Orthogonal Estimation of Wasserstein Distances
This work addresses computational bottlenecks in Wasserstein distance estimation for machine learning applications, but appears incremental as it builds on existing sliced methods.
The paper tackled the problem of efficiently estimating Wasserstein distances by proposing a new variant of sliced Wasserstein distance and studying orthogonal coupling in Monte Carlo estimation, with experimental evaluation in generative modeling and reinforcement learning.
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.