Title :

An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization

Author(s) :

Alquier, Pierre [Auteur]
Centre de Recherche en Économie et Statistique [CREST]
Université Paris-Saclay
Guedj, Benjamin [Auteur]
MOdel for Data Analysis and Learning [MODAL]

Journal title :

Mathematical Methods of Statistics

Pages :

55 - 67

Publisher :

Springer

Publication date :

2017

ISSN :

1066-5307

English keyword(s) :

Oracle inequality
Blockwise coordinate optimization
PAC-Bayesian theory
Gibbs sampler
Non-negative matrix factorization

HAL domain(s) :

Statistiques [stat]/Machine Learning [stat.ML]
Statistiques [stat]/Théorie [stat.TH]
Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

The aim of this paper is to provide some theoretical understanding of Bayesian non-negative matrix factorization methods. We derive an oracle inequality for a quasi-Bayesian estimator. This result holds for a very general ...
Show more >The aim of this paper is to provide some theoretical understanding of Bayesian non-negative matrix factorization methods. We derive an oracle inequality for a quasi-Bayesian estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence. We illustrate our theoretical results with a short numerical study along with a discussion on existing implementations .Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL