In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at enhancing model robustness against variations in data distribution, with safe screening (SS), a sparse optimization technique designed to identify irrelevant samples and features prior to model training. The core concept of the DRSS method involves reformulating the DR covariate-shift problem as a weighted empirical risk minimization problem, where the weights are subject to uncertainty within a predetermined range. By extending the SS technique to accommodate this weight uncertainty, the DRSS method is capable of reliably identifying unnecessary samples and features under any future distribution within a specified range. We provide a theoretical guarantee of the DRSS method and validate its performance through numerical experiments on both synthetic and real-world datasets.

我们提出了一种名为分布鲁棒安全筛选（DRSS）的方法，用于在DR协变量转变设置中识别不必要的样本和特征。该方法有效地将DR学习与安全筛选相结合，对模型训练之前的无关样本和特征进行了稀疏优化，实现了在特定范围内可靠地识别任何未来分布的不必要样本和特征。我们提供了DRSS方法的理论保证，并通过在合成和现实世界数据集上进行数值实验证实了其性能。