This paper studies distributed estimation and support recovery for
high-dimensional linear regression model with heavy-tailed noise. To deal with
heavy-tailed noise whose variance can be infinite, we adopt the quantile
regression loss function instead of the commonly used squared loss. However,
the non-smooth quantile loss poses new challenges to high-dimensional
distributed estimation in both computation and theoretical development. To
address the challenge, we transform the response variable and establish a new
connection between quantile regression and ordinary linear regression. Then, we
provide a distributed estimator that is both computationally and
communicationally efficient, where only the gradient information is
communicated at each iteration. Theoretically, we show that, after a constant
number of iterations, the proposed estimator achieves a near-oracle convergence
rate without any restriction on the number of machines. Moreover, we establish
the theoretical guarantee for the support recovery. The simulation analysis is
provided to demonstrate the effectiveness of our method.

本文研究了具有重尾噪声的高维线性回归模型的分布式估计和支持恢复，并采用分位数回归损失函数来处理噪声。我们提出了一种计算和通信效率高的分布式估计器，理论上表明该方法在少数迭代后即能达到近乎理想的收敛速度，并且还为支持恢复提供了理论保证。