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.

References in corpus (5)

• High-dimensional additive modeling
• Rates of contraction of posterior distributions based on Gaussian process priors
• Additive Gaussian Processes
• High-Dimensional Non-Linear Variable Selection through Hierarchical Kernel Learning
• Minimax-optimal rates for sparse additive models over kernel classes via convex programming

Cited by in corpus (1)

• Polynomial-Chaos-based Kriging