# Federated Causal Discovery via Regression-Directed Cumulants

arXiv: https://arxiv.org/abs/2609.03705 · HTML: https://mlsanity.com/paper/2609.03705/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Causal machine learning for single-cell genomics](https://mlsanity.com/paper/2310.14935/) (2023)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [A causal learning framework for the analysis and interpretation of COVID-19 clinical data](https://mlsanity.com/paper/2105.06998/) (2021)
- [Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants](https://mlsanity.com/paper/2507.06888/) (2025)

## Abstract (arXiv)

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.