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

Antanas Žilinskas; Anatoly Zhigljavsky; Vladimir Nekrutkin; Vladimir Kornikov

doi:10.1063/1.5090010

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 language	English
Title of host publication	14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO)
Editors	Andre H. Deutz, Sander C. Hille, Yaroslav D. Sergeyev, Michael T. M. Emmerich
Publisher	American Institute of Physics
Number of pages	4
Volume	2070
ISBN (Electronic)	9780735417984
DOIs	https://doi.org/10.1063/1.5090010
Publication status	Published - 12 Feb 2019
Event	14th International Global Optimization Workshop, LeGO 2018 - Leiden Duration: 18 Sep 2018 → 21 Sep 2018

Publication series

Name	AIP Conference Proceedings
Publisher	AMER INST PHYSICS
Volume	2070
ISSN (Print)	0094-243X

Conference

Conference	14th International Global Optimization Workshop, LeGO 2018
Country	Netherlands
City	Leiden
Period	18/09/18 → 21/09/18

Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/1.5090010

http://www.scopus.com/inward/record.url?scp=85061906735&partnerID=8YFLogxK

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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 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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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.",

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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, 14th International Global Optimization Workshop, LeGO 2018, 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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AU - Žilinskas, Antanas

AU - Zhigljavsky, Anatoly

AU - Nekrutkin, Vladimir

AU - Kornikov, Vladimir

PY - 2019/2/12

Y1 - 2019/2/12

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.

AB - 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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M3 - Conference contribution

AN - SCOPUS:85061906735

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T3 - AIP Conference Proceedings

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A2 - Sergeyev, Yaroslav D.

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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