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Additive Covariance kernels for high-dimensional Gaussian Process modeling

Nicolas DurrandeDavid GinsbourgerOlivier Roustant — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

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...

Argumentwise invariant kernels for the approximation of invariant functions

David GinsbourgerXavier BayOlivier RoustantLaurent Carraro — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two subclasses of argumentwise kernels are considered, involving a fundamental domain or a double sum over orbits. We then derive invariance properties...

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