Abstract Many supervised learning problems involve learning from samples whose labels are corrupted in some way. For example, each label may be flipped with some constant probability (learning with label noise), or one may have a pool of unlabelled samples in lieu of negative samples (learning from positive and unlabelled data). This paper uses class-probability estimation to study these and other corruption processes belonging to the mutually contaminated distributions framework Learning from corrupted binary labels In many practical scenarios involving learning from binary labels, one observes samples whose labels are corrupted versions of the actual ground truth. For example, in learning from class-conditional label noise (CCN learning), the labels are flipped with some constant probability A fundamental question is whether one can minimise a given performance measure with respect to D, given access only to samples from D corr . Intuitively, in general this requires knowledge of the parameters of the corruption process that determines D corr . This yields two further questions: are there measures for which knowledge of these corruption parameters is unnecessary, and for other measures, can we estimate these parameters? In this paper, we consider corruption problems belonging to the mutually contaminated distributions framework While some of our results are known for the special cases of CCN and PU learning, our interest is in determining to what extent they generalise to other label corruption problems. This is a step towards a unified treatment of these problems. We now fix notation and formalise the problem
