报告人：陈昱鑫 (美国宾夕法尼亚大学沃顿商学院)

邀请人：潘灯

报告时间：2022年12月2日（星期五）8:30-10:00

报告地点：腾讯会议：828 391 627

报告题目：Nonconvex Low-Rank Models

报告摘要：Many high-dimensional problems involve reconstruction of a low-rank matrix from incomplete and corrupted observations. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained low-rank estimates, and how to construct valid yet short confidence intervals for the unknown low-rank matrix. In this talk, I will discuss how to perform inference and uncertainty quantification for two examples of low-rank models: (1) heteroskedastic PCA with missing data, and (2) noisy matrix completion. For both problems, we identify statistically efficient estimators that admit non-asymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals for, say, the unseen entries of the low-rank matrix of interest. All this is accomplished by a powerful leave-one-out analysis framework that originated from probability and random matrix theory.

This is based on joint work with Yuling Yan, Cong Ma, and Jianqing Fan. See arXiv:2107.12365 and arXiv:1906.04159.

报告人简介：陈昱鑫，美国宾夕法尼亚大学沃顿商学院统计与数据科学系副教授，于斯坦福大学获得电气工程博士学位，并曾在斯坦福大学进行博士后研究。曾担任普林斯顿大学电子与计算机工程助理教授。获得Alfred P. Sloan Research Fellowship, the ICCM best paper award (gold medal), the AFOSR and ARO Young Investigator Awards, the Google Research Scholar Award等荣誉。他目前的研究方向包括高维统计、非凸优化和强化学习等。