Characterizing interactions between drugs is important to avoid potentially harmful combinations, to reduce off-target effects of treatments and to fight antibiotic resistant pathogens, among others. Here we present a network inference algorithm to predict uncharacterized drug-drug interactions. Our algorithm takes, as its only input, sets of previously reported interactions, and does not require any pharmacological or biochemical information about the drugs, their targets or their mechanisms of action. Because the models we use are abstract, our approach can deal with adverse interactions, synergistic/antagonistic/suppressing interactions, or any other type of drug interaction. We show that our method is able to accurately predict interactions, both in exhaustive pairwise interaction data between small sets of drugs, and in large-scale databases. We also demonstrate that our algorithm can be used efficiently to discover interactions of new drugs as part of the drug discovery process. 