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SUMMARY:Estimation of Low-Rank Matrices via Approximate Message Passing - 
 Dr Ramji Venkataramanan
DTSTART:20181031T140000Z
DTEND:20181031T150000Z
UID:TALK110518@talks.cam.ac.uk
CONTACT:J.W.Stevens
DESCRIPTION:We consider the problem of estimating a low-rank symmetric mat
 rix when its entries are perturbed by Gaussian noise\, a setting often cal
 led the "spiked model".  If the empirical distribution of the entries of t
 he spikes is known\, optimal estimators that exploit this knowledge can su
 bstantially outperform simple spectral approaches. We discuss an estimator
  that uses Approximate Message Passing (AMP) in conjunction with a spectra
 l initialization.  The analysis of this estimator builds on a decoupling b
 etween the outlier eigenvectors and the bulk in the spiked random matrix m
 odel.  As illustrations\, we use our main result to derive detailed predic
 tions for estimating a rank-one matrix and a block-constant low-rank matri
 x ("Gaussian block model"). Special cases of these models are closely rela
 ted to the community detection problem.  We show how the proposed estimato
 r can be used to construct asymptotically valid confidence intervals\, and
  find that in many cases of interest\, it can achieve Bayes-optimal accura
 cy above the spectral threshold. \n\nJoint work with Andrea Montanari.  Th
 e talk will be based on the following paper: https://arxiv.org/abs/1711.01
 682
LOCATION:CMS\, MR15
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