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Empirical Bayes matrix completion

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  • Matsuda, Takeru
  • Komaki, Fumiyasu

Abstract

We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris. Since the EB algorithm is derived as the Expectation–Maximization algorithm applied to a simple model, it does not require heuristic parameter tuning other than tolerance. Also, it can account for the heterogeneity in variance of observation noise. Numerical results demonstrate that the EB algorithm attains at least comparable accuracy to existing algorithms for matrices not close to square and that it works particularly well when the rank is relatively large or the proportion of observed entries is small. Application to real data also shows the practical utility of the EB algorithm.

Suggested Citation

  • Matsuda, Takeru & Komaki, Fumiyasu, 2019. "Empirical Bayes matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 195-210.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:195-210
    DOI: 10.1016/j.csda.2019.02.006
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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. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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    Cited by:

    1. Li, Xiao & Matsuda, Takeru & Komaki, Fumiyasu, 2024. "Empirical Bayes Poisson matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    2. T Matsuda & W E Strawderman, 2022. "Estimation under matrix quadratic loss and matrix superharmonicity [Shrinkage estimation with a matrix loss function]," Biometrika, Biometrika Trust, vol. 109(2), pages 503-519.

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