Time-adaptive functional Gaussian Process regression
This provides a domain-specific method for spatiotemporal regression on manifolds, which is incremental as it builds on existing Gaussian Process frameworks.
The paper tackles functional Gaussian Process regression on manifolds by developing an Empirical Bayes approach using tight Gaussian measures and exploiting covariance kernel invariance under manifold isometries. The result is a regression predictor with demonstrated finite sample and asymptotic properties through simulation studies and synthetic data applications.
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.