[Paper] Regret-Based Federated Causal Discovery with Unknown Interventions

Source: arXiv - 2512.23626v1

Overview

Federated causal discovery aims to learn cause‑effect relationships from data that lives on many devices or institutions without moving the raw data. Existing methods assume every participant shares the same underlying causal graph, an assumption that breaks down when, for example, hospitals follow different treatment protocols that act as unknown interventions. This paper introduces I‑PERI, a federated algorithm that can uncover a richer causal structure even when each client’s data has been subtly altered by its own hidden interventions.

Key Contributions

• Novel federated algorithm (I‑PERI) that first learns a CPDAG for the union of all client graphs and then refines edge orientations by exploiting differences caused by unknown client‑level interventions.
• Definition of the Φ‑Markov Equivalence Class and its compact representation, the Φ‑CPDAG, which is strictly tighter than the traditional CPDAG when heterogeneous interventions are present.
• Theoretical guarantees: convergence of the distributed learning process and formal privacy bounds (regret‑based analysis showing limited information leakage across rounds).
• Empirical validation on synthetic federated datasets, demonstrating that I‑PERI recovers more correct edge directions than baseline federated causal discovery methods that ignore intervention heterogeneity.
• Open‑source implementation (released with the paper) that integrates with popular federated learning frameworks (e.g., TensorFlow Federated, PySyft).

Methodology

1. Local Phase – Structure Learning

   • Each client runs a standard causal discovery routine (e.g., PC or GES) on its own data, producing a local CPDAG.
   • The local algorithm is intervention‑agnostic: it treats the data as purely observational, which is safe because the true interventions are unknown.

2. Global Aggregation – Union CPDAG

   • The server collects the local CPDAGs (only the graph skeletons and edge marks, not raw data).
   • By taking the union of all skeletons and intersecting the edge orientations, it builds a global CPDAG that captures every edge that appears in any client.

3. Intervention Exploitation – Φ‑Orientation

   • I‑PERI leverages the fact that an unknown intervention on a node removes incoming edges to that node in the intervened graph.
   • By comparing the presence/absence of edges across clients, the algorithm infers which edges must have been “cut” by an intervention, allowing it to orient previously ambiguous edges.
   • This step is performed iteratively: after each orientation round, the refined graph is re‑broadcast to clients for another local update, reducing regret over time.

4. Privacy‑Preserving Communication

   • Only graph summaries (edge lists) are exchanged; no raw feature values leave the client.
   • The authors prove a differential‑privacy‑like bound on the regret of the algorithm, showing that an adversary cannot reconstruct a client’s exact intervention pattern from the exchanged messages.

Results & Findings

• Tighter equivalence class: The Φ‑CPDAG recovered by I‑PERI contains on average 30 % fewer undirected edges than the standard CPDAG, meaning more causal directions are known.
• Robustness to noise: Even when 20 % of clients have spurious interventions (random edge deletions), I‑PERI still outperforms baselines by a large margin.
• Scalability: Experiments with up to 50 clients and 100 variables show linear communication overhead and sub‑linear runtime growth thanks to the local‑first design.

Practical Implications

• Healthcare analytics: Hospitals can collaboratively learn causal pathways (e.g., risk factors for readmission) without exposing patient records, while automatically accounting for differing treatment protocols.
• A/B testing platforms: Companies running heterogeneous experiments across regions can fuse causal insights without revealing which variant was deployed where.
• Edge‑AI and IoT: Devices that perform local interventions (e.g., firmware updates that change sensor behavior) can still contribute to a global causal model, enabling better fault diagnosis and predictive maintenance.
• Regulatory compliance: By limiting data exchange to graph structures and providing formal privacy regret bounds, I‑PERI aligns with GDPR‑style data minimization requirements.

Developers can plug I‑PERI into existing federated pipelines, using the provided Python API to replace the usual “average model weights” step with a “merge causal graphs” step, thereby gaining richer interpretability without sacrificing privacy.

Limitations & Future Work

• Synthetic focus: The evaluation is limited to simulated data; real‑world deployments (e.g., multi‑hospital studies) are needed to confirm robustness against messy, non‑Gaussian noise.
• Assumption of acyclicity: I‑PERI inherits the DAG restriction; cyclic causal structures (common in feedback systems) remain out of scope.
• Intervention detection granularity: The method can infer that an intervention occurred on a node but does not identify the exact intervention type or magnitude.
• Future directions suggested by the authors include extending the framework to handle latent confounders, integrating differential privacy mechanisms for stronger guarantees, and testing the approach on large‑scale real federated datasets (e.g., national health registries).

Authors

• Federico Baldo
• Charles K. Assaad

Paper Information

• arXiv ID: 2512.23626v1
• Categories: cs.AI, cs.LG
• Published: December 29, 2025
• PDF: Download PDF