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TZID:Europe/Vienna
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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20200122T211538Z
UID:5de64562a6f01130082093@ist.ac.at
DTSTART:20200319T100000
DTEND:20200319T110000
DESCRIPTION:Speaker: Ramji Venkataramanan\nhosted by Marco Mondelli\nAbstra
ct: Large datasets often have an underlying low-dimensional structure that
can be captured by modeling the data matrix as the sum of a low-rank matr
ix and a noise matrix. The goal is to estimate the low-rank part from the
data matrix. A natural approach for estimating the low-rank part is via th
e spectrum of the data matrix. However\, if the empirical distribution of
the entries in the low-rank part is known\, one can design estimators that
substantially outperform simple spectral approaches.In this talk we discu
ss an estimator that consists of an Approximate Message Passing (AMP) algo
rithm initialized with a spectral estimate. We obtain a sharp asymptotic c
haracterization of the performance of this estimator\, and use the result
to derive detailed predictions for estimating a rank-one matrix and a bloc
k-constant low-rank matrix in Gaussian noise. Special cases of these model
s 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 interest\, it can ac
hieve Bayes-optimal accuracy above the spectral threshold. The talk will b
e self-contained\, and will not assume familiarity with message passing al
gorithms. Joint work with Andrea Montanari.
LOCATION:Mondi Seminar Room 2\, Central Building\, IST Austria
ORGANIZER:slandaue@ist.ac.at
SUMMARY:Estimating low-rank matrices via approximate message passing
URL:https://talks-calendar.app.ist.ac.at/events/2439
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