Papers › Scalable Exact Inference in Multi-Output Gaussian Processes

Scalable Exact Inference in Multi-Output Gaussian Processes

14 Nov 2019ICML 2020 1arXiv:1911.06287archive 2025-07-28

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

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(n³ p³), 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(n³ m³). 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.

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