Nothing but Regrets --- Privacy-Preserving Federated Causal Discovery

In critical applications, causal models are the prime choice for their trustworthiness and explainability. If data is inherently distributed and privacy-sensitive, federated learning allows for collaboratively training a joint model. Existing approaches for federated causal discovery share locally discovered causal model in every iteration, therewith not only revealing local structure but also leading to very high communication costs. Instead, we propose an approach for privacy-preserving federated causal discovery by distributed min-max regret optimization. We prove that max-regret is a consistent scoring criterion that can be used within the well-known Greedy Equivalence Search to discover causal networks in a federated setting and is provably privacy-preserving at the same time. Through extensive experiments, we show that our approach reliably discovers causal networks without ever looking at local data and beats the state of the art both in terms of the quality of discovered causal networks as well as communication efficiency.