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arXiv · 1308.1359

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

David Ginsbourger·Olivier Roustant·Nicolas Durrande
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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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David Ginsbourger, Olivier Roustant, Nicolas Durrande. 2013-08-06. Invariances of random fields paths, with applications in Gaussian Process Regression. https://arxiv.org/abs/1308.1359

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