A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression

Penalized quantile regression (PQR) provides a useful tool for analyzing high-dimensional data with heterogeneity. However, its computation is challenging due to the nonsmoothness and (sometimes) the nonconvexity of the objective function. An iterative coordinate descent algorithm (QICD) was recentl...

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Vydané v:Journal of computational and graphical statistics Ročník 26; číslo 4; s. 935 - 939
Hlavní autori: Yu, Liqun, Lin, Nan, Wang, Lan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Alexandria Taylor & Francis 02.10.2017
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Predmet:
ADMM
Algorithms
Computation
Descent
Dimensional analysis
Iterative methods
Nonconvex penalty
Parallelization
Quantile regression and single-loop algorithm
Regression analysis
Short Technical Notes
Statistical analysis
Studies
ISSN:1061-8600, 1537-2715
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Popis
Shrnutí:Penalized quantile regression (PQR) provides a useful tool for analyzing high-dimensional data with heterogeneity. However, its computation is challenging due to the nonsmoothness and (sometimes) the nonconvexity of the objective function. An iterative coordinate descent algorithm (QICD) was recently proposed to solve PQR with nonconvex penalty. The QICD significantly improves the computational speed but requires a double-loop. In this article, we propose an alternative algorithm based on the alternating direction method of multiplier (ADMM). By writing the PQR into a special ADMM form, we can solve the iterations exactly without using coordinate descent. This results in a new single-loop algorithm, which we refer to as the QPADM algorithm. The QPADM demonstrates favorable performance in both computational speed and statistical accuracy, particularly when the sample size n and/or the number of features p are large. Supplementary material for this article is available online.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2017.1328366