Orthogonal Estimation of Wasserstein Distances

Mark Rowland, Jiri Hron, Yunhao Tang, Krzysztof Choromanski, Tamas Sarlos, Adrian Weller
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:186-195, 2019.

Abstract

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-rowland19a, title = {Orthogonal Estimation of Wasserstein Distances}, author = {Rowland, Mark and Hron, Jiri and Tang, Yunhao and Choromanski, Krzysztof and Sarlos, Tamas and Weller, Adrian}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {186--195}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/rowland19a/rowland19a.pdf}, url = {https://proceedings.mlr.press/v89/rowland19a.html}, abstract = {Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.} }
Endnote
%0 Conference Paper %T Orthogonal Estimation of Wasserstein Distances %A Mark Rowland %A Jiri Hron %A Yunhao Tang %A Krzysztof Choromanski %A Tamas Sarlos %A Adrian Weller %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-rowland19a %I PMLR %P 186--195 %U https://proceedings.mlr.press/v89/rowland19a.html %V 89 %X Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.
APA
Rowland, M., Hron, J., Tang, Y., Choromanski, K., Sarlos, T. & Weller, A.. (2019). Orthogonal Estimation of Wasserstein Distances. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:186-195 Available from https://proceedings.mlr.press/v89/rowland19a.html.

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