通用线性模型中用于生物医学应用的简洁子集选择
Parsimonious Subset Selection for Generalized Linear Models with Biomedical Applications
AI总结：
本文提出了一种高效的子集选择方法COMBSS-GLM，用于高维生物医学研究，通过连续布尔松弛和Frank-Wolfe算法实现稀疏且可解释的模型，同时在生物医学应用中表现出色。
摘要：
高维生物医学研究需要同时准确、稀疏且可解释的模型，但精确的最佳子集选择对于广义线性模型在计算上是不可行的。我们开发了一种可扩展的方法，结合了子集问题的连续布尔松弛和由包络梯度驱动的Frank-Wolfe算法。所提出的方法COMBSS-GLM简单易用，每迭代只需拟合一个惩罚广义线性模型，且能沿模型大小路径产生稀疏模型。理论上，我们识别出一个基于曲率的参数域，在该域内松弛的目标函数在选择权重上是凹的，这意味着全局最小值出现在二进制角点。经验上，在逻辑和多项式模拟中，该方法在低维和高维相关设置中均优于已有的惩罚似然竞争者，同时保持了强大的预测性能。在生物医学应用中，它在二元结局稻基因组关联研究中恢复了已知位点，并在Khan SRBCT癌症数据集上使用少量基因实现了完美的多类测试准确率。开源实现可在R和Python中获得。
英文摘要：
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.
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