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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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https://hal.archives-ouvertes.fr/hal-00850436
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Submitted on : Tuesday, August 6, 2013 - 2:32:48 PM
Last modification on : Sunday, April 4, 2021 - 10:22:03 AM
Long-term archiving on: : Wednesday, April 5, 2017 - 7:39:42 PM

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  • HAL Id : hal-00850436, version 1
  • ARXIV : 1308.1359

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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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