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SUMMARY:Robust low-rank matrix completion with adversarial noise
DTSTART:20230303T151500
DTEND:20230303T170000
DTSTAMP:20260407T030042Z
UID:8f69bdf87be73e97e96bf51b897e17f66d840f3357f14183c1a67937
CATEGORIES:Conferences - Seminars
DESCRIPTION:Felix Krahmer\, Technische Universität München\nThe problem 
 of recovering a high-dimensional low-rank matrix from a limited set of ran
 dom measurements has enjoyed various applications and gained a detailed th
 eoretical foundation over the last 15 years. An instance of particular int
 erest is the matrix completion problem where the measurements are entry ob
 servations. The first rirgorous recovery guarantees for this problem were 
 derived for the nuclear norm minimization approach\, a convex proxy for th
 e NP-hard problem of constrained rank minimization. For matrices whose ent
 ries are ”spread out” well enough\, this convex problem admits a uniqu
 e solution which corresponds to the ground truth. In the presence of rando
 m measurement noise\, the reconstruction performance is also well-studied\
 , but the performance for adversarial noise remains less understood.\nWhil
 e some error bounds have been derived for both convex and nonconvex approa
 ches\, these bounds exhibit a gap to information-theoretic lower bounds an
 d provable performance for Gaussian measurements. However\, a recent analy
 sis of the problem suggests that under small-scale adversarsial noise\, th
 e reconstruction error can be significantly amplified.\nIn this talk\, we 
 investigate this amplification quantitatively and provide new reconstructi
 on bounds for both small and large noise levels that suggest a quadratic d
 ependence between the reconstruction error and the noise level.\nThis is j
 oint work with Julia Kostin (TUM/ETH) and Dominik Stöger (KU Eichstätt-I
 ngolstadt).\n\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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