8 papers
Learning Monge maps with constrained drifting models
Théo Dumont, Théo Lacombe, François-Xavier Vialard
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold.…
Persistence-based topological optimization: a survey
Mathieu Carriere, Yuichi Ike, Théo Lacombe +1
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can…
The Wasserstein gradient flow of the Sinkhorn divergence between Gaussian distributions
Mathis Hardion, Théo Lacombe
We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the…
Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approach
Marc Janthial, Théo Lacombe
The Sliced Wasserstein Kernel (SWK) for persistence diagrams was introduced in (Carri{è}re et al. 2017) as a powerful tool to implicitly embed persistence diagrams in a Hilbert sp…
On the existence of Monge maps for the Gromov-Wasserstein problem
Théo Dumont, Théo Lacombe, François-Xavier Vialard
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipp…
Diffeomorphic interpolation for efficient persistence-based topological optimization
Mathieu Carriere, Marc Theveneau, Théo Lacombe
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functio…