Nonparametric Gaussian Process Covariances via Multidimensional Convolutions

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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, eg 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.
Original languageEnglish
Title of host publicationProceedings of Machine Learning Research
Subtitle of host publicationInternational Conference on Artificial Intelligence and Statistics, 25-27 April 2023, Palau de Congressos, Valencia, Spain
Number of pages15
Publication statusPublished - 20 Aug 2023

Publication series

NameProceedings of Machine Learning Research


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