The Annals of Applied Statistics

Network exploration via the adaptive LASSO and SCAD penalties

Jianqing Fan, Yang Feng, and Yichao Wu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 2 (2009), 521-541.

Dates
First available in Project Euclid: 22 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1245676184

Digital Object Identifier
doi:10.1214/08-AOAS215

Mathematical Reviews number (MathSciNet)
MR2750671

Zentralblatt MATH identifier
1166.62040

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

Citation

Fan, Jianqing; Feng, Yang; Wu, Yichao. Network exploration via the adaptive LASSO and SCAD penalties. Ann. Appl. Stat. 3 (2009), no. 2, 521--541. doi:10.1214/08-AOAS215. https://projecteuclid.org/euclid.aoas/1245676184


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