Belief update in CLG Bayesian networks with lazy propagation

In recent years, Bayesian networks with a mixture of continuous and discrete variables have received an increasing level of attention. In this paper, we focus on the restricted class of mixture Bayesian networks known as conditional linear Gaussian Bayesian networks (CLG Bayesian networks) and present an architecture for exact belief update for this class of mixture networks.The proposed architecture is an extension of lazy propagation using operations of Lauritzen and Jensen [S.L. Lauritzen, F. Jensen, Stable local computation with mixed Gaussian distributions, Statistics and Computing 11(2) (2001) 191–203] and Cowell [R.G. Cowell, Local propagation in conditional Gaussian Bayesian networks, Journal of Machine Learning Research 6 (2005) 1517–1550]. By decomposing clique and separator potentials into sets of factors, the proposed architecture takes advantage of independence and irrelevance properties induced by the structure of the graph and the evidence. The resulting benefits are illustrated by examples and assessed by experiments.The performance of the proposed architecture has been evaluated using a set of randomly generated networks. The results indicate a significant potential of the proposed architecture.