FedECE: Federated Estimation of Causal Effect Based on Causal Graphical Modeling

Causal effect estimation as a basic task in causal inference has been widely studied in past decades. In recent years, preserving data privacy has gained significant attention due to increasing incidents of data abuse and data leakage, however, most existing methods do not consider the problem of protecting data privacy when calculating causal effects. Thus in this article, we propose a FedECE (federated estimation of causal effect) framework for causal effect estimation in a federated setting using causal graphical modeling, which comprises two modules: a federated causal structure learning (FedCSL) module and a federated causal effect (FedCE) module. We first instantiate the FedECE framework with a basic FedECE algorithm, called FedECE-B. FedECE-B presents a layer-wise cooperative optimization strategy to learn a global skeleton by the consideration of preserving data privacy. In addition, a distributed optimal consensus strategy for V-structure identification is proposed to orient edges in the learned global skeleton. To tackle the CPDAG problem in the learned causal structure, FedECE-B presents a progressively integrated multiset strategy for federated causal effect computation. To further improve the computational efficiency and accuracy of FedECE-B, we also propose the FedECE-L and FedECE-O algorithms. The extensive experiments validate the effectiveness of the proposed methods.