Computing marginals for arbitrary subsets from marginal representation in Markov trees

Abstract

Markov trees and clique trees are the alternative representations of valuation networks and belief networks that are used by local computational techniques for efficient reasoning. However, once the Markov tree has been created, the existing techniques can only compute the marginals for the vertices of the Markov tree or for a subset of variables which is contained in one vertex. This paper presents a method for computing the marginal for a subset which may not be contained in one vertex, but is a subset of the union of several vertices. The proposed method allows us to change the Markov tree to include a vertex containing the new subset without changing any information in the original vertices, thus avoiding possible repeated computations. Moreover, it can compute marginals for any subsets from the marginal representation in the Markov tree. By using the presented method, we can easily update belief for some variables given some observations.