Fig. 3.

Error of the Wasserstein distance: We compare the numerical estimation of the Wasserstein distance between two data sets of cardinality N and M. The datasets are sampled from multivariate normal distributions of different dimensionality. They differ in their mean, i.e., a zero vector and a vector filled with ones, but share the covariance matrix $C_{\mathit{ij}}={\delta }_{\mathit{ij}}+0.2·(1-{\delta }_{\mathit{ij}})$. For each combination (N, M), we sample 1000 datasets. The confidence interval in a highlights the area between the first and third quartiles. Numerical computation follows (Flamary et al. 2021; Dutta et al. 2021; Bonneel et al. 2011), the analytic solution was discovered by Dowson and Landau (1982)