题 目：Estimating Double Sparse Structures over $\ell_u(\ell_q)$-Balls: Minimax Rates and Phase Transition

报告人：尹建鑫 副教授（中国人民大学统计学院）

摘要: In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise and element-wise sparsity. By combining the Gilbert-Varshamov bound and its variants, we develop a novel lower bound technique for the metric entropy of the parameter space, specifically tailored for the double sparse structure over $\ell_u(\ell_q)$-balls with $u,q \in [0,1]$. We prove lower bounds on the estimation error using an information-theoretic approach, leveraging our proposed lower bound technique and Fano's inequality. To complement the lower bounds, we establish matching upper bounds through a direct analysis of constrained least-squares estimators and utilize results from empirical processes. A significant finding of our study is the discovery of a phase transition phenomenon on the minimax rates for $u,q \in (0, 1]$.Furthermore, we extend the theoretical results to the double sparse regression model and determine its minimax rate for estimation error.

  To tackle double sparse linear regression, we develop the Double Sparse Iterative Hard Thresholding (DSIHT) algorithm, demonstrating its optimality in the minimax sense. Finally, we demonstrate the superiority of our method through numerical experiments.

报告人简介：尹建鑫，中国人民大学统计学院副教授，副院长，博士生导师。从事高维数据分析、图模型学习、文本分析等方向的研究。2015年获教育部第七届高等学校科学研究优秀成果奖（人文社会科学）统计学三等奖，2021年作为主要获奖者之一获得北京市教学成果一等奖、多次获得学校优秀本科论文指导教师奖等。

报告时间：2024年5月23日（周一）上午10：00

报告地点：教二楼927

联系人：胡涛