Federated Learning of Dynamic Bayesian Network via Continuous Optimization from Time Series Data

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.