Bayesian Quadrature, Energy Minimization, and Space-Filling Design
| Autor: | Anatoly Zhigljavsky, Luc Pronzato |
|---|---|
| Přispěvatelé: | Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SYSTEMES, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), School of Mathematics [Cardiff], Cardiff University |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Optimal design potential energy minimization Computer science Positive-definite matrix Directional derivative Energy minimization 01 natural sciences 010104 statistics & probability BLUE [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] discrepancy Discrete Mathematics and Combinatorics Applied mathematics 0101 mathematics space-filling design Applied Mathematics 010102 general mathematics Computer experiment AMS 62K99 65D30 65D99 Quadrature (mathematics) Modeling and Simulation Minification Statistics Probability and Uncertainty Convex function Bayesian quadrature |
| Zdroj: | SIAM/ASA Journal on Uncertainty Quantification SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2020, 8 (3), pp.959-1011 |
| ISSN: | 2166-2525 |
| DOI: | 10.1137/18m1210332 |
| Popis: | A standard objective in computer experiments is to approximate the behavior 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, covering radius) or a discrepancy criterion measuring distance to uniformity. The paper investigates connections between design for integration (quadrature design), construction of the (continuous) best linear unbiased estimator (BLUE) for the location model, space-filling design, 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, showing the strong relation between discrepancy minimization and more traditional design of optimal experiments. In particular, kernel herding algorithms, which are special instances of vertex-direction methods used in optimal design, can be applied to the construction of point sequences with suitable space-filling properties. |
| Databáze: | OpenAIRE |
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