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DTSTART:20210328T030000
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DTSTAMP:20201201T032948Z
UID:5fb2637f9d798315748536@ist.ac.at
DTSTART:20201123T140000
DTEND:20201123T150000
DESCRIPTION:Speaker: Marco Mondelli\nhosted by Kseniia Khudiakova\, Raimund
o Saona\nAbstract: In a generalized linear model (GLM)\, the goal is to es
timate a d-dimensional signal x from an n-dimensional observation of the f
orm f(Ax\, w)\, where A is a design matrix and w is a noise vector. Well-k
nown examples of GLMs include phase retrieval\, 1-bit compressed sensing\,
and logistic regression. We focus on the high-dimensional setting in whic
h both the number of measurements n and the signal dimension d diverge\, w
ith their ratio tending to a fixed constant.Linear and spectral methods ar
e two popular solutions to obtain an initial estimate\, which can also be
used as a warm start for other algorithms. In particular\, the linear esti
mator is a data-dependent linear combination of the columns of the design
matrix\, and its analysis is quite simple\; the spectral estimator is the
principal eigenvector of a data-dependent matrix\, whose spectrum exhibits
a phase transition. In this talk\, I will first analyze the spectral meth
od and prove that it leads to the information-theoretically optimal thresh
old for weak recovery in phase retrieval. Second\, I will show how to opti
mally combine the linear and spectral estimators. Finally\, I will conside
r estimators based on approximate message passing (AMP) and prove how to i
nitialize them with the spectral method.Based on joint work with Andrea Mo
ntanari\, Christos Thrampoulidis and Ramji Venkataraman [https://arxiv.org
/abs/1708.05932\, https://arxiv.org/abs/2008.03326\, https://arxiv.org/abs
/2010.03460].
LOCATION:Online Event ()\, IST Austria
ORGANIZER:kkhudiak@ist.ac.at
SUMMARY:Stochastic seminar: Inference in High Dimensions for Generalized Li
near Models: the Linear\, the Spectral and the Approximate
URL:https://talks-calendar.app.ist.ac.at/events/2974
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