Concave 1-norm group selection

Dingfeng Jiang; Jian Huang

doi:10.1093/biostatistics/kxu050

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Journal article

Open access

Peer reviewed

Concave 1-norm group selection

Dingfeng Jiang and Jian Huang

Biostatistics (Oxford, England), Vol.16(2), pp.252-267

04/2015

DOI: 10.1093/biostatistics/kxu050

PMCID: PMC4441102

PMID: 25417206

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https://doi.org/10.1093/biostatistics/kxu050View

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Abstract

Grouping structures arise naturally in many high-dimensional problems. Incorporation of such information can improve model fitting and variable selection. Existing group selection methods, such as the group Lasso, require correct membership. However, in practice it can be difficult to correctly specify group membership of all variables. Thus, it is important to develop group selection methods that are robust against group mis-specification. Also, it is desirable to select groups as well as individual variables in many applications. We propose a class of concave [Formula: see text]-norm group penalties that is robust to grouping structure and can perform bi-level selection. A coordinate descent algorithm is developed to calculate solutions of the proposed group selection method. Theoretical convergence of the algorithm is proved under certain regularity conditions. Comparison with other methods suggests the proposed method is the most robust approach under membership mis-specification. Simulation studies and real data application indicate that the [Formula: see text]-norm concave group selection approach achieves better control of false discovery rates. An R package grppenalty implementing the proposed method is available at CRAN.

Models, Theoretical

Algorithms

Breast Neoplasms - genetics

Humans

Middle Aged

Female

Breast Neoplasms - diagnosis

Details

Title: Subtitle: Concave 1-norm group selection
Creators: Dingfeng Jiang - Department of Biostatistics, University of Iowa, Iowa City, IA 52246, USA dingfeng-jiang@uiowa.edu
Jian Huang - Department of Biostatistics, University of Iowa, Iowa City, IA 52246, USA and Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52246, USA
Resource Type: Journal article
Publication Details: Biostatistics (Oxford, England), Vol.16(2), pp.252-267
Publisher: England
DOI: 10.1093/biostatistics/kxu050
PMID: 25417206
PMCID: PMC4441102
ISSN: 1468-4357
eISSN: 1468-4357
Grant note: R01CA142774 / NCI NIH HHS
Language: English
Date published: 04/2015
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9983985891502771

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