报告人：王经铭（弗吉尼亚大学）
报告时间：2026年6月15日（周一）上午9:30 - 10:30
报告地点：国交二号楼315会议室
报告摘要：Many datasets exhibit a low-rank signal plus noise structure, which arises in applications such as networks, text data, and gene expression data. Spectral method is a standard tool for analyzing such data, with eigenvectors playing a central role in recovering hidden information. To understand the performance, it is important to compare empirical eigenvectors with their population counterparts and study the large deviation bounds. In many settings, especially with heterogeneous noise, sharp entrywise eigenvector analysis is necessary but relatively underdeveloped. In this talk, I will discuss entrywise eigenvector analysis for low-rank models and demonstrate its usefulness in two applications: membership estimation in network models and topic estimation in topic modeling. I will show that sharp entrywise control of eigenvectors can guide the design of optimal procedures and provide rigorous theoretical guarantees.
