Recurrent high-order networks for probabilistic explanation

Bayesian belief networks are a popular connectionist knowledge representation for reasoning under uncertainty. An important problem on belief networks is finding the most probable explanation for a given set of observances ε, known as the evidence. The objective is to find the network assignment A with highest conditional probability P(A/ε). In this paper, we show how a (k+1)-order recurrent network can be used to find high-probability assignments for a belief network with a maximum in-degree of k. We describe the results of applying our method to a number of belief networks with maximum in-degrees of two, three and four