Kriging via variably scaled kernels

Fuente: arXiv
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Main Authors: Audone, Gianluca, Marchetti, Francesco, Perracchione, Emma, Rossini, Milvia
Format: Preprint
Published: 2026
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author Audone, Gianluca
Marchetti, Francesco
Perracchione, Emma
Rossini, Milvia
author_facet Audone, Gianluca
Marchetti, Francesco
Perracchione, Emma
Rossini, Milvia
contents 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
format Preprint
id arxiv_https___arxiv_org_abs_2603_16950
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Kriging via variably scaled kernels
Audone, Gianluca
Marchetti, Francesco
Perracchione, Emma
Rossini, Milvia
Machine Learning
Methodology
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
title Kriging via variably scaled kernels
topic Machine Learning
Methodology
url https://arxiv.org/abs/2603.16950