论文标题
通过双限制球
l1-norm quantile regression screening rule via the dual circumscribed sphere
论文作者
论文摘要
如果在高维数据集中存在异常值或重尾误差，则L1-norm分位数回归是一个常见的选择。但是，当数据的特征大小超高时，解决此问题在计算上昂贵。据我们所知，现有的筛选规则无法加快L1-Norm分位回归的计算，这使分位数函数/弹球损失的非差异性可降低。在本文中，我们介绍了双限制的球体技术，并提出了一种新型的L1-norm分位回归筛选规则。我们的规则表示为给定数据的闭合形式功能，并消除了低计算成本的非活动特征。在某些仿真和实际数据集上进行的数值实验表明，该筛选规则可用于消除几乎所有不活动的特征。此外，与没有筛查规则的计算相比，该规则可以帮助减少计算时间的23倍。
l1-norm quantile regression is a common choice if there exists outlier or heavy-tailed error in high-dimensional data sets. However, it is computationally expensive to solve this problem when the feature size of data is ultra high. As far as we know, existing screening rules can not speed up the computation of the l1-norm quantile regression, which dues to the non-differentiability of the quantile function/pinball loss. In this paper, we introduce the dual circumscribed sphere technique and propose a novel l1-norm quantile regression screening rule. Our rule is expressed as the closed-form function of given data and eliminates inactive features with a low computational cost. Numerical experiments on some simulation and real data sets show that this screening rule can be used to eliminate almost all inactive features. Moreover, this rule can help to reduce up to 23 times of computational time, compared with the computation without our screening rule.
