A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression
针对非凸惩罚分位数回归计算困难的问题，提出一种基于交替方向乘子法的单循环算法QPADM，在样本量和特征数大时计算更快、统计精度更高。
Penalized quantile regression (PQR) provides a useful tool for analyzing high-dimensional data with heterogeneity. However, its computation is challenging due to the nonsmoothness and (sometimes) the nonconvexity of the objective function. An iterative coordinate descent algorithm (QICD) was recently proposed to solve PQR with nonconvex penalty. The QICD significantly improves the computational speed but requires a double-loop. In this article, we propose an alternative algorithm based on the alternating direction method of multiplier (ADMM). By writing the PQR into a special ADMM form, we can solve the iterations exactly without using coordinate descent. This results in a new single-loop algorithm, which we refer to as the QPADM algorithm. The QPADM demonstrates favorable performance in both computational speed and statistical accuracy, particularly when the sample size n and/or the number of features p are large. Supplementary material for this article is available online.