  The molecular characterization of tumor samples by multiple omics data sets
of different types or modalities (e.g. gene expression, mutation, CpG
methylation) has become an invaluable source of information for assessing the
expected performance of individual drugs and their combinations. Merging the
relevant information from the omics data modalities provides the statistical
basis for determining suitable therapies for specific cancer patients.
Different data modalities may each have their specific structures that need to
be taken into account during inference. In this paper, we assume that each
omics data modality has a low-rank structure with only few relevant features
that affect the prediction and we propose to use a composite local nuclear norm
penalization for learning drug sensitivity. Numerical results show that the
composite low-rank structure can improve the prediction performance compared to
using a global low-rank approach or elastic net regression.
