Stochastic Wasserstein Barycenters

Sebastian Claici, Edward Chien, Justin Solomon
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:999-1008, 2018.

Abstract

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-claici18a, title = {Stochastic {W}asserstein Barycenters}, author = {Claici, Sebastian and Chien, Edward and Solomon, Justin}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {999--1008}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/claici18a/claici18a.pdf}, url = {https://proceedings.mlr.press/v80/claici18a.html}, abstract = {We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.} }
Endnote
%0 Conference Paper %T Stochastic Wasserstein Barycenters %A Sebastian Claici %A Edward Chien %A Justin Solomon %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-claici18a %I PMLR %P 999--1008 %U https://proceedings.mlr.press/v80/claici18a.html %V 80 %X We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and allows the support of the barycenter to be adjusted in each iteration. We tackle the problem without regularization, allowing us to recover a sharp output whose support is contained within the support of the true barycenter. We give examples where our algorithm recovers a more meaningful barycenter than previous work. Our method is versatile and can be extended to applications such as generating super samples from a given distribution and recovering blue noise approximations.
APA
Claici, S., Chien, E. & Solomon, J.. (2018). Stochastic Wasserstein Barycenters. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:999-1008 Available from https://proceedings.mlr.press/v80/claici18a.html.

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