To date, most directed acyclic graphs (DAGs) structure learning approaches require data to be stored in a central server. However, due to the consideration of privacy protection, data owners gradually refuse to share their personalized raw data to avoid private information leakage, making this task more troublesome by cutting off the first step. Thus, a puzzle arises: \textit{how do we discover the underlying DAG structure from decentralized data?} In this paper, focusing on the additive noise models (ANMs) assumption of data generation, we take the first step in developing a gradient-based learning framework named FedDAG, which can learn the DAG structure without directly touching the local data and also can naturally handle the data heterogeneity. Our method benefits from a two-level structure of each local model. The first level structure learns the edges and directions of the graph and communicates with the server to get the model information from other clients during the learning procedure, while the second level structure approximates the mechanisms among variables and personally updates on its own data to accommodate the data heterogeneity. Moreover, FedDAG formulates the overall learning task as a continuous optimization problem by taking advantage of an equality acyclicity constraint, which can be solved by gradient descent methods to boost the searching efficiency. Extensive experiments on both synthetic and real-world datasets verify the efficacy of the proposed method.
翻译:至今为止,大多数定向的环形图(DAGs)结构学习方法要求将数据储存在中央服务器中。然而,由于对隐私保护的考虑,数据所有人逐渐拒绝分享其个人化原始数据以避免私人信息泄漏,从而使这项任务更加麻烦。因此,产生了一个难题:\ textit{我们如何从分散的数据中发现基本的DAG结构?}在侧重于数据生成的添加噪声模型假设的本文件中,我们迈出了第一步,开发了一个以梯度为基础的学习框架,名为FDDDAAG,它可以在不直接接触当地数据的情况下学习DAG结构,也可以自然地处理数据繁杂性。我们的方法得益于每个地方模型的两层结构。第一层结构了解了图形的边缘和方向,并与服务器沟通,以便在学习过程中从其他客户那里获得模型信息,而第二级结构则接近了变量之间的机制,并亲自更新了自己的数据,以适应数据的多样性。此外,FDDAGAG制定了总体学习任务,即通过不断的周期性化实验方法,通过不断的周期性效率来提升数据效率,从而通过持续地压压压平化的方法,从而提升数据效率的优势,从而解决了不断的升级化方法的优势。