Using Qualitative Relationships for Bounding Probability Distributions

Abstract

We exploit qualitative probabilistic relationships among variables for computing bounds of con- ditional probability distributions of interest in Bayesian networks. Using the signs of qualita- tive relationships, we can implement abstraction operations that are guaranteed to bound the dis- tributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distri- butions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well.