标题： 分布鲁棒组正则化估计量 显示英文标题

标题： Distributionally Robust Groupwise Regularization Estimator

摘要： 在群组变量的背景下，正则化估计量已成功应用于模型和特征选择以保持可解释性。 我们提出了一个分布鲁棒优化 (DRO) 问题，该问题恢复了流行的估计量，例如群组平方根套索 (GSRL)。 我们的 DRO 公式使我们可以将 GSRL 解释为一种博弈，在这种博弈中，我们在学习回归参数的同时，对手会选择数据的扰动。 我们希望选择参数以最小化对手可能选择的任何合理模型下的期望损失——而对手则希望增加期望损失。 事实证明，正则化参数恰好由对手允许的训练数据的扰动量精确确定。 在本文中，我们引入了一个基于数据的（统计学）准则，用于最优正则化的选择，并在训练集规模增大时渐近地以封闭形式对其进行评估。 我们的易于计算的正则化公式与交叉验证进行了比较，显示出良好的（有时更优）性能。 显示英文摘要

摘要： Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers popular estimators, such as Group Square Root Lasso (GSRL). Our DRO formulation allows us to interpret GSRL as a game, in which we learn a regression parameter while an adversary chooses a perturbation of the data. We wish to pick the parameter to minimize the expected loss under any plausible model chosen by the adversary - who, on the other hand, wishes to increase the expected loss. The regularization parameter turns out to be precisely determined by the amount of perturbation on the training data allowed by the adversary. In this paper, we introduce a data-driven (statistical) criterion for the optimal choice of regularization, which we evaluate asymptotically, in closed form, as the size of the training set increases. Our easy-to-evaluate regularization formula is compared against cross-validation, showing good (sometimes superior) performance.