# Time-adaptive infinite-dimensional Gaussian process regression on manifolds

arXiv: https://arxiv.org/abs/2603.21144 · HTML: https://mlsanity.com/paper/2603.21144/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming](https://mlsanity.com/paper/2004.11408/) (2020)
- [The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running](https://mlsanity.com/paper/2111.01084/) (2021)
- [Bayesian inference for spatio-temporal spike-and-slab priors](https://mlsanity.com/paper/1509.04752/) (2015)
- [LRD spectral analysis of multifractional functional time series on manifolds](https://mlsanity.com/paper/2212.06228/) (2022)
- [Computationally efficient multi-level Gaussian process regression for functional data observed under completely or partially regular sampling designs](https://mlsanity.com/paper/2406.13691/) (2024)
- [Climate change analysis from LRD manifold functional regression](https://mlsanity.com/paper/2407.00381/) (2024)

## Abstract (arXiv)

This paper proposes a new formulation of functional Gaussian Process regression on 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 via characteristic function of these measures with the infinite product of one-dimensional Gaussian measures is then obtained, in terms of the eigenfunctions of the Laplace-Beltrami operator on the manifold. The involved time-varying angular spectrum constitutes 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 illustrate the performance of the proposed functional regression predictor.