Invariances of random fields paths, with applications in Gaussian Process Regression
Statistics Theory
2013-08-07 v1 Probability
Methodology
Machine Learning
Statistics Theory
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 Lo\`eve 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.
Cite
@article{arxiv.1308.1359,
title = {Invariances of random fields paths, with applications in Gaussian Process Regression},
author = {David Ginsbourger and Olivier Roustant and Nicolas Durrande},
journal= {arXiv preprint arXiv:1308.1359},
year = {2013}
}