Multivariate response regression with low-rank and generalized sparsity

Abstract

In this study, we propose a multivariate-response regression by imposing structural conditions on the underlying regression coefficient matrix motivated by an analysis of Cancer Cell Line Encyclopedia (CCLE) data consisting of resistance responses to multiple drugs and gene expression of cancer cell lines. It is important to estimate the drug resistance response from gene information and identify those genes responsible for the sensitivity of the resistance response to each drug. We consider a penalized multiple-response regression estimator using both generalized l(1) norm and nuclear norm regularizers based on the motivations that only a few genes are relevant to the effect of drug resistance responses and that some genes could have similar effects on multiple responses. For the statistical properties, we developed non-asymptotic error bounds of the proposed estimator. In our numerical analysis using simulated and CCLE data, the proposed method better predicts the drug responses than the other methods.