Ross, M., Smith, M.T. and Álvarez, M.A. (Submitted: 2021) Learning nonparametric Volterra kernels with Gaussian processes. arXiv. (Submitted)
Abstract
This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels model (NVKM). When the input function to the operator is unobserved and has a GP prior, the NVKM constitutes a powerful method for both single and multiple output regression, and can be viewed as a nonlinear and nonparametric latent force model. When the input function is observed, the NVKM can be used to perform Bayesian system identification. We use recent advances in efficient sampling of explicit functions from GPs to map process realisations through the Volterra series without resorting to numerical integration, allowing scalability through doubly stochastic variational inference, and avoiding the need for Gaussian approximations of the output processes. We demonstrate the performance of the model for both multiple output regression and system identification using standard benchmarks.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). For reuse permissions, please contact the Author(s). |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council EP/R034303/1; EP/T00343X/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Jun 2021 08:47 |
Last Modified: | 30 Jun 2021 08:47 |
Published Version: | https://arxiv.org/abs/2106.05582 |
Status: | Submitted |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175742 |