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Positive-unlabeled learning (PU learning) is known as a special case ofsemi-supervised binary classification where only a fraction of positiveexamples are labeled. The challenge is then to find the correct classifierdespite this lack of information. Recently, new methodologies have beenintroduced to address the case where the probability of being labeled maydepend on the covariates. In this paper, we are interested in establishing riskbounds for PU learning under this general assumption. In addition, we quantifythe impact of label noise on PU learning compared to standard classificationsetting. Finally, we provide a lower bound on minimax risk proving that theupper bound is almost optimal.

Risk bounds for PU learning under Selected At Random assumption