Recent advances in biomedical and sequencing technologies have revealed the genomic landscape of common forms of human cancer in unprecedented detail. Of the genes that drive tumorigenesis when altered, for most cancers it is believed that there exist a small number of “mountains” (genes altered at high frequencies across the population), and a much larger number of “hills” (much less frequently altered genes). This challenging mutational profile of the cancer genome calls for approaches that can integrate data from different genomic platforms to more reliably prioritize driver genes with lower alteration frequencies. Here the authors propose a novel, biologically-motivated, Bayesian multitask approach, which explicitly models gene-centric dependencies across multiple and distinct genomic platforms. The authors demonstrate that accounting for the gene-centric dependencies enables leveraging information from multi-omic input data and improves prediction and feature selection performance. They further demonstrate the applicability of their method in an unsupervised dimensionality reduction application by inferring genes essential to tumorigenesis in the pancreatic ductal adenocarcinoma and lung adenocarcinoma patient cohorts from The Cancer Genome Atlas.