Nested Junction Trees

TL;DR

This paper introduces nested junction trees to optimize message passing in Bayesian network inference, significantly reducing computational costs by exploiting independence relations within clique potentials.

Contribution

It presents a structured method for using nested junction trees to improve inference efficiency in Bayesian networks, with empirical validation.

Findings

Reduced space and time complexity in inference algorithms

Effective in large real-world Bayesian networks

Empirical results demonstrate significant efficiency gains

Abstract

The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy architectures can be improved by exploiting the independence relations induced by the incoming messages of a clique. That is, the message to be sent from a clique can be computed via a factorization of the clique potential in the form of a junction tree. In this paper we show that by exploiting such nested junction trees in the computation of messages both space and time costs of the conventional propagation methods may be reduced. The paper presents a structured way of exploiting the nested junction trees technique to achieve such reductions. The usefulness of the method is emphasized through a thorough empirical evaluation involving ten large real-world Bayesian networks and the Hugin inference algorithm.