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VERSION:2.0
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CALSCALE:GREGORIAN
X-WR-CALNAME:Probability and Statistics Seminar: Non-convex matrix sensing:
  Breaking the quadratic rank barrier in the sample complexity
X-WR-TIMEZONE:Pacific Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260908T085655Z
UID:tag:localist.com\,2008:EventInstance_47872627755240
DTSTART:20241025T223000Z
DTEND:20241025T233000Z
DESCRIPTION:Yizhe Zhu\, USC\n\nTitle: Non-convex matrix sensing: Breaking t
 he quadratic rank barrier in the sample complexity\n\nAbstract: For the pr
 oblem of reconstructing a low-rank matrix from a few linear measurements\,
  two classes of algorithms have been widely studied in the literature: con
 vex approaches based on nuclear norm minimization\, and non-convex approac
 hes that use factorized gradient descent. Under certain statistical model 
 assumptions\, it is known that nuclear norm minimization recovers the grou
 nd truth as soon as the number of samples scales linearly with the number 
 of degrees of freedom of the ground truth. In contrast\, while non-convex 
 approaches are computationally less expensive\, existing recovery guarante
 es assume that the number of samples scales at least quadratically with th
 e rank. In this talk\, we consider the problem of reconstructing a positiv
 e semidefinite matrix from a few Gaussian measurements. We improve the pre
 vious rank-dependence in the sample complexity of non-convex matrix factor
 ization from quadratic to linear. Our proof relies on a probabilistic deco
 upling argument\, where we show that the gradient descent iterates are onl
 y weakly dependent on the individual entries of the measurement matrices. 
 Joint work with Dominik Stöger (KU Eichstätt-Ingolstadt).
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 414
SUMMARY:Probability and Statistics Seminar: Non-convex matrix sensing: Brea
 king the quadratic rank barrier in the sample complexity
URL;VALUE=URI:https://calendar.usc.edu/event/probability-and-statistics-sem
 inar-non-convex-matrix-sensing-breaking-the-quadratic-rank-barrier-in-the-
 sample-complexity
CATEGORIES:Lecture / Talk / Workshop
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