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Empirical Bayes Poisson matrix completion

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  • Li, Xiao
  • Matsuda, Takeru
  • Komaki, Fumiyasu

Abstract

An empirical Bayes method for the Poisson matrix denoising and completion problems is proposed, and a corresponding algorithm called EBPM (Empirical Bayes Poisson Matrix) is developed. This approach is motivated by the non-central singular value shrinkage prior, which was used for the estimation of the mean matrix parameter of a matrix-variate normal distribution. Numerical experiments show that the EBPM algorithm outperforms the common nuclear norm penalized method in both matrix denoising and completion. The EBPM algorithm is highly efficient and does not require heuristic parameter tuning, as opposed to the nuclear norm penalized method, in which the regularization parameter should be selected. The EBPM algorithm also performs better than others in real-data applications.

Suggested Citation

  • Li, Xiao & Matsuda, Takeru & Komaki, Fumiyasu, 2024. "Empirical Bayes Poisson matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:csdana:v:197:y:2024:i:c:s0167947324000604
    DOI: 10.1016/j.csda.2024.107976
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    References listed on IDEAS

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    1. Takeru Matsuda & Fumiyasu Komaki, 2015. "Singular value shrinkage priors for Bayesian prediction," Biometrika, Biometrika Trust, vol. 102(4), pages 843-854.
    2. Matsuda, Takeru & Komaki, Fumiyasu, 2019. "Empirical Bayes matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 195-210.
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    5. Jesse R. Dixon & Siddarth Selvaraj & Feng Yue & Audrey Kim & Yan Li & Yin Shen & Ming Hu & Jun S. Liu & Bing Ren, 2012. "Topological domains in mammalian genomes identified by analysis of chromatin interactions," Nature, Nature, vol. 485(7398), pages 376-380, May.
    6. Bigot, Jérémie & Deledalle, Charles, 2022. "Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
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