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Sparse Matrix Graphical Models

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  • Chenlei Leng
  • Cheng Yong Tang

Abstract

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this article, we propose a novel sparse matrix graphical model for these types of statistical problems. By penalizing, respectively, two precision matrices corresponding to the rows and columns, our method yields a sparse matrix graphical model that synthetically characterizes the underlying conditional independence structure. Our model is more parsimonious and is practically more interpretable than the conventional sparse vector-variate graphical models. Asymptotic analysis shows that our penalized likelihood estimates enjoy better convergent rates than that of the vector-variate graphical model. The finite sample performance of the proposed method is illustrated via extensive simulation studies and several real datasets analysis.

Suggested Citation

  • Chenlei Leng & Cheng Yong Tang, 2012. "Sparse Matrix Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1187-1200, September.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1187-1200
    DOI: 10.1080/01621459.2012.706133
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    Cited by:

    1. Andrea Bucci, 2022. "A smooth transition autoregressive model for matrix-variate time series," Papers 2212.08615, arXiv.org.
    2. Gagliardini, Patrick & Gouriéroux, Christian, 2017. "Double instrumental variable estimation of interaction models with big data," Journal of Econometrics, Elsevier, vol. 201(2), pages 176-197.
    3. Suprateek Kundu & Benjamin B. Risk, 2021. "Scalable Bayesian matrix normal graphical models for brain functional networks," Biometrics, The International Biometric Society, vol. 77(2), pages 439-450, June.
    4. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    5. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    6. Fang, Qian & Yu, Chen & Weiping, Zhang, 2020. "Regularized estimation of precision matrix for high-dimensional multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    7. 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.
    8. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    9. Yin Xia & Lexin Li, 2017. "Hypothesis testing of matrix graph model with application to brain connectivity analysis," Biometrics, The International Biometric Society, vol. 73(3), pages 780-791, September.
    10. Xiao Guo & Hai Zhang, 2020. "Sparse directed acyclic graphs incorporating the covariates," Statistical Papers, Springer, vol. 61(5), pages 2119-2148, October.
    11. Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
    12. Wei Lan & Ronghua Luo & Chih-Ling Tsai & Hansheng Wang & Yunhong Yang, 2015. "Testing the Diagonality of a Large Covariance Matrix in a Regression Setting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 76-86, January.
    13. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    14. 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.
    15. Ding, Hao & Qin, Shanshan & Wu, Yuehua & Wu, Yaohua, 2021. "Asymptotic properties on high-dimensional multivariate regression M-estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    16. Pircalabelu, Eugen & Claeskens, Gerda, 2021. "Linear manifold modeling and graph estimation based on multivariate functional data with different coarseness scales," LIDAM Discussion Papers ISBA 2021032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Fangting Zhou & Kejun He & Kunbo Wang & Yanxun Xu & Yang Ni, 2023. "Functional Bayesian networks for discovering causality from multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3279-3293, December.
    18. 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.
    19. Wang, Dong & Liu, Xialu & Chen, Rong, 2019. "Factor models for matrix-valued high-dimensional time series," Journal of Econometrics, Elsevier, vol. 208(1), pages 231-248.
    20. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a multiplicative covariance structure in the large dimensional case," CeMMAP working papers 52/16, Institute for Fiscal Studies.

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