Original title: Federated Causal Discovery via Regression-Directed Cumulants
Pablo Torrijos, Fabio Stella, José A. Gámez, José M. Puerta · September 2026
Researchers want to find cause-and-effect links in data spread across multiple computers without moving the raw records, which privacy rules like GDPR forbid. Standard tools like DirectLiNGAM work well on one computer, but they cannot be directly adapted to this shared, private setup. Earlier shared methods like FedISHC break down when the data noise is nearly symmetric. To solve this, the researchers created FedRCD, a new family of causal discovery tools. They use higher-order cumulants, which are mathematical summaries that can be added together across groups in just one message round. This works across horizontal, vertical, and hybrid data splits. Single-round versions can also easily delete any data, from one record to a whole client. However, tests show these methods do not actually order variables by noise asymmetry as intended. Instead, they follow variance differences along paths. Standardising the variables makes all cumulant methods drop to near-random ordering.
Imagine a group of friends each keeping a private journal about their daily activities. They want to figure out who influences whom without showing their journals. If everyone writes in a similar style, it's hard to tell connections apart. In this paper, multiple organizations have sensitive data and can't share it. By combining specific summaries, called higher-order cumulants, from each set, they can uncover causal links even when the data is similar enough to confuse earlier methods.
For organizations handling sensitive data under privacy laws like GDPR, this work enables accurate causal analysis without centralizing data. The new FedRCD family fixes breakdowns that plagued previous federated methods, making private collaboration practical.
The abstract indicates that at typical sample sizes, the cumulant-based methods do not rank by true asymmetry but by a variance ladder. Also, marginal standardisation causes these methods to perform poorly, approaching random ordering. The work may not address non-linear cases or compare to all other federated approaches.
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Federated Causal Discovery via Regression-Directed Cumulants — Pablo Torrijos, Fabio Stella, José A. Gámez et al.
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.