  Machine learning classifiers have been demonstrated, both empirically and
theoretically, to be robust to label noise under certain conditions -- notably
the typical assumption is that label noise is independent of the features given
the class label. We provide a theoretical framework that generalizes beyond
this typical assumption by modeling label noise as a distribution over feature
space. We show that both the scale and the shape of the noise distribution
influence the posterior likelihood; and the shape of the noise distribution has
a stronger impact on classification performance if the noise is concentrated in
feature space where the decision boundary can be moved. For the special case of
uniform label noise (independent of features and the class label), we show that
the Bayes optimal classifier for $c$ classes is robust to label noise until the
ratio 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 of
class-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 the
noise distribution targets decision boundaries (label noise is directly
dependent on feature space), classification robustness can drop off even at a
small scale of noise. Even when evaluating recent label-noise mitigation
methods we see reduced accuracy when label noise is dependent on features.
These findings explain why machine learning often handles label noise well if
the noise distribution is uniform in feature-space; yet it also points to the
difficulty of overcoming label noise when it is concentrated in a region of
feature space where a decision boundary can move.
