Combination of High-Dimensional Kriging Sub-models
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 due to the shape of the likelihood function, to the exponential growth of the search space with the dimension, and to over-fitting issues when there are too few observations. It often fails to provide correct hyperparameter values. In this article, we propose a method for high-dimensional problems which avoids the hyperparameter optimization by combining Kriging sub-models with fixed 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 based on the designs and on the employed kernel. We also compare different approaches to compute the weights in the combination. We show for a 50-dimensional test problem that our combination provides a more accurate surrogate model than the classical Kriging approach using MLE.
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