# Regret-Based Federated Causal Discovery with Unknown Interventions

arXiv: https://arxiv.org/abs/2512.23626 · HTML: https://mlsanity.com/paper/2512.23626/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [Causal Inference with a Graphical Hierarchy of Interventions](https://mlsanity.com/paper/1411.2127/) (2014)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)

## Built on by (most cited first, 2 of 2)

- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)
- [When Do Causal World Models Help Modular LLM Agents](https://mlsanity.com/paper/2610.00012/) (2026)

## Abstract (arXiv)

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 Phi-Markov Equivalence Class, represented by the Phi-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.