2025/04/23 by Peiwen Xiao, Xiao, Peiwen, Xiaohui Liu +5
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2504.16535
openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
In this paper, we introduce a novel decentralized surrogate gradient-based algorithm for quantile regression in a feature-distributed setting, where global features are dispersed across multiple machines within a decentralized network. The proposed algorithm, DSG-cqr, utilizes a convolution-type smoothing approach to address the non-smooth nature of the quantile loss function. DSG-cqr is fully decentralized, conjugate-free, easy to implement, and achieves linear convergence up to statistical precision. To ensure privacy, we adopt the Gaussian mechanism to provide (ε,δ)-differential privacy. To overcome the exact residual calculation problem, we estimate residuals using auxiliary variables and develop a confidence interval construction method based on Wald statistics. Theoretical properties are established, and the practical utility of the methods is also demonstrated through extensive simulations and a real-world data application.