Wen Jiawei, Yang Songshan, Wang Christina Dan, Jiang Yifan, Li Runze
Meta Platforms Inc., 1 Hacker Way, Menlo Park, CA 94025, USA.
The Center for Applied Statistics and Institute of Statistics and Big Data, Renmin University of China, Beijing 100872, China.
J Econom. 2025 May;249(Pt A). doi: 10.1016/j.jeconom.2023.01.028. Epub 2023 Mar 24.
This paper is concerned with computational issues related to penalized quantile regression (PQR) with ultrahigh dimensional predictors. Various algorithms have been developed for PQR, but they become ineffective and/or infeasible in the presence of ultrahigh dimensional predictors due to the storage and scalability limitations. The variable updating schema of the feature-splitting algorithm that directly applies the ordinary alternating direction method of multiplier (ADMM) to ultrahigh dimensional PQR may make the algorithm fail to converge. To tackle this hurdle, we propose an efficient and parallelizable algorithm for ultrahigh dimensional PQR based on the three-block ADMM. The compatibility of the proposed algorithm with parallel computing alleviates the storage and scalability limitations of a single machine in the large-scale data processing. We establish the rate of convergence of the newly proposed algorithm. In addition, Monte Carlo simulations are conducted to compare the finite sample performance of the proposed algorithm with that of other existing algorithms. The numerical comparison implies that the proposed algorithm significantly outperforms the existing ones. We further illustrate the proposed algorithm via an empirical analysis of a real-world data set.
本文关注与具有超高维预测变量的惩罚分位数回归（PQR）相关的计算问题。针对PQR已经开发了各种算法，但由于存储和可扩展性限制，在存在超高维预测变量的情况下，这些算法变得无效和/或不可行。直接将普通交替方向乘子法（ADMM）应用于超高维PQR的特征分裂算法的变量更新模式可能会使算法无法收敛。为克服这一障碍，我们基于三块ADMM提出了一种用于超高维PQR的高效且可并行化的算法。所提出算法与并行计算的兼容性减轻了单机在大规模数据处理中的存储和可扩展性限制。我们建立了新提出算法的收敛速度。此外，进行了蒙特卡罗模拟，以比较所提出算法与其他现有算法的有限样本性能。数值比较表明，所提出的算法明显优于现有算法。我们通过对一个真实数据集的实证分析进一步说明了所提出的算法。
