Space-filling designs based on Rényi entropy
Résumé
Simulations using computationally intensive computer models need to be organized according to a design of experiments. Space-filling designs spread out the training examples in the experimental domain with the aim to catch the irregularities of the computer response. Among the existing space-filling designs, the uniform designs have the characteristic of having a distribution of their points close to the uniform distribution. In this paper we propose three uniformity criteria to build space-filling designs, defined from three methods of estimating the Rényi entropy: a plug-in estimation, a nearest neighbor estimation and a method based on the minimum spanning tree of the design points. An optimization algorithm is used to build optimal Latin hypercube designs. The space-filling properties of the resulting designs are studied with numerical tests.
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