  Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous
variables, arise naturally in many application areas (e.g., image
understanding, data fusion, medical diagnosis, fraud detection). This paper
concerns inference in an important subclass of HBNs, the conditional Gaussian
(CG) networks, in which all continuous random variables have Gaussian
distributions and all children of continuous random variables must be
continuous. Inference in CG networks can be NP-hard even for special-case
structures, such as poly-trees, where inference in discrete Bayesian networks
can be performed in polynomial time. Therefore, approximate inference is
required. In approximate inference, it is often necessary to trade off accuracy
against solution time. This paper presents an extension to the Hybrid Message
Passing inference algorithm for general CG networks and an algorithm for
optimizing its accuracy given a bound on computation time. The extended
algorithm uses Gaussian mixture reduction to prevent an exponential increase in
the number of Gaussian mixture components. The trade-off algorithm performs
pre-processing to find optimal run-time settings for the extended algorithm.
Experimental results for four CG networks compare performance of the extended
algorithm with existing algorithms and show the optimal settings for these CG
networks.
