Learning on mm spaces based on Gromov’s reconstruction theorem

lundi 21 sept. 2026, 14:30 → 15:30 Europe/Paris

Salle Fokko du CLoux, 1er étage du bât Braconnier

In this talk, we focus on the questions of testing and learning for datasets represented by a matrix of pairwise
distances between datapoints. Such datasets can be considered as discrete versions of metric measure spaces
(mm spaces). We recall the Gromov’s mm spaces reconstruction theorem in [1], that states that mm spaces can
be represented by the distribution of pairwise distance matrices. We give an alternative proof to this theorem.
Then we introduce a new metric between mm spaces, based on this theorem, as an alternative to the Gromov-
Wasserstein distance, and prove stability results and in particular parametric rates. As the Gromov-Wasserstein
distance, this metric allows to account for variations of both density and shape of datasets. We provide new
goodness-of-fit and two-sample tests for mm spaces, but also new classification methods for data given by mm
spaces (or pairwise distance matrices), based on this new metric.

References
[1] M. Gromov. Metric structures for Riemannian and non-Riemannian spaces. Modern Birkhäuser Classics, 2007.