Probabilistic Decision Graphs - Combining Verification and AI Techniques for Probabilistic Inference

We adopt probabilistic decision graphs developed in the field of automated verification as a tool for probabilistic model representation and inference. We show that probabilistic inference has linear time complexity in the size of the probabilistic decision graph, that the smallest probabilistic decision graph for a given distribution is at most as large as the smallest junction tree for the same distribution, and that in some cases it can in fact be much smaller. Behind these very promising features of probabilistic decision graphs lies the fact that they integrate into a single coherent framework a number of representational and algorithmic optimizations developed for Bayesian networks (use of hidden variables, context-specific independence, structured representation of conditional probability tables).