Journal article
Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
Journal of computational and graphical statistics, Vol.26(3), pp.547-557
07/03/2017
DOI: 10.1080/10618600.2016.1256816
Abstract
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.
Details
- Title: Subtitle
- Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
- Creators
- Congrui Yi - University of IowaJian Huang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of computational and graphical statistics, Vol.26(3), pp.547-557
- Publisher
- Taylor & Francis
- DOI
- 10.1080/10618600.2016.1256816
- ISSN
- 1061-8600
- eISSN
- 1537-2715
- Language
- English
- Date published
- 07/03/2017
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257617402771
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