Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

Anton Mallasto; Aasa Feragen

Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

Anton Mallasto, Aasa Feragen

Datalogisk Institut

15 Citationer (Scopus)

Abstract

We introduce a novel framework for statistical analysis of populations of nondegenerate
Gaussian processes (GPs), which are natural representations of uncertain
curves. This allows inherent variation or uncertainty in function-valued data to be
properly incorporated in the population analysis. Using the 2-Wasserstein metric we
geometrize the space of GPs with L2 mean and covariance functions over compact
index spaces. We prove uniqueness of the barycenter of a population of GPs, as well
as convergence of the metric and the barycenter of their finite-dimensional counterparts.
This justifies practical computations. Finally, we demonstrate our framework
through experimental validation on GP datasets representing brain connectivity and
climate development. A MATLAB library for relevant computations will be published
at https://sites.google.com/view/antonmallasto/software.

Originalsprog	Engelsk
Titel	Neural Information Processing Systems 2017
Redaktører	I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett
Antal sider	11
Forlag	NIPS Proceedings
Publikationsdato	2017
Status	Udgivet - 2017
Begivenhed	31st Annual Conference on Neural Information Processing Systems - Long Beach, USA Varighed: 4 dec. 2017 → 9 dec. 2017 Konferencens nummer: 31

Konference

Konference	31st Annual Conference on Neural Information Processing Systems
Nummer	31
Land/Område	USA
By	Long Beach
Periode	04/12/2017 → 09/12/2017

Navn	Advances in Neural Information Processing Systems
Vol/bind	30
ISSN	1049-5258

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Citationsformater

Learning from uncertain curves : The 2-Wasserstein metric for Gaussian processes. / Mallasto, Anton; Feragen, Aasa.

Neural Information Processing Systems 2017. red. / I. Guyon; U. V. Luxburg; S. Bengio; H. Wallach; R. Fergus; S. Vishwanathan; R. Garnett. NIPS Proceedings, 2017. (Advances in Neural Information Processing Systems, Bind 30).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Mallasto, A & Feragen, A 2017, Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes. i I Guyon, UV Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan & R Garnett (red), Neural Information Processing Systems 2017. NIPS Proceedings, Advances in Neural Information Processing Systems, bind 30, 31st Annual Conference on Neural Information Processing Systems, Long Beach, California, USA, 04/12/2017.

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title = "Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes",

abstract = "We introduce a novel framework for statistical analysis of populations of nondegenerateGaussian processes (GPs), which are natural representations of uncertaincurves. This allows inherent variation or uncertainty in function-valued data to beproperly incorporated in the population analysis. Using the 2-Wasserstein metric wegeometrize the space of GPs with L2 mean and covariance functions over compactindex spaces. We prove uniqueness of the barycenter of a population of GPs, as wellas convergence of the metric and the barycenter of their finite-dimensional counterparts.This justifies practical computations. Finally, we demonstrate our frameworkthrough experimental validation on GP datasets representing brain connectivity andclimate development. A MATLAB library for relevant computations will be publishedat https://sites.google.com/view/antonmallasto/software.",

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language = "English",

series = "Advances in Neural Information Processing Systems",

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AU - Feragen, Aasa

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N2 - We introduce a novel framework for statistical analysis of populations of nondegenerateGaussian processes (GPs), which are natural representations of uncertaincurves. This allows inherent variation or uncertainty in function-valued data to beproperly incorporated in the population analysis. Using the 2-Wasserstein metric wegeometrize the space of GPs with L2 mean and covariance functions over compactindex spaces. We prove uniqueness of the barycenter of a population of GPs, as wellas convergence of the metric and the barycenter of their finite-dimensional counterparts.This justifies practical computations. Finally, we demonstrate our frameworkthrough experimental validation on GP datasets representing brain connectivity andclimate development. A MATLAB library for relevant computations will be publishedat https://sites.google.com/view/antonmallasto/software.

AB - We introduce a novel framework for statistical analysis of populations of nondegenerateGaussian processes (GPs), which are natural representations of uncertaincurves. This allows inherent variation or uncertainty in function-valued data to beproperly incorporated in the population analysis. Using the 2-Wasserstein metric wegeometrize the space of GPs with L2 mean and covariance functions over compactindex spaces. We prove uniqueness of the barycenter of a population of GPs, as wellas convergence of the metric and the barycenter of their finite-dimensional counterparts.This justifies practical computations. Finally, we demonstrate our frameworkthrough experimental validation on GP datasets representing brain connectivity andclimate development. A MATLAB library for relevant computations will be publishedat https://sites.google.com/view/antonmallasto/software.

M3 - Article in proceedings

T3 - Advances in Neural Information Processing Systems

BT - Neural Information Processing Systems 2017

A2 - Guyon, I.

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Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes

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