时 间：2026-04-24 10:30 - 2026-04-24 11:30
地 点：普陀校区理科大楼A1214室
报告人：杨青 中国科学技术大学副教授
主持人：王亚平 华东师范大学教授
摘 要：
In this paper, we investigate the geometric fluctuations of principal subspaces for high-dimensional covariance matrices. Specifically, we establish the asymptotic distribution of the sin$\Theta$ distance between the sample eigenspace associated with the $r_p$ largest eigenvalues and its population counterpart. Our central limit theorem is derived under notably mild conditions, particularly accommodating a diverging number of spiked eigenvalues $r_p$, a diverging covariance spectral norm, and the presence of highly heterogeneous spikes. Furthermore, our theoretical results yield deep insights into existing upper bounds in the literature, demonstrating that several known bounds can be strictly sharpened and confirming the minimax optimality of the sample covariance matrix under specific population structures. Various numerical studies further empirically support our theoretical findings.
报告人简介：
杨青，中国科学技术大学管理学院副教授，博士生导师。研究主要围绕复杂数据统计推断展开，相关成果发表在AOS、JASA、JMLR、ICML等学术期刊和会议上。