  Positive-unlabeled learning (PU learning) is known as a special case of
semi-supervised binary classification where only a fraction of positive
examples are labeled. The challenge is then to find the correct classifier
despite this lack of information. Recently, new methodologies have been
introduced to address the case where the probability of being labeled may
depend on the covariates. In this paper, we are interested in establishing risk
bounds for PU learning under this general assumption. In addition, we quantify
the impact of label noise on PU learning compared to standard classification
setting. Finally, we provide a lower bound on minimax risk proving that the
upper bound is almost optimal.
