Learning from Uncertain Curves: The 2-Wasserstein Metric for Gaussian Processes
Abstract
We introduce a novel framework for statistical analysis of populations of non-degenerate 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.
Cite
Text
Mallasto and Feragen. "Learning from Uncertain Curves: The 2-Wasserstein Metric for Gaussian Processes." Neural Information Processing Systems, 2017.Markdown
[Mallasto and Feragen. "Learning from Uncertain Curves: The 2-Wasserstein Metric for Gaussian Processes." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/mallasto2017neurips-learning/)BibTeX
@inproceedings{mallasto2017neurips-learning,
title = {{Learning from Uncertain Curves: The 2-Wasserstein Metric for Gaussian Processes}},
author = {Mallasto, Anton and Feragen, Aasa},
booktitle = {Neural Information Processing Systems},
year = {2017},
pages = {5660-5670},
url = {https://mlanthology.org/neurips/2017/mallasto2017neurips-learning/}
}