Advances in applying stochastic-dominance relationships to bounding probability distributions in Bayesian networks

Abstract

Bounds of probability distributions are useful for many reasoning tasks, including resolving the qualitative ambi- guities in qualitative probabilistic networks and search- ing the best path in stochastic transportation networks. This paper investigates a subclass of the state-space ab- straction methods that are designed to approximately evaluate Bayesian networks. Taking advantage of par- ticular stochastic-dominance relationships among ran- dom variables, these special methods aggregate states of random variables to obtain bounds of probability dis- tributions 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 stochastic- dominance relationships confines their applicability. Also, designed for general Bayesian networks, these methods might not achieve their best performance in spe- cial domains, such as fastest-path planning problems. The author elaborates on these problems, and offers ex- tensions to improve the existing approximation tech- niques.