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Online graph topology learning from matrix-valued time series

Author

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  • Jiang, Yiye
  • Bigot, Jérémie
  • Maabout, Sofian

Abstract

The focus is on the statistical analysis of matrix-valued time series, where data is collected over a network of sensors, typically at spatial locations, over time. Each sensor records a vector of features at each time point, creating a vectorial time series for each sensor. The goal is to identify the dependency structure among these sensors and represent it with a graph. When only one feature per sensor is observed, vector auto-regressive (VAR) models are commonly used to infer Granger causality, resulting in a causal graph. The first contribution extends VAR models to matrix-variate models for the purpose of graph learning. Additionally, two online procedures are proposed for both low and high dimensions, enabling rapid updates of coefficient estimates as new samples arrive. In the high-dimensional setting, a novel Lasso-type approach is introduced, and homotopy algorithms are developed for online learning. An adaptive tuning procedure for the regularization parameter is also provided. Given that the application of auto-regressive models to data typically requires detrending, which is not feasible in an online context, the proposed AR models are augmented by incorporating trend as an additional parameter, with a particular focus on periodic trends. The online algorithms are adapted to these augmented data models, allowing for simultaneous learning of the graph and trend from streaming samples. Numerical experiments using both synthetic and real data demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Jiang, Yiye & Bigot, Jérémie & Maabout, Sofian, 2025. "Online graph topology learning from matrix-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
  • Handle: RePEc:eee:csdana:v:202:y:2025:i:c:s016794732400149x
    DOI: 10.1016/j.csda.2024.108065
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    References listed on IDEAS

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    1. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
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    4. Kristjan Greenewald & Shuheng Zhou & Alfred Hero, 2019. "Tensor graphical lasso (TeraLasso)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(5), pages 901-931, November.
    5. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
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