Orthogonal Estimation of Wasserstein Distances

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Mark Rowland, Jiri Hron, Yunhao Tang, Krzysztof Choromanski, Tamas Sarlos, Adrian Weller ;
Proceedings of Machine Learning Research, 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.

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