An oracle inequality for quasi-Bayesian nonnegative matrix factorization

Abstract

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods of nonnegative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence.

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Correspondence to P. Alquier.

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Alquier, P., Guedj, B. An oracle inequality for quasi-Bayesian nonnegative matrix factorization. Math. Meth. Stat. 26, 55–67 (2017). https://doi.org/10.3103/S1066530717010045

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Keywords

  • nonnegative matrix factorization
  • oracle inequality
  • PAC-Bayesian bounds

2010 Mathematics Subject Classification

  • primary 62H99
  • secondary 62F35
  • 68T05
  • 65C05