Adaptive Lasso for High Dimensional Regression and Gaussian Graphical Modeling

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.

30 pages

References in corpus (4)

• Simultaneous analysis of Lasso and Dantzig selector
• The Dantzig selector and sparsity oracle inequalities
• Model Selection Through Sparse Maximum Likelihood Estimation
• High-dimensional covariance estimation by minimizing ${\ell }_1$-penalized log-determinant divergence

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• Adaptive Inferential Method for Monotone Graph Invariants
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• Structure Adaptive Elastic-Net
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