Enhancing Causal Discovery in Federated Settings with Limited Local Samples

Causal discovery from observational data is crucial for understanding complex systems, but traditional methods often require centralized data, conflicting with growing privacy concerns. Although federated causal discovery (FCD) has emerged as a solution, existing methods struggle when individual clients possess limited local samples. This paper introduces FedECD, a novel approach addressing causal discovery in federated settings with limited local samples. FedECD comprises two phases: 1) Federated Causal Skeleton Optimization and 2) Federated Causal Structure Refinement, both leveraging Bootstrapping techniques to enhance robustness and accuracy across distributed clients. Both phases employ a two-layer aggregation strategy: client-layer aggregates results from Bootstrapped sub-datasets within each client, while server-layer aggregates across all clients. The first phase uses weighted aggregation to iteratively remove false causal edges based on conditional independence tests. In contrast, the second phase utilizes majority voting to determine edge directions, ensuring robust estimation of the true causal structure. Extensive experiments on eight benchmark Bayesian network datasets demonstrate the superiority of FedECD over existing FCD methods, particularly with limited sample sizes. FedECD achieves an average improvement of 7.53% in the Ar_F1 score compared to the best baseline, addressing a critical challenge in FCD.