Positive-Unlabeled Learning with Non-Negative Risk Estimator

摘要

From only positive (P) and unlabeled (U) data, a binary classifier can be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, its empirical risk on training data wall go negative and we will suffer from serious overfitting. In this paper, we propose a non-negative risk estimator for PU learning. When being minimized, it is more robust against overfitting and thus we are able to train very flexible models given limited P data. Moreover, we analyze the bias, consistency and mean-squared-error reduction of the proposed risk estimator and the estimation error of the corresponding risk minimizer. Experiments show that the proposed risk estimator successfully fixes the overfitting problem of its unbiased counterparts.