# Nested Kriging predictions for datasets with a large number of observations

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## Abstract

This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function. The Kriging interpolation technique (or Gaussian process regression) is often considered to tackle such a problem, but the method suffers from its computational burden when the number of observation points is large. We introduce in this article nested Kriging predictors which are constructed by aggregating sub-models based on subsets of observation points. This approach is proven to have better theoretical properties than other aggregation methods that can be found in the literature. Contrarily to some other methods it can be shown that the proposed aggregation method is consistent. Finally, the practical interest of the proposed method is illustrated on simulated datasets and on an industrial test case with \(10^4\) observations in a 6-dimensional space.

### Keywords

Gaussian process regression Big data Aggregation methods Best linear unbiased predictor Spatial processes## Notes

### Acknowledgements

Part of this research was conducted within the frame of the Chair in Applied Mathematics OQUAIDO, gathering partners in technological research (BRGM, CEA, IFPEN, IRSN, Safran, Storengy) and academia (Ecole Centrale de Lyon, Mines Saint-Etienne, University of Grenoble, University of Nice, University of Toulouse and CNRS) around advanced methods for Computer Experiments. The authors would like to warmly thank Dr. Géraud Blatman and EDF R&D for providing us the industrial test case. They also thank both editor and reviewers for very precise and constructive comments on this paper. This paper has been finished during a stay of D. Rullière at Vietnam Institute for Advanced Study in Mathematics, the latter author thanks the VIASM institute and DAMI research chair (Data Analytics & Models for Insurance) for their support.

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