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Joint graphical lasso with regularized aggregation

Author

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  • Chung, Jongik
  • Zhang, Qihu
  • Mcdowell, Jennifer E.
  • Park, Cheolwoo

Abstract

We present methods for estimating multiple precision matrices for high-dimensional time series within the framework of Gaussian graphical models, with a specific focus on analyzing functional magnetic resonance imaging (fMRI) data collected from multiple subjects. Our goal is to estimate both individual brain networks and a collective structure representing a group of subjects. To achieve this, we propose a method that utilizes group Graphical Lasso and regularized aggregation to simultaneously estimate individual and group precision matrices, assigning varying weights to each individual based on their outlier status within the group. We investigate the convergence rates of precision matrix estimators under various norms and expectations, assessing their performance with sub-Gaussian and heavy-tailed data. The effectiveness of our methods is demonstrated through simulations and real fMRI data analysis.

Suggested Citation

  • Chung, Jongik & Zhang, Qihu & Mcdowell, Jennifer E. & Park, Cheolwoo, 2026. "Joint graphical lasso with regularized aggregation," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001046
    DOI: 10.1016/j.jmva.2025.105509
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    References listed on IDEAS

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    1. Zhang, Qihu & Park, Cheolwoo & Chung, Jongik, 2021. "Minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory," Statistics & Probability Letters, Elsevier, vol. 177(C).
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    9. Zhang, Qihu & Chung, Jongik & Park, Cheolwoo, 2025. "Joint estimation of precision matrices for long-memory time series," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
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