Nested Kriging predictions for datasets with large number of observations

TL;DR

This paper introduces nested Kriging predictors that efficiently handle large datasets by aggregating sub-models, offering better theoretical properties and consistency, demonstrated through simulations and an industrial case with 10,000 observations.

Contribution

The paper proposes a novel nested Kriging aggregation method that improves computational efficiency and theoretical consistency for large datasets.

Findings

The method is consistent unlike some existing aggregation techniques.

It performs well on simulated data and a real industrial dataset with 10,000 observations.

The approach offers better theoretical properties than other aggregation methods.

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.