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Bayesian quadrature, energy minimization and kernel herding for space filling design

Presented by: 
Luc Pronzato Université de Nice Sophia Antipolis, CNRS (Centre national de la recherche scientifique)
Date: 
Friday 13th April 2018 - 09:00 to 10:00
Venue: 
INI Seminar Room 1
Abstract: 
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, points of evaluation spread out across the available space are obtained by minimizing a geometrical (for instance, minimax-distance) or a discrepancy criterion measuring distance to uniformity. We shall make a survey of some recent results on energy functionals, and investigate connections between design for integration (quadrature design), construction of the (continuous) BLUE for the location model, and minimization of energy (kernel discrepancy) for signed measures. Integrally strictly positive definite kernels define strictly convex energy functionals, with an equivalence between the notions of potential and directional derivative for smooth kernels, showing the strong relation between discrepancy minimization and more traditional design of optimal experiments. In particular, kernel herding algorithms are special instances of vertex-direction methods used in optimal design, and can be applied to the construction of point sequences with suitable space-filling properties. The presentation is based on recent work with A.A. Zhigljavsky (Cardiff University).
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons