Federated Causal Structure Learning with Non-identical Variable Sets

Federated causal structure learning aims to infer causal relationships from data stored on individual clients, with privacy concerns. Most existing methods assume identical variable sets across clients and present federated strategies for aggregating local updates. However, in practice, clients often observe overlapping but non-identical variable sets, and non-overlapping variables may introduce spurious dependencies. Moreover, existing strategies typically reflect only the overall quality of local graphs, ignoring the varying importance of relationships within each graph. In this paper, we study federated causal structure learning with non-identical variable sets, aiming to design an effective strategy for aggregating "correct" and "good" causal relationships across distributed datasets. Specifically, we first develop theories for detecting spurious dependencies, examining whether the learned causal and noncausal relationships are "correct" or not. Furthermore, we define stable relationships as those that are both "correct" and "good" across multiple graphs, and finally design a two-level priority selection strategy for aggregating local updates, obtaining a global causal graph over the integrated variables. Experimental results on synthetic, benchmark and real-world datasets demonstrate the effectiveness of our proposed method.