eprintid: 10181903 rev_number: 7 eprint_status: archive userid: 699 dir: disk0/10/18/19/03 datestamp: 2023-11-24 16:39:16 lastmod: 2023-11-24 16:39:16 status_changed: 2023-11-24 16:39:16 type: proceedings_section metadata_visibility: show sword_depositor: 699 creators_name: Hutchinson, Michael creators_name: Terenin, Alexander creators_name: Borovitskiy, Viacheslav creators_name: Takao, So creators_name: Teh, Yee Whye creators_name: Deisenroth, Marc Peter title: Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2021 date_type: published publisher: NeurIPS 2021 official_url: https://proceedings.neurips.cc/paper_files/paper/2021/hash/8e7991af8afa942dc572950e01177da5-Abstract.html oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2110246 isbn_13: 9781713845393 lyricists_name: Deisenroth, Marc lyricists_id: MDEIS71 actors_name: Deisenroth, Marc actors_id: MDEIS71 actors_role: owner full_text_status: public pres_type: paper series: Advances in Neural Information Processing Systems publication: NeurIPS volume: 34 pagerange: 17160-17169 event_title: 35th Conference on Neural Information Processing Systems (NeurIPS 2021) book_title: Proccedings of the 35th Conference on Neural Information Processing Systems (NeurIPS 2021) editors_name: Ranzato, Marc'Aurelio editors_name: Beygelzimer, Alina editors_name: Dauphin, Yann N editors_name: Liang, Percy editors_name: Vaughan, Jennifer Wortman citation: 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 Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10181903/1/2110.14423.pdf