通过构建最小局部化网络，大幅降低贝叶斯网络规模并提升推理效率。
Structural Dimension Reduction in Bayesian Networks
- 提出有向凸包结构，实现贝叶斯网络的最小局部化压缩。
- 实测在真实网络中可显著减少维度，推理速度优于变量消元等传统方法。
- 适合需要高效推理的大规模贝叶斯网络应用，如医疗诊断与风险评估。
本文提出一种名为结构维度缩减的新技术，可将贝叶斯网络压缩为最小且局部化的形式，同时保证原始网络与简化后网络间的概率推断结果一致。为此，我们引入了有向无环图中的一种新组合结构——有向凸包，并证明其等价于最小局部化贝叶斯网络。我们设计了一种高效的多项式时间算法，通过确定包含目标变量的唯一有向凸包来识别该结构。实验表明，该技术在真实网络中具有显著的维度压缩能力，基于有向凸包的概率推理效率相比传统的变量消元法和信念传播算法大幅提升。相关代码已开源，详见 https://github.com/Balance-H/Algorithms，主要结论的证明见附录。
原文摘要 · Abstract (English)
This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain consistent. To this end, we propose a new combinatorial structure in directed acyclic graphs called the directed convex hull, which has turned out to be equivalent to their minimum localized Bayesian networks. An efficient polynomial-time algorithm is devised to identify them by determining the unique directed convex hulls containing the variables of interest from the original networks. Experiments demonstrate that the proposed technique has high dimension reduction capability in real networks, and the efficiency of probabilistic inference based on directed convex hulls can be significantly improved compared with traditional methods such as variable elimination and belief propagation algorithms. The code of this study is open at \href{https://github.com/Balance-H/Algorithms}{https://github.com/Balance-H/Algorithms} and the proofs of the results in the main body are postponed to the appendix.
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