Federated learning (FL) demonstrates its advantages in integrating distributed infrastructure, communication, computing and learning in a privacy-preserving manner. However, the robustness and capabilities of existing FL methods are challenged by limited and dynamic data and conditions, complexities including heterogeneities and uncertainties, and analytical explainability. Bayesian federated learning (BFL) has emerged as a promising approach to address these issues. This survey presents a critical overview of BFL, including its basic concepts, its relations to Bayesian learning in the context of FL, and a taxonomy of BFL from both Bayesian and federated perspectives. We categorize and discuss client- and server-side and FL-based BFL methods and their pros and cons. The limitations of the existing BFL methods and the future directions of BFL research further address the intricate requirements of real-life FL applications.

翻译：联邦学习（FL）在兼顾隐私保护地集成分布式基础设施、通信、计算与学习方面展现其优势。然而，现有联邦学习方法的鲁棒性与能力受到有限且动态的数据与条件、包括异质性与不确定性在内的复杂性，以及分析可解释性的挑战。贝叶斯联邦学习（BFL）已成为应对这些问题的有前景方法。本综述对BFL进行了批判性概述，涵盖其基本概念、在联邦学习背景下与贝叶斯学习的关系，以及从贝叶斯与联邦双视角提出的BFL分类体系。我们分类并讨论了客户端侧、服务器侧及基于FL的BFL方法及其优缺点。现有BFL方法的局限性以及BFL研究的未来方向进一步回应了现实联邦学习应用的复杂需求。