Message Passing for Hybrid Bayesian Networks: Representation, Propagation, and Integration

The traditional message passing algorithm was originally developed by Pearl in the 1980s for computing exact inference solutions for discrete polytree Bayesian networks (BN). When a loop is present in the network, propagating messages are not exact, but the loopy algorithm usually converges and provides good approximate solutions. However, in general hybrid BNs, the message representation and manipulation for arbitrary continuous variable and message propagation between different types of variables are still open problems. The novelty of the work presented here is to propose a framework to compute, propagate, and integrate the messages for hybrid models. First, we combine unscented transformation and Pearl's message passing algorithm to deal with the arbitrary functional relationships between continuous variables in the network. For the general hybrid model, we partition the network into separate parts by introducing the concept of interface node. We then apply different algorithms for each subnetwork. Finally we integrate the information through the channel of interface nodes and then estimate the posterior distributions for all hidden variables. The numerical experiments show that the algorithm works well for nonlinear hybrid BNs.