报告人：魏玉婷 (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）10:00-11:30

报告地点：腾讯会议：828 391 627

报告题目：High-dimensional Statistical Methods

报告摘要：Statistical methods have been a major driving force towards interpretable machine learning. However, existing statistical theory remains highly inadequate in explaining many new phenomena that emerge in modern machine learning. In this talk, I present two recent works that adapt the high-dimensional statistics toolbox to contemporary settings. In the first part of the talk, we pursue theoretical understandings for interpolating estimators --- the ones that achieve zero training error --- which are of growing empirical interest in over-parameterized machine learning. We observe, and provide rigorous theoretical justifications for, a curious multi-descent phenomenon of the minimum L1-norm interpolator, via the machinery of approximate message passing (AMP). In the second part of the talk, we develop a non-asymptotic framework towards understanding AMP in spiked matrix estimation. Built upon new decomposition of AMP updates and controllable residual terms, we lay out an analysis recipe to characterize the finite-sample behavior of AMP in the presence of an independent initialization, which is further generalized to allow for spectral initialization. We give two examples to demonstrate the power of this general recipe.

报告人简介：魏玉婷，宾夕法尼亚大学沃顿商学院统计与数据科学系助理教授，于加州大学伯克利分校获得统计学博士学位。曾在卡内基梅隆大学担任统计学助理教授，曾在斯坦福大学担任Stein研究员。获得2022年NSF Career award 和2018年the Erich L. Lehmann Citation from the Berkeley statistics department。她的研究兴趣包括高维和非参数统计，统计机器学习和强化学习等。