Marginalising over Stationary Kernels with Bayesian Quadrature
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.
Cite
@article{arxiv.2106.07452,
title = {Marginalising over Stationary Kernels with Bayesian Quadrature},
author = {Saad Hamid and Sebastian Schulze and Michael A. Osborne and Stephen J. Roberts},
journal= {arXiv preprint arXiv:2106.07452},
year = {2023}
}