Causal discovery, the inference of causal relations from data, is a core task of fundamental importance in all scientific domains, and several new machine learning methods for addressing the causal discovery problem have been proposed recently. However, existing machine learning methods for causal discovery typically require that the data used for inference is pooled and available in a centralized location. In many domains of high practical importance, such as in healthcare, data is only available at local data-generating entities (e.g. hospitals in the healthcare context), and cannot be shared across entities due to, among others, privacy and regulatory reasons. In this work, we address the problem of inferring causal structure - in the form of a directed acyclic graph (DAG) - from a distributed data set that contains both observational and interventional data in a privacy-preserving manner by exchanging updates instead of samples. To this end, we introduce a new federated framework, FED-CD, that enables the discovery of global causal structures both when the set of intervened covariates is the same across decentralized entities, and when the set of intervened covariates are potentially disjoint. We perform a comprehensive experimental evaluation on synthetic data that demonstrates that FED-CD enables effective aggregation of decentralized data for causal discovery without direct sample sharing, even when the contributing distributed data sets cover disjoint sets of interventions. Effective methods for causal discovery in distributed data sets could significantly advance scientific discovery and knowledge sharing in important settings, for instance, healthcare, in which sharing of data across local sites is difficult or prohibited.

翻译：因果发现（即从数据中推断因果关系）是各科学领域具有根本重要性的核心任务，近年来涌现了多种基于机器学习的新方法。然而，现有用于因果发现的机器学习方法通常要求用于推断的数据集中存储于同一中心节点。在医疗健康等具有高度实际重要性的领域中，数据仅存储在本地数据生成实体（如医疗机构），且因隐私保护、法规限制等原因无法跨实体共享。本研究针对分布式数据集的因果结构推断问题——以有向无环图（DAG）形式呈现——提出通过交换更新参数而非原始样本的方式，在保护隐私的前提下处理同时包含观测数据与干预数据的分布式数据集。为此，我们构建了新型联邦学习框架FED-CD，该框架既能处理各去中心化实体间干预变量集相同的情况，也能处理干预变量集可能互不相交的情形。基于合成数据的全面实验评估表明：即使在贡献数据的分布式数据集覆盖不相交干预变量的情况下，FED-CD也能在不直接共享样本的前提下实现分散数据的有效聚合。针对分布式数据集开发有效的因果发现方法，将显著推动医疗健康等难以或禁止跨本地站点共享数据重要场景的科学发现与知识共享进程。