# Distributed High-Dimensional Quantile Regression: Estimation Efficiency and Support Recovery

arXiv: https://arxiv.org/abs/2405.07552 · HTML: https://mlsanity.com/paper/2405.07552/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 16 of 16)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [Smoothing quantile regressions](https://mlsanity.com/paper/1905.08535/) (2019)
- [Distributed High-dimensional Regression Under a Quantile Loss Function](https://mlsanity.com/paper/1906.05741/) (2019)
- [A Distributed One-Step Estimator](https://mlsanity.com/paper/1511.01443/) (2015)
- [Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guarantees](https://mlsanity.com/paper/2110.13113/) (2021)
- [Communication-Efficient Distributed Optimization of Self-Concordant Empirical Loss](https://mlsanity.com/paper/1501.00263/) (2015)
- [L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs](https://mlsanity.com/paper/1511.08102/) (2015)
- [Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores](https://mlsanity.com/paper/1702.06209/) (2017)
- [A General Framework for Robust Testing and Confidence Regions in High-Dimensional Quantile Regression](https://mlsanity.com/paper/1412.8724/) (2014)
- [An Algorithm for Quadratic ℓ1-Regularized Optimization with a Flexible Active-Set Strategy](https://mlsanity.com/paper/1412.1844/) (2014)

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.02117/) (2026)

## Abstract (arXiv)

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and data heterogeneity. However, the non-smoothness of the check loss function poses big challenges to both computation and theory in the distributed setting. To tackle these problems, we transform the original quantile regression into the least-squares optimization. By applying a double-smoothing approach, we extend a previous Newton-type distributed approach without the restrictive independent assumption between the error term and covariates. An efficient algorithm is developed, which enjoys high computation and communication efficiency. Theoretically, the proposed distributed estimator achieves a near-oracle convergence rate and high support recovery accuracy after a constant number of iterations. Extensive experiments on synthetic examples and a real data application further demonstrate the effectiveness of the proposed method.