2D-FedSMKL：面向模态缺失与站点异质性的混合联邦多模态融合方法
Hybrid Federated Learning for Multimodal Fusion under Missing Modalities and Site Heterogeneity
一篇搞联邦多模态融合的论文，数据缺模态、各站点分布还不一样时怎么训练，给出了理论保证加基准结果，做医疗或跨机构数据合作的可以看看。
arXiv 论文提出二维联邦平滑多核大间隔学习方法 2D-FedSMKL，处理按样本与特征块混合划分的联邦数据。方法整合可用性校正的模态评分、组核正则化和平滑的最坏站点风险聚合，目标函数在固定映射与倾向下为凸且平滑，并给出条件加速收敛率。理论部分包含 oracle 倾向二分类风险界与倾向扰动结果。在两个公开活动识别基准上，最坏站点聚合提升了异质场景下最坏站点的性能，验证集选择的校正模型在最坏站点不显著弱于最强参照方法。
Hybrid Federated Learning for Multimodal Fusion under Missing Modalities and Site Heterogeneity
Multimodal fusion is studied under hybrid federation, where data are partitioned across samples and feature blocks. The proposed two-dimensional federated smooth multiple-kernel large-margin learning method (2D-FedSMKL) integrates availability-corrected modality scores, group-kernel regularization, and smooth worst-site risk aggregation. For fixed maps and propensities, the objective is convex and smooth. Curvature bounds and exact synchronous block-gradient equivalence are established for binary and multiclass scores, giving a conditional accelerated rate. An oracle-propensity binary risk bound and a propensity-perturbation result are also derived. Simulations and two public activity-recognition benchmarks assess site heterogeneity and modality absence. Worst-site aggregation improves worst-site performance under heterogeneity, including reversed and size-balanced designs. On the benchmarks, validation selects the correction; the selected model is not significantly worse than the strongest reference at the worst site, and group-regularization benefits vary by dataset.