报告题目：Modern Perspectives in High-dimensional Statistics: Two Recent Stories

报告时间：2022-12-02  10:30 - 11:30

报告人：Prof. Yuting Wei   University of Pennsylvania

腾讯会议ID：828-391-627

报告链接：https://meeting.tencent.com/dm/2OXytd62Rpaj

Abstract：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.

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