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 | |
| 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 |
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Scopus subject areas
- Physics and Astronomy(all)
Cite this
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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
TY - GEN
T1 - Selection of a covariance kernel for a Gaussian random field aimed for modeling global optimization problems
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.
UR - http://www.scopus.com/inward/record.url?scp=85061906735&partnerID=8YFLogxK
U2 - 10.1063/1.5090010
DO - 10.1063/1.5090010
M3 - Conference contribution
AN - SCOPUS:85061906735
VL - 2070
T3 - AIP Conference Proceedings
BT - 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP (LEGO)
A2 - Deutz, Andre H.
A2 - Hille, Sander C.
A2 - Sergeyev, Yaroslav D.
A2 - Emmerich, Michael T. M.
PB - American Institute of Physics
ER -