Nested Kriging predictions for datasets with 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.

References in corpus (5)

• Gaussian Processes for Data-Efficient Learning in Robotics and Control
• Gaussian Processes for Big Data
• Bayesian Nonstationary Spatial Modeling for Very Large Datasets
• Blitzkriging: Kronecker-structured Stochastic Gaussian Processes
• Properties and comparison of some Kriging sub-model aggregation methods

Cited by in corpus (9)

• When Gaussian Process Meets Big Data: A Review of Scalable GPs
• Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes
• Composite likelihood estimation for a gaussian process under fixed domain asymptotics
• A Bayesian neural network approach to Multi-fidelity surrogate modelling
• Aggregating Dependent Gaussian Experts in Local Approximation
• Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey
• Incorporating Subsampling into Bayesian Models for High-Dimensional Spatial Data
• Gaussian Experts Selection using Graphical Models
• Healing Products of Gaussian Processes