  Conventional causal discovery methods rely on centralized data, which is
inconsistent with the decentralized nature of data in many real-world
situations. This discrepancy has motivated the development of federated causal
discovery (FCD) approaches. However, existing FCD methods may be limited by
their potentially restrictive assumptions of identifiable functional causal
models or homogeneous data distributions, narrowing their applicability in
diverse scenarios. In this paper, we propose a novel FCD method attempting to
accommodate arbitrary causal models and heterogeneous data. We first utilize a
surrogate variable corresponding to the client index to account for the data
heterogeneity across different clients. We then develop a federated conditional
independence test (FCIT) for causal skeleton discovery and establish a
federated independent change principle (FICP) to determine causal directions.
These approaches involve constructing summary statistics as a proxy of the raw
data to protect data privacy. Owing to the nonparametric properties, FCIT and
FICP make no assumption about particular functional forms, thereby facilitating
the handling of arbitrary causal models. We conduct extensive experiments on
synthetic and real datasets to show the efficacy of our method. The code is
available at https://github.com/lokali/FedCDH.git.
