Fusion Learning of Functional Linear Regression with Application to Genotype-by-Environment Interaction Studies

We propose a sparse multi-group functional linear regression model to simultaneously estimate multiple coefficient functions and identify groups, such that coefficient functions are identical within groups and distinct across groups. By borrowing information from relevant subgroups of subjects, our method enhances estimation efficiency while preserving heterogeneity in model parameters and coefficient functions. We use an adaptive fused lasso penalty to shrink coefficient estimates to a common value within each group. We also establish theoretical properties of the proposed estimators. To enhance computation efficiency and incorporate neighborhood information, we propose to use graph-constrained adaptive lasso with a computationally efficient algorithm. Two Monte Carlo simulation studies have been conducted to study the finite-sample performance of the proposed method. The proposed method is applied to sorghum flowering-time data and hybrid maize grain yields from the Genomes to Fields consortium. Supplementary materials accompanying this paper appear online.