A talk by Moritz Piening (Mathematics, Technische Universität Berlin)

Wasserstein distances define metrics between probability measures on arbitrary metric spaces, including measures over measures. In this talk, we focus on the computation of the resulting Wasserstein-over-Wasserstein (WoW) distance and its connection to the Gromov–Wasserstein (GW) distance, a metric between arbitrary geometries. To mitigate the computational cost of WoW and GW, we consider slicing algorithms based on random one-dimensional projections. Leveraging the isometry between the one-dimensional Wasserstein space and quantile functions in the space of square-integrable functions, we construct slicing procedures for both WoW and GW. Finally, we present exemplary applications in shape analysis and point cloud comparison.

If you want to speak with Moritz, please contact koharu.komiyama@oist.jp