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SUMMARY:Bayesian quadrature\, energy minimization and kernel herding for s
 pace filling design - Luc Pronzato (Université de Nice Sophia Antipolis\;
  CNRS (Centre national de la recherche scientifique))
DTSTART:20180413T080000Z
DTEND:20180413T090000Z
UID:TALK103750@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A standard objective in computer experiments is to predict the
  behaviour of an unknown function on a compact domain from a few evaluatio
 ns inside the domain. When little is known about the function\, space-fill
 ing design is advisable: typically\, points of evaluation spread out acros
 s the available space are obtained by minimizing a geometrical (for instan
 ce\, minimax-distance) or a discrepancy criterion measuring distance to un
 iformity.  We shall make a survey of some recent results on energy functio
 nals\, and investigate connections between design for integration (quadrat
 ure design)\, construction of the (continuous) BLUE for the location model
 \, and minimization of energy (kernel discrepancy) for signed measures. In
 tegrally strictly positive definite kernels define strictly convex energy 
 functionals\, with an equivalence between the notions of potential and dir
 ectional derivative for smooth kernels\, showing the strong relation betwe
 en discrepancy minimization and more traditional design of optimal experim
 ents. In particular\, kernel herding algorithms are special instances of v
 ertex-direction methods used in optimal design\, and can be applied to the
  construction of point sequences with suitable space-filling properties. T
 he presentation is based on recent work with A.A. Zhigljavsky (Cardiff Uni
 versity).
LOCATION:Seminar Room 1\, Newton Institute
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