Subadditivity and optimal matching of unbounded samples - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Subadditivity and optimal matching of unbounded samples

Abstract

We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents $p$ and dimensions $d$. Moreover we identify the exact prefactor when $p\le d$. We cover in particular the Gaussian case, going far beyond the currently known bounds. Our proof technique is based on approximate sub- and super-additivity bounds along a geometric decomposition adapted to some features the density, such as its radial symmetry and its decay at infinity.
Fichier principal
Vignette du fichier
Gaux_final.pdf (477.18 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04639188 , version 1 (08-07-2024)

Identifiers

  • HAL Id : hal-04639188 , version 1

Cite

Emanuele Caglioti, Michael Goldman, Francesca Pieroni, Dario Trevisan. Subadditivity and optimal matching of unbounded samples. 2024. ⟨hal-04639188⟩
0 View
0 Download

Share

Gmail Mastodon Facebook X LinkedIn More