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DTSTAMP:20170820T054436Z
UID:57f7915881fe3520818363@ist.ac.at
DTSTART:20170627T160000
DTEND:20170627T180000
DESCRIPTION:Speaker: Nicolas Trillos\, Brown University\nhosted by Jan Maas
\nAbstract: We consider the problem of recovering a function input of a di
fferential equation formulated on an unknown domain $M$. We assume to have
access to a discrete domain $M_n=\\{x_1\, \\dots\, x_n\\} \\subset M$\, a
nd to noisy measurements of the output solution at $p\\le n$ of those poi
nts. We introduce a graph-based Bayesian inverse problem\, and show that t
he graph-posterior measures over functions in $M_n$ converge\, in the larg
e $n$ limit\, to a posterior over functions in $M$ that solves a Bayesian
inverse problem with known domain. The proofs rely on the variational form
ulation of the Bayesian update\, and on a new topology for the study of co
nvergence of measures over functions on point clouds to a measure over fun
ctions on the continuum. Our framework\, techniques\, and results may serv
e to lay the foundations of robust uncertainty quantification of graph-bas
ed tasks in machine learning. The ideas are presented in the concrete sett
ing of recovering the 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
T Austria
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Continuum limit of posteriors in graph-Bayesian inverse
URL:https://talks-calendar.app.ist.ac.at/events/63
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