  We consider multi-response and multitask regression models, where the
parameter matrix to be estimated is expected to have an unknown grouping
structure. The groupings can be along tasks, or features, or both, the last one
indicating a bi-cluster or "checkerboard" structure. Discovering this grouping
structure along with parameter inference makes sense in several applications,
such as multi-response Genome-Wide Association Studies. This additional
structure can not only can be leveraged for more accurate parameter estimation,
but it also provides valuable information on the underlying data mechanisms
(e.g. relationships among genotypes and phenotypes in GWAS). In this paper, we
propose two formulations to simultaneously learn the parameter matrix and its
group structures, based on convex regularization penalties. We present
optimization approaches to solve the resulting problems and provide numerical
convergence guarantees. Our approaches are validated on extensive simulations
and real datasets concerning phenotypes and genotypes of plant varieties.
