Feature splitting parallel algorithm for Dantzig selectors

The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets into manageable subsets that can be stored and processed more...

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Vydáno v:	Statistics and computing Ročník 35; číslo 5
Hlavní autoři:	Wu, Xiaofei, Chao, Yue, Liang, Rongmei, Tang, Shi, Zhang, Zhimin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.10.2025 Springer Nature B.V
Témata:	Algorithms Artificial Intelligence Computer Science Convergence Original Paper Probability and Statistics in Computer Science Selectors Splitting Statistical Theory and Methods Statistics and Computing/Statistics Programs Partition-insensitive Parallel computing Proximal point algorithm Dantzig selector Feature splitting
ISSN:	0960-3174, 1573-1375
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Abstract	The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets into manageable subsets that can be stored and processed more easily on a single machine. This paper proposes a variable splitting parallel algorithm for solving both convex and nonconvex Dantzig selectors based on the proximal point algorithm. The primary advantage of our parallel algorithm, compared to existing parallel approaches, is the significantly reduced number of iteration variables, which greatly enhances computational efficiency and accelerates the convergence speed of the algorithm. Furthermore, we show that our solution remains unchanged regardless of how the data is partitioned, a property referred to as partition-insensitive. In theory, we use a concise proof framework to demonstrate that the algorithm exhibits linear convergence. Numerical experiments indicate that our algorithm performs competitively in both parallel and nonparallel environments. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/PPADS .
AbstractList	The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets into manageable subsets that can be stored and processed more easily on a single machine. This paper proposes a variable splitting parallel algorithm for solving both convex and nonconvex Dantzig selectors based on the proximal point algorithm. The primary advantage of our parallel algorithm, compared to existing parallel approaches, is the significantly reduced number of iteration variables, which greatly enhances computational efficiency and accelerates the convergence speed of the algorithm. Furthermore, we show that our solution remains unchanged regardless of how the data is partitioned, a property referred to as partition-insensitive. In theory, we use a concise proof framework to demonstrate that the algorithm exhibits linear convergence. Numerical experiments indicate that our algorithm performs competitively in both parallel and nonparallel environments. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/PPADS. The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets into manageable subsets that can be stored and processed more easily on a single machine. This paper proposes a variable splitting parallel algorithm for solving both convex and nonconvex Dantzig selectors based on the proximal point algorithm. The primary advantage of our parallel algorithm, compared to existing parallel approaches, is the significantly reduced number of iteration variables, which greatly enhances computational efficiency and accelerates the convergence speed of the algorithm. Furthermore, we show that our solution remains unchanged regardless of how the data is partitioned, a property referred to as partition-insensitive. In theory, we use a concise proof framework to demonstrate that the algorithm exhibits linear convergence. Numerical experiments indicate that our algorithm performs competitively in both parallel and nonparallel environments. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/PPADS .
ArticleNumber	116
Author	Tang, Shi Zhang, Zhimin Liang, Rongmei Wu, Xiaofei Chao, Yue
Author_xml	– sequence: 1 givenname: Xiaofei surname: Wu fullname: Wu, Xiaofei organization: College of Mathematics and Statistics, Chongqing University – sequence: 2 givenname: Yue surname: Chao fullname: Chao, Yue organization: Department of Statistics and Data Science, Xiamen University – sequence: 3 givenname: Rongmei surname: Liang fullname: Liang, Rongmei organization: Department os Statistics and Data Science, Southern University of Science and Technology – sequence: 4 givenname: Shi surname: Tang fullname: Tang, Shi organization: Big Data and Intelligence Engineering School, Chongqing College of International Business and Economics – sequence: 5 givenname: Zhimin surname: Zhang fullname: Zhang, Zhimin email: zmzhang@cqu.edu.cn organization: College of Mathematics and Statistics, Chongqing University
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Snippet	The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing...
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SubjectTerms	Algorithms Artificial Intelligence Computer Science Convergence Original Paper Probability and Statistics in Computer Science Selectors Splitting Statistical Theory and Methods Statistics and Computing/Statistics Programs
Title	Feature splitting parallel algorithm for Dantzig selectors
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