Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes

Published: 22 Apr 2024, Last Modified: 22 Apr 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art sparse variational methods have $O(NM^2)$ cost. Recently, methods have been proposed using more sophisticated features; these promise $O(M^3)$ cost, with good performance in low dimensional tasks such as spatial modelling, but they only work with a very limited class of kernels, excluding some of the most commonly used. In this work, we propose integrated Fourier features, which extends these performance benefits to a very broad class of stationary covariance functions. We motivate the method and choice of parameters from a convergence analysis and empirical exploration, and show practical speedup in synthetic and real world spatial regression tasks.
Submission Length: Long submission (more than 12 pages of main content)
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Submission Number: 1518