鈥� Gabriel Rioux (Imperial College London, UK)
Title: 鈥淕romov-Wasserstein Distances: Computation and Statistics鈥�
Abstract:
In recent years, the statistical and computational study of optimal transport (OT) has advanced significantly, driven, in part, by its broad applicability across data science, statistics, economics, and physics. While OT distances, such as the Wasserstein metric, are well suited for comparing distributions on the same space and endow the space of probabilities on a given space with a rich geometry, comparing datasets of different types -- such as text and images -- requires specifying an ad hoc cost function, which may fail to capture a meaningful correspondence between data points.
To address this limitation, Gromov-Wasserstein (GW) distances have been proposed as a natural extension of the OT framework for comparing metric measure (mm) spaces based only on their intrinsic structure. Notably, GW distances define a metric on the space of all mm spaces and provide a means by which to align them. Despite their broad applicability to comparing heterogeneous datasets, the statistical and computational study of GW distances remained limited until quite recently.
This talk will outline recent progress in the statistical and computational study of GW distances and will discuss ongoing and future directions for this line of work.
This is joint work with Ziv Goldfeld and Kengo Kato.
馃敆 Zoom:
Meeting ID: 872 4362 3765
