2022/05/05 by Rebeka Man, Man, Rebeka, Xiaoou Pan +6 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #Algorithm #Artificial intelligence #Artificial neural network #Computer science #Convolution (computer science) #Lasso (programming language) #Machine learning #Mathematical optimization #Mathematics #Quantile #Quantile regression #Smoothness #Statistical Methods and Inference #Statistics #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.2205.02432
published in arXiv (Cornell University) (Cornell University)
arxiv created 2022/05/05 · openalex publication_date 2022/05/05 · arxiv updated 2022/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable algorithms for fitting penalized QR are lacking due to the non-differentiable piecewise linear loss function. To overcome the lack of smoothness, a recently proposed convolution-type smoothed method brings an interesting tradeoff between statistical accuracy and computational efficiency for both standard and penalized quantile regressions. In this paper, we propose a unified algorithm for fitting penalized convolution smoothed quantile regression with various commonly used convex penalties, accompanied by an R-language package conquer available from the Comprehensive R Archive Network. We perform extensive numerical studies to demonstrate the superior performance of the proposed algorithm over existing methods in both statistical and computational aspects. We further exemplify the proposed algorithm by fitting a fused lasso additive QR model on the world happiness data.