Statistical Theory for Gromov-Wasserstein Distances
KENGO KATO – CORNELL UNIVERSITY
ABSTRACT
The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This property is particularly useful for comparing datasets that naturally admit isomorphic representations, such as unlabeled graphs or objects embedded in space. However, a statistical theory of valid estimation and inference for the GW distance remains largely obscure. In this talk, I will discuss my recent work on statistical aspects of the Gromov-Wasserstein distance, including sample complexity, minimax lower bounds, limiting distributions, and an application to testing for graph isomorphism.