  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.
