Approximation Algorithms for Wasserstein Distance

Develop efficient approximation algorithms for computing the Wasserstein distance between probability distributions given explicit specifications (e.g., parametric forms such as multivariate Gaussians), with provable guarantees similar to those established for total variation distance.

Background

While the paper focuses on TV distance, the authors explicitly identify approximations for other distance notions—particularly the Wasserstein distance—as an open direction.

Wasserstein distance is central in optimal transport, statistics, and machine learning; efficient, guaranteed approximation methods would be valuable across these domains.