Open AccessNETWORK EXPLORATION VIA THE ADAPTIVE LASSO AND SCAD PENALTIES.
Author(s) -
Jianqing Fan,
Yang Feng,
Yichao Wu
Publication year - 2009
Publication title -
pubmed
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.674
H-Index - 75
pISSN - 1932-6157
DOI - 10.1214/08-aoas215supp
Subject(s) - lasso (programming language) , scad , mathematical optimization , computer science , algorithm , penalty method , sequence (biology) , matrix (chemical analysis) , set (abstract data type) , mathematics , optimization problem , psychology , psychiatry , world wide web , myocardial infarction , materials science , biology , composite material , genetics , programming language
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 non-concave penalties and the adaptive LASSO penalty to attenuate the bias problem in the network estimation. Through the local linear approximation to the non-concave 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. (2008). Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.