Network exploration via the adaptive LASSO and SCAD penalties
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, positivedefiniteness 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 $L_1$ penalty and solved using the efficient algorithm of Friedman et al. [Biostatistics 9 (2008) 432441]. Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 arXiv:
 arXiv:0908.2053
 Bibcode:
 2009arXiv0908.2053F
 Keywords:

 Statistics  Applications
 EPrint:
 Published in at http://dx.doi.org/10.1214/08AOAS215 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)