Kriging via variably scaled kernels

TL;DR

This paper introduces variably scaled kernels to enhance Gaussian process models, allowing them to better capture non-stationary and heterogeneous correlation structures in data, especially with abrupt changes or discontinuities.

Contribution

It proposes a novel approach using variably scaled kernels to construct non-stationary Gaussian processes, improving modeling flexibility and accuracy over classical stationary kernels.

Findings

Improved reconstruction accuracy with variably scaled kernels

Enhanced uncertainty estimates reflecting data structure

Effective modeling of abrupt changes and discontinuities

Abstract

Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance between scattered data. While this assumption ensures analytical tractability, it limits the ability of Gaussian processes to represent heterogeneous correlation structures. In this work, we investigate variably scaled kernels as an effective tool for constructing non-stationary Gaussian processes by explicitly modifying the correlation structure of the data. Through a scaling function, variably scaled kernels alter the correlations between data and enable the modeling of targets exhibiting abrupt changes or discontinuities. We analyse the resulting predictive uncertainty via the variably scaled kernel power function and clarify the relationship between variably scaled kernels-based constructions and classical non-stationary kernels. Numerical experiments demonstrate that variably scaled kernels-based Gaussian processes yield improved reconstruction accuracy and provide uncertainty estimates that reflect the underlying structure of the data