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.

本文主要探讨 PU（和 NU）学习相对于 PN 学习的上界估计误差，并发现了简单的条件，当先验概率和 P 与 N 数据的大小给定时，PU 或 NU 学习具有无限 U 数据将优于 PN 学习。