<> <http://www.w3.org/2000/01/rdf-schema#comment> "The repository administrator has not yet configured an RDF license."^^<http://www.w3.org/2001/XMLSchema#string> .
<> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10181903> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/title> "Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/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."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/date> "2021" .
<https://discovery.ucl.ac.uk/id/document/1680201> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/volume> "34" .
<https://discovery.ucl.ac.uk/id/org/ext-7a2cc8511960a41d6c7b3228bf46afc6> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Organization> .
<https://discovery.ucl.ac.uk/id/org/ext-7a2cc8511960a41d6c7b3228bf46afc6> <http://xmlns.com/foaf/0.1/name> "NeurIPS 2021"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/publisher> <https://discovery.ucl.ac.uk/id/org/ext-7a2cc8511960a41d6c7b3228bf46afc6> .
<https://discovery.ucl.ac.uk/id/publication/ext-9d06671690dff3df7627ebee8b0d62a5> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Collection> .
<https://discovery.ucl.ac.uk/id/publication/ext-9d06671690dff3df7627ebee8b0d62a5> <http://xmlns.com/foaf/0.1/name> "NeurIPS"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/publication/ext-9d06671690dff3df7627ebee8b0d62a5> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/status> <http://purl.org/ontology/bibo/status/published> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_4> <https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_5> <https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#authors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_6> <https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_4> <https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.loc.gov/loc.terms/relators/EDT> <https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/editorList> <https://discovery.ucl.ac.uk/id/eprint/10181903#editors> .
<https://discovery.ucl.ac.uk/id/eprint/10181903#editors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_5> <https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> .
<https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> <http://xmlns.com/foaf/0.1/givenName> "Marc'Aurelio"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> <http://xmlns.com/foaf/0.1/familyName> "Ranzato"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-998179fdde0661ed3d5815a4ed3a8293> <http://xmlns.com/foaf/0.1/name> "Marc'Aurelio Ranzato"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> <http://xmlns.com/foaf/0.1/givenName> "So"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> <http://xmlns.com/foaf/0.1/familyName> "Takao"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-9f3a8dcf9b2b6d64285129707ec31688> <http://xmlns.com/foaf/0.1/name> "So Takao"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> <http://xmlns.com/foaf/0.1/givenName> "Yann N"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> <http://xmlns.com/foaf/0.1/familyName> "Dauphin"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-bd6f5fdb6da58fcabb14f085869f7dbb> <http://xmlns.com/foaf/0.1/name> "Yann N Dauphin"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> <http://xmlns.com/foaf/0.1/givenName> "Viacheslav"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> <http://xmlns.com/foaf/0.1/familyName> "Borovitskiy"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-28d51e0c64d8cc768fa910bb1b1ff7df> <http://xmlns.com/foaf/0.1/name> "Viacheslav Borovitskiy"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> <http://xmlns.com/foaf/0.1/givenName> "Michael"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> <http://xmlns.com/foaf/0.1/familyName> "Hutchinson"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-1b3a3574783c7a68f79cf5b0ef279ba5> <http://xmlns.com/foaf/0.1/name> "Michael Hutchinson"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> <http://xmlns.com/foaf/0.1/givenName> "Alina"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> <http://xmlns.com/foaf/0.1/familyName> "Beygelzimer"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-cf9ac6541e57c9c8dcbdb376d02cd0f3> <http://xmlns.com/foaf/0.1/name> "Alina Beygelzimer"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> <http://xmlns.com/foaf/0.1/givenName> "Marc Peter"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> <http://xmlns.com/foaf/0.1/familyName> "Deisenroth"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-acdfe882dfd5dba73b9c303c4cf6912e> <http://xmlns.com/foaf/0.1/name> "Marc Peter Deisenroth"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> <http://xmlns.com/foaf/0.1/givenName> "Yee Whye"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> <http://xmlns.com/foaf/0.1/familyName> "Teh"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-ead0c8f6fd59f5bf4cff57de5ccde3cc> <http://xmlns.com/foaf/0.1/name> "Yee Whye Teh"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> <http://xmlns.com/foaf/0.1/givenName> "Percy"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> <http://xmlns.com/foaf/0.1/familyName> "Liang"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-e9ddc9f0cff878f118d85af0b47ed684> <http://xmlns.com/foaf/0.1/name> "Percy Liang"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> <http://xmlns.com/foaf/0.1/givenName> "Jennifer Wortman"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> <http://xmlns.com/foaf/0.1/familyName> "Vaughan"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-edfb02e5c5bb894718f6a5fbe4584ed0> <http://xmlns.com/foaf/0.1/name> "Jennifer Wortman Vaughan"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> .
<https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> <http://xmlns.com/foaf/0.1/givenName> "Alexander"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> <http://xmlns.com/foaf/0.1/familyName> "Terenin"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/person/ext-fb981f5d6657df2b4d0711cb0502696e> <http://xmlns.com/foaf/0.1/name> "Alexander Terenin"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/ontology/bibo/presentedAt> <https://discovery.ucl.ac.uk/id/event/ext-c523f3a0bfd2454933ce5b945e05a869> .
<https://discovery.ucl.ac.uk/id/event/ext-c523f3a0bfd2454933ce5b945e05a869> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Conference> .
<https://discovery.ucl.ac.uk/id/event/ext-c523f3a0bfd2454933ce5b945e05a869> <http://purl.org/dc/terms/title> "35th Conference on Neural Information Processing Systems (NeurIPS 2021)"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/EPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/ProceedingsSectionEPrint> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://purl.org/dc/terms/isPartOf> <https://discovery.ucl.ac.uk/id/repository> .
<https://discovery.ucl.ac.uk/id/eprint/10181903> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/1680201> .
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