Simultaneous Parameter Learning and Bi-Clustering for Multi-Response Models

TL;DR

This paper introduces methods for jointly estimating parameters and uncovering grouping structures in multi-response models, enhancing both accuracy and interpretability in applications like GWAS.

Contribution

It proposes two convex regularization-based formulations for simultaneous parameter learning and bi-clustering, with optimization algorithms and convergence guarantees.

Findings

Effective in simulations and real GWAS datasets

Improves parameter estimation accuracy

Reveals meaningful biological groupings

Abstract

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.