On state-space abstraction for anytime evaluation of Bayesian networks

Despite the increasing popularity of Bayesian networks for representing and reasoning about uncertain situations, the complexity of inference in this formalism remains a significant concern. A viable approach to relieving the problem is trading off accuracy for computational efficiency. To this end, varying the granularity of state space of state variables appears to be a feasible strategy for controlling the evaluation process. We consider an anytime procedure for approximate evaluation of Bayesian networks based on this idea. On application to some simple networks, the procedure exhibits a smooth improvement in approximation quality as computation time increases. With the aim of developing principled control techniques, we also conduct a theoretical analysis of the quality of approximation. Our main result demonstrates that the error induced by state-space abstraction deceases with the distance from the abstracted nodes, where "distance" is defined in terms of d-separation. While the empirical results suggest that incremental state-space abstraction offers a viable performance profile, the theoretical results represent a starting point for the deliberation scheduling of our anytime approximation method.