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Journal Articles Mathematical Methods of Statistics Year : 2017

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

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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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Dates and versions

hal-01251878 , version 1 (06-01-2016)
hal-01251878 , version 2 (07-06-2016)
hal-01251878 , version 3 (25-08-2016)
hal-01251878 , version 4 (26-06-2018)

Licence

Attribution - NonCommercial - NoDerivatives - CC BY 4.0

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Cite

Pierre Alquier, Benjamin Guedj. An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization. Mathematical Methods of Statistics, 2017, 26 (1), pp.55 - 67. ⟨10.3103/S1066530717010045⟩. ⟨hal-01251878v4⟩
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