Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914414475608064 |
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| author | Mathur, Anant Liquet, Benoit Muller, Samuel Moka, Sarat |
| author_facet | Mathur, Anant Liquet, Benoit Muller, Samuel Moka, Sarat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications Mathur, Anant Liquet, Benoit Muller, Samuel Moka, Sarat Methodology Computation 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. |
| title | Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2603.21952 |