Kernels and designs for modelling invariant functions: From group invariance to additivity

Abstract : We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of "axis designs" outperfoms latin hypercubes in terms of the IMSE criterion.
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David Ginsbourger, Nicolas Durrande, Olivier Roustant. Kernels and designs for modelling invariant functions: From group invariance to additivity. MODA-10, Physica-Verlag HD, 2013. 〈hal-00731657〉

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