?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Vector-valued+Gaussian+Processes+on+Riemannian+Manifolds+via+Gauge+Independent+Projected+Kernels&rft.creator=Hutchinson%2C+Michael&rft.creator=Terenin%2C+Alexander&rft.creator=Borovitskiy%2C+Viacheslav&rft.creator=Takao%2C+So&rft.creator=Teh%2C+Yee+Whye&rft.creator=Deisenroth%2C+Marc+Peter&rft.description=Gaussian+processes+are+machine+learning+models+capable+of+learning+unknown+functions+in+a+way+that+represents+uncertainty%2C+thereby+facilitating+construction+of+optimal+decision-making+systems.+Motivated+by+a+desire+to+deploy+Gaussian+processes+in+novel+areas+of+science%2C+a+rapidly-growing+line+of+research+has+focused+on+constructively+extending+these+models+to+handle+non-Euclidean+domains%2C+including+Riemannian+manifolds%2C+such+as+spheres+and+tori.+We+propose+techniques+that+generalize+this+class+to+model+vector+fields+on+Riemannian+manifolds%2C+which+are+important+in+a+number+of+application+areas+in+the+physical+sciences.+To+do+so%2C+we+present+a+general+recipe+for+constructing+gauge+independent+kernels%2C+which+induce+Gaussian+vector+fields%2C+i.e.+vector-valued+Gaussian+processes+coherent+withgeometry%2C+from+scalar-valued+Riemannian+kernels.+We+extend+standard+Gaussian+process+training+methods%2C+such+as+variational+inference%2C+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.&rft.publisher=NeurIPS+2021&rft.contributor=Ranzato%2C+Marc'Aurelio&rft.contributor=Beygelzimer%2C+Alina&rft.contributor=Dauphin%2C+Yann+N&rft.contributor=Liang%2C+Percy&rft.contributor=Vaughan%2C+Jennifer+Wortman&rft.date=2021&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A+Ranzato%2C+Marc'Aurelio+and+Beygelzimer%2C+Alina+and+Dauphin%2C+Yann+N+and+Liang%2C+Percy+and+Vaughan%2C+Jennifer+Wortman%2C+(eds.)+Proccedings+of+the+35th+Conference+on+Neural+Information+Processing+Systems+(NeurIPS+2021).++(pp.+pp.+17160-17169).++NeurIPS+2021+(2021)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10181903%2F1%2F2110.14423.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10181903%2F&rft.rights=open