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

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

Standard

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

Harvard

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.

APA

Mallasto, A., & Feragen, A. (2017). Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes. In I. Guyon, U. V. 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

Vancouver

Mallasto A, Feragen A. Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes. In Guyon I, Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R, editors, Neural Information Processing Systems 2017. NIPS Proceedings. 2017. (Advances in Neural Information Processing Systems, Vol. 30).

Author

Mallasto, Anton ; Feragen, Aasa. / Learning from uncertain curves : The 2-Wasserstein metric for Gaussian processes. Neural Information Processing Systems 2017. editor / 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).

Bibtex

@inproceedings{97b311d0d0434dda971a1ee08afaf380,
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.",
author = "Anton Mallasto and Aasa Feragen",
year = "2017",
language = "English",
series = "Advances in Neural Information Processing Systems",
publisher = "NIPS Proceedings",
editor = "I. Guyon and Luxburg, {U. V.} and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett",
booktitle = "Neural Information Processing Systems 2017",
note = "null ; Conference date: 04-12-2017 Through 09-12-2017",

}

RIS

TY - GEN

T1 - Learning from uncertain curves

AU - Mallasto, Anton

AU - Feragen, Aasa

N1 - Conference code: 31

PY - 2017

Y1 - 2017

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.

A2 - Fergus, R.

A2 - Vishwanathan, S.

A2 - Garnett, R.

PB - NIPS Proceedings

Y2 - 4 December 2017 through 9 December 2017

ER -

ID: 194814290