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Consistent group selection in high-dimensional linear regression.

Fengrong Wei1, Jian Huang

  • 1Department of Mathematics, University of West Georgia, 1601 Maple Street, Carrollton, GA 30118, USA.

Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability
|November 11, 2011
PubMed
Summary
This summary is machine-generated.

The group Lasso method for variable selection in high-dimensional data can be inconsistent. An adaptive group Lasso improves selection accuracy by building upon initial group Lasso estimates.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Group Lasso is effective for variable selection when covariates have natural groupings.
  • High-dimensional settings, where the number of groups exceeds sample size, pose challenges for standard methods.
  • Understanding the selection and estimation properties of Group Lasso in these settings is crucial.

Purpose of the Study:

  • To analyze the selection and estimation performance of the Group Lasso in high-dimensional scenarios.
  • To develop an improved method, the adaptive Group Lasso, for more accurate variable selection.
  • To establish conditions for the consistency of the adaptive Group Lasso.

Main Methods:

  • Investigated the theoretical properties of the Group Lasso in high-dimensional settings.
  • Proposed an adaptive Group Lasso method, generalizing the adaptive Lasso.
  • Analyzed the consistency of the adaptive Group Lasso using the Group Lasso as an initial estimator.

Main Results:

  • The Group Lasso can achieve model dimension comparable to the true model and is estimation consistent under certain conditions.
  • The Group Lasso is generally not selection consistent and may select irrelevant groups.
  • The proposed adaptive Group Lasso demonstrates consistency in group selection under specific conditions.

Conclusions:

  • While Group Lasso offers benefits in structured high-dimensional data, its selection consistency is limited.
  • The adaptive Group Lasso provides a more reliable approach for variable selection in such scenarios.
  • The adaptive Group Lasso's performance is contingent on the quality of the initial estimator, ideally Group Lasso.