for gas detection is discussed that is used as a running example throughout the chapter and in Section 3.4 we discuss the corresponding factor graph of the causal model, which provides a basis for the investigation of properties of distributed system.In Section 3.5 we formalize the notions of modular inference systems and in Section 3.6 we discuss the design and assembly rules to construct modular inference systems that support globally coherent inference.In this section we also discuss an algorithm for distributed inference through message passing between local inference models.Finally, in Section 3.7 we conclude the chapter with a discussion.