Exploiting Contextual Independence and Approximation in Belief Network Inference

Recently there has been some evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network is too coarse; it is unlikely that a parent will make little difference for all values of the other parents. A representation in terms of rules or trees, is at a more appropriate level; in some contexts the differences in values may be insignificant. This paper presents (a) a formal definition of a parent context that allows a structured decomposition of a probability distribution, (b) a way to simplify a probabilistic model by ignoring distinctions which have similar probabilities, (c) a method to exploit the simpler model, (d) a bound on the resulting errors, and (e) some empirical results on simple networks. 1 Introduction Bayesian networks (Pearl 1988) are a representation of independence amongst random variables. They are of in..