A Selective Review of Group Selection in High-Dimensional Models

• Published in: Statistical science Vol. 27; no. 4; pp. 481 - 499
• Main Authors: Huang, Jian, Breheny, Patrick, Ma, Shuangge
• Format: Journal Article
• Language: English
• Published: United States Institute of Mathematical Statistics 01-11-2012; The Institute of Mathematical Statistics
• Subjects: Algorithms; Bi-level selection; concave group selection; Coordinate systems; Dimensional analysis; Estimation methods; Estimators; group LASSO; Group selection; Least squares; Linear regression; Machine learning; Modeling; oracle property; Oracles; penalized regression; Regression analysis; Sparsity; Variables; Bi-level selection; group LASSO; sparsity; concave group selection; penalized regression; oracle property
• ISSN: 0883-4237; 2168-8745
• DOI: 10.1214/12-sts392

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.