Regularization Paths for Huber Loss Regression and Quantile Regression via Semismooth Newton Coordinate Descent

• Activity Number: 696
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Congrui Yi* and Jian Huang
• Companies: The University of Iowa and The University of Iowa
• Keywords: Huber loss regression ; quantile regression ; robust ; elastic-net ; strong rule ; semismooth Newton coordinate descent

Abstract

We propose semismooth Newton coordinate descent (SNCD), a fast algorithm for elastic-net penalized robust regression models. SNCD is a novel combination of the semismooth Newton and coordinate descent algorithms. It is designed for loss functions with only first order derivatives, including Huber loss in particular, and is scalable to high-dimensional models. In addition, an adaptive version of the "strong rule" for screening predictors is incorporated to gain extra efficiency. We establish convergence properties of the algorithm. As an important application, we show that SNCD can be adopted to compute the solution paths of penalized quantile regression. Through numerical experiments, we demonstrate that the proposed algorithm works well on high-dimensional data with heavy-tailed errors or high correlations between predictors, and that for quantile regression SNCD is considerably faster than the existing method and has better optimization performance. A breast cancer gene expression dataset is used to illustrate the proposed algorithm.