Decentralized Sparse Quantile Regression
Abstract
Distributed statistical learning has recently attracted significant attention owing to its computational efficiency and scalability in large-scale systems. However, the non-smooth quantile loss poses substantial challenges to the development of efficient decentralized algorithms for quantile regression. Existing methods may either suffer from slow convergence or rely on smoothing-based approximations that require additional stringent assumptions, particularly in high-dimensional settings. To address these issues, we propose a decentralized framework that integrates gradient tracking with iterative hard thresholding for sparse quantile estimation. The proposed method avoids smoothing approximations and relaxes the initialization requirement. Theoretically, we show that the proposed algorithm achieves linear convergence under stated regularity conditions and that the resulting estimator attains the same order of statistical accuracy as its centralized counterpart. We further develop a decentralized information criterion for selecting the working sparsity level and establish support screening guarantees. Numerical experiments and a real-data study illustrate the finite-sample performance of the proposed method.
Related
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BibTeX
@misc{yang2026decentralized,
title = {{Decentralized Sparse Quantile Regression}},
author = {Changxin Yang and Jianwei Shi and Zhongyi Zhu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04612},
eprint = {2611.04612},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04612},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Decentralized Sparse Quantile Regression
AU - Changxin Yang
AU - Jianwei Shi
AU - Zhongyi Zhu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04612
UR - https://arxiv.org/abs/2611.04612
AB - Distributed statistical learning has recently attracted significant attention owing to its computational efficiency and scalability in large-scale systems. However, the non-smooth quantile loss poses substantial challenges to the development of efficient decentralized algorithms for quantile regression. Existing methods may either suffer from slow convergence or rely on smoothing-based approximations that require additional stringent assumptions, particularly in high-dimensional settings. To address these issues, we propose a decentralized framework that integrates gradient tracking with iterative hard thresholding for sparse quantile estimation. The proposed method avoids smoothing approximations and relaxes the initialization requirement. Theoretically, we show that the proposed algorithm achieves linear convergence under stated regularity conditions and that the resulting estimator attains the same order of statistical accuracy as its centralized counterpart. We further develop a decentralized information criterion for selecting the working sparsity level and establish support screening guarantees. Numerical experiments and a real-data study illustrate the finite-sample performance of the proposed method.
ER -