A Selective Review of Group Selection in High-Dimensional Models

Abstract

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study.

Published in at http://dx.doi.org/10.1214/12-STS392 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (14)

• Nearly unbiased variable selection under minimax concave penalty
• Pathwise coordinate optimization
• Consistency of the group Lasso and multiple kernel learning
• One-step sparse estimates in nonconcave penalized likelihood models
• Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
• The composite absolute penalties family for grouped and hierarchical variable selection
• Component selection and smoothing in multivariate nonparametric regression
• Variable selection in nonparametric additive models
• Coordinate descent algorithms for lasso penalized regression
• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• The sparsity and bias of the Lasso selection in high-dimensional linear regression
• The Dantzig selector and sparsity oracle inequalities
• Some sharp performance bounds for least squares regression with $L_1$ regularization
• Consistent group selection in high-dimensional linear regression

Cited by in corpus (2)

• The iterative reweighted Mixed-Norm Estimate for spatio-temporal MEG/EEG source reconstruction
• Introduction to the Special Issue on Sparsity and Regularization Methods