Minimal Assumption Distribution Propagation in Belief Networks

As belief networks are used to model in­ creasingly complex situations, the need to automatically construct them from large databases will become paramount. This pa­ per concentrates on solving a part of the belief network induction problem: that of learning the quantitative structure (the con­ ditional probabilities), given the qualitative structure. In particular, a theory is presented that shows how to propagate inference dis­ tributions in a belief network, with the only assumption being that the given qualitative structure is correct. Most inference algo­ rithms must make at least this assumption. The theory is based on four network transfor­ mations that are sufficient for any inference in a belief network. Furthermore, the claim is made that contrary to popular belief, er­ ror will not necessarily grow as the inference chain grows. Instead, for QBN belief nets in­ duced from large enough samples, the error is more likely to decrease as the size of the inference chain increases.