Regret-Based Federated Causal Discovery with Unknown Interventions

Most causal discovery methods recover a completed partially directed acyclic graph (CPDAG) representing a Markov equivalence class from observational data. Recent work has extended these methods to federated settings to address data decentralization and privacy constraints, but often under idealized assumptions that all clients share the same causal model. Such assumptions are unrealistic in practice, as client-specific policies, for instance, across hospitals, naturally induce heterogeneous and unknown interventions. In this work, we address federated causal discovery under unknown client-level interventions. We propose I-PERI, a novel federated algorithm that first recovers the CPDAG common to all clients and then orients additional edges by exploiting structural differences induced by interventions across clients. This yields a tighter equivalence class, which we call the $\mathbf{\Phi}$-Markov Equivalence Class, represented by an augmented version of the CPDAG, namely, a $\mathbf{\Phi}$-CPDAG. We provide theoretical guarantees on the convergence of I-PERI, as well as on its privacy-preserving properties, and present empirical evaluations demonstrating the effectiveness of the proposed algorithm.

In many real-world settings, data is collected across multiple sites, such as hospitals, each operating under different, often undisclosed local policies. For example, one hospital might routinely prescribe a particular drug while another does not. These differences silently alter the statistical relationships in each site's data, making it hard to recover the true underlying cause-and-effect structure. Existing methods either assume all sites are identical or require knowing exactly what each site's policies are, which may be unavailable or even a privacy violation to share. We introduce I-PERI, an algorithm that turns this heterogeneity from a problem into an opportunity. Rather than ignoring site-level differences, I-PERI exploits them to resolve causal ambiguities that no single site's data could resolve alone, without any site ever revealing which interventions it applied, and with formal privacy guarantees ensuring individual records cannot be reconstructed from shared information. We prove that I-PERI correctly recovers the tightest possible causal structure achievable in this setting, and demonstrate experimentally that it consistently outperforms existing methods. This opens the door to more realistic causal discovery from distributed, privacy-sensitive data.