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Pseudo-marginal Markov Chain Monte Carlo for Nonnegative Matrix Factorization

Abstract

A pseudo-marginal Markov chain Monte Carlo (PMCMC) method is proposed for nonnegative matrix factorization (NMF). The sampler jointly simulates the joint posterior distribution for the nonnegative matrices and the matrix dimensions which indicate the number of the nonnegative components in the NMF model. We show that the PMCMC sampler is a generalization of a version of the reversible jump Markov chain Monte Carlo. An illustrative synthetic data was used to demonstrate the ability of the proposed PMCMC sampler in inferring the nonnegative matrices and as well as the matrix dimensions. The proposed sampler was also applied to a nuclear magnetic resonance spectroscopy data to infer the number of nonnegative components.

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Acknowledgments

This work is supported by the fundamental research funds for the central universities in China.

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Correspondence to Mingjun Zhong.

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Du, J., Zhong, M. Pseudo-marginal Markov Chain Monte Carlo for Nonnegative Matrix Factorization. Neural Process Lett 45, 553–562 (2017). https://doi.org/10.1007/s11063-016-9542-x

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Keywords

  • Pseudo-marginal Markov Chain Monte Carlo
  • Nonnegative matrix factorization
  • Reversible jump Markov Chain Monte Carlo
  • Importance sampling