Wasserstein Distributional Normalization For Robust Distributional Certification of Noisy Labeled Data

We propose a novel Wasserstein distributional normalization method that can classify noisy labeled data accurately. Recently, noisy labels have been successfully handled based on small-loss criteria, but have not been clearly understood from the theoretical point of view. In this paper, we address this problem by adopting distributionally robust optimization (DRO). In particular, we present a theoretical investigation of the distributional relationship between uncertain and certain samples based on the small-loss criteria. Our method takes advantage of this relationship to exploit useful information from uncertain samples. To this end, we normalize uncertain samples into the robustly certified region by introducing the non-parametric Ornstein-Ulenbeck type of Wasserstein gradient flows called Wasserstein distributional normalization, which is cheap and fast to implement. We verify that network confidence and distributional certification are fundamentally correlated and show the concentration inequality when the network escapes from over-parameterization. Experimental results demonstrate that our non-parametric classification method outperforms other parametric baselines on the Clothing1M and CIFAR-10/100 datasets when the data have diverse noisy labels.