IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v137y2019icp195-210.html
   My bibliography  Save this article

Empirical Bayes matrix completion

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300556
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.02.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Takeru Matsuda & Fumiyasu Komaki, 2015. "Singular value shrinkage priors for Bayesian prediction," Biometrika, Biometrika Trust, vol. 102(4), pages 843-854.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Hassairi, Abdelhamid & Roula, Amel, 2022. "Exponential and related probability distributions on symmetric matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).
    4. Nardo, Elvira Di, 2020. "Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    5. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate stochastic volatility with co-heteroscedasticity," CAMA Working Papers 2018-52, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    6. Mark Bognanni, 2018. "A Class of Time-Varying Parameter Structural VARs for Inference under Exact or Set Identification," Working Papers (Old Series) 1811, Federal Reserve Bank of Cleveland.
    7. Matsuda, Takeru & Strawderman, William E., 2019. "Improved loss estimation for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 300-311.
    8. Shokofeh Zinodiny & Saralees Nadarajah, 2022. "Matrix Variate Two-Sided Power Distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 179-194, March.
    9. Dette, Holger & Tomecki, Dominik, 2019. "Determinants of block Hankel matrices for random matrix-valued measures," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5200-5235.
    10. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.
    11. Saralees Nadarajah, 2009. "A bivariate distribution with gamma and beta marginals with application to drought data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(3), pages 277-301.
    12. Alfelt, Gustav & Bodnar, Taras & Javed, Farrukh & Tyrcha, Joanna, 2020. "Singular conditional autoregressive Wishart model for realized covariance matrices," Working Papers 2021:1, Örebro University, School of Business.
    13. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Apr 2023.
    14. Bauder, David & Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2020. "Bayesian inference of the multi-period optimal portfolio for an exponential utility," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    15. Wang, Dong & Liu, Xialu & Chen, Rong, 2019. "Factor models for matrix-valued high-dimensional time series," Journal of Econometrics, Elsevier, vol. 208(1), pages 231-248.
    16. Daya K. Nagar & Raúl Alejandro Morán-Vásquez & Arjun K. Gupta, 2015. "Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-15, January.
    17. Li, Xiao, 2024. "Nearly minimax empirical Bayesian prediction of independent Poisson observables," Statistics & Probability Letters, Elsevier, vol. 208(C).
    18. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    19. Phong, Duong Thanh & Thu, Pham-Gia & Thanh, Dinh Ngoc, 2019. "Exact distribution of the non-central Wilks’s statistic of the second kind," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 80-89.
    20. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2017. "Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 138-150.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:195-210. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.