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

Pierre Alquier 1, 2 Benjamin Guedj 3 
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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 .
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Submitted on : Tuesday, June 26, 2018 - 10:08:04 AM
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Pierre Alquier, Benjamin Guedj. An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2017, 26 (1), pp.55 - 67. ⟨10.3103/S1066530717010045⟩. ⟨hal-01251878v4⟩



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