Importance Sampling for General Hybrid Bayesian Networks

Some real problems are more naturally modeled by hybrid Bayesian networks that consist of mixtures of continuous and discrete variables with their interactions described by equations and continuous probability distributions. However, inference in such general hybrid models is hard. Therefore, existing approaches either only deal with special instances, such as Conditional Linear Gaussians (CLGs), or approximate a general model with a restricted version and then perform inference on the simpler model. However, results thus obtained highly depend on the quality of the approximations. This paper describes an importance sampling-based algorithm that directly deals with hybrid Bayesian networks constructed in the most general settings and guarantees to converge to the correct answers given enough time.