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Edge detection in sparse Gaussian graphical models

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  • Luo, Shan
  • Chen, Zehua

Abstract

In this paper, we consider the problem of detecting edges in a Gaussian graphical model. The problem is equivalent to the identification of non-zero entries of the concentration matrix of a normally distributed random vector. Following the methodology initiated in Meinshausen and Bühlmann (2006), we tackle the problem through regression models where each component of the random vector is regressed on the remaining components. We adapt a method called SLasso cum EBIC (sequential LASSO cum extended Bayesian information criterion) recently developed in Luo and Chen (2011) for feature selection in sparse regression models to suit the special nature of the concentration matrix, and propose two approaches, dubbed SR-SLasso and JR-SLasso, for the identification of non-zero entries of the concentration matrix. Comprehensive numerical studies are conducted to compare the proposed approaches with other available competing methods. The numerical studies demonstrate that the proposed approaches are more accurate than the other methods for the identification of non-zero entries of the concentration matrix.

Suggested Citation

  • Luo, Shan & Chen, Zehua, 2014. "Edge detection in sparse Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 138-152.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:138-152
    DOI: 10.1016/j.csda.2013.09.002
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    3. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    4. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    5. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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    Cited by:

    1. Zehua Chen & Yiwei Jiang, 2020. "A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 65-90, February.
    2. Luo, Shan & Chen, Zehua, 2020. "A procedure of linear discrimination analysis with detected sparsity structure for high-dimensional multi-class classification," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    3. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.

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