Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity
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” outperforms Latin hypercubes in terms of the IMSE criterion.
KeywordsFinite Group Composition Operator Kriging Model Integrate Mean Square Error Additive Path
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