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Labelling of data for supervised learning can be costly and time-consumingand the risk of incorporating label noise in large data sets is imminent. Whentraining a flexible discriminative model using a strictly proper loss, suchnoise will inevitably shift the solution towards the conditional distributionover noisy labels. Nevertheless, while deep neural networks have proven capableof fitting random labels, regularisation and the use of robust loss functionsempirically mitigate the effects of label noise. However, such observationsconcern robustness in accuracy, which is insufficient if reliable uncertaintyquantification is critical. We demonstrate this by analysing the properties ofthe conditional distribution over noisy labels for an input-dependent noisemodel. In addition, we evaluate the set of robust loss functions characterisedby noise-insensitive, asymptotic risk minimisers. We find that strictly properand robust loss functions both offer asymptotic robustness in accuracy, butneither guarantee that the final model is calibrated. Moreover, even withrobust loss functions, overfitting is an issue in practice. With these results,we aim to explain observed robustness of common training practices, such asearly stopping, to label noise. In addition, we aim to encourage thedevelopment of new noise-robust algorithms that not only preserve accuracy butthat also ensure reliability.

Robustness and Reliability When Training With Noisy Labels