Hutchinson, Michael;
Terenin, Alexander;
Borovitskiy, Viacheslav;
Takao, So;
Teh, Yee Whye;
Deisenroth, Marc Peter;
(2021)
Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels.
In: Ranzato, Marc'Aurelio and Beygelzimer, Alina and Dauphin, Yann N and Liang, Percy and Vaughan, Jennifer Wortman, (eds.)
Proccedings of the 35th Conference on Neural Information Processing Systems (NeurIPS 2021).
(pp. pp. 17160-17169).
NeurIPS 2021
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Abstract
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian processes in novel areas of science, a rapidly-growing line of research has focused on constructively extending these models to handle non-Euclidean domains, including Riemannian manifolds, such as spheres and tori. We propose techniques that generalize this class to model vector fields on Riemannian manifolds, which are important in a number of application areas in the physical sciences. To do so, we present a general recipe for constructing gauge independent kernels, which induce Gaussian vector fields, i.e. vector-valued Gaussian processes coherent withgeometry, from scalar-valued Riemannian kernels. We extend standard Gaussian process training methods, such as variational inference, to this setting. This enables vector-valued Gaussian processes on Riemannian manifolds to be trained using standard methods and makes them accessible to machine learning practitioners.
| Type: | Proceedings paper |
|---|---|
| Title: | Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels |
| Event: | 35th Conference on Neural Information Processing Systems (NeurIPS 2021) |
| ISBN-13: | 9781713845393 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.neurips.cc/paper_files/paper/2... |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10181903 |
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