Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning
This work addresses a theoretical gap in understanding performance differences in binary classification for researchers in machine learning, though it is incremental as it builds on existing PU learning frameworks.
The paper tackles the problem of explaining why Positive-Unlabeled (PU) learning sometimes outperforms Positive-Negative (PN) learning by providing theoretical analysis based on upper bounds on estimation errors, finding conditions under which PU or NU learning is likely to be better and proving that with infinite unlabeled data, one will improve over PN learning, with experimental results on artificial and benchmark data supporting these findings.
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. Our theoretical findings well agree with the experimental results on artificial and benchmark data even when the experimental setup does not match the theoretical assumptions exactly.