报告题目：A minimax optimal approach to high-dimensional double sparse linear regression

报告时间：2023-12-30   10:00-10:30

报 告 人 ：尹建鑫  教授  中国人民大学

报告地点：理学院东北楼三楼报告厅（302）

Abstract：In this talk, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding) procedure that dynamically updates the threshold at each step. We establish the matching upper and lower bounds for parameter estimation, showing the optimality of our proposal in the minimax sense. Coupled with a novel sparse group information criterion, we develop a fully adaptive procedure to handle unknown group sparsity and noise levels.   We show that our adaptive procedure achieves optimal statistical accuracy with fast convergence. Finally, we demonstrate the superiority of our method by comparing it with several state-of-the-art algorithms on both synthetic and real-world datasets.