Federated Causal Structure Learning with a Bi-Level Optimization Model

Learning causal structure from observational data is crucial across many scientific fields. Conventional causal structure learning methods mostly rely on centralized data, which may be unsuitable to real-world situations. Due to increasing privacy concerns, gathering data from different sources is challenging as owners may reluctant to share their data. Therefore, in this paper, we propose a federated causal structure learning (FedCASL) method based on contiunous optimization to learn causal structure from distributed data in a privacy-preserving way. Specifically, FedCASL consists of a bi-level optimization model, involving client and server components. During the learning process, both ends only need to exchange model parameters without exposing data, and obtain the final causal graph under acyclic constraint. Furthermore, a carefully designed sparse penalty term is introduced to guide the optimization to a desired direction. Experimental results on synthetic and real datasets show that FedCASL exhibits superior performance compared to other benchmarks.