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Properties and comparison of some Kriging sub-model aggregation methods

Abstract : Kriging is a widely employed technique, in particular for computer experiments, in machine learning or in geostatistics. An important challenge for Kriging is the computational burden when the data set is large. This article focuses on a class of methods aiming at decreasing this computational cost, consisting in aggregating Kriging predictors based on smaller data subsets. It proves that aggregation methods that ignore the covariance between sub-models can yield an inconsistent final Kriging prediction. In contrast, a theoretical study of the nested Kriging method shows additional attractive properties for it: First, this predictor is consistent, second it can be interpreted as an exact conditional distribution for a modified process and third, the conditional covariances given the observations can be computed efficiently. This article also includes a theoretical and numerical analysis of how the assignment of the observation points to the sub-models can affect the prediction ability of the aggregated model. Finally, the nested Kriging method is extended to measurement errors and to universal Kriging.
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https://hal.archives-ouvertes.fr/hal-01561747
Contributor : Didier Rullière Connect in order to contact the contributor
Submitted on : Thursday, February 25, 2021 - 10:37:48 PM
Last modification on : Friday, July 22, 2022 - 10:45:26 AM

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François Bachoc, Nicolas Durrande, Didier Rullière, Clément Chevalier. Properties and comparison of some Kriging sub-model aggregation methods. Mathematical Geosciences, Springer Verlag, 2022, 54, pp.941--977. ⟨10.1007/s11004-021-09986-2⟩. ⟨hal-01561747v2⟩

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