Combination of optimization-free kriging models for high-dimensional problems

Tanguy Appriou (), Didier Rullière and David Gaudrie
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Tanguy Appriou: Univ Clermont Auvergne
Didier Rullière: Univ Clermont Auvergne
David Gaudrie: Stellantis, Centre Technique Velizy

Computational Statistics, 2024, vol. 39, issue 6, No 7, 3049-3071

Abstract: Abstract 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.

Keywords: Kriging; Gaussian process regression; High dimension; Hyperparameter optimization; Length-scales bounds; Model aggregation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01424-7

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