Personalized Federated Vector Autoregression with Personalization Diversity

2026-10-03

AI Summary

This study addresses the ambiguity between shared and personalized structures caused by parameter heterogeneity in personalized federated learning by proposing the PerFeCT-VAR framework. Grounded in a principle of personalized diversity, this method introduces a cross-client frequency capping threshold to precisely decompose time series dynamics into shared low-rank, sparse linkage, and personalized bias components. Furthermore, a distributed-compatible algorithm with joint linear convergence is developed. The proposed approach successfully achieves sample-level gains for shared components and client-specific accuracy for personalized components, thereby significantly enhancing both predictive performance and model interpretability.

Abstract

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.

Problem

• Personalized Federated Learning
• High-dimensional Time Series
• Parameter Heterogeneity
• Vector Autoregression

Innovation

• Personalized Federated Learning
• Vector Autoregression
• Personalization Diversity
• Frequency-Capped Thresholding
• Low-rank and Sparse Decomposition