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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY:Estimating low-rank matrices via approximate messa
ge passing - Ramji Venkataramanan\, CUED
DTSTART;TZID=Europe/London:20181115T150000
DTEND;TZID=Europe/London:20181115T160000
UID:TALK114532AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/114532
DESCRIPTION:Large datasets often have an underlying low-dimens
ional structure that can be captured by modeling t
he data matrix as the sum of a low-rank matrix and
a noise matrix. The goal is to estimate the low-r
ank part from the data matrix. A natural approach
for estimating the low-rank part is via the spect
rum of the data matrix. However\, if the empirical
distribution of the entries in the low-rank part
is known\, one can design estimators that substant
ially outperform simple spectral approaches.\n\nIn
this talk we discuss an estimator that consists o
f an Approximate Message Passing (AMP) algorithm i
nitialized with a spectral estimate. We obtain a s
harp asymptotic characterization of the performanc
e of this estimator\, and use the result to deriv
e detailed predictions for estimating a rank-one m
atrix and a block-constant low-rank matrix in Gaus
sian noise. Special cases of these models are clos
ely related to the problem of community detection
in stochastic block models. We show how the propos
ed estimator can be used to construct confidence i
ntervals\, and find that in many cases of interest
\, it can achieve Bayes-optimal accuracy above the
spectral threshold. \n\n(The talk will be self-co
ntained\, and will not assume familiarity with mes
sage passing algorithms.)
LOCATION:LT6\, Baker Building\, CUED
CONTACT:Prof. Ramji Venkataramanan
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