Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems

Antanas Žilinskas, Anatoly Zhigljavsky, Vladimir Nekrutkin, Vladimir Kornikov

Research output

Abstract

Bayesian approach is actively used to develop global optimization algorithms aimed at expensive black box functions. One of the challenges in this approach is the selection of an appropriate model for the objective function. Normally, a Gaussian random field is chosen as a theoretical model. However, the problem of estimation of parameters, using objective function values, is not thoroughly researched. In this paper, we consider the behavior of maximum likelihood estimators (MLEs) of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function. We also compare properties of exponential covariance function models.

Original languageEnglish
Title of host publication14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO)
EditorsAndre H. Deutz, Sander C. Hille, Yaroslav D. Sergeyev, Michael T. M. Emmerich
PublisherAmerican Institute of Physics
Number of pages4
Volume2070
ISBN (Electronic)9780735417984
DOIs
Publication statusPublished - 12 Feb 2019
Event14th International Global Optimization Workshop, LeGO 2018 - Leiden
Duration: 18 Sep 201821 Sep 2018

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume2070
ISSN (Print)0094-243X

Conference

Conference14th International Global Optimization Workshop, LeGO 2018
CountryNetherlands
CityLeiden
Period18/09/1821/09/18

Fingerprint

optimization
estimators
boxes

Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Žilinskas, A., Zhigljavsky, A., Nekrutkin, V., & Kornikov, V. (2019). Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems. In A. H. Deutz, S. C. Hille, Y. D. Sergeyev, & M. T. M. Emmerich (Eds.), 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO) (Vol. 2070). [20043] (AIP Conference Proceedings; Vol. 2070). American Institute of Physics. https://doi.org/10.1063/1.5090010
Žilinskas, Antanas ; Zhigljavsky, Anatoly ; Nekrutkin, Vladimir ; Kornikov, Vladimir. / Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems. 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO). editor / Andre H. Deutz ; Sander C. Hille ; Yaroslav D. Sergeyev ; Michael T. M. Emmerich. Vol. 2070 American Institute of Physics, 2019. (AIP Conference Proceedings).
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Žilinskas, A, Zhigljavsky, A, Nekrutkin, V & Kornikov, V 2019, Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems. in AH Deutz, SC Hille, YD Sergeyev & MTM Emmerich (eds), 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO). vol. 2070, 20043, AIP Conference Proceedings, vol. 2070, American Institute of Physics, Leiden, 18/09/18. https://doi.org/10.1063/1.5090010

Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems. / Žilinskas, Antanas; Zhigljavsky, Anatoly; Nekrutkin, Vladimir; Kornikov, Vladimir.

14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO). ed. / Andre H. Deutz; Sander C. Hille; Yaroslav D. Sergeyev; Michael T. M. Emmerich. Vol. 2070 American Institute of Physics, 2019. 20043 (AIP Conference Proceedings; Vol. 2070).

Research output

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T1 - Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems

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N2 - Bayesian approach is actively used to develop global optimization algorithms aimed at expensive black box functions. One of the challenges in this approach is the selection of an appropriate model for the objective function. Normally, a Gaussian random field is chosen as a theoretical model. However, the problem of estimation of parameters, using objective function values, is not thoroughly researched. In this paper, we consider the behavior of maximum likelihood estimators (MLEs) of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function. We also compare properties of exponential covariance function models.

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Žilinskas A, Zhigljavsky A, Nekrutkin V, Kornikov V. Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems. In Deutz AH, Hille SC, Sergeyev YD, Emmerich MTM, editors, 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO). Vol. 2070. American Institute of Physics. 2019. 20043. (AIP Conference Proceedings). https://doi.org/10.1063/1.5090010