Inference and Learning in Hybrid Bayesian Networks
Kevin P. Murphy · 1998
We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities. 1 1 Introduction We discuss Bayesian networks (BNs [Jen96]) in which each node is either discrete or continuous, scalar or vector-valued, and in which the joint distribution over all the nodes is Conditional Gaussian (CG) [LW89, Lau92] i.e., for each instantiation i of the discrete nodes Y, the distribution over the continuous nodes X has the form f(xjY = i) = N (x; ~¯(i); \\Sigma(i)), where N () represents a multivariate Gaussian (MVG) or Normal density. (Note...