Group COMBSS: Group Selection via Continuous Optimization

TL;DR

This paper introduces Group COMBSS, a continuous optimization approach for group selection in linear regression, improving variable selection by leveraging group structures, especially in high-dimensional genetic data.

Contribution

It proposes a novel continuous optimization method for the challenging group selection problem, outperforming existing strategies in simulations and real genetic data.

Findings

Outperforms state-of-the-art variable selection methods in simulations

Effectively identifies groupings in genetic marker data

Handles high-dimensional predictor spaces efficiently

Abstract

We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the response. The incorporation of group structure in a predictor matrix is a key factor in obtaining better estimators and identifying associations between response and predictors. Such a discrete constrained problem is well-known to be hard, particularly in high-dimensional settings where the number of predictors is much larger than the number of observations. We propose to tackle this problem by framing the underlying discrete binary constrained problem into an unconstrained continuous optimization problem. The performance of our proposed approach is compared to state-of-the-art variable selection strategies on simulated data sets. We illustrate the effectiveness of our approach on a genetic dataset to identify grouping of markers across chromosomes.