Accurate Graph-Based PU Learning without Class Prior

How can we classify graph-structured data only with positive labels? Graph-based positive-unlabeled (PU) learning is to train a binary classifier given only the positive labels when the relationship between examples is given as a graph. The problem is of great importance for various tasks such as detecting malicious accounts in a social network, which are difficult to be modeled by supervised learning when the true negative labels are absent. Previous works for graph-based PU learning assume that the prior distribution of positive nodes is known in advance, which is not true in many real-world cases. In this work, we propose GRAB (Graph-based Risk minimization with iterAtive Belief propagation), a novel end-to-end approach for graph-based PU learning that requires no class prior. GRAB models a given graph as a Markov network and runs the marginalization and update steps iteratively. The marginalization step estimates the marginals of latent variables, while the update step trains a classifier network utilizing the computed priors in the objective function. Extensive experiments on five datasets show that GRAB achieves state-of-the-art accuracy, even compared with previous methods that are given the true prior.