Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
提出一种半光滑牛顿坐标下降算法，用于高维弹性网惩罚Huber损失回归和分位数回归，通过同时更新系数和次梯度解决计算难题，数值实验表明算法高效且可扩展至超高维。
We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates a regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the “strong rule” for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultrahigh dimensions. We illustrate the application via a real data example. Supplementary materials for this article are available online.