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Invariances of random fields paths, with applications in Gaussian Process Regression

Abstract

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended to a broader class of operators in the Gaussian case, via the Loève isometry. Several covariance-driven pathwise invariances are illustrated, including fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process regression.
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Dates and versions

hal-00850436 , version 1 (06-08-2013)

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David Ginsbourger, Olivier Roustant, Nicolas Durrande. Invariances of random fields paths, with applications in Gaussian Process Regression. 2013. ⟨hal-00850436⟩
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