Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression

Congrui Yi, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

39 Citations (Scopus)


We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates a regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the “strong rule” for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultrahigh dimensions. We illustrate the application via a real data example. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)547-557
Number of pages11
JournalJournal of Computational and Graphical Statistics
Issue number3
Publication statusPublished - 3 Jul 2017
Externally publishedYes


  • Elastic-net
  • High-dimensional data
  • Nonsmooth optimization
  • Robust regression
  • Solution path

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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