Research

Paper

TESTING March 23, 2026

Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications

Authors

Anant Mathur, Benoit Liquet, Samuel Muller, Sarat Moka

Abstract

High-dimensional biomedical studies require models that are simultaneously accurate, sparse, and interpretable, yet exact best subset selection for generalized linear models is computationally intractable. We develop a scalable method that combines a continuous Boolean relaxation of the subset problem with a Frank--Wolfe algorithm driven by envelope gradients. The resulting method, which we refer to as COMBSS-GLM, is simple to implement, requires one penalized generalized linear model fit per iteration, and produces sparse models along a model-size path. Theoretically, we identify a curvature-based parameter regime in which the relaxed objective is concave in the selection weights, implying that global minimizers occur at binary corners. Empirically, in logistic and multinomial simulations across low- and high-dimensional correlated settings, the proposed method consistently improves variable-selection quality relative to established penalised likelihood competitors while maintaining strong predictive performance. In biomedical applications, it recovers established loci in a binary-outcome rice genome-wide association study and achieves perfect multiclass test accuracy on the Khan SRBCT cancer dataset using a small subset of genes. Open-source implementations are available in R at https://github.com/benoit-liquet/COMBSS-GLM-R and in Python at https://github.com/saratmoka/COMBSS-GLM-Python.

Metadata

arXiv ID: 2603.21952
Provider: ARXIV
Primary Category: stat.ME
Published: 2026-03-23
Fetched: 2026-03-24 06:02

Related papers

Raw Data (Debug)
{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.21952v1</id>\n    <title>Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications</title>\n    <updated>2026-03-23T13:09:57Z</updated>\n    <link href='https://arxiv.org/abs/2603.21952v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.21952v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>High-dimensional biomedical studies require models that are simultaneously accurate, sparse, and interpretable, yet exact best subset selection for generalized linear models is computationally intractable. We develop a scalable method that combines a continuous Boolean relaxation of the subset problem with a Frank--Wolfe algorithm driven by envelope gradients. The resulting method, which we refer to as COMBSS-GLM, is simple to implement, requires one penalized generalized linear model fit per iteration, and produces sparse models along a model-size path. Theoretically, we identify a curvature-based parameter regime in which the relaxed objective is concave in the selection weights, implying that global minimizers occur at binary corners. Empirically, in logistic and multinomial simulations across low- and high-dimensional correlated settings, the proposed method consistently improves variable-selection quality relative to established penalised likelihood competitors while maintaining strong predictive performance. In biomedical applications, it recovers established loci in a binary-outcome rice genome-wide association study and achieves perfect multiclass test accuracy on the Khan SRBCT cancer dataset using a small subset of genes. Open-source implementations are available in R at https://github.com/benoit-liquet/COMBSS-GLM-R and in Python at https://github.com/saratmoka/COMBSS-GLM-Python.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='stat.ME'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='stat.CO'/>\n    <published>2026-03-23T13:09:57Z</published>\n    <arxiv:primary_category term='stat.ME'/>\n    <author>\n      <name>Anant Mathur</name>\n    </author>\n    <author>\n      <name>Benoit Liquet</name>\n    </author>\n    <author>\n      <name>Samuel Muller</name>\n    </author>\n    <author>\n      <name>Sarat Moka</name>\n    </author>\n  </entry>"
}