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TZID:Europe/Vienna
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DTSTART:20170326T030000
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DTSTART:20171029T020000
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DTSTAMP:20220817T005214Z
UID:57f7915881fe3520818363@ist.ac.at
DTSTART:20170627T160000
DTEND:20170627T180000
DESCRIPTION:Speaker: Nicolas Trillos\nhosted by Jan Maas\nAbstract: We cons
ider the problem of recovering a function input of a differential equation
formulated on an unknown domain $M$. We assume to have access to a discre
te domain $M_n=\\{x_1\, \\dots\, x_n\\} \\subset M$\, and to noisy measure
ments of the output solution at $p\\le n$ of those points. We introduce a
graph-based Bayesian inverse problem\, and show that the graph-posterior
measures over functions in $M_n$ converge\, in the large $n$ limit\, to a
posterior over functions in $M$ that solves a Bayesian inverse problem wit
h known domain. The proofs rely on the variational formulation of the Baye
sian update\, and on a new topology for the study of convergence of measur
es over functions on point clouds to a measure over functions on the conti
nuum. Our framework\, techniques\, and results may serve to lay the founda
tions of robust uncertainty quantification of graph-based tasks in machine
learning. The ideas are presented in the concrete setting of recovering t
he initial condition of the heat equation on an unknown manifold. This is
joint work with Daniel Sanz-Alonso
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Nicolas Trillos: Continuum limit of posteriors in graph-Bayesian in
verse
URL:https://talks-calendar.app.ist.ac.at/events/654
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