Ord-NLL: Negative Label Learning for Ordinal Noisy Labels

Abstract

Disease severity is often annotated using a small number of discrete severity levels with an inherent order, yet such labels are subjective and often corrupted by label noise biased toward adjacent levels. Conventional methods for learning with noisy labels typically treat label noise as random class flips, overlooking the ordinal structure of these misannotations. We propose Ordinal Negative Label Learning (Ord-NLL), an extension of negative label learning that explicitly incorporates ordinal structure into negative-label sampling. Ord-NLL constructs an ordinal negative-label distribution that assigns higher sampling probability to levels farther from the observed label, thereby encouraging learning that respects ordinal relationships. The method uses a single-term objective derived theoretically and requires neither the noise rate nor the label-transition matrix, making it practical when prior knowledge about the noise process is unavailable. We further introduce Ord-NLL+, which leverages the confidence estimates produced by Ord-NLL for sample selection and retraining. Experiments on two multi-expert ulcerative colitis (UC) endoscopic-image datasets under two ordinal-noise models show that Ord-NLL is competitive with or superior to strong baselines while reducing mean absolute error, and that Ord-NLL+ often yields further gains. Across controlled ordinal-noise experiments, Ord-NLL and Ord-NLL + consistently outperformed conventional NLL and remained competitive with strong noisy-label baselines. In a representative severe-noise setting, Ord-NLL + achieved 0.715 accuracy, 0.305 MAE, and 0.625 macro-F1, outperforming both conventional NLL and the best competing baseline. These results suggest that explicitly incorporating ordinal structure into negative-label learning is an effective strategy for robust severity estimation under noisy ordinal annotations.