Structural Dimension Reduction in Bayesian Networks

TL;DR

This paper presents a new method called structural dimension reduction for Bayesian networks, using directed convex hulls to simplify networks while maintaining inference accuracy, leading to improved efficiency over traditional methods.

Contribution

It introduces the concept of directed convex hulls and an algorithm to identify minimal localized Bayesian networks, enhancing dimension reduction and inference efficiency.

Findings

High dimension reduction capability demonstrated in real networks

Significant improvement in inference efficiency over traditional methods

Open-source implementation available for further use

Abstract

This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain consistent. To this end, we propose a new combinatorial structure in directed acyclic graphs called the directed convex hull, which has turned out to be equivalent to their minimum localized Bayesian networks. An efficient polynomial-time algorithm is devised to identify them by determining the unique directed convex hulls containing the variables of interest from the original networks. Experiments demonstrate that the proposed technique has high dimension reduction capability in real networks, and the efficiency of probabilistic inference based on directed convex hulls can be significantly improved compared with traditional methods such as variable elimination and belief propagation algorithms. The code of this study is open at \href{https://github.com/Balance-H/Algorithms}{https://github.com/Balance-H/Algorithms} and the proofs of the results in the main body are postponed to the appendix.