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SUMMARY:Estimating low-rank matrices via approximate message passing - Ram
 ji Venkataramanan\, CUED
DTSTART:20181115T150000Z
DTEND:20181115T160000Z
UID:TALK114532@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:Large datasets often have an underlying low-dimensional struct
 ure that can be captured by modeling the data matrix as the sum of a low-r
 ank matrix and a noise matrix. The goal is to estimate the low-rank part f
 rom the data matrix.  A natural approach for estimating the low-rank part 
 is via the spectrum of the data matrix. However\, if the empirical distrib
 ution of the entries in the low-rank part is known\, one can design estima
 tors that substantially outperform simple spectral approaches.\n\nIn this 
 talk we discuss an estimator that consists of an Approximate Message Passi
 ng (AMP) algorithm initialized with a spectral estimate. We obtain a sharp
  asymptotic characterization of the performance of this estimator\,  and u
 se the result to derive detailed predictions for estimating a rank-one mat
 rix and a block-constant low-rank matrix in Gaussian noise. Special cases 
 of these models are closely related to the problem of community detection 
 in stochastic block models. We show how the proposed estimator can be used
  to construct confidence intervals\, and find that in many cases of intere
 st\, it can achieve Bayes-optimal accuracy above the spectral threshold. \
 n\n(The talk will be self-contained\, and will not assume familiarity with
  message passing algorithms.)
LOCATION:LT6\, Baker Building\, CUED
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