Additive Covariance kernels for high-dimensional Gaussian Process modeling

Abstract

Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian Process modeling with the advantages of generalized additive models, and to describe some properties of the resulting models.