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.

提出了一种新的面向任意因果模型和异构数据的联邦因果探索方法，通过使用代理变量来解决不同客户端之间的数据异构性，并利用联邦条件独立性检验和联邦独立性改变原则来确定因果方向，无需对特定函数形式进行任何假设，以以保护数据隐私的方式构建摘要统计量，实验证明了该方法的有效性。

异构数据的联邦因果推断

Federated Causal Discovery from Heterogeneous Data

Discovering the causality from observational data is a crucial task in
various scientific domains. With increasing awareness of privacy, data are not
allowed to be exposed, and it is very hard to learn causal graphs from
dispersed data, since these data may have different distributions. In this
paper, we propose a federated causal discovery strategy (FedCausal) to learn
the unified global causal graph from decentralized heterogeneous data. We
design a global optimization formula to naturally aggregate the causal graphs
from client data and constrain the acyclicity of the global graph without
exposing local data. Unlike other federated causal learning algorithms,
FedCausal unifies the local and global optimizations into a complete directed
acyclic graph (DAG) learning process with a flexible optimization objective. We
prove that this optimization objective has a high interpretability and can
adaptively handle homogeneous and heterogeneous data. Experimental results on
synthetic and real datasets show that FedCausal can effectively deal with
non-independently and identically distributed (non-iid) data and has a superior
performance.

通过联邦因果发现策略 (FedCausal) ，在去中心化的异构数据中学习统一的全局因果图，不暴露本地数据，解决非独立同分布数据的问题。