Discrete Mixtures of Kernels for Kriging-based Optimization

Autor: David Ginsbourger, Laurent Carraro, Céline Helbert
Přispěvatelé: Ginsbourger, David, Six, Grégory, Département Méthodes et Modèles Mathématiques pour l'Industrie (3MI-ENSMSE), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Centre G2I, DICE Consortium
Jazyk: angličtina
Rok vydání: 2008
Předmět:
Mathematical optimization
0211 other engineering and technologies
Multikernel
02 engineering and technology
[STAT.OT]Statistics [stat]/Other Statistics [stat.ML]
Management Science and Operations Research
01 natural sciences
010104 statistics & probability
symbols.namesake
Kriging
Applied mathematics
Statistics::Methodology
0101 mathematics
Safety
Risk
Reliability and Quality
Variogram
Global optimization
Gaussian process
Gaussian Processes
ComputingMilieux_MISCELLANEOUS
Parametric statistics
Mathematics
021103 operations research
Global Optimization
Covariance
Kernel Selection
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
[STAT.OT] Statistics [stat]/Other Statistics [stat.ML]
Statistics::Computation
Kernel (statistics)
symbols
[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation
Mixture of Experts
Zdroj: Quality and Reliability Engineering International
Quality and Reliability Engineering International, Wiley, 2008, 24 (6), pp.681-691
ISSN: 0748-8017
1099-1638
Popis: Kriging-based exploration strategies often rely on a single Ordinary Kriging model which parametric covariance kernel is selected a priori or on the basis of an initial data set. Since choosing an unadapted kernel can radically harm the results, we wish to reduce the risk of model misspecification. Here we consider the simultaneous use of multiple kernels within Kriging. We give the equations of discrete mixtures of Ordinary Krigings, and derive a multikernel version of the expected improvement optimization criterion. We finally provide an illustration of the Ef- ficient Global Optimization algorithm with mixed exponential and Gaussian kernels, where the parameters are estimated by Maximum Likelihood and the mixing weights are likelihood ratios. The global optimization of numerical simulators is a challenging problem since the number of runs is severely limited by computation time. Furthermore, the derivatives are generally not available. For the past decade, Kriging-based derivative-free algorithms like EGO ((5)) have been developed to address this issue. Kriging metamodels are indeed convenient for building exploration strate- gies since they provide for every potential input vector both a mean predicted response value (Kriging mean) and an associated measure of accuracy (Kriging variance). Along this paper, the simulator is seen as a determinist numerical black-box function y with d-dimensional input
Databáze: OpenAIRE
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