{"ID":5937231,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T04:06:17.856186522Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04650","arxiv_id":"2607.04650","title":"Decomposition for Bayesian Networks: Local and Parallel 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.","short_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 principle...","url_abs":"https://arxiv.org/abs/2607.04650","url_pdf":"https://arxiv.org/pdf/2607.04650v1","authors":"[\"Pei Heng\",\"Xinyi Hu\",\"Yi Sun\"]","published":"2026-07-06T04:08:15Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}