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Motivation: Large-scale cancer omics studies have highlighted the diversity of patient molecular profiles and the importance of leveraging this information to deliver the right drug to the right patient at the right time. Key challenges in learning predictive models for this include the high-dimensionality of omics data and heterogeneity in biological and clinical factors affecting patient response. The use of multi-task learning techniques has been widely explored to address dataset limitations for in vitro drug response models, while domain adaptation (DA) has been employed to extend them to predict in vivo response. In both of these transfer learning settings, noisy data for some tasks (or domains) can substantially reduce the performance for others compared to single-task (domain) learners, i.e. lead to negative transfer (NT)., Results: We describe a novel multi-task unsupervised DA method (TUGDA) that addresses these limitations in a unified framework by quantifying uncertainty in predictors and weighting their influence on shared feature representations. TUGDA's ability to rely more on predictors with low-uncertainty allowed it to notably reduce cases of NT for in vitro models (94% overall) compared to state-of-the-art methods. For DA to in vivo settings, TUGDA improved over previous methods for patient-derived xenografts (9 out of 14 drugs) as well as patient datasets (significant associations in 9 out of 22 drugs). TUGDA's ability to avoid NT thus provides a key capability as we try to integrate diverse drug-response datasets to build consistent predictive models with in vivo utility., Availabilityand Implementation: https://github.com/CSB5/TUGDA., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2021. Published by Oxford University Press.)