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Concave 1-norm group selection.

Dingfeng Jiang1, Jian Huang2

  • 1Department of Biostatistics, University of Iowa, Iowa City, IA 52246, USA dingfeng-jiang@uiowa.edu.

Biostatistics (Oxford, England)
|November 24, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a robust group selection method using concave penalties, improving model fitting and variable selection even with incorrect group assignments. The new approach offers better control over false discovery rates in high-dimensional data analysis.

Keywords:
Bi-level selectionConcave penaltiesCoordinate descentSparse group Lassop > n problems

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional data analysis often benefits from incorporating grouping structures.
  • Existing group selection methods, like group Lasso, are sensitive to incorrect group membership specification.
  • Robust methods are needed to handle potential mis-specification in grouping structures.

Purpose of the Study:

  • To develop a group selection method robust to grouping structure mis-specification.
  • To enable bi-level selection of both groups and individual variables.
  • To improve model fitting and variable selection accuracy in high-dimensional settings.

Main Methods:

  • Proposal of a novel class of concave $L_q$-norm group penalties.
  • Development and theoretical convergence proof of a coordinate descent algorithm for solution computation.
  • Comparison with existing methods through simulation studies and real data application.

Main Results:

  • The proposed concave $L_q$-norm group penalty method demonstrates robustness against group membership mis-specification.
  • Bi-level selection of groups and individual variables is effectively achieved.
  • The method shows improved control of false discovery rates compared to other approaches.
  • An R package `grppenalty` is available for implementation.

Conclusions:

  • The proposed concave $L_q$-norm group selection method offers a robust and effective solution for high-dimensional data analysis.
  • It addresses the limitations of existing methods concerning group membership mis-specification.
  • The approach facilitates simultaneous selection of groups and variables, enhancing analytical capabilities.