Traditionally, learning the structure of a Dynamic Bayesian Network has been centralized, requiring all data to be pooled in one location. However, in real-world scenarios, data are often distributed across multiple entities (e.g., companies, devices) that seek to collaboratively learn a Dynamic Bayesian Network while preserving data privacy and security. More importantly, due to the presence of diverse clients, the data may follow different distributions, resulting in data heterogeneity. This heterogeneity poses additional challenges for centralized approaches. In this study, we first introduce a federated learning approach for estimating the structure of a Dynamic Bayesian Network from homogeneous time series data that are horizontally distributed across different parties. We then extend this approach to heterogeneous time series data by incorporating a proximal operator as a regularization term in a personalized federated learning framework. To this end, we propose \texttt{FDBNL} and \texttt{PFDBNL}, which leverage continuous optimization, ensuring that only model parameters are exchanged during the optimization process. Experimental results on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art techniques, particularly in scenarios with many clients and limited individual sample sizes.

翻译：传统上，动态贝叶斯网络的结构学习采用集中式方法，要求将所有数据汇集至单一位置。然而，在实际应用场景中，数据通常分布在多个实体（如公司、设备）之间，这些实体希望在保护数据隐私与安全的前提下协作学习动态贝叶斯网络。更重要的是，由于客户端存在多样性，数据可能服从不同分布，从而导致数据异质性。这种异质性给集中式方法带来了额外挑战。本研究首先提出一种联邦学习方法，用于从水平分布在多方间的同质时间序列数据中估计动态贝叶斯网络结构。随后，通过在个性化联邦学习框架中引入近端算子作为正则化项，将该方法扩展至异质时间序列数据。为此，我们提出 \texttt{FDBNL} 和 \texttt{PFDBNL} 方法，其利用连续优化技术，确保在优化过程中仅交换模型参数。在合成数据集和真实数据集上的实验结果表明，我们的方法优于现有先进技术，尤其在客户端数量众多且个体样本量有限的场景中表现突出。