AI 中文总结
本文针对多机构张量数据的隐私、高维性和客户端异质性问题，提出个性化联邦张量回归框架，经模拟和MRI-ADHD实验验证其性能优于纯局部方法。
AI 中文摘要
多机构间张量值数据的日益普及为协同分析创造了机会，但也带来了数据隐私、高维性和客户端异质性相关挑战。本文提出一种个性化联邦张量回归框架，同时解决这三个问题：将每个客户端的系数张量分解为全局共享的低Tucker秩分量和局部稀疏偏差，通过两阶段隐私保护流程进行估计。我们建立了量化隐私-精度权衡的有限样本上界和极小极大下界，并证明了支撑初始化和秩选择步骤的一致性。模拟研究证实，该联邦方法相比纯局部方法提升了估计和预测性能，尤其在每个客户端数据稀缺时效果显著；基于MRI的ADHD研究则表明其在真实隐私约束下表现优异。
英文摘要
The growing availability of tensor-valued data across multiple institutions creates opportunities for collaborative analysis, but also raises challenges related to data privacy, high dimensionality, and client heterogeneity. This paper introduces a personalized federated tensor regression framework that addresses all three simultaneously. Each client's coefficient tensor is decomposed into a globally shared low-Tucker-rank component and a locally sparse deviation, estimated via a two-stage privacy-preserving procedure. We establish finite-sample upper bounds and minimax lower bounds that quantify the privacy-accuracy trade-off, and prove the consistency of the supporting initialization and rank-selection steps. Simulation studies confirm that the federated approach improves estimation and prediction over purely local methods, especially when per-client data are scarce, and an MRI-based ADHD study illustrates its strong performance under real privacy constraints.
