Gromov-Wasserstein Distances between Gaussian Distributions - Archive ouverte HAL Access content directly
Journal Articles Journal of Applied Probability Year : 2022

Gromov-Wasserstein Distances between Gaussian Distributions


The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures living on Euclidean spaces of different dimensions. In this paper, we focus on the Gromov-Wasserstein distance with a ground cost defined as the squared Euclidean distance and we study the form of the optimal plan between Gaussian distributions. We show that when the optimal plan is restricted to Gaussian distributions, the problem has a very simple linear solution, which is also solution of the linear Gromov-Monge problem. We also study the problem without restriction on the optimal plan, and provide lower and upper bounds for the value of the Gromov-Wasserstein distance between Gaussian distributions.
Fichier principal
Vignette du fichier
Gromov_Wasserstein(3).pdf (740.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03197398 , version 1 (13-04-2021)
hal-03197398 , version 2 (16-04-2021)
hal-03197398 , version 3 (24-01-2022)



Antoine Salmona, Julie Delon, Agnès Desolneux. Gromov-Wasserstein Distances between Gaussian Distributions. Journal of Applied Probability, 2022, 59 (4), ⟨10.1017/jpr.2022.16⟩. ⟨hal-03197398v3⟩
556 View
1501 Download



Gmail Facebook Twitter LinkedIn More