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arXiv · 2106.07452

Marginalising over Stationary Kernels with Bayesian Quadrature

Saad Hamid·Sebastian Schulze·Michael A. Osborne·Stephen J. Roberts
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Abstract

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of the maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.

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Saad Hamid, Sebastian Schulze, Michael A. Osborne, Stephen J. Roberts. 2021-06-14. Marginalising over Stationary Kernels with Bayesian Quadrature. https://arxiv.org/abs/2106.07452

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