Federated learning (FL) allows for collaborative model training across decentralized clients while preserving privacy by avoiding data sharing. However, current FL methods assume conditional independence between client models, limiting the use of priors that capture dependence, such as Gaussian processes (GPs). We introduce the Structured Independence via deep Generative Model Approximation (SIGMA) prior which enables FL for non-factorizable models across clients, expanding the applicability of FL to fields such as spatial statistics, epidemiology, environmental science, and other domains where modeling dependencies is crucial. The SIGMA prior is a pre-trained deep generative model that approximates the desired prior and induces a specified conditional independence structure in the latent variables, creating an approximate model suitable for FL settings. We demonstrate the SIGMA prior's effectiveness on synthetic data and showcase its utility in a real-world example of FL for spatial data, using a conditional autoregressive prior to model spatial dependence across Australia. Our work enables new FL applications in domains where modeling dependent data is essential for accurate predictions and decision-making.

翻译：联邦学习（FL）允许在去中心化的客户端之间进行协作式模型训练，同时通过避免数据共享来保护隐私。然而，当前的联邦学习方法假设客户端模型之间条件独立，这限制了使用能够捕捉依赖关系的先验（例如高斯过程）。我们引入了基于深度生成模型近似的结构化独立（SIGMA）先验，该先验使得跨客户端的非可分解模型能够进行联邦学习，从而将联邦学习的适用性扩展到空间统计、流行病学、环境科学以及其他建模依赖关系至关重要的领域。SIGMA先验是一个预训练的深度生成模型，它近似期望的先验并在潜在变量中引入指定的条件独立结构，从而创建一个适用于联邦学习设置的近似模型。我们在合成数据上证明了SIGMA先验的有效性，并通过一个使用条件自回归先验对澳大利亚全境空间依赖性进行建模的真实世界空间数据联邦学习案例，展示了其实用性。我们的工作使得联邦学习能够在依赖数据建模对于准确预测和决策至关重要的新领域中得到应用。