Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning

Niu, Gang, Plessis, Marthinus Christoffel du, Sakai, Tomoya, Ma, Yao, Sugiyama, Masashi

Neural Information Processing Systems 

In PU learning, a binary classifier is trained from positive (P) and unlabeled (U) data without negative (N) data. Although N data is missing, it sometimes outperforms PN learning (i.e., ordinary supervised learning). Hitherto, neither theoretical nor experimental analysis has been given to explain this phenomenon. In this paper, we theoretically compare PU (and NU) learning against PN learning based on the upper bounds on estimation errors. We find simple conditions when PU and NU learning are likely to outperform PN learning, and we prove that, in terms of the upper bounds, either PU or NU learning (depending on the class-prior probability and the sizes of P and N data) given infinite U data will improve on PN learning.