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

Department of Computer Science

15 Citations (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.

Original language	English
Title of host publication	Neural Information Processing Systems 2017
Editors	I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett
Number of pages	11
Publisher	NIPS Proceedings
Publication date	2017
Publication status	Published - 2017
Event	31st Annual Conference on Neural Information Processing Systems - Long Beach, United States Duration: 4 Dec 2017 → 9 Dec 2017 Conference number: 31

Conference

Conference	31st Annual Conference on Neural Information Processing Systems
Number	31
Country/Territory	United States
City	Long Beach
Period	04/12/2017 → 09/12/2017

Series	Advances in Neural Information Processing Systems
Volume	30
ISSN	1049-5258

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

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

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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

A2 - Luxburg, U. V.

A2 - Bengio, S.

A2 - Wallach, H.

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A2 - Garnett, R.

PB - NIPS Proceedings

Y2 - 4 December 2017 through 9 December 2017

ER -

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

Abstract

Conference

UN SDGs

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