Contraction rates for sparse variational approximations in Gaussian process regression
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866911399702167552 |
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| author | Nieman, Dennis Szabo, Botond van Zanten, Harry |
| author_facet | Nieman, Dennis Szabo, Botond van Zanten, Harry |
| contents | We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009a) and derive sufficient conditions for obtaining contraction rates for the corresponding variational Bayes (VB) posterior. As examples we show that for three particular covariance kernels (Matérn, squared exponential, random series prior) the VB approach can achieve optimal, minimax contraction rates for a sufficiently large number of appropriately chosen inducing variables. The theoretical findings are demonstrated by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10755 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Contraction rates for sparse variational approximations in Gaussian process regression Nieman, Dennis Szabo, Botond van Zanten, Harry Statistics Theory We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009a) and derive sufficient conditions for obtaining contraction rates for the corresponding variational Bayes (VB) posterior. As examples we show that for three particular covariance kernels (Matérn, squared exponential, random series prior) the VB approach can achieve optimal, minimax contraction rates for a sufficiently large number of appropriately chosen inducing variables. The theoretical findings are demonstrated by numerical experiments. |
| title | Contraction rates for sparse variational approximations in Gaussian process regression |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2109.10755 |