A Coordinate-Descent-Based Approach to Solving the Sparse Group Elastic Net

Group sparse approaches to regression modeling are finding ever increasing utility in an array of application areas. While group sparsity can help assess certain data structures, it is desirable in many instances to also capture element-wise sparsity. Recent work exploring the latter has been conduc...

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Bibliographic Details
Published in:Technometrics 2017-01, Vol.59 (4), p.437
Main Authors: Samarov, Daniel V, Allen, David, Hwang, Jeeseong, Lee, Young Jong, Litorjae, Maritoni
Format: Article
Language:English
Subjects:
Algorithms
Data analysis
Data structures
Descent
Hyperspectral imaging
Regression analysis
Sparsity
Online Access:Get full text
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Summary:Group sparse approaches to regression modeling are finding ever increasing utility in an array of application areas. While group sparsity can help assess certain data structures, it is desirable in many instances to also capture element-wise sparsity. Recent work exploring the latter has been conducted in the context of l2/l1 penalized regression in the form of the sparse group lasso (SGL). Here, we present a novel model, called the sparse group elastic net (SGEN), which uses an l∞/l1/ridge-based penalty.We showthat the l∞-norm,which induces group sparsity is particularly effective in the presence of noisy data.We solve the SGENmodel using a coordinate-descent-based procedure and compare its performance to the SGL and relatedmethods in the context of hyperspectral imaging in the presence of noisy observations. Supplementary materials for this article are available online.
ISSN:0040-1706
1537-2723
DOI:10.1080/004017062016.1273138