A Selective Review of Group Selection in High-Dimensional Models

TL;DR

This paper reviews recent advances in group selection methods for high-dimensional models, focusing on methodological, theoretical, and computational aspects, especially those involving concave penalties and bi-level selection.

Contribution

It provides a comprehensive overview of group selection techniques, highlighting developments, applications, and open issues in high-dimensional statistical modeling.

Findings

Summarizes key group selection methods like group LASSO and concave penalties.

Discusses applications in genomics and nonparametric models.

Identifies areas needing further research.

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.