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

TL;DR

This paper provides a theoretical analysis comparing positive-unlabeled (PU) learning with positive-negative (PN) learning, revealing conditions under which PU can outperform PN and supporting findings with experiments.

Contribution

It offers the first theoretical comparison of PU and PN learning based on estimation error bounds, explaining when PU learning can be more effective.

Findings

PU and NU learning can outperform PN under certain conditions.

Theoretical bounds predict PU/NU outperform PN with infinite unlabeled data.

Experimental results align with theoretical predictions.

Abstract

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.