论文标题
总体上保持稀疏线性回归，并具有强大的损失功能
Aggregated hold out for sparse linear regression with a robust loss function
论文作者
论文摘要
稀疏的线性回归方法通常具有自由的超参数，可以控制稀疏性的数量，并且要经受偏差差异的权衡。本文认为，在线性回归的背景下，使用汇总的固定来汇总该超参数的值。汇总固定（Agghoo）是一个程序，该过程平均按hold-out选择估计器（单个分裂的交叉验证）。在本文的理论部分中，证明Agghoo将其应用于由其零 - 标记参数化的稀疏估计器时，满足了非反应性甲骨文的不平等。特别是，这包括Zou，Hasti {é}和Tibshirani引入的套索变体。模拟用于将Agghoo与交叉验证进行比较。他们表明，当固有维度较高时，当存在混杂因素与预测协变量相关时，Agghoo的性能要比CV更好。
Sparse linear regression methods generally have a free hyperparameter which controls the amount of sparsity, and is subject to a bias-variance tradeoff. This article considers the use of Aggregated hold-out to aggregate over values of this hyperparameter, in the context of linear regression with the Huber loss function. Aggregated hold-out (Agghoo) is a procedure which averages estimators selected by hold-out (cross-validation with a single split). In the theoretical part of the article, it is proved that Agghoo satisfies a non-asymptotic oracle inequality when it is applied to sparse estimators which are parametrized by their zero-norm. In particular , this includes a variant of the Lasso introduced by Zou, Hasti{é} and Tibshirani. Simulations are used to compare Agghoo with cross-validation. They show that Agghoo performs better than CV when the intrinsic dimension is high and when there are confounders correlated with the predictive covariates.
