Actually Sparse Variational Gaussian Processes

• URL: http://arxiv.org/abs/2304.05091v1
• Date: Tue, 11 Apr 2023 09:38:58 GMT
• Title: Actually Sparse Variational Gaussian Processes
• Authors: Harry Jake Cunningham, Daniel Augusto de Souza, So Takao, Mark van der Wilk, Marc Peter Deisenroth
• Abstract summary: We propose a new class of inter-domain variational GP constructed by projecting a GP onto a set of compactly supported B-spline basis functions. This allows us to very efficiently model fast-varying spatial phenomena with tens of thousands of inducing variables.
• Score: 20.71289963037696
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables designed to summarise the data. In practice however, for large datasets requiring many inducing variables, such as low-lengthscale spatial data, even sparse GPs can become computationally expensive, limited by the number of inducing variables one can use. In this work, we propose a new class of inter-domain variational GP, constructed by projecting a GP onto a set of compactly supported B-spline basis functions. The key benefit of our approach is that the compact support of the B-spline basis functions admits the use of sparse linear algebra to significantly speed up matrix operations and drastically reduce the memory footprint. This allows us to very efficiently model fast-varying spatial phenomena with tens of thousands of inducing variables, where previous approaches failed.

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