Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
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DOI：
10.1080/10618600.2016.1256816
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发表时间：
2017-01-01
影响因子：
2.4
通讯作者：
Huang, Jian
中科院分区：
文献类型：
--
作者：
Yi, Congrui;Huang, Jian
提出了高维环境下弹性网罚Huber损失回归和分位数回归的半光滑牛顿坐标下降(SNCD)算法。与现有的坐标下降型算法不同，SNCD算法在每次迭代中同时更新回归系数及其对应的次梯度。它结合了坐标下降法和半光滑牛顿算法的优点，有效地解决了高维和非光滑性带来的计算挑战。我们建立了该算法的收敛性质。此外，我们提出了强规则的自适应版本，用于筛选预报器以获得额外的效率。通过数值实验，我们证明了所提出的算法是非常有效的，并且可以扩展到超高维。通过一个真实的数据实例说明了该方法的应用。这篇文章的补充材料可以在网上找到。
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.