Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe)

Abstract

We propose a new method for the simultaneous selection and estimation of multivariate sparse additive models with correlated errors. Our method called Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe) simultaneously selects among null, linear, and smooth non-linear effects for each predictor while incorporating joint estimation of the sparse residual structure among responses, with the motivation that accounting for inter-response correlation structure can lead to improved accuracy in variable selection and estimation efficiency. CoMPAdRe is constructed in a computationally efficient way that allows the selection and estimation of linear and non-linear covariates to be conducted in parallel across responses. Compared to single-response approaches that marginally select linear and non-linear covariate effects, we demonstrate in simulation studies that the joint multivariate modeling leads to gains in both estimation efficiency and selection accuracy, of greater magnitude in settings where signal is moderate relative to the level of noise. We apply our approach to protein-mRNA expression levels from multiple breast cancer pathways obtained from The Cancer Proteome Atlas and characterize both mRNA-protein associations and protein-protein subnetworks for each pathway. We find non-linear mRNA-protein associations for the Core Reactive, EMT, PIK-AKT, and RTK pathways. Supplementary Materials are available online.

Keywords: Multivariate analysis; Multivariate regression; Non-convex optimization; Semi-parametric regression; Variable selection.