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CATEGORIES:CCIMI Seminars
SUMMARY:Estimation of Low-Rank Matrices via Approximate Me
ssage Passing - Dr Ramji Venkataramanan
DTSTART;TZID=Europe/London:20181031T140000
DTEND;TZID=Europe/London:20181031T150000
UID:TALK110518AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/110518
DESCRIPTION:We consider the problem of estimating a low-rank s
ymmetric matrix when its entries are perturbed by
Gaussian noise\, a setting often called the "spike
d model". If the empirical distribution of the en
tries of the spikes is known\, optimal estimators
that exploit this knowledge can substantially outp
erform simple spectral approaches. We discuss an e
stimator that uses Approximate Message Passing (AM
P) in conjunction with a spectral initialization.
The analysis of this estimator builds on a decoup
ling between the outlier eigenvectors and the bulk
in the spiked random matrix model. As illustrati
ons\, we use our main result to derive detailed pr
edictions for estimating a rank-one matrix and a b
lock-constant low-rank matrix ("Gaussian block mod
el"). Special cases of these models are closely re
lated to the community detection problem. We show
how the proposed estimator can be used to constru
ct asymptotically valid confidence intervals\, and
find that in many cases of interest\, it can achi
eve Bayes-optimal accuracy above the spectral thre
shold. \n\nJoint work with Andrea Montanari. The
talk will be based on the following paper: https:/
/arxiv.org/abs/1711.01682
LOCATION:CMS\, MR15
CONTACT:J.W.Stevens
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