Decomposition for Bayesian Networks: Local and Parallel Inference

2026-07-06

AI Summary

This work addresses the computational intractability of probabilistic inference in high-dimensional Bayesian networks, which stems from the exponential complexity of their joint distributions. The authors propose a novel framework based on directed convex subgraph decomposition, introducing a minimal d-decomposition tree as an alternative to conventional junction trees. This structure decomposes the joint distribution into low-dimensional submodels that can be learned and stored independently. The approach inherently supports localized and parallelized inference, achieving substantial gains in computational efficiency while preserving inference accuracy—particularly advantageous for low-dimensional queries. The core contributions lie in an improved structural decomposition mechanism and highly efficient algorithms for parallel parameter estimation and inference.

Abstract

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

Problem

• Bayesian networks
• probabilistic inference
• high-dimensional
• computational complexity
• joint distribution

Innovation

• Bayesian networks
• d-decomposition tree
• parallel inference
• probabilistic inference
• graph decomposition