Learning from graphs with structural variation

Rune Kok Nielsen; Andreas Nugaard Holm; Aasa Feragen

Learning from graphs with structural variation

Rune Kok Nielsen, Andreas Nugaard Holm, Aasa Feragen

Department of Computer Science

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	5
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

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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Learning from graphs with structural variation. / Nielsen, Rune Kok; Holm, Andreas Nugaard; 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

Nielsen, RK, Holm, AN & Feragen, A 2017, Learning from graphs with structural variation. 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 graphs with structural variation",

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year = "2017",

language = "English",

series = "Advances in Neural Information Processing Systems",

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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.

A2 - Fergus, R.

A2 - Vishwanathan, S.

A2 - Garnett, R.

PB - NIPS Proceedings

T2 - 31st Annual Conference on Neural Information Processing Systems

Y2 - 4 December 2017 through 9 December 2017

ER -

Learning from graphs with structural variation

Abstract

Conference

UN SDGs

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