Edge detection in sparse Gaussian graphical models
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 70 (2014)
Issue (Month): C ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/csda|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:138-152. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.