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Edge detection in sparse Gaussian graphical models

Listed author(s):
  • Luo, Shan
  • Chen, Zehua
Registered author(s):

    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313003174
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 70 (2014)
    Issue (Month): C ()
    Pages: 138-152

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    Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:138-152
    DOI: 10.1016/j.csda.2013.09.002
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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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. 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.
    3. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    4. 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.
    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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