Hybrid loopy belief propagation

We propose an algorithm called Hybrid Loopy Belief Propagation (HLBP), which extends the Loopy Belief Propagation (LBP) (Murphy et al., 1999) and Nonparametric Belief Propagation (NBP) (Sudderth et al., 2003) algorithms to deal with general hybrid Bayesian networks. The main idea is to represent the LBP messages with mixture of Gaussians and formulate their calculation as Monte Carlo integration problems. The new algorithm is general enough to deal with hybrid models that may represent linear or nonlinear equations and arbitrary probability distributions.