Christophe Vauthier

collaborators

4 papers

stat.ML2026

Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions

Christophe Vauthier, Quentin MÃ©rigot, Anna Korba

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along rando…

math.OC2025

Variational Analysis in the Wasserstein Hierarchy

Christophe Vauthier

Let $M$ be a complete connected Riemannian manifold. For $n \geq 0$ , we endow the Wasserstein space $P_{2}^{(n)} (M) = P_{2} (\dots P_{2} (M) \dots)$ , equipped with the Wasserstein distanc…

stat.ML2025

Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis

In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the…

cs.LG2025

Flowing Datasets with Wasserstein over Wasserstein Gradient Flows

Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable grad…