Cost-Sensitive Unbiased Risk Estimation for Multi-Class Positive-Unlabeled Learning

Abstract

Positive--Unlabeled (PU) learning considers settings in which only positive and unlabeled data are available, while negatives are missing or left unlabeled. This situation is common in real applications where annotating reliable negatives is difficult or costly. Despite substantial progress in PU learning, the multi-class case (MPU) remains challenging: many existing approaches do not ensure \emph{unbiased risk estimation}, which limits performance and stability. We propose a cost-sensitive multi-class PU method based on \emph{adaptive loss weighting}. Within the empirical risk minimization framework, we assign distinct, data-dependent weights to the positive and \emph{inferred-negative} (from the unlabeled mixture) loss components so that the resulting empirical objective is an unbiased estimator of the target risk. We formalize the MPU data-generating process and establish a generalization error bound for the proposed estimator. Extensive experiments on \textbf{eight} public datasets, spanning varying class priors and numbers of classes, show consistent gains over strong baselines in both accuracy and stability.