Combination of Optimization-free Kriging Models for High-Dimensional Problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computational Statistics Année : 2023

Combination of Optimization-free Kriging Models for High-Dimensional Problems

Résumé

Kriging metamodeling (also called Gaussian Process regression) is a popular approach to predict the output of a function based on few observations. The Kriging method involves length-scale hyperparameters whose optimization is essential to obtain an accurate model and is typically performed using maximum likelihood estimation (MLE). However, for high-dimensional problems, the hyperparameter optimization is problematic and often fails to provide correct values. This is especially true for Kriging-based design optimization where the dimension is often quite high. In this article, we propose a method for building high-dimensional surrogate models which avoids the hyperparameter optimization by combining Kriging sub-models with randomly chosen length-scales. Contrarily to other approaches, it does not rely on dimension reduction techniques and it provides a closed-form expression for the model. We present a recipe to determine a suitable range for the sub-models length-scales. We also compare different approaches to compute the weights in the combination. We show for a high-dimensional test problem and a real-world application that our combination is more accurate than the classical Kriging approach using MLE.
Fichier principal
Vignette du fichier
Combination of Optimization-free Kriging Models for High-Dimensional Problems.pdf (767.96 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03812073 , version 1 (12-10-2022)
hal-03812073 , version 2 (26-07-2023)

Identifiants

Citer

Tanguy Appriou, Didier Rullière, David Gaudrie. Combination of Optimization-free Kriging Models for High-Dimensional Problems. Computational Statistics, In press, ⟨10.1007/s00180-023-01424-7⟩. ⟨hal-03812073v2⟩
143 Consultations
114 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More