发表机构
Institute of Statistics and Big Data, Renmin University of China; Department of Statistics and Actuarial Science, University of Waterloo（中国人民大学统计与大数据研究院; 滑铁卢大学统计与精算科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对路由预测联邦学习中未考虑客户端内潜在亚群致双重异质性影响路由和预测的问题，提出FedSPM框架，用特定客户端潜在组件表示客户端，结合分类预测与路由特征分布，开发算法并证明收敛，实验验证其有效性。
AI 中文摘要
路由预测联邦学习将客户端间异质性视为系统智能资源。现有方法忽略客户端内潜在亚群。我们提出FedSPM，一个支持路由的半参数混合框架，用特定客户端潜在组件表示客户端。每个组件结合分类预测分布和路由特征分布。为灵活建模特征分布并跨客户端有效共享信息，FedSPM通过经验似然估计相对于共同非参数度量的密度比。我们开发联邦期望最大化算法，证明在适当控制替代误差时，精确剖析目标以标准\(\mathcal{O}(1/\sqrt{T})\)速率收敛。在受控基准和真实世界医疗数据上的实验表明，在双重异质性下，路由和预测有持续改进。代码可在这个https URL获取。
英文摘要
Routing-prediction federated learning has emerged as a new paradigm that reframes inter-client heterogeneity as a resource for system-level intelligence: at inference time, the server routes each external query to the best-matched client for prediction. Existing approaches, however, typically treat each client as internally homogeneous, overlooking latent subpopulations within local data. For example, patients with the same diagnosis at one hospital may exhibit morphologically distinct disease subtypes. The coexistence of inter-client and intra-client heterogeneity, which we call dual heterogeneity, can impair both routing and prediction. To address this challenge, we propose FedSPM, a routing-enabled semiparametric mixture framework that represents each client using client-specific latent components. Each component combines a predictive distribution for classification with a feature distribution for routing. To flexibly model feature distributions while effectively sharing information across clients, FedSPM models their density ratios relative to a common nonparametric measure estimated via empirical likelihood. We develop a federated expectation-maximization algorithm that optimizes a tractable surrogate and prove convergence of the exact profiled objective at the standard $\mathcal{O}(1/\sqrt{T})$ rate when the surrogate errors are properly controlled. Experiments on controlled benchmarks and real-world medical data demonstrate consistent improvements in routing and prediction under dual heterogeneity. Code is available at https://github.com/zijianwang0510/FedSPM.
