Centered plug-in estimation of Wasserstein distances

Understand

The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative.

• We eliminate most of this bias using a simple centering procedure based on linear combinations.
• We construct a pair of centered plug-in estimators that decrease with the true Wasserstein distance, and are therefore guaranteed to be informative, for any finite sample size.
• Crucially, we demonstrate that these estimators can often be viewed as complementary upper and lower bounds on the squared Wasserstein distance.