Accéder directement au contenu Accéder directement à la navigation
Pré-publication, Document de travail

Factored couplings in multi-marginal optimal transport via difference of convex programming

Abstract : Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build upon a traditional OT setup with two distributions, while leaving a more general multi-marginal OT formulation somewhat unexplored. In this paper, we study the multi-marginal OT (MMOT) problem and unify several popular OT methods under its umbrella by promoting structural information on the coupling. We show that incorporating such structural information into MMOT results in an instance of a different of convex (DC) programming problem allowing us to solve it numerically. Despite high computational cost of the latter procedure, the solutions provided by DC optimization are usually as qualitative as those obtained using currently employed optimization schemes.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-03381198
Contributeur : Tran Quang Huy Connectez-vous pour contacter le contributeur
Soumis le : lundi 18 octobre 2021 - 09:12:43
Dernière modification le : samedi 25 juin 2022 - 10:57:35

Fichier

Factored couplings in multi-ma...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-03381198, version 2
  • ARXIV : 2110.00629

Citation

Huy Quang Tran, Hicham Janati, Ievgen Redko, Rémi Flamary, Nicolas Courty. Factored couplings in multi-marginal optimal transport via difference of convex programming. 2021. ⟨hal-03381198v2⟩

Partager

Métriques

Consultations de la notice

59

Téléchargements de fichiers

10