Titre :

High-dimensional Gaussian sampling: a review and a unifying approach based on a stochastic proximal point algorithm

Auteur(s) :

Vono, Maxime [Auteur]
Signal et Communications [IRIT-SC]
Huawei Technologies France
Dobigeon, Nicolas [Auteur]
Institut universitaire de France [IUF]
Signal et Communications [IRIT-SC]
Chainais, Pierre [Auteur]
Centre de Recherche Réseau Image SysTème Architecture et MuLtimédia [CRISTAL]

Titre de la revue :

SIAM Review

Pagination :

3-56

Éditeur :

Society for Industrial and Applied Mathematics

Date de publication :

2022-02

ISSN :

0036-1445

Discipline(s) HAL :

Informatique [cs]/Intelligence artificielle [cs.AI]
Informatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV]
Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
Informatique [cs]/Apprentissage [cs.LG]
Informatique [cs]/Traitement des images [eess.IV]
Informatique [cs]/Traitement du signal et de l'image [eess.SP]

Résumé en anglais : [en]

Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stake issue. Vanilla Cholesky samplers imply a computational cost and memory requirements which can rapidly become prohibitive in high ...
Lire la suite >Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stake issue. Vanilla Cholesky samplers imply a computational cost and memory requirements which can rapidly become prohibitive in high dimension. To tackle these issues, multiple methods have been proposed from different communities ranging from iterative numerical linear algebra to Markov chain Monte Carlo (MCMC) approaches. Surprisingly, no complete review and comparison of these methods have been conducted. This paper aims at reviewing all these approaches by pointing out their differences, close relations, benefits and limitations. In addition to this state of the art, this paper proposes a unifying Gaussian simulation framework by deriving a stochastic counterpart of the celebrated proximal point algorithm in optimization. This framework offers a novel and unifying revisit of most of the existing MCMC approaches while extending them. Guidelines to choose the appropriate Gaussian simulation method for a given sampling problem in high dimension are proposed and illustrated with numerical examples.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Artificial and Natural Intelligence Toulouse Institute

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL