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SUMMARY:Statistical physics approach to compressed sensing and generalized
linear regression
DTSTART;VALUE=DATE-TIME:20171207T133000Z
DTEND;VALUE=DATE-TIME:20171207T143000Z
DTSTAMP;VALUE=DATE-TIME:20210227T072818Z
UID:indico-event-2610@indico.math.cnrs.fr
DESCRIPTION:Bayesian inference and statistical physics are formally closel
y related. Therefore methodology and concepts developed in statistical phy
sics to understand disordered materials such as glasses and spin glasses c
an be elevated to analyze models of statistical inference. We will present
this approach in a rather general setting that covers analysis of compres
sed sensing\, generalized linear regression\, and the perceptron - a kind
of a single layer neural network. At the one hand\, this approach leads to
the approximate message passing algorithm that is gaining its place among
other widely used regression and classification algorithms. At the other
hand\, the related analyses leads to identification of phase transitions i
n the performance of Bayes-optimal estimators. We will discuss relation be
tween these phase transitions and algorithmic hardness\, and in the case o
f compressed sensing we will show how this understanding leads to a design
of optimal measurement protocols.\n\nBased partly on "Statistical-physics
-based reconstruction in compressed sensing" PRX 2012 and reviewed in "Sta
tistical physics of inference: Thresholds and algorithms" Advances of Phys
ics 2016.\n\nhttps://indico.math.cnrs.fr/event/2610/
LOCATION:UMPA salle 435
URL:https://indico.math.cnrs.fr/event/2610/
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