报告题目：Sparse estimation via ?q-minimization in high dimensional linear regression

主讲人：李冲教授（浙江大学）

时间：2025年11月4日（周二）14:30 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：In this talk, we consider the problem of estimating a sparse parameter from noisy observations in high dimensional linear regression. First, we shall an alyze the reconstruction procedure with a deterministic design through ?q (0 < q ≤ 1) minimization, and then extend the obtained results to problems with a random design using some probabilistic discussions. By introducing a notion of lower-order restricted eigenvalue condition, we show that stable recovery of any s-sparse vector can be achieved via ?q minimization in both deterministic and random cases. Then, we consider the ?q regularization problems and investigate the statistical properties of the optimal solutions. We derive the oracle inequalities for the purpose of prediction and coefficient approximation for both deterministic and random designs. Finally, we will validate the established theoretical results via some numerical simulations. The numerical results meet well with the scaling of the recovery bound predicted by our theoretical results in high-dimensional settings.

主讲人简介：

李冲，浙江大学数学科学学院教授，博士生导师，现聘为云南财经大学银龄教师。目前主要从事非光滑分析、数值泛函分析、最优化理论和方法等领域的研究，先后主持国家自然科学基金、或以主研人员参加国家自然科学基金重大和重点项目等10余项的研究，在优化理论，科学计算以及机器学习领域的顶级刊物SIAM J Optim.，SIAM J. Control Optim.，Math. Program，SIAM J Numer Anal以及JMLR等发表学术论文30余篇。 先后获教育部新世纪优秀人才，享受国务院政府特殊津贴专家、商业部有突出贡献的中青年专家、教育部优秀骨干教师，江苏省青年科学家等称号。