Nonconvex Dantzig selector and its parallel computing algorithm

The Dantzig selector is a popular ℓ 1 -type variable selection method widely used across various research fields. However, ℓ 1 -type methods may not perform well for variable selection without complex irrepresentable conditions. In this article, we introduce a nonconvex Dantzig selector for ultrahig...

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Bibliographic Details
Published in:Statistics and computing Vol. 34; no. 6
Main Authors: Wen, Jiawei, Yang, Songshan, Zhao, Delin
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2024
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Computer Science
Computing time
Feature selection
Linear programming
Original Paper
Probability and Statistics in Computer Science
Regularization
Regularization methods
Splitting
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
Local linear approximation
Parallel computing
SCAD
High-dimensional regularization model
ISSN:0960-3174, 1573-1375
Online Access:Get full text
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Summary:The Dantzig selector is a popular ℓ 1 -type variable selection method widely used across various research fields. However, ℓ 1 -type methods may not perform well for variable selection without complex irrepresentable conditions. In this article, we introduce a nonconvex Dantzig selector for ultrahigh-dimensional linear models. We begin by demonstrating that the oracle estimator serves as a local optimum for the nonconvex Dantzig selector. In addition, we propose a one-step local linear approximation estimator, called the Dantzig-LLA estimator, for the nonconvex Dantzig selector, and establish its strong oracle property. The proposed regularization method avoids the restrictive conditions imposed by ℓ 1 regularization methods to guarantee the model selection consistency. Furthermore, we propose an efficient and parallelizable computing algorithm based on feature-splitting to address the computational challenges associated with the nonconvex Dantzig selector in high-dimensional settings. A comprehensive numerical study is conducted to evaluate the performance of the nonconvex Dantzig selector and the computing efficiency of the feature-splitting algorithm. The results demonstrate that the Dantzig selector with nonconvex penalty outperforms the ℓ 1 penalty-based selector, and the feature-splitting algorithm performs well in high-dimensional settings where linear programming solver may fail. Finally, we generalize the concept of nonconvex Dantzig selector to deal with more general loss functions.
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ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-024-10492-8