TY  - GEN
A1  - Hutchinson, Michael
A1  - Terenin, Alexander
A1  - Borovitskiy, Viacheslav
A1  - Takao, So
A1  - Teh, Yee Whye
A1  - Deisenroth, Marc Peter
T3  - Advances in Neural Information Processing Systems
N2  - 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.
ID  - discovery10181903
UR  - https://proceedings.neurips.cc/paper_files/paper/2021/hash/8e7991af8afa942dc572950e01177da5-Abstract.html
PB  - NeurIPS 2021
N1  - This version is the version of record. For information on re-use, please refer to the publisher?s terms and conditions.
TI  - Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels
AV  - public
SP  - 17160
Y1  - 2021///
EP  - 17169
ER  -