Hierarchical Junction Trees: Conditional Independence Preservation and Forecasting in Dynamic Bayesian Networks with Heterogeneous Evolution

Abstract

Propagation in decomposable Bayesian networks with junction trees is inferentially efficient: no conditional independence in the Bayesian network is ignored in the junction tree construction and in any propagation task. For nondecomposable Bayesian networks, the junction tree construction uses moralisation and triangulation that ignore some of the conditional independence. The junction tree, therefore, trades inferential efficiency with generality: it can be used to compute the distribution of any set of target nodes given any set of conditioning nodes.In this chapter inferential efficiency for non-decomposable Bayesian networks is addressed. We present the hierarchical junction tree, a framework that transparently represents the conditional independence in the Bayesian network. We discuss propagation tasks where conditional independence is not ignored in the construction of the hierarchical junction tree and in the propagation tasks. We also discuss their use for efficient exact forecasting in dynamic Bayesian network with heterogeneous evolution.