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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Bibliographic Details
Published in:Statistics and computing Vol. 35; no. 5
Main Authors: Wu, Xiaofei, Chao, Yue, Liang, Rongmei, Tang, Shi, Zhang, Zhimin
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2025
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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 .
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ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-025-10658-y