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 -