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On estimation of surrogate models for multivariate computer experiments

  • Benedikt Bauer
  • Felix Heimrich
  • Michael Kohler
  • Adam KrzyżakEmail author
Article
  • 75 Downloads

Abstract

Estimation of surrogate models for computer experiments leads to nonparametric regression estimation problems without noise in the dependent variable. In this paper, we propose an empirical maximal deviation minimization principle to construct estimates in this context and analyze the rate of convergence of corresponding quantile estimates. As an application, we consider estimation of computer experiments with moderately high dimension by neural networks and show that here we can circumvent the so-called curse of dimensionality by imposing rather general assumptions on the structure of the regression function. The estimates are illustrated by applying them to simulated data and to a simulation model in mechanical engineering.

Keywords

Computer experiments Curse of dimensionality Neural networks Nonparametric regression without noise in the dependent variable Quantile estimates Rate of convergence Surrogate models 

Notes

Acknowledgements

The first three authors would like to thank the German Research Foundation (DFG) for funding this project within the Collaborative Research Centre 805. The last author would like to thank the Natural Sciences and Engineering Research Council of Canada for additional support under Grant RGPIN-2015-06412.

Supplementary material

10463_2017_627_MOESM1_ESM.pdf (189 kb)
Supplementary material 1 (pdf 188 KB)

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  • Benedikt Bauer
    • 1
  • Felix Heimrich
    • 2
  • Michael Kohler
    • 1
  • Adam Krzyżak
    • 3
    Email author
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Fachbereich MaschinenbauTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada

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