Large-scale data from various research fields are not only heterogeneous and sparse but also difficult to store on a single machine. Expectile regression is a popular alternative for modeling heterogeneous data. In this paper, we devise a distributed optimization approach to SCAD and adaptive LASSO penalized expectile regression, where the observations are randomly partitioned across multiple machines. We construct a penalized communication-efficient surrogate loss (CSL) function. Computationally, our method based on the CSL function requires only the master machine to solve a regular M-estimation problem, while other worker machines compute the gradient of the loss function on local data. Our method matches the estimation error bound of the centralized method during consecutive rounds of communication. Under some mild assumptions, we establish the oracle properties of the SCAD and adaptive LASSO penalized expectile regression. We then develop a modified alternating direction method of multipliers (ADMM) algorithm for the implementation of the proposed estimator. A series of simulation studies are conducted to assess the finite-sample performance of the proposed estimator. Applications to an HIV study demonstrate the practicability of the proposed method.

来自各个研究领域的大规模数据不仅异构且稀疏，而且难以存储在单个计算机上。期望回归是用于建模异构数据的流行替代方法。在本文中，我们设计了一种针对SCAD和自适应LASSO惩罚性期望回归的分布式优化方法，该方法将观测值随机分配到多台计算机上。我们构造了一种惩罚有效的通信效率代理损失（CSL）函数。通过计算，我们基于CSL函数的方法仅需要主机即可解决常规的M估计问题，而其他工作机则可根据本地数据计算损失函数的梯度。我们的方法在连续几轮通信中匹配集中式方法的估计误差范围。在一些温和的假设下，我们建立了SCAD的Oracle属性和自适应LASSO惩罚性预期回归。然后，我们为提出的估算器的实现开发了一种改进的乘数交替方向法（ADMM）算法。进行了一系列模拟研究，以评估所提出估计量的有限样本性能。一项HIV研究的申请证明了该方法的实用性。