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June 2009 Network exploration via the adaptive LASSO and SCAD penalties
Jianqing Fan, Yang Feng, Yichao Wu
Ann. Appl. Stat. 3(2): 521-541 (June 2009). DOI: 10.1214/08-AOAS215


Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. We introduce nonconcave penalties and the adaptive LASSO penalty to attenuate the bias problem in the network estimation. Through the local linear approximation to the nonconcave penalty functions, the problem of precision matrix estimation is recast as a sequence of penalized likelihood problems with a weighted L1 penalty and solved using the efficient algorithm of Friedman et al. [Biostatistics 9 (2008) 432–441]. Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.


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Jianqing Fan. Yang Feng. Yichao Wu. "Network exploration via the adaptive LASSO and SCAD penalties." Ann. Appl. Stat. 3 (2) 521 - 541, June 2009.


Published: June 2009
First available in Project Euclid: 22 June 2009

zbMATH: 1166.62040
MathSciNet: MR2750671
Digital Object Identifier: 10.1214/08-AOAS215

Keywords: Adaptive LASSO , covariance selection , Gaussian concentration graphical model , genetic network , Lasso , precision matrix , SCAD

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 2 • June 2009
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