Scalable exact inference in multi-output Gaussian processes

Wessel Bruinsma*, Eric Perim, Will Tebbutt, Scott Hosking, Arno Solin, Richard E. Turner

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is their computational scaling O(n3p3), which is cubic in the number of both inputs n (e.g., time points or locations) and outputs p. For this reason, a popular class of MOGPs assumes that the data live around a low-dimensional linear subspace, reducing the complexity to O(n3m3). However, this cost is still cubic in the dimensionality of the subspace m, which is still prohibitively expensive for many applications. We propose the use of a sufficient statistic of the data to accelerate inference and learning in MOGPs with orthogonal bases. The method achieves linear scaling in m in practice, allowing these models to scale to large m without sacrificing significant expressivity or requiring approximation. This advance opens up a wide range of real-world tasks and can be combined with existing GP approximations in a plug-and-play way. We demonstrate the efficacy of the method on various synthetic and real-world data sets.
Original languageEnglish
Title of host publicationProceedings of the 37th International Conference on Machine Learning
Pages1190-1201
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Machine Learning - Vienna, Austria
Duration: 12 Jul 202018 Jul 2020
Conference number: 37

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume119
ISSN (Electronic)2640-3498

Conference

ConferenceInternational Conference on Machine Learning
Abbreviated titleICML
Country/TerritoryAustria
CityVienna
Period12/07/202018/07/2020

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