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UID:431@fds.yale.edu
DTSTART;TZID=America/New_York:20221216T130000
DTEND;TZID=America/New_York:20221216T140000
DTSTAMP:20240226T190412Z
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\n\nAbstract: Many statistical
estimation problems can be reduced to the reconstruction of a low-rank n×
d matrix when observed through a noisy channel. While tremendous positive
results have been established\, relatively few works focus on understandin
g the fundamental limitations of the proposed models and algorithms. Under
standing such limitations not only provides practitioners with guidance on
algorithm selection\, but also spurs the development of cutting-edge meth
odologies. In this talk\, I will present some recent progress in this dire
ction from two perspectives in the context of low-rank matrix estimation.
From an information-theoretic perspective\, I will give an exact character
ization of the limiting minimum estimation error. Our results apply to the
high-dimensional regime n\,d→∞ and d/n→∞ (or d/n→0) and general
ize earlier works that focus on the proportional asymptotics n\,d→∞\,
d/n→δ∈(0\,∞). From an algorithmic perspective\, large-dimensional m
atrices are often processed by iterative algorithms like power iteration a
nd gradient descent\, thus encouraging the pursuit of understanding the fu
ndamental limits of these approaches. We introduce a class of general firs
t order methods (GFOM)\, which is broad enough to include the aforemention
ed algorithms and many others. I will describe the asymptotic behavior of
any GFOM\, and provide a sharp characterization of the optimal error achie
ved by the GFOM class.This is based on joint works with Michael Celentano
and Andrea Montanari.\n\n\n\nThis seminar was held virtually over zoom and
a recording is not available.\n
CATEGORIES:Postdoctoral Applicants,Seminar Series
LOCATION:\, \,
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