Adaptive Lasso for High Dimensional Regression and Gaussian Graphical Modeling

2009/03/13 by Zhou, Shuheng, van de Geer, Sara, Bühlmann, Peter
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0903.2515

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.

Related

• High-dimensional Penalized Linear IV Estimation & Inference using BRIDGE and Adaptive LASSO
• Some Two-Step Procedures for Variable Selection in High-Dimensional Linear Regression
• New Error Analysis for Lasso
• Thresholded Lasso for high dimensional variable selection and statistical estimation
• Bayesian Adaptive Lasso