Polar Gaussian Processes and Experimental Designs in Circular Domains

Abstract : Predicting on circular domains is a central issue that can be addressed by Gaus- sian process (GP) regression. However, usual GP models do not take into account the geometry of the disk in their covariance structure (or kernel), which may be a drawback at least for industrial processes involving a rotation or a diffusion from the center of the disk. We introduce so-called polar GPs defined on the space of polar coordinates. Their kernels are obtained as a combination of a kernel for the radius and a kernel for the angle, based on either chordal or geodesic distances on the circle. Their efficiency is illustrated on two industrial applications. We further consider the problem of designing experiments on the disk. Two new Latin hypercube designs are obtained, by defining a valid maximin criterion for polar coordinates. Finally, an extension of the whole methodology to higher dimensions is investigated.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01119942
Contributeur : Olivier Roustant <>
Soumis le : mercredi 30 mars 2016 - 17:18:23
Dernière modification le : dimanche 4 septembre 2016 - 17:40:26
Document(s) archivé(s) le : lundi 14 novembre 2016 - 09:37:51

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polarGP_HAL.pdf
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  • HAL Id : hal-01119942, version 4

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Espéran Padonou, O Roustant. Polar Gaussian Processes and Experimental Designs in Circular Domains. 2016. <hal-01119942v4>

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