Federated Nonlinear Causal Discovery via Divide-and-Conquer Learning

Federated causal discovery aims to learn causal structures from distributed data without sharing raw samples. Existing federated nonlinear methods adopt a monolithic global strategy that optimizes the entire graph simultaneously, suffering from catastrophic error propagation: a single misidentified edge cascades through the global structure, severely degrading accuracy under heterogeneous and limited local data. We propose DC-FNCD (Divide-and-Conquer based Federated Nonlinear Causal Discovery), which decomposes the global problem into independent per-variable neighborhood learning tasks. The core mechanism is a characteristic function-based conditional independence test whose empirical statistics admit exact linear decomposition across clients, enabling lossless federated aggregation without raw data exchange. Local neighborhoods are merged via conflict-aware skeleton construction and oriented through federated additive noise model testing. Extensive experiments demonstrate that DC-FNCD significantly outperforms state-of-the-art federated baselines. The source code is available at https://github.com/Xianjie-Guo/DC-FNCD.