Network Exploration via the Adaptive LASSO and SCAD Penalties

• Activity Number: 562
• Type: Contributed
• Date/Time: Thursday, August 6, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jianqing Fan and Yang Feng*+ and Yichao Wu
• Companies: Princeton University and Princeton University and North Carolina State University
• Keywords: Adaptive LASSO ; covariance selection ; precision matrix ; genetic network ; LASSO ; SCAD

Abstract

Graphical models are frequently used to explore networks, such as genetic networks. 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 L1 penalty and solved using the efficient algorithm of Friedman et al.(2008). Our estimation schemes are applied to two real data sets. Simulation experiments and asymptotic theory are used to justify our methods.