A Proximal Point Algorithm for Minimum Divergence Estimators with Application to Mixture Models

Abstract : Estimators derived from a divergence criterion such as ϕ−divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called minimum dual ϕ–divergence estimator (MDϕDE), an estimator built using a dual representation of ϕ–divergences. We present in this paper an iterative proximal point algorithm that permits the calculation of such an estimator. The algorithm contains by construction the well-known Expectation Maximization (EM) algorithm. Our work is based on the paper of Tseng on the likelihood function. We provide some convergence properties by adapting the ideas of Tseng. We improve Tseng's results by relaxing the identifiability condition on the proximal term, a condition which is not verified for most mixture models and is hard to be verified for " non mixture " ones. Convergence of the EM algorithm in a two-component Gaussian mixture is discussed in the spirit of our approach. Several experimental results on mixture models are provided to confirm the validity of the approach.
Type de document :
Article dans une revue
Entropy, MDPI, 2016, 18 (8), pp.277. 〈10.3390/e18080277〉
Liste complète des métadonnées

Littérature citée [22 références]  Voir  Masquer  Télécharger

https://hal.sorbonne-universite.fr/hal-01375424
Contributeur : Gestionnaire Hal-Upmc <>
Soumis le : lundi 3 octobre 2016 - 11:00:02
Dernière modification le : jeudi 21 mars 2019 - 13:12:17
Document(s) archivé(s) le : vendredi 3 février 2017 - 13:52:18

Fichier

entropy-18-00277.pdf
Publication financée par une institution

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

Citation

Diaa Al Mohamad, Michel Broniatowski. A Proximal Point Algorithm for Minimum Divergence Estimators with Application to Mixture Models. Entropy, MDPI, 2016, 18 (8), pp.277. 〈10.3390/e18080277〉. 〈hal-01375424〉

Partager

Métriques

Consultations de la notice

262

Téléchargements de fichiers

121