Computational Drug Discovery, which uses computational techniques to facilitate and improve the drug discovery process, has aroused considerable interests in recent years. Drug Repositioning (DR) and Drug- Drug Interaction (DDI) prediction are two key problems in drug discovery and many computational techniques have been proposed for them in the last decade. Although these two problems have mostly been researched separately in the past, both DR and DDI can be formulated as the problem of detecting positive interactions between data entities (DR is between drug and disease, and DDI is between pairwise drugs). The challenge in both problems is that we can only observe a very small portion of positive interactions. In this paper, we propose a novel framework called Dyadic Positive-Unlabeled learning (DyPU) to solve the problem of detecting positive interactions. DyPU forces positive data pairs to rank higher than the average score of unlabeled data pairs. Moreover, we also derive the dual formulation of the proposed method with the rectifier scoring function and we show that the associated non-trivial proximal operator admits a closed form solution. Extensive experiments are conducted on real drug data sets and the results show that our method achieves superior performance comparing with the state-of-the-art.