Time-adaptive functional Gaussian Process regression

• URL: http://arxiv.org/abs/2603.21144v1
• Date: Sun, 22 Mar 2026 09:40:09 GMT
• Title: Time-adaptive functional Gaussian Process regression
• Abstract summary: This paper proposes a new formulation of functional Gaussian Process regression in manifold, based on an Empirical Bayes approach in the context of the random field.<n>The identified measures are then obtained via the eigensfunction of the Laplace-Beltrami operator on the manifold.<n>The involved time spectra constitute the key tool for dimension reduction in the implementation of this regression approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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