While supervised federated learning approaches have enjoyed significant success, the domain of unsupervised federated learning remains relatively underexplored. In this paper, we introduce a novel federated gradient EM algorithm designed for the unsupervised learning of mixture models with heterogeneous mixture proportions across tasks. We begin with a comprehensive finite-sample theory that holds for general mixture models, then apply this general theory on Gaussian Mixture Models (GMMs) and Mixture of Regressions (MoRs) to characterize the explicit estimation error of model parameters and mixture proportions. Our proposed federated gradient EM algorithm demonstrates several key advantages: adaptability to unknown task similarity, resilience against adversarial attacks on a small fraction of data sources, protection of local data privacy, and computational and communication efficiency.

翻译：尽管有监督联邦学习方法取得了显著成功，但无监督联邦学习领域仍相对探索不足。本文提出了一种新颖的联邦梯度EM算法，用于在任务间混合比例异构的情况下实现混合模型的无监督学习。我们首先建立了适用于一般混合模型的综合有限样本理论，随后将该理论应用于高斯混合模型（GMMs）和混合回归模型（MoRs），以刻画模型参数与混合比例的显式估计误差。所提出的联邦梯度EM算法展现出若干关键优势：对未知任务相似性的自适应能力、对少量数据源对抗攻击的鲁棒性、本地数据隐私保护，以及计算与通信效率。