通过分解图结构实现贝叶斯网络高效并行推理
Decomposition for Bayesian Networks: Local and Parallel Inference
- 基于有向凸子图构建最小d-分解树，拆分联合分布
- 相比经典枝形图方法，计算效率显著提升，精度不降
- 适合高维网络中低维查询的并行化处理场景
高维贝叶斯网络中的概率推理困难，因联合分布的精确操作随网络规模呈指数增长。本文提出基于有向凸子图的分解框架，并引入最小d-分解树，为经典枝形图构造提供一种原则性替代方案。该框架将联合分布表示为可独立学习与存储的低维子模型，降低计算成本并天然支持并行计算。基于最小d-分解树，进一步设计两种参数估计与概率推理的并行算法。实验表明，该方法在保持推理精度的同时，显著优于枝形图方法，尤其在低维查询下表现更优。
原文摘要 · Abstract (English)
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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