From the 1 of 9 linked papers with an AI index.
9 papers
Gluing methods for quantitative stability of optimal transport maps
Cyril Letrouit, Quentin Mérigot
The paper proves that the optimal quadratic transport map from a fixed density to a varying measure depends bi‑Hölder continuously on the target measure, establishing quantitative…
Highly Data Parallelizable Estimation of the Sliced-Wasserstein Distance Using Cumulative Distribution Functions
Christophe Vauthier, Quentin Mérigot, 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…
Semi-discrete convex order and Laguerre tessellation fitting
David P. Bourne, Thomas Gallouët, Quentin Mérigot +1
Laguerre tessellations offer an efficient way to parameterize a large class of convex partitions of Euclidean space using only a set of points and scalar weights. For this reason,…
Polynomial diagrams for microstructure modelling
David P. Bourne, Maciej Buze, Thomas Gallouët +1
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to b…
Particle method for a nonlinear multimarginal optimal transport problem
Adrien Cances, Quentin Mérigot, Luca Nenna
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling…
Sharp comparisons between sliced and standard -Wasserstein distances
Guillaume Carlier, Alessio Figalli, Quentin Mérigot +1
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoret…