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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| Published in: | Statistics and computing Vol. 34; no. 6 |
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| Language: | English |
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01.12.2024
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| ISSN: | 0960-3174, 1573-1375 |
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| Abstract | 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. |
|---|---|
| AbstractList | The Dantzig selector is a popular ℓ1-type variable selection method widely used across various research fields. However, ℓ1-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 ℓ1 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 ℓ1 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. 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. |
| ArticleNumber | 180 |
| Author | Zhao, Delin Wen, Jiawei Yang, Songshan |
| Author_xml | – sequence: 1 givenname: Jiawei surname: Wen fullname: Wen, Jiawei organization: Meta – sequence: 2 givenname: Songshan surname: Yang fullname: Yang, Songshan organization: Center for Applied Statistics and Institute of Statistics and Big Data, Renmin University of China – sequence: 3 givenname: Delin surname: Zhao fullname: Zhao, Delin email: delin1997@ruc.edu.cn organization: Center for Applied Statistics and Institute of Statistics and Big Data, Renmin University of China |
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| Cites_doi | 10.1111/j.1467-9868.2008.00668.x 10.1214/13-AOS1198 10.1198/jasa.2008.tm08516 10.3150/12-BEJSP17 10.1080/00401706.1995.10484371 10.1080/10618600.2022.2143785 10.1214/10-AOAS388 10.1137/140964357 10.1080/01621459.2012.656014 10.1214/08-AOS620 10.1093/nsr/nwt032 10.18637/jss.v033.i01 10.1214/009053607000000604 10.1109/TSP.2018.2868269 10.1111/j.2517-6161.1996.tb02080.x 10.1093/biomet/asp013 10.1109/TIP.2019.2924339 10.1198/jasa.2009.0127 10.1016/j.csda.2012.04.019 10.1214/09-AOS729 10.1198/016214501753382273 10.1080/00401706.1970.10488634 10.1201/9780429096280 10.1016/j.jeconom.2022.04.004 10.1080/01621459.2023.2202433 10.1198/016214506000000735 10.1007/s10444-017-9559-3 10.1080/01621459.2020.1840989 10.1111/j.1467-9868.2005.00503.x 10.1017/9781108627771 10.1214/15-AOAS842 10.1016/j.jeconom.2023.01.028 10.1109/ICASSP.2019.8683703 |
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| Snippet | 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... The Dantzig selector is a popular ℓ1-type variable selection method widely used across various research fields. However, ℓ1-type methods may not perform well... |
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| SubjectTerms | 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 |
| Title | Nonconvex Dantzig selector and its parallel computing algorithm |
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