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CATEGORIES:Statistics
SUMMARY:Robust Matrix Completion - Olga Klopp\, Université
Paris Ouest
DTSTART;TZID=Europe/London:20150501T160000
DTEND;TZID=Europe/London:20150501T170000
UID:TALK58610AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58610
DESCRIPTION:We consider the problem of recovery of a low-rank
matrix in\nthe situation when most of its entries
are not observed and a fraction of observed entrie
s are corrupted. The observations are noisy realiz
ations of the sum of a low rank matrix\, which we
wish to recover\, with a second matrix having a c
omplementary sparse structure such as element-wise
or column-wise sparsity. We analyse a class of es
timators obtained by solving a constrained convex
optimization problem that combines the nuclear nor
m and a convex relaxation for a sparse constraint
. Our results are obtained for the simultaneous p
resence of random and deterministic patterns in th
e sampling scheme. We provide guarantees for recov
ery of low-rank and sparse components from partial
and corrupted observations in the presence of noi
se and show that the obtained rates of convergence
are minimax optimal. This is a joint work with K.
Lounici and A. Tsybakov.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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