Distribution of Gaussian process arc lengths
We present the first treatment of the arc length of the Gaussian Process (gp) with more than a single output dimension. Gps are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, wit...
| Główni autorzy: | , , , |
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| Format: | Conference item |
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Proceedings of Machine Learning Research
2017
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| _version_ | 1826268317247078400 |
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| author | Bewsher, J Tosi, A Osborne, M Roberts, S |
| author_facet | Bewsher, J Tosi, A Osborne, M Roberts, S |
| author_sort | Bewsher, J |
| collection | OXFORD |
| description | We present the first treatment of the arc length of the Gaussian Process (gp) with more than a single output dimension. Gps are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary gp with multiple output dimensions. A new method is used to derive the mean of a one-dimensional gp over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued gp in Rn by moment matching the distribution. Numerical simulations confirm our theoretical derivations. |
| first_indexed | 2024-03-06T21:07:50Z |
| format | Conference item |
| id | oxford-uuid:3d10b509-e060-41c9-b021-8f5ee96825fb |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:07:50Z |
| publishDate | 2017 |
| publisher | Proceedings of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:3d10b509-e060-41c9-b021-8f5ee96825fb2022-03-26T14:17:29ZDistribution of Gaussian process arc lengthsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:3d10b509-e060-41c9-b021-8f5ee96825fbSymplectic Elements at OxfordProceedings of Machine Learning Research2017Bewsher, JTosi, AOsborne, MRoberts, SWe present the first treatment of the arc length of the Gaussian Process (gp) with more than a single output dimension. Gps are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary gp with multiple output dimensions. A new method is used to derive the mean of a one-dimensional gp over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued gp in Rn by moment matching the distribution. Numerical simulations confirm our theoretical derivations. |
| spellingShingle | Bewsher, J Tosi, A Osborne, M Roberts, S Distribution of Gaussian process arc lengths |
| title | Distribution of Gaussian process arc lengths |
| title_full | Distribution of Gaussian process arc lengths |
| title_fullStr | Distribution of Gaussian process arc lengths |
| title_full_unstemmed | Distribution of Gaussian process arc lengths |
| title_short | Distribution of Gaussian process arc lengths |
| title_sort | distribution of gaussian process arc lengths |
| work_keys_str_mv | AT bewsherj distributionofgaussianprocessarclengths AT tosia distributionofgaussianprocessarclengths AT osbornem distributionofgaussianprocessarclengths AT robertss distributionofgaussianprocessarclengths |