Relative-Error Approximation Algorithms for Wasserstein Distance

Develop polynomial-time algorithms that approximate, to a prescribed relative error, the Wasserstein distance (e.g., W_2) between pairs of multivariate probability distributions, in particular extending the techniques developed for total variation distance to the Wasserstein metric.

Background

The paper focuses on total variation distance and achieves relative-error approximation algorithms for multivariate Gaussians; however, many applications use other metrics, notably the Wasserstein distance.

The authors explicitly mention approximations for other notions of distance such as Wasserstein as an open direction, motivating the development of analogous algorithmic frameworks for Wasserstein distance.