Motivation: A key goal of computational personalized medicine is to systematically utilize genomic and other molecular features of samples to predict drug responses for a previously unseen sample. Such predictions are valuable for developing hypotheses for selecting therapies tailored for individual patients. This is especially valuable in oncology, where molecular and genetic heterogeneity of the cells has a major impact on the response. However, the prediction task is extremely challenging, raising the need for methods that can effectively model and predict drug responses.Results: In this study, we propose a novel formulation of multi-task matrix factorization that allows selective data integration for predicting drug responses. To solve the modeling task, we extend the state-of-the-art kernelized Bayesian matrix factorization (KBMF) method with component-wise multiple kernel learning. In addition, our approach exploits the known pathway information in a novel and biologically meaningful fashion to learn the drug response associations. Our method quantitatively outperforms the state of the art on predicting drug responses in two publicly available cancer datasets as well as on a synthetic dataset. In addition, we validated our model predictions with lab experiments using an in-house cancer cell line panel. We finally show the practical applicability of the proposed method by utilizing prior knowledge to infer pathway-drug response associations, opening up the opportunity for elucidating drug action mechanisms. We demonstrate that pathway-response associations can be learned by the proposed model for the well-known EGFR and MEK inhibitors.Availability and implementation: The source code implementing the method is available at http://research.cs.aalto.fi/pml/software/cwkbmf/.Contacts: email@example.com or firstname.lastname@example.orgSupplementary information: Supplementary data are available at Bioinformatics online.