Browsing by Author "Tebbutt, Will"

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    Combining pseudo-point and state space approximations for sum-separable Gaussian processes
    (PMLR, 2021) Tebbutt, Will; Solin, Arno; Turner, Richard E.; University of Cambridge; Department of Computer Science
    Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support large numbers of off-the-grid spatial data-points and long time-series which is a hallmark of many applications. Pseudo-point approximations, one of the gold-standard methods for scaling GPs to large data sets, are well suited for handling off-the-grid spatial data. However, they cannot handle long temporal observation horizons effectively reverting to cubic computational scaling in the time dimension. State space GP approximations are well suited to handling temporal data, if the temporal GP prior admits a Markov form, leading to linear complexity in the number of temporal observations, but have a cubic spatial cost and cannot handle off-the-grid spatial data. In this work we show that there is a simple and elegant way to combine pseudo-point methods with the state space GP approximation framework to get the best of both worlds. The approach hinges on a surprising conditional independence property which applies to space–time separable GPs. We demonstrate empirically that the combined approach is more scalable and applicable to a greater range of spatio-temporal problems than either method on its own.
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    Scalable exact inference in multi-output Gaussian processes
    (PMLR, 2020) Bruinsma, Wessel; Perim, Eric; Tebbutt, Will; Hosking, Scott; Solin, Arno; Turner, Richard E.; University of Cambridge; Invenia Labs; British Antarctic Survey; Professorship Solin A.; Department of Computer Science
    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.