报告人：曾靖 副教授
报告题目：Second-Order Sparse Sufficient Dimension Reduction with Applications to Quadratic Discriminant Analysis
报告时间：2025年06月04日（周三）下午4：00
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
曾靖，中国科学技术大学管理学院特任副教授。2017年本科毕业于中国科学技术大学，2022年博士毕业于佛罗里达州立大学。目前主要研究方向为数据降维，高维数据分析，张量数据分析，以及稳健统计。有多篇论文发表在Journal of the American Statistical Association, Statistica Sinica期刊上。目前主持国家自然科学基金项目一项。
报告摘要：
Motivated by exploratory data analysis, sufficient dimension reduction (SDR) methods, especially inverse regression methods such as sliced inverse regression (SIR) and sliced averaged variance estimation (SAVE), have been central to multivariate analysis for more than three decades. Despite their popularity, the extension of these methods to high-dimensional settings remains challenging. This paper addresses the computational and theoretical limitations of the less explored second-order SDR methods in high dimensions. We introduce a novel approach for sparse subspace estimation that utilizes quadratic convex optimization and leverages the group structure of tensor parameters, achieving significant parameter reduction. The proposed two-step estimator achieves consistency in dimension selection, variable selection, and subspace estimation at a high convergence rate under mild conditions. The effectiveness and efficiency of the proposed method are further demonstrated through extensive simulation studies and real data examples. Additionally, the proposed sparse second-order SDR techniques are applied to quadratic discriminant analysis (QDA) problems and provide practitioners a sparse projective classification method that is theoretically guaranteed and empirically well-performed.