Using Qualitative Relationships for Bounding Probability Distributions
This work addresses the challenge of efficient probabilistic inference in Bayesian networks, which is incremental as it builds on existing qualitative methods.
The paper tackles the problem of bounding conditional probability distributions in Bayesian networks by exploiting qualitative probabilistic relationships, resulting in an algorithm that provides monotonically tightening bounds converging to exact distributions.
We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well.