Minimal Assumption Distribution Propagation in Belief Networks

TL;DR

This paper introduces a theory for propagating inference distributions in belief networks with minimal assumptions, showing that error may decrease with larger inference chains in large-sample networks.

Contribution

It presents a novel method for distribution propagation in belief networks based on four transformations, requiring only correct qualitative structure assumptions.

Findings

Error does not necessarily grow with inference chain length.

In large-sample belief networks, error may decrease as inference chains lengthen.

The theory is applicable to automatically constructing belief networks from large databases.

Abstract

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