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

Pierre Alquier (1, 2) , Benjamin Guedj (3)

1 CREST - Centre de Recherche en Économie et Statistique
2 Université Paris-Saclay
3 MODAL - MOdel for Data Analysis and Learning

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 .

Mots clés: Non-negative matrix factorization; Gibbs sampler; PAC-Bayesian theory; Oracle inequality; Blockwise coordinate optimization

Domaines: Machine Learning [stat.ML]; Théorie [stat.TH]; Statistiques [math.ST]

Pierre Alquier, Benjamin Guedj. An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization. Mathematical Methods of Statistics, 2017. ⟨hal-01251878v3⟩