机器学习与数据科学博士生系列论坛（第八十八期）——Properties and Applications of the ESD of i.i.d. Random Matrices with Random Perturbations
报告人：陈坤 (北京大学)
时间：2025-05-15 16:00-17:00
地点：腾讯会议 531-8098-3912
摘要：
The spectral properties of large i.i.d. random matrices with low-rank perturbations have been extensively investigated, particularly in the aspects of their ESD (Empirical Spectral Distribution), eigenvectors and eigenvalue outliers. Meanwhile, random matrix theory serves as a powerful analytical tool across diverse fields including statistical inference and numerical linear algebra. For example, Simchowitz (2020) established an optimal query complexity lower bound for eigenvector approximation in symmetric matrices through analysis of spiked Wigner matrix models.
In this talk, we introduce recent work on the i.i.d. random matrix subjected to random perturbation, which provides parallel results for eigenvalue outliers, ESD and eigenvectors to those in deterministic perturbation case. As an application, we develop a similar optimal query complexity lower bound for approximating eigenvectors of asymmetric matrices. The corresponding upper bound can be achieved by the power method.
论坛介绍：该线上论坛是由张志华教授机器学习实验室组织，每两周主办一次（除了公共假期）。论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍，主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。
