A Selective Review of Group Selection in High-Dimensional Models

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Grouping structures are common in statistical modeling.
• Existing methods like group LASSO address variable selection with groups.
• Concave group selection methods offer advanced approaches.

Purpose of the Study:

• To provide a selective review of group selection methods.
• To focus on methodological developments, theoretical properties, and algorithms.
• To emphasize group selection methods with concave penalties.

Main Methods:

• Reviewing existing group selection techniques.
• Analyzing theoretical properties and computational algorithms.
• Investigating bi-level selection methods.

Main Results:

• Group selection methods, especially those with concave penalties, are effective.
• These methods are applicable to various models including nonparametric additive models, semiparametric regression, and seemingly unrelated regressions.
• Applications extend to genomic data analysis and genome-wide association studies.

Conclusions:

• Group selection with concave penalties is a significant area of statistical modeling.
• Further research is needed to address outstanding issues in group selection methods.
• The reviewed methods offer powerful tools for variable selection in complex datasets.