Kernel Interpolation for Scalable Online Gaussian Processes

03/02/2021

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by   Samuel Stanton, et al.

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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 fashion. However, updating a GP posterior to accommodate even a single new observation after having observed n points incurs at least O(n) computations in the exact setting. We show how to use structured kernel interpolation to efficiently recycle computations for constant-time 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. Code is available at https://github.com/wjmaddox/online_gp.