Nested Kriging predictions for datasets with a large number of observations

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.

Gaussian processes for computer experiments

“…We present in this section some results from a joint work with F. Bachoc, C. Chevalier, N. Durrande and D. Rullière [49].…”

“…Compared to [49], we focus here on the simplified context of Kriging submodels relying on centered Gaussian Processes, but results can be adapted to more general settings, such as non-Gaussian processes, or other types of submodels.…”

“…corresponds exactly to the full model M full (.). The detail of all these properties is given in [49].…”

“…The other methods that are considered in this benchmarck are the (generalized) product of Experts: PoE, GPoE, the (robust) Bayesian Committee Machine: BCM, RBCM, and the smallest Prediction Variance (SPV), see [21,49].…”

“…The contributions which are presented in Sections 2, 3 and 4 correspond to the references [14,35], [49] and [12,13].…”