cs.LGSep 3, 2026

Federated Causal Discovery via Regression-Directed Cumulants

Authors: Pablo Torrijos, Fabio Stella, José A. Gámez, José M. Puerta

Organizations: Departamento de Sistemas Inform´aticos Universidad de Castilla-La Mancha Albacete, Spain · Dipartimento di Informatica, Sistemistica e Comunicazione Universit`a degli Studi di Milano Bicocca Milano, Italy · Departamento de Sistemas Inform´aticos2026 Universidad de Castilla-La Mancha Albacete, Spain

Abstract

In this paper we study linear non-Gaussian acyclic models (LiNGAM) when used in federated environments. These causal models allow one to go beyond Markov equivalence. However, in many domains data are scarce, and increasing the sample size by centralising data from different clients is not advisable due to regulations such as the GDPR. The federated environment offers an attractive option to balance privacy and causal discovery accuracy. Unfortunately, the standard centralised estimator in the LiNGAM setting, i.e., DirectLiNGAM, cannot be straightforwardly federated. Higher-order cumulant tensors offer a way around this obstacle: they depend only on the joint distribution of the variables involved and add exactly across independent sample groups, so a single communication round suffices in horizontal, vertical, and hybrid partitions. However, FedISHC, i.e., the current federated method along these lines, breaks down under near-symmetric noise. To overcome the above limitation, we introduce the FedRCD family of causal discovery algorithms, and investigate three variants that trade off communication rounds against algebraic noise; two of them are exact federated counterparts of the centralised high-order cumulant (HC) and HC-LiNGAM algorithms, and the single-round variants further effectively support exact unlearning at any granularity, from a single observation to a whole client. Numerical experiments show that at sample sizes typical of real deployments, the entire cumulant-based federated family does not actually rank variables by the population asymmetry that the scores encode at zero. It ranks them by a variance ladder induced by the DAG along its directed paths, the cumulant counterpart of varsortability. Marginal standardisation collapses every cumulant method to near-random ordering, while scale-invariant DirectLiNGAM, not federable under this protocol, is unaffected.

Explore similar work

CardsList
Jun 21, 2026cs.LG

A Survey on Federated Causal Discovery and Inference

Causal reasoning, which encompasses the discovery of causal structures and the inference of causal effects, is fundamental to data-driven decision making. In practice, data for reliable causal analysis are often distributed across institutions and cannot be centralized due to privacy regulations or communication constraints. Federated learning (FL) addresses this by enabling collaborative analysis without raw data sharing, giving rise to the rapidly growing field of federated causal discovery (FCD) and inference (FCI). However, the interdisciplinary nature of this field and the absence of a comprehensive survey present barriers to entry for researchers. This paper bridges that gap by providing a systematic review through multi-dimensional taxonomies. Grounded in the three core design decisions underlying any FCD solution, namely how structures are learned, how data are partitioned, and what structural knowledge each party obtains, we organize FCD along three axes: methodological paradigm, federation topology, and structural scope. We further examine key practical dimensions, including temporal dynamics, data heterogeneity, missing data, and non-identical variable sets. For FCI, we categorize methods by target estimand (average versus individualized/conditional treatment effects) and by estimation strategy, from classical weighting methods to modern deep generative architectures. Unlike prior works that treat FCD and FCI separately, we formalize their connection as complementary stages of a unified federated causal reasoning pipeline, where FCD supplies the structural knowledge required for valid effect estimation in FCI. Finally, we highlight their shared concerns regarding privacy, communication efficiency, theoretical guarantees, and application domains, and conclude by identifying open challenges for future research.
Xianjie Guo, Yuwei Wang, Guodu Xiang +4
Causal Foundation ModelsFederated LearningCausal ReasoningSurvey
AskPDF
Jun 21, 2026cs.LG

Fed-CausalDiff: Decoupled Synchronization for Federated Do-Simulation and Policy Evaluation

While federated learning enables collaborative modelling on decentralised data, standard methods merely fit historical observations. This purely observational approach is fundamentally insufficient for interventional inference and policy evaluation, as sequential actions dynamically alter future states. We propose \textbf{Fed-CausalDiff}, a federated causal diffusion framework for do-simulation. The architecture decomposes the evolution of the latent state into a global causal score function and a local confounding score function. This design enables \emph{decoupled synchronisation} (DSS), where clients aggregate only the shared causal mechanism while retaining site-specific confounders locally to handle heterogeneity. Experiments on four datasets demonstrate that Fed-CausalDiff achieves better ATE and policy-value estimation accuracy, offering a favorable trade-off between communication cost and inference fidelity.
Pengfei Li, Mohammad Khalil
Federated LearningDiffusion PoliciesDecouplingValue Functions
AskPDF
May 6, 2026stat.ME

Causal discovery under mean independence and linearity

Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.
Geert Mesters, Alvaro Ribot, Anna Seigal +1
Causal Foundation ModelsConditional IndependenceMarket
AskPDF