Decomposition for Bayesian Networks: Local and Parallel Inference

• URL: http://arxiv.org/abs/2607.04650v1
• Date: Mon, 06 Jul 2026 04:08:15 GMT
• Title: Decomposition for Bayesian Networks: Local and Parallel Inference
• Abstract summary: Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size.<n>We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree.
• Score: 9.547272742835615
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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