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UID:601@fds.yale.edu
DTSTART;TZID=America/New_York:20221216T130000
DTEND;TZID=America/New_York:20221216T140000
DTSTAMP:20250916T142119Z
URL:https://fds.yale.edu/events/fds-seminar-yuchen-wu-stanford-university/
SUMMARY:FDS Seminar: Yuchen Wu (Stanford University)
DESCRIPTION:Fundamental Limits of Low-Rank Matrix Estimation: Information-T
 heoretic and Computational Perspectives\n\n\nAbstract: Many statistical es
 timation problems can be reduced to the reconstruction of a low-rank n×d 
 matrix when observed through a noisy channel. While tremendous positive re
 sults have been established\, relatively few works focus on understanding 
 the fundamental limitations of the proposed models and algorithms. Underst
 anding such limitations not only provides practitioners with guidance on a
 lgorithm selection\, but also spurs the development of cutting-edge method
 ologies. In this talk\, I will present some recent progress in this direct
 ion from two perspectives in the context of low-rank matrix estimation. Fr
 om an information-theoretic perspective\, I will give an exact characteriz
 ation of the limiting minimum estimation error. Our results apply to the h
 igh-dimensional regime n\,d→∞ and d/n→∞ (or d/n→0) and generaliz
 e earlier works that focus on the proportional asymptotics n\,d→∞\, d/
 n→δ∈(0\,∞). From an algorithmic perspective\, large-dimensional mat
 rices are often processed by iterative algorithms like power iteration and
  gradient descent\, thus encouraging the pursuit of understanding the fund
 amental limits of these approaches. We introduce a class of general first 
 order methods (GFOM)\, which is broad enough to include the aforementioned
  algorithms and many others. I will describe the asymptotic behavior of an
 y GFOM\, and provide a sharp characterization of the optimal error achieve
 d by the GFOM class.This is based on joint works with Michael Celentano an
 d Andrea Montanari.\n\n\n\nThis seminar was held virtually over zoom and a
  recording is not available.\n
CATEGORIES:FDS Events,Postdoctoral Applicants,Seminar Series
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