A Sharp Oracle Inequality for Bayesian Non-Negative Matrix Factorization

The aim of this paper is to provide some theoretical understanding of Bayesian non-negative matrix factorization methods. We prove a sharp 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.