Evidence Absorption and Propagation through Evidence Reversals

TL;DR

This paper introduces evidence reversal, an extension of arc reversal for probabilistic inference that handles instantiated evidence, offering a unified view of existing algorithms and insights into belief network computations.

Contribution

It extends arc reversal to evidence reversal for belief networks with evidence, unifying and clarifying the relationship among key inference algorithms.

Findings

Evidence reversal enables computing posterior distributions with evidence.

All three algorithms are identical on forest-structured networks.

Provides new insights into Pearl's and Lauritzen-Spiegelhalter's methods.

Abstract

The arc reversal/node reduction approach to probabilistic inference is extended to include the case of instantiated evidence by an operation called "evidence reversal." This not only provides a technique for computing posterior joint distributions on general belief networks, but also provides insight into the methods of Pearl [1986b] and Lauritzen and Spiegelhalter [1988]. Although it is well understood that the latter two algorithms are closely related, in fact all three algorithms are identical whenever the belief network is a forest.