Advances in Applying Stochastic-Dominance Relationships to Bounding Probability Distributions in Bayesian Networks

Bounds of probability distributions are useful for many reasoning tasks, including resolving the qualitative ambiguities in qualitative probabilistic networks and searching the best path in stochastic transportation networks. This paper investigates a subclass of the state-space abstraction methods that are designed to approximately evaluate Bayesian networks. Taking advantage of particular stochastic-dominance relationships among random variables, these special methods aggregate states of random variables to obtain bounds of probability distributions at much reduced computational costs, thereby achieving high responsiveness of the overall system. The existing methods demonstrate two drawbacks, however. The strict reliance on the particular stochasticdominance relationships confines their applicability. Also, designed for general Bayesian networks, these methods might not achieve their best performance in special domains, such as fastest-path planning problems. The author elaborates on these problems, and offers extensions to improve the existing approximation techniques.