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Multiple matrix Gaussian graphs estimation

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  • Yunzhang Zhu
  • Lexin Li

Abstract

Matrix‐valued data, where the sampling unit is a matrix consisting of rows and columns of measurements, are emerging in numerous scientific and business applications. Matrix Gaussian graphical models are a useful tool to characterize the conditional dependence structure of rows and columns. We employ non‐convex penalization to tackle the estimation of multiple graphs from matrix‐valued data under a matrix normal distribution. We propose a highly efficient non‐convex optimization algorithm that can scale up for graphs with hundreds of nodes. We establish the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results. We demonstrate the efficacy of our proposed method through both simulations and real functional magnetic resonance imaging analyses.

Suggested Citation

  • Yunzhang Zhu & Lexin Li, 2018. "Multiple matrix Gaussian graphs estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 927-950, November.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:5:p:927-950
    DOI: 10.1111/rssb.12278
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    Cited by:

    1. Jiadong Ji & Yong He & Lei Liu & Lei Xie, 2021. "Brain connectivity alteration detection via matrix‐variate differential network model," Biometrics, The International Biometric Society, vol. 77(4), pages 1409-1421, December.
    2. Keskiner, Hilal & Gür, Bekir S., 2023. "Questioning merit-based scholarships at nonprofit private universities: Lessons from Turkey," International Journal of Educational Development, Elsevier, vol. 97(C).
    3. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.
    4. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    5. Katal, Ali & Mortezazadeh, Mohammad & Wang, Liangzhu (Leon), 2019. "Modeling building resilience against extreme weather by integrated CityFFD and CityBEM simulations," Applied Energy, Elsevier, vol. 250(C), pages 1402-1417.
    6. Zhou Tang & Zhangsheng Yu & Cheng Wang, 2020. "A fast iterative algorithm for high-dimensional differential network," Computational Statistics, Springer, vol. 35(1), pages 95-109, March.

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