Comparing Metric Spaces (and Molecules) with the Gromov-Wasserstein Metric

Marco Cuturi
Kyoto University

Optimal transport metrics can be used to compare probability measures defined on the same metric space. Recent results show that a computational approach known as entropic regularization can be used to speed up significantly the computation of OT distances, improve their performance in inference tasks, and notably, show that they can be useful in some quantum chemistry tasks. Mémoli introduced almost 10 years ago a generalization of OT metrics which can be used to compare distributions defined on different metric spaces, the Gromov-Wasserstein (GW) distance. I present in this talk new numerical approaches to compute GW distances, using also entropic regularization. I will also show how this technique can be used to compute barycenters of metric spaces and compare molecules.

This is joint work with G. Peyré and J. Solomon.

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