McDonald, T.M., Ross, M., Smith, M.T. et al. (1 more author) (2023) Nonparametric gaussian process covariances via multidimensional convolutions. In: Ruiz, F., Dy, J. and van de Meent, J-W, (eds.) Proceedings of Machine Learning Research. International Conference on Artificial Intelligence and Statistics, 25-27 Apr 2023, Palau de Congressos, Valencia, Spain. ML Research Press , pp. 8279-8293.
Abstract
A key challenge in the practical application of Gaussian processes (GPs) is selecting a proper covariance function. The process convolutions construction of GPs allows some additional flexibility, but still requires choosing a proper smoothing kernel, which is non-trivial. Previous approaches have built covariance functions by using GP priors over the smoothing kernel, and by extension the covariance, as a way to bypass the need to specify it in advance. However, these models have been limited in several ways: they are restricted to single dimensional inputs, e.g. time; they only allow modelling of single outputs and they do not scale to large datasets since inference is not straightforward. In this paper, we introduce a nonparametric process convolution formulation for GPs that alleviates these weaknesses. We achieve this using a functional sampling approach based on Matheron's rule to perform fast sampling using interdomain inducing variables. We test the performance of our model on benchmarks for single output, multi-output and large-scale GP regression, and find that our approach can provide improvements over standard GP models, particularly for larger datasets.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © 2023 The Authors. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Aug 2023 11:03 |
Last Modified: | 16 Aug 2023 11:03 |
Published Version: | https://proceedings.mlr.press/v206/mcdonald23a.htm... |
Status: | Published |
Publisher: | ML Research Press |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202432 |