Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 8th January of 2024
Place : 3001

Clément BONET (CREST) – Sliced-Wasserstein Distances on Cartan-Hadamard Manifolds

Abstract:

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on these spaces is the Wasserstein distance which suffers from a heavy computational burden. On Euclidean spaces, a popular alternative is the Sliced-Wasserstein distance, which leverages a closed-form solution of the Wasserstein distance in one dimension, but which is not readily available on manifolds. In this work, we derive general constructions of Sliced-Wasserstein distances on Hadamard manifolds, Riemannian manifolds with non-positive curvature, which include among others hyperbolic spaces or the space of symmetric positive definite matrices. Additionally, we derive non-parametric schemes to minimize these new distances by approximating their Wasserstein gradient flows.

Organizers:
Cristina BUTUCEA (CREST), Anna KORBA (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP