MPE inference in conditional linear gaussian networks

Given evidence on a set of variables in a Bayesian network, the most probable explanation (MPE) is the problem of finding a configuration of the remaining variables with maximum posterior probability. This problem has previously been addressed for discrete Bayesian networks and can be solved using inference methods similar to those used for finding posterior probabilities. However, when dealing with hybrid Bayesian networks, such as conditional linear Gaussian (CLG) networks, the MPE problem has only received little attention. In this paper, we provide insights into the general problem of finding an MPE configuration in a CLG network. For solving this problem, we devise an algorithm based on bucket elimination and with the same computational complexity as that of calculating posterior marginals in a CLG network. We illustrate the workings of the algorithm using a detailed numerical example, and discuss possible extensions of the algorithm for handling the more general problem of finding a maximum a posteriori hypothesis (MAP).