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Ranking Edges and Model Selection in High-Dimensional Graphs

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  • Zamar, Rubén
  • Nogales Martín, Francisco Javier
  • Lafit, Ginette

Abstract

In this article we present an approach to rank edges in a network modeled through a Gaussian Graphical Model. We obtain a path of precision matrices such that, in each step of the procedure, an edge is added. We also guarantee that the matrices along the path are symmetric and positive definite. To select the edges, we estimate the covariates that have the largest absolute correlation with a node conditional to the set of edges estimated in previous iterations. Simulation studies show that the procedure is able to detect true edges until the sparsity level of the population network is recovered. Moreover, it can add efficiently true edges in the first iterations avoiding to enter false ones. We show that the top-rank edges are associated with the largest partial correlated variables. Finally, we compare the graph recovery performance with that of Glasso under different settings.

Suggested Citation

  • Zamar, Rubén & Nogales Martín, Francisco Javier & Lafit, Ginette, 2015. "Ranking Edges and Model Selection in High-Dimensional Graphs," DES - Working Papers. Statistics and Econometrics. WS ws1511, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws1511
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    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/20778/ws1511.pdf?sequence=1
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. 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.
    3. 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.
    4. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    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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    Keywords

    Precision Matrix;

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