Positive Unlabeled Learning with Class-prior Approximation

The positive unlabeled (PU) learning aims to train a binary classifier from a set of positive labeled samples and other unlabeled samples. Much research has been done on this special branch of weakly supervised classification problems. Since only part of the positive class is labeled, the classical PU model trains the classifier assuming the class-prior is known. However, the true class prior is usually difficult to obtain and must be learned from the given data, and the traditional methods may not work. In this paper, we formulate a convex formulation to jointly solve the class-prior unknown problem and train an accurate classifier with no need of any class-prior assumptions or additional negative samples. The class prior is estimated by pursuing the optimal solution of gradient thresholding and the classifier is simultaneously trained by performing empirical unbiased risk. The detailed derivation and theoretical analysis of the proposed model are outlined, and a comparison of our experiments with other representative methods prove the superiority of our method.