Zobrazeno 1 - 10
of 123
pro vyhledávání: '"Mérigot Quentin"'
Autor:
Letrouit, Cyril, Mérigot, Quentin
We establish quantitative stability bounds for the quadratic optimal transport map $T_\mu$ between a fixed probability density $\rho$ and a probability measure $\mu$ on $\mathbb{R}^d$. Under general assumptions on $\rho$, we prove that the map $\mu\m
Externí odkaz:
http://arxiv.org/abs/2411.04908
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 75, Pp 1-1 (2023)
Externí odkaz:
https://doaj.org/article/d9cc93cef2794d48867ed4c28cf30e1b
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight H\"older-behavior for this operation under minimal assumptions. Our proof essent
Externí odkaz:
http://arxiv.org/abs/2401.01088
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an equivalence
Externí odkaz:
http://arxiv.org/abs/2211.07694
Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures
Externí odkaz:
http://arxiv.org/abs/2209.10217
The stability of solutions to optimal transport problems under variation of the measures is fundamental from a mathematical viewpoint: it is closely related to the convergence of numerical approaches to solve optimal transport problems and justifies
Externí odkaz:
http://arxiv.org/abs/2207.11042
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a set of $N$ p
Externí odkaz:
http://arxiv.org/abs/2106.07911
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The dissipative coun
Externí odkaz:
http://arxiv.org/abs/2105.12605
This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for the numeri
Externí odkaz:
http://arxiv.org/abs/2104.05682
Autor:
Delalande, Alex, Merigot, Quentin
This work studies the quantitative stability of the quadratic optimal transport map between a fixed probability density $\rho$ and a probability measure $\mu$ on R^d , which we denote T$\mu$. Assuming that the source density $\rho$ is bounded from ab
Externí odkaz:
http://arxiv.org/abs/2103.05934