Christoph Weitkamp

• 
  Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference
  Christoph Weitkamp
  In this talk, we present a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently computable symptotic statistical test for pose invariant object discrimination. This is based on an empirical version of a ß- trimmed lower bound of the Gromov-Wasserstein distance. We derive for ß € [0; 1=2) distributional limits of this test statistic. To this end, we introduce a novel U-type process indexed in ß and show its weak convergence. Finally, the theory developed is investigated in Monte Carlo simulations and applied to structural protein comparisons.