Classification with Asymmetric Label Noise

In many real-world classification problems, the labels of training examples are randomly corrupted. That is, the set of training examples for each class is contaminated by examples of the other class. Existing approaches to this problem assume that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. We introduce a general framework for classification with label noise that eliminates these assumptions. In particular, we identify necessary and sufficient distributional assumptions for the existence of a consistent estimator of the optimal risk, with associated estimation strategies. We find that learning in the presence of label noise is possible even when the class-conditional distributions overlap and the label noise is not symmetric. A key to our approach is a universally consistent estimator of the maximal proportion of one distribution that is present in another, or equivalently, of the so-called “separation distance” between two distributions.
The methodology is motivated by a problem in nuclear particle classification. Connections to domain adaptation and learning with positive and unlabeled examples will also be given.