Biomedicine produces copious information it cannot fully exploit. Specifically, there is considerable need to integrate knowledge from disparate studies to discover connections across domains. Here, we used a Collaborative Filtering approach, inspired by online recommendation algorithms, in which non-negative matrix factorization (NMF) predicts interactions among chemicals, genes, and diseases only from pairwise information about their interactions. Our approach, applied to matrices derived from the Comparative Toxicogenomics Database, successfully recovered Chemical-Disease, Chemical-Gene, and Disease-Gene networks in 10-fold cross-validation experiments. Additionally, we could predict each of these interaction matrices from the other two. Integrating all three CTD interaction matrices with NMF led to good predictions of STRING, an independent, external network of protein-protein interactions. Finally, this approach could integrate the CTD and STRING interaction data to improve Chemical-Gene cross-validation performance significantly, and, in a time-stamped study, it predicted information added to CTD after a given date, using only data prior to that date. We conclude that collaborative filtering can integrate information across multiple types of biological entities, and that as a first step towards precision medicine it can compute drug repurposing hypotheses.