Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians
This work addresses a bottleneck in probabilistic modeling for researchers and practitioners by extending exact inference capabilities to more complex hybrid Bayesian networks, though it is incremental as it builds on existing MoG methods.
The paper tackles the problem of exact inference in hybrid Bayesian networks with mixed discrete and continuous variables by approximating them as mixtures of Gaussians, enabling the use of the fast Lauritzen-Jensen algorithm for a broader class of networks, including those with non-Gaussian distributions and nonlinear dependencies.
The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG Bayesian networks, and there exists a commercial implementation of this algorithm. However, this algorithm can only be used for MoG BNs. Some limitations of such networks are as follows. All continuous chance variables must have conditional linear Gaussian distributions, and discrete chance nodes cannot have continuous parents. The methods described in this paper will enable us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This includes networks with continuous chance nodes with non-Gaussian distributions, networks with no restrictions on the topology of discrete and continuous variables, networks with conditionally deterministic variables that are a nonlinear function of their continuous parents, and networks with continuous chance variables whose variances are functions of their parents.