A Sparse-Group Pliable Lasso

2026-08-21

AI Summary

本文提出了一种稀疏组可塑Lasso方法，通过结合稀疏组正则化和预测器级别的耦合惩罚来同时进行组级别选择、组内稀疏性和主效应与交互作用之间的层次结构，并通过仿真研究及实际应用验证了其有效性。

Abstract

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.

Problem

• sparse-group pliable Lasso
• group-level selection
• within-group sparsity
• hierarchical structure

Innovation

• Sparse-Group Pliable Lasso
• blockwise coordinate descent
• hierarchical structure