Given only positive examples and unlabeled examples (from both positive and negative classes), we might hope nevertheless to estimate an accurate positive-versus-negative classifier. Formally, this task is broken down into two subtasks: (i) Mixture Proportion Estimation (MPE)—determining the fraction of positive examples in the unlabeled data; and (ii) PU-learning—given such an estimate, learning the desired positive-versus-negative classifier. Unfortunately, classical methods for both problems…