# Decomposition for Bayesian Networks: Local and Parallel Inference

arXiv: https://arxiv.org/abs/2607.04650 · HTML: https://mlsanity.com/paper/2607.04650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 1 of 1)

- [Structural Dimension Reduction in Bayesian Networks](https://mlsanity.com/paper/2601.08236/) (2026)

## Abstract (arXiv)

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.