  From only positive (P) and unlabeled (U) data, a binary classifier could be
trained with PU learning, in which the state of the art is unbiased PU
learning. However, if its model is very flexible, empirical risks on training
data will go negative, and we will suffer from serious overfitting. In this
paper, we propose a non-negative risk estimator for PU learning: when getting
minimized, it is more robust against overfitting, and thus we are able to use
very flexible models (such as deep neural networks) given limited P data.
Moreover, we analyze the bias, consistency, and mean-squared-error reduction of
the proposed risk estimator, and bound the estimation error of the resulting
empirical risk minimizer. Experiments demonstrate that our risk estimator fixes
the overfitting problem of its unbiased counterparts.
