Learning from corrupted binary labels via class-probability estimation

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 (Scott et al., 2013), with three conclusions. First, one can optimise balanced error and AUC without knowledge of the corruption parameters. Second, given estimates of the corruption parameters, one can minimise a range of classification risks. Third, one can estimate corruption parameters via a class-probability estimator (e.g. kernel logistic regression) trained solely on corrupted data. Experiments on label noise tasks corroborate our analysis.