## Kernel Interpolation for Scalable Online Gaussian Processes

### Samuel Stanton · Wesley Maddox · Ian Delbridge · Andrew Gordon Wilson

Keywords: [ Models and Methods ] [ Gaussian Processes ]

[ Abstract ]
Wed 14 Apr 12:45 p.m. PDT — 2:45 p.m. PDT

Abstract: Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential online setting. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $\mathcal{O}(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently reuse computations for constant-time $\mathcal{O}(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting.

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