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SUMMARY:Matrix completion with adversarial noise
DTSTART:20220408T153000
DTEND:20220408T170000
DTSTAMP:20260502T104730Z
UID:ccb5ad6dde87f1702e3123701abcf3cdf201f9fb05b2d026de2d756b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Felix Krahmer\, Technical University of Munich\nLow-rank
  matrix recovery from structured measurements has been a topic of intense 
 study in the last decades. An instance of this problem that is of particul
 ar interest due to its relevance for many applications such as recommender
  systems is the matrix completion problem\, where the observations consist
  of randomly selected matrix entries. An important benchmark method to sol
 ve this problem is to minimize the nuclear norm\, a convex proxy for the r
 ank. A common approach to establish recovery guarantees for this convex pr
 ogram relies on the construction of a so-called approximate dual certifica
 te. However\, this approach provides only limited insight in various respe
 cts. In particular\, the best-known bounds for the reconstruction error un
 der adversarial noise involve seemingly spurious dimensional factors.\n\nI
 n this talk\, we analyze the problem from a geometric perspective and show
  that these dimension factors in the noise bounds are not an artefact of t
 he proof\, but cannot be avoided in the framework commonly applied for the
  analysis\, which aims to establish a linear scaling of the error in terms
  of the noise level. At the same time\, we establish that these factors on
 ly arise for very small noise levels\, and if one accepts a square root sc
 aling\, the constants can be chosen independently of the dimension and dep
 ending only mildly on the rank.\n\nThis is joint work with Yulia Kostina (
 TUM) and Dominik Stöger (KU Eichstätt/Ingolstadt).\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021 https://epfl.zoom
 .us/j/66136073806
STATUS:CANCELLED
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