Adaptive Lasso for High Dimensional Regression and Gaussian Graphical Modeling

TL;DR

This paper demonstrates that the two-stage adaptive Lasso method is consistent for high-dimensional model selection in linear and Gaussian graphical models, extending previous conditions to more general cases.

Contribution

It proves the consistency of the adaptive Lasso in high-dimensional settings under broader restricted eigenvalue conditions.

Findings

Adaptive Lasso is consistent for high-dimensional model selection.

Restricted eigenvalue conditions are sufficient for sparse structure estimation.

Extends previous work to more general situations.

Abstract

We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse structure estimation.