  We consider the problem of learning a binary classifier from a training set
of positive and unlabeled examples, both in the inductive and in the
transductive setting. This problem, often referred to as \emph{PU learning},
differs from the standard supervised classification problem by the lack of
negative examples in the training set. It corresponds to an ubiquitous
situation in many applications such as information retrieval or gene ranking,
when we have identified a set of data of interest sharing a particular
property, and we wish to automatically retrieve additional data sharing the
same property among a large and easily available pool of unlabeled data. We
propose a conceptually simple method, akin to bagging, to approach both
inductive and transductive PU learning problems, by converting them into series
of supervised binary classification problems discriminating the known positive
examples from random subsamples of the unlabeled set. We empirically
demonstrate the relevance of the method on simulated and real data, where it
performs at least as well as existing methods while being faster.
