Kriging via variably scaled kernels
This work addresses the problem of modeling non-stationary data in Gaussian processes for researchers and practitioners in fields like spatial statistics and machine learning, representing an incremental advancement over classical non-stationary kernels.
The paper tackled the limitation of stationary kernels in Gaussian processes and Kriging models by introducing variably scaled kernels to handle heterogeneous correlation structures, such as abrupt changes or discontinuities, resulting in improved reconstruction accuracy and better uncertainty estimates.
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