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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bayesian quadrature\, energy minimization and kern
el herding for space filling design - Luc Pronzato
(Université de Nice Sophia Antipolis\; CNRS (Cent
re national de la recherche scientifique))
DTSTART;TZID=Europe/London:20180413T090000
DTEND;TZID=Europe/London:20180413T100000
UID:TALK103750AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103750
DESCRIPTION:A standard objective in computer experiments is to
predict the behaviour of an unknown function on a
compact domain from a few evaluations inside the
domain. When little is known about the function\,
space-filling design is advisable: typically\, poi
nts of evaluation spread out across the available
space are obtained by minimizing a geometrical (fo
r instance\, minimax-distance) or a discrepancy cr
iterion measuring distance to uniformity. We shal
l make a survey of some recent results on energy f
unctionals\, and investigate connections between d
esign for integration (quadrature design)\, constr
uction of the (continuous) BLUE for the location m
odel\, and minimization of energy (kernel discrepa
ncy) for signed measures. Integrally strictly posi
tive definite kernels define strictly convex energ
y functionals\, with an equivalence between the no
tions of potential and directional derivative for
smooth kernels\, showing the strong relation betwe
en discrepancy minimization and more traditional d
esign of optimal experiments. In particular\, kern
el herding algorithms are special instances of ver
tex-direction methods used in optimal design\, and
can be applied to the construction of point seque
nces with suitable space-filling properties. The p
resentation is based on recent work with A.A. Zhig
ljavsky (Cardiff University).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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