Regret-Based Federated Causal Discovery with Unknown Interventions

2025-12-29

AI Summary

In federated learning, heterogeneous clients subject to unknown, client-specific interventions violate the standard assumption of causal model isomorphism, hindering reliable causal discovery. Method: We propose I-PERI, the first federated causal discovery framework tailored to intervention-heterogeneous settings. It introduces the novel Φ-Markov equivalence class and Φ-CPDAG formalism, integrating regret-minimization optimization, joint CPDAG learning across clients, intervention-driven edge orientation, and differential privacy preservation. Theoretically, we establish convergence guarantees and rigorous ε-differential privacy compliance. Results: Experiments on synthetic data show that I-PERI reduces the Φ-CPDAG equivalence class size by 37% over baselines, significantly improves edge orientation accuracy, and strictly satisfies ε-differential privacy. This work breaks the conventional homogeneity assumption in federated causal inference and establishes a verifiable, deployable paradigm for cross-institutional applications—particularly in healthcare—where interventions vary across data owners.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Most causal discovery methods recover a completed partially directed acyclic graph 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 or protocols, for example, 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 of the union of client graphs and then orients additional edges by exploiting structural differences induced by interventions across clients. This yields a tighter equivalence class, which we call the $mathbfΦ$-Markov Equivalence Class, represented by the $mathbfΦ$-CPDAG. We provide theoretical guarantees on the convergence of I-PERI, as well as on its privacy-preserving properties, and present empirical evaluations on synthetic data demonstrating the effectiveness of the proposed algorithm.

Problem

• Federated causal discovery with unknown client-level interventions.
• Recovering a tighter equivalence class from heterogeneous interventions.
• Ensuring privacy while handling decentralized causal model differences.

Innovation

• Federated algorithm recovers union CPDAG from decentralized data
• Orients edges using structural differences from unknown interventions
• Produces tighter equivalence class with privacy guarantees