Time-adaptive functional Gaussian Process regression

Fuente: arXiv
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Autores principales: Ruiz-Medina, MD, Madrid, AE, Torres-Signes, A, Angulo, JM
Formato: Preprint
Publicado: 2026
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author Ruiz-Medina, MD
Madrid, AE
Torres-Signes, A
Angulo, JM
author_facet Ruiz-Medina, MD
Madrid, AE
Torres-Signes, A
Angulo, JM
contents This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable Hilbert spaces, exploiting the invariance property of covariance kernels under the group of isometries of the manifold. The identification of these measures with infinite-product Gaussian measures is then obtained via the eigenfunctions of the Laplace-Beltrami operator on the manifold. The involved time-varying angular spectra constitute the key tool for dimension reduction in the implementation of this regression approach, adopting a suitable truncation scheme depending on the functional sample size. The simulation study and synthetic data application undertaken illustrate the finite sample and asymptotic properties of the proposed functional regression predictor.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21144
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Time-adaptive functional Gaussian Process regression
Ruiz-Medina, MD
Madrid, AE
Torres-Signes, A
Angulo, JM
Machine Learning
60F99, 60E10, 60G15, 60G60
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable Hilbert spaces, exploiting the invariance property of covariance kernels under the group of isometries of the manifold. The identification of these measures with infinite-product Gaussian measures is then obtained via the eigenfunctions of the Laplace-Beltrami operator on the manifold. The involved time-varying angular spectra constitute the key tool for dimension reduction in the implementation of this regression approach, adopting a suitable truncation scheme depending on the functional sample size. The simulation study and synthetic data application undertaken illustrate the finite sample and asymptotic properties of the proposed functional regression predictor.
title Time-adaptive functional Gaussian Process regression
topic Machine Learning
60F99, 60E10, 60G15, 60G60
url https://arxiv.org/abs/2603.21144