提出环形分布式算法，高效学习高维贝叶斯网络。
A Ring-Based Distributed Algorithm for Learning High-Dimensional Bayesian Networks
- 用环形结构分治边集，每节点仅处理分配子集。
- 实验显示在400-1000变量数据上比GES快，收敛稳定。
- 保留GES理论性质，适合大规模网络建模任务。
从高维数据中学习贝叶斯网络（BNs）是一项复杂且耗时的任务。尽管已有基于水平（样本）或垂直（变量）划分的方法，但除基于GES算法本身外，均无法保证与贪婪等价搜索（GES）相同的理论性质。本文提出一种基于有向环的分布式方法，以GES作为局部学习算法，确保与GES相同的理论性质，同时减少CPU时间。该方法将可能边集进行划分，限制环中每个处理器仅处理接收到的子集。全局学习过程为迭代算法，持续多轮直至满足收敛条件。每轮中，各处理器接收前一处理器的BN模型，与本地模型融合后，作为局部学习的初始解，限定在自身边集上执行；随后将结果传递给环中下一处理器。在包含400至1000个变量的三个大型数据集上进行实验，结果表明本方法相比GES及其快速版本fGES具有更优性能。
原文摘要 · Abstract (English)
Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although there are approaches based on horizontal (instances) or vertical (variables) partitioning in the literature, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. In this paper, we propose a directed ring-based distributed method that uses GES as the local learning algorithm, ensuring the same theoretical properties as GES but requiring less CPU time. The method involves partitioning the set of possible edges and constraining each processor in the ring to work only with its received subset. The global learning process is an iterative algorithm that carries out several rounds until a convergence criterion is met. In each round, each processor receives a BN from its predecessor in the ring, fuses it with its own BN model, and uses the result as the starting solution for a local learning process constrained to its set of edges. Subsequently, it sends the model obtained to its successor in the ring. Experiments were carried out on three large domains (400-1000 variables), demonstrating our proposal's effectiveness compared to GES and its fast version (fGES).
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