You can robustly learn from contaminated data by selecting the subset of samples that maximizes Wasserstein distance from the full dataset—this works as a model-agnostic preprocessing tool before training any model.
This paper introduces Wasserstein Filtering, a method to clean contaminated datasets by selecting samples whose distribution is most different from the full dataset. The approach uses optimal transport theory to identify and remove outliers, with theoretical guarantees and practical algorithms that work as a preprocessing step for any downstream task.