Wrapped Gaussian Process Regression on Riemannian Manifolds

Anton Mallasto; Aasa Feragen

doi:10.1109/CVPR.2018.00585

Wrapped Gaussian Process Regression on Riemannian Manifolds

Anton Mallasto, Aasa Feragen

5 Citations (Scopus)

Abstract

Gaussian process (GP) regression is a powerful tool in non-parametric regression providing uncertainty estimates. However, it is limited to data in vector spaces. In fields such as shape analysis and diffusion tensor imaging, the data often lies on a manifold, making GP regression nonviable, as the resulting predictive distribution does not live in the correct geometric space. We tackle the problem by defining wrapped Gaussian processes (WGPs) on Riemannian manifolds, using the probabilistic setting to generalize GP regression to the context of manifold-valued targets. The method is validated empirically on diffusion weighted imaging (DWI) data, directional data on the sphere and in the Kendall shape space, endorsing WGP regression as an efficient and flexible tool for manifold-valued regression.

Original language	English
Title of host publication	Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
Number of pages	9
Publisher	IEEE
Publication date	2018
Pages	5580-5588
Article number	8578683
ISBN (Electronic)	9781538664209
DOIs	https://doi.org/10.1109/CVPR.2018.00585
Publication status	Published - 2018
Event	31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018 - Salt Lake City, United States Duration: 18 Jun 2018 → 22 Jun 2018

Conference

Conference	31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
Country/Territory	United States
City	Salt Lake City
Period	18/06/2018 → 22/06/2018

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10.1109/CVPR.2018.00585

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Mallasto, A & Feragen, A 2018, Wrapped Gaussian Process Regression on Riemannian Manifolds. in Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018., 8578683, IEEE, pp. 5580-5588, 31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, United States, 18/06/2018. https://doi.org/10.1109/CVPR.2018.00585

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author = "Anton Mallasto and Aasa Feragen",

year = "2018",

doi = "10.1109/CVPR.2018.00585",

language = "English",

pages = "5580--5588",

booktitle = "Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018",

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AB - Gaussian process (GP) regression is a powerful tool in non-parametric regression providing uncertainty estimates. However, it is limited to data in vector spaces. In fields such as shape analysis and diffusion tensor imaging, the data often lies on a manifold, making GP regression nonviable, as the resulting predictive distribution does not live in the correct geometric space. We tackle the problem by defining wrapped Gaussian processes (WGPs) on Riemannian manifolds, using the probabilistic setting to generalize GP regression to the context of manifold-valued targets. The method is validated empirically on diffusion weighted imaging (DWI) data, directional data on the sphere and in the Kendall shape space, endorsing WGP regression as an efficient and flexible tool for manifold-valued regression.

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BT - Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018

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T2 - 31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018

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ER -

Wrapped Gaussian Process Regression on Riemannian Manifolds

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