NETWORK EXPLORATION VIA THE ADAPTIVE LASSO AND SCAD PENALTIES.

TLDR

Graphical models are used to explore networks, such as genetic networks, by exploiting sparsity in the precision matrix, but positive‑definiteness constraints make penalized likelihood optimization challenging. The study introduces non‑concave penalties and an adaptive LASSO penalty to reduce bias in network estimation. Using a local linear approximation, the authors recast precision‑matrix estimation as a sequence of weighted L1 penalized likelihood problems solved with Friedman et al.’s algorithm, and validate the approach on two real datasets and through simulation and asymptotic theory. Published in 2008.

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 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.