个性化联邦向量自回归及其个性化多样性

中文摘要 AI 辅助

个性化联邦学习可以在保留客户端特定动态的同时，改进高维时间序列的估计。然而，参数异质性在共享结构与个性化结构之间造成了根本性的模糊性。我们引入了个性化多样性原则，在该原则下，真正个性化的效应仅在一小部分客户端中重复出现。基于这一原则，我们提出了PerFeCT-VAR，即通过频率上限阈值法实现的个性化联邦向量自回归，该方法将每个客户端特定的转移矩阵分解为共享低秩动态、共享稀疏链接和个性化稀疏偏离三部分。跨客户端的频率上限产生了清晰的共享-个性化分离阈值，并推动了用于联邦估计的频率上限阈值法。我们的理论进一步通过分布兼容性条件考虑了异构的客户端分布，并建立了共享与个性化分量的联合线性收敛性。在充分的个性化多样性下，共享动态保留了联邦总样本量的增益，而个性化分量则达到了客户端级别的精度。模拟实验以及对多门店零售收入数据的应用，展示了所提出框架在预测和解释方面的优势。

英文摘要

Personalized federated learning can improve estimation for high-dimensional time series while preserving client-specific dynamics. However, parameter heterogeneity creates a fundamental ambiguity between shared and personalized structure. We introduce the principle of personalization diversity, under which genuinely personalized effects recur in only a limited fraction of clients. Based on this principle, we propose PerFeCT-VAR, Personalized Federated Vector Autoregression via Frequency-Capped Thresholding, which decomposes each client-specific transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures. A cross-client frequency cap yields a sharp shared--personalized separation threshold and motivates frequency-capped thresholding for federated estimation. Our theory further accounts for heterogeneous client distributions through a distributional compatibility condition and establishes joint linear convergence of the shared and personalized components. Under sufficient personalization diversity, the shared dynamics retain federated total-sample-size gains while the personalized components achieve client-level accuracy. Simulations and an application to multi-store retail revenue data demonstrate the predictive and interpretive benefits of the proposed framework.

发表机构

• Shanghai Jiao Tong University（上海交通大学）
• Tongji University（同济大学）
• University of Hong Kong（香港大学）

机构由 AI 辅助整理，请以论文原文为准。