Hybrid message passing for mixed bayesian networks

The traditional message passing algorithm developed by Pearl in 1980s provides exact inference for discrete poly-tree Bayesian networks. When there are multiple paths (loops) in the network, we can still apply Pearl\´s algorithm to provide approximate solutions and it is so-called "loopy propagation". However, when mixed random variables (continuous and discrete variables) are present in the network, there is no theoretical sound method so far for efficient message passing. In this paper, we propose a novel approach to compute, propagate and integrate the messages for hybrid models. Specifically, we propose to first partition the network into separate parts by introducing the concept of interface nodes. We then apply different algorithms for each sub-network. Finally we integrate the information through the channel of interface nodes and then calculate the posterior distributions for all hidden variables. The numerical experiment results show that the algorithm works well for hybrid Bayesian networks.