cPU: Consistent Risk Estimator for Positive-Unlabeled Learning.

Abstract

As one of the classical strategies for positive-unlabeled (PU) learning, the cost-sensitive methods achieve binary classification by minimizing the overall risk. To achieve this goal, the class prior is usually exploited to guide model learning in many state-of-the-art cost-sensitive approaches. However, how to effectively mine the underlying supervision information using the class prior remains a major challenging problem. It is known that the distribution of positive and negative samples is fixed in unlabeled samples when the class prior is available. Based on this knowledge, we derive a novel supervision formulation from a risk perspective: if the class prior is known, the ratio between the positive risk distribution of negative samples and the negative risk distribution of positive samples converges to a fixed value in unlabeled samples. By fully exploiting this brand-new constraint, we construct a consistent risk estimator to impose consistency between the negative expected risk of the positive samples and the positive expected risk of the negative samples. Moreover, we introduce Mixup regularization to mitigate the confirmation bias of the learned model, and meanwhile employ the entropy minimization technique to improve the separability of samples, which can further enhance classification performance. Experimental results on four benchmark datasets demonstrate the advantage of our model over several baseline methods. The code is available at https://github.com/yunbao520/cPU.