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SUMMARY:Robust Matrix Completion - Olga Klopp\, Université Paris Ouest
DTSTART:20150501T150000Z
DTEND:20150501T160000Z
UID:TALK58610@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:We consider the problem of recovery of a low-rank matrix in\nt
 he situation when most of its entries are not observed and a fraction of o
 bserved entries are corrupted. The observations are noisy realizations of 
 the sum of a low rank matrix\, which we wish to recover\, with a second ma
 trix having  a complementary sparse structure such as element-wise or colu
 mn-wise sparsity. We analyse a class of estimators obtained by solving a c
 onstrained convex optimization problem that combines the nuclear norm  and
  a convex relaxation for a sparse constraint. Our results are obtained for
  the simultaneous  presence of random and deterministic patterns in the sa
 mpling scheme. We provide guarantees for recovery of low-rank and sparse c
 omponents from partial and corrupted observations in the presence of noise
  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\, Wilberforce Road\, Cam
 bridge
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