Improving Search-Based Inference in Bayesian Networks

A method for improving search-based inference techniques in Bayesian networks by obtaining a prior estimation of the error is presented. The method is based on a recently introduced algorithm for calculating the contribution of a given set of instantiations to the total probability mass. If a certain accuracy for the solution is desired, the method provides us with the number of replications (i.e., the sample size) needed for obtaining the approximated values with the desired accuracy. In addition to providing a prior stopping rule, the method substantially reduces the structure of the search tree and, hence, the computer time required for the process. Important savings are obtained in the case of Bayesian networks with extreme probabilities, as it is shown with the examples reported in the paper. As an example of several possible applications of the method, the problem of finding a maximal posteriori (MAP) instantiation of the Bayesian network variables, given a partial value assignment as an initial constraint, is presented.