AI 中文总结
该研究提出稀疏组柔性Lasso（SGPL）模型及分块坐标下降算法，经模拟与真实数据验证，其预测性能优、交互项估计误差小，可用于微生物组与癌症基因组相关研究。
AI 中文摘要
稀疏组柔性Lasso（SGPL）通过结合稀疏组正则化与预测变量水平的耦合惩罚项，扩展了柔性Lasso和组柔性Lasso，可同时实现组水平选择、组内稀疏性以及主效应与交互项间的层级结构。我们提出一种用于拟合SGPL的分块坐标下降算法，该算法利用目标函数的凸性与结构，建立了凸性和Karush-Kuhn-Tucker最优性条件，并证明该算法收敛到全局极小值。模拟研究显示，SGPL的预测性能具有竞争力，且与柔性Lasso和组柔性Lasso相比，交互项估计误差更小，尽管在支持集恢复中存在预期的精确率-召回率权衡。我们进一步使用帕金森病肠道微生物组研究和癌症基因组图谱的肾上腺皮质癌（ACC）拷贝数数据集说明所提方法：帕金森病应用识别出微生物丰度与饮食变量间可解释的交互作用，而ACC应用表明，组结构正则化的有效性取决于预先指定的分组对潜在信号结构的反映程度。
英文摘要
The sparse-group pliable Lasso (SGPL) extends the pliable Lasso and group pliable Lasso by combining sparse-group regularization with a predictor-level coupling penalty, enabling simultaneous group-level selection, within-group sparsity, and hierarchical structure between main effects and interactions. We propose a blockwise coordinate descent algorithm for fitting the SGPL that exploits the convexity and structure of the objective function, establish convexity and Karush--Kuhn--Tucker optimality conditions, and prove that the algorithm converges to a global minimizer. Simulation studies demonstrate competitive predictive performance and smaller interaction estimation error than the pliable Lasso and group pliable Lasso, albeit with the expected precision--recall trade-off in support recovery. We further illustrate the proposed method using a Parkinson's disease gut microbiome study and an adrenocortical carcinoma (ACC) copy-number dataset from The Cancer Genome Atlas. The Parkinson's application identifies interpretable interactions between microbial abundances and dietary variables, while the ACC application illustrates that the effectiveness of group-structured regularization depends on how well the prespecified grouping reflects the underlying signal structure.
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