ADMM for High-Dimensional Sparse Penalized Quantile Regression

Yuwen Gu, Jun Fan, Lingchen Kong, Shiqian Ma, Hui Zou

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Sparse penalized quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection in high-dimensional data analysis. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to nonsmoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. The convergence properties of the proposed algorithms are established. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)319-331
Number of pages13
JournalTechnometrics
Volume60
Issue number3
DOIs
StatePublished - Jul 3 2018

Fingerprint

Method of multipliers
Penalized Regression
Alternating Direction Method
Quantile Regression
High-dimensional
Fast Solvers
Heteroscedasticity
Robust Estimation
Regression Function
High-dimensional Data
Variable Selection
Loss Function
Convergence Properties
Data analysis
Numerical Examples
Computing
Demonstrate

Keywords

  • Alternating direction method of multipliers
  • Lasso
  • Nonconvex penalty
  • Quantile regression
  • Variable selection

Cite this

ADMM for High-Dimensional Sparse Penalized Quantile Regression. / Gu, Yuwen; Fan, Jun; Kong, Lingchen; Ma, Shiqian; Zou, Hui.

In: Technometrics, Vol. 60, No. 3, 03.07.2018, p. 319-331.

Research output: Contribution to journalArticle

Gu, Yuwen ; Fan, Jun ; Kong, Lingchen ; Ma, Shiqian ; Zou, Hui. / ADMM for High-Dimensional Sparse Penalized Quantile Regression. In: Technometrics. 2018 ; Vol. 60, No. 3. pp. 319-331.
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