  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.
