Personalized Federated Vector Autoregression with Personalization Diversity
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.
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BibTeX
@misc{fan2026personalized,
title = {{Personalized Federated Vector Autoregression with Personalization Diversity}},
author = {Zhiyun Fan and Xiaoyu Zhang and Guodong Li and Di Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04474},
eprint = {2610.04474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04474},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Personalized Federated Vector Autoregression with Personalization Diversity
AU - Zhiyun Fan
AU - Xiaoyu Zhang
AU - Guodong Li
AU - Di Wang
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04474
UR - https://arxiv.org/abs/2610.04474
AB - 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.
ER -