标题： 高维正则化Huber回归的精确坐标下降法 显示英文标题

标题： Exact Coordinate Descent for High-Dimensional Regularized Huber Regression

摘要： 我们开发了一种用于高维正则化Huber回归的精确坐标下降算法。 与复合梯度下降方法相比，我们的算法在底层模型稀疏时充分利用了坐标下降的优势。 此外，与文献中之前引入的现有二阶近似方法不同，即使由于从重尾分布中抽取的协变量之间的高度相关性导致Hessian矩阵病态，该算法仍然有效。 关键思想是，对于每个坐标，边际增量仅来自内群观测，而导数在由部分残差构建的网格上保持单调递增。 在传统坐标下降策略的基础上，我们进一步提出了变量筛选规则，有选择地确定每次迭代中要更新的变量，从而加速收敛。 据我们所知，这是第一项为惩罚Huber损失最小化开发一阶坐标下降算法的工作。 我们通过扩展用于Lasso的论证，界定了所提出算法的非渐近收敛速率，并正式描述了所提出筛选规则的操作。 在重尾和高度相关的预测因子下的大量模拟研究，以及一个实际数据应用，展示了该方法的实际效率和计算增强的好处。 显示英文摘要

摘要： We develop an exact coordinate descent algorithm for high-dimensional regularized Huber regression. In contrast to composite gradient descent methods, our algorithm fully exploits the advantages of coordinate descent when the underlying model is sparse. Moreover, unlike existing second-order approximation methods previously introduced in the literature, it remains effective even when the Hessian becomes ill-conditioned due to high correlations among covariates drawn from heavy-tailed distributions. The key idea is that, for each coordinate, marginal increments arise only from inlier observations, while the derivatives remain monotonically increasing over a grid constructed from the partial residuals. Building on conventional coordinate descent strategies, we further propose variable screening rules that selectively determine which variables to update at each iteration, thereby accelerating convergence. To the best of our knowledge, this is the first work to develop a first-order coordinate descent algorithm for penalized Huber loss minimization. We bound the nonasymptotic convergence rate of the proposed algorithm by extending arguments developed for the Lasso and formally characterize the operation of the proposed screening rule. Extensive simulation studies under heavy-tailed and highly-correlated predictors, together with a real data application, demonstrate both the practical efficiency of the method and the benefits of the computational enhancements.