Efficient belief propagation in second-order Bayesian networks for singly-connected graphs

Second-order Bayesian networks extend Bayesian networks by incorporating uncertainty in the conditional probabilities. This paper develops a method for inference in a binary second-order Bayesian network with a singly-connected graph that builds upon the message-passing algorithm for regular belief propagation by leveraging recent developments in subjective logic. The method applies the moment-matching approach to the Beta representation of the uncertain probabilities. We provide experimental analysis which shows that the introduced method effectively captures the bounds for the actual error in a consistent manner and, at the same time, does not decrease the efficiency of the performance compared to the other similar approaches.