Belief Updating by Enumerating High-Probability Independence-Based Assignments

TL;DR

This paper introduces a method for belief updating in Bayesian networks using high-probability independence-based assignments, which are more efficient and effective especially in highly-connected networks, by approximating marginal probabilities.

Contribution

The paper proposes novel algorithms for finding high-probability IB assignments, improving the efficiency of belief updating in complex Bayesian networks.

Findings

IB assignments contain fewer variables, leading to higher probability mass per assignment.

The proposed methods are effective for highly-connected networks where standard algorithms struggle.

Experimental results demonstrate the feasibility of the approach in complex network structures.

Abstract

Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially supported variables. We use IB assignments to approximate marginal probabilities in Bayesian belief networks. Recent work in belief updating for Bayes networks attempts to approximate posterior probabilities by finding a small number of the highest probability complete (or perhaps evidentially supported) assignments. Under certain assumptions, the probability mass in the union of these assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly-connected networks, where the maximum clique size or the cutset size make the standard algorithms intractable. Since IB assignments contain fewer assigned variables, the probability mass in each assignment is greater than in the respective complete assignment. Thus, fewer IB assignments are sufficient, and a good approximation can be obtained more efficiently. IB assignments can be used for efficiently approximating posterior node probabilities even in cases which do not obey the rather strict skewness assumptions used in previous research. Two algorithms for finding the high probability IB assignments are suggested: one by doing a best-first heuristic search, and another by special-purpose integer linear programming. Experimental results show that this approach is feasible for highly connected belief networks.