A Time and Space Efficient Junction Tree Architecture

TL;DR

This paper introduces two novel junction tree architectures, ARCH-1 and ARCH-2, that improve computational efficiency by combining the speed of Hugin propagation with lower space requirements, addressing limitations of existing methods.

Contribution

The paper proposes two new architectures for junction tree belief propagation that optimize time and space efficiency, outperforming existing architectures in various scenarios.

Findings

ARCH-1 combines Hugin speed with Shafer-Shenoy space efficiency.

ARCH-2 offers improved speed and space complexity, especially with high-degree vertices.

Both architectures outperform traditional methods in computational benchmarks.

Abstract

The junction tree algorithm is a way of computing marginals of boolean multivariate probability distributions that factorise over sets of random variables. The junction tree algorithm first constructs a tree called a junction tree who's vertices are sets of random variables. The algorithm then performs a generalised version of belief propagation on the junction tree. The Shafer-Shenoy and Hugin architectures are two ways to perform this belief propagation that tradeoff time and space complexities in different ways: Hugin propagation is at least as fast as Shafer-Shenoy propagation and in the cases that we have large vertices of high degree is significantly faster. However, this speed increase comes at the cost of an increased space complexity. This paper first introduces a simple novel architecture, ARCH-1, which has the best of both worlds: the speed of Hugin propagation and the low space requirements of Shafer-Shenoy propagation. A more complicated novel architecture, ARCH-2, is then introduced which has, up to a factor only linear in the maximum cardinality of any vertex, time and space complexities at least as good as ARCH-1 and in the cases that we have large vertices of high degree is significantly faster than ARCH-1.