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

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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 languageEnglish
Title of host publicationNeural Information Processing Systems 2017
EditorsI. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett
Number of pages11
PublisherNIPS Proceedings
Publication date2017
Publication statusPublished - 2017
Event31st Annual Conference on Neural Information Processing Systems - Long Beach, United States
Duration: 4 Dec 20179 Dec 2017
Conference number: 31

Conference

Conference31st Annual Conference on Neural Information Processing Systems
Nummer31
LandUnited States
ByLong Beach
Periode04/12/201709/12/2017
SeriesAdvances in Neural Information Processing Systems
Volume30
ISSN1049-5258

ID: 194814290