Sample Complexity for the 2-Gromov-Wasserstein Distance
In this paper, we study the sample complexity of the empirical plug-in estimator for the $2$-Gromov-Wasserstein distance $D_2$ between compactly supported probability measures on Euclidean spaces. Let $\mu$ and $\nu$ be supported on compact subsets of $\mathbb{R}^{d_x}$ and $\mathbb{R}^{d_y}$, respectively, and let $\w...