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Machine learning classifiers have been demonstrated, both empirically andtheoretically, to be robust to label noise under certain conditions -- notablythe typical assumption is that label noise is independent of the features giventhe class label. We provide a theoretical framework that generalizes beyondthis typical assumption by modeling label noise as a distribution over featurespace. We show that both the scale and the shape of the noise distributioninfluence the posterior likelihood; and the shape of the noise distribution hasa stronger impact on classification performance if the noise is concentrated infeature space where the decision boundary can be moved. For the special case ofuniform label noise (independent of features and the class label), we show thatthe Bayes optimal classifier for $c$ classes is robust to label noise until theratio of noisy samples goes above $\frac{c-1}{c}$ (e.g. 90% for 10 classes),which we call the tipping point. However, for the special case ofclass-dependent label noise (independent of features given the class label),the tipping point can be as low as 50%. Most importantly, we show that when thenoise distribution targets decision boundaries (label noise is directlydependent on feature space), classification robustness can drop off even at asmall scale of noise. Even when evaluating recent label-noise mitigationmethods we see reduced accuracy when label noise is dependent on features.These findings explain why machine learning often handles label noise well ifthe noise distribution is uniform in feature-space; yet it also points to thedifficulty of overcoming label noise when it is concentrated in a region offeature space where a decision boundary can move.

Robustness to Label Noise Depends on the Shape of the Noise Distribution in Feature Space