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Orthogonal Estimation of Wasserstein Distances

Mark Rowland
Jiri Hron
Yunhao Tang
Adrian Weller
The 22nd International Conference on Artificial Intelligence and Statistics (AISTATS 2019)


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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