IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v137y2019icp181-194.html
   My bibliography  Save this article

Lasso ANOVA decompositions for matrix and tensor data

Author

Listed:
  • Griffin, Maryclare
  • Hoff, Peter D.

Abstract

Consider the problem of estimating the entries of an unknown mean matrix or tensor given a single noisy realization. In the matrix case, this problem can be addressed by decomposing the mean matrix into a component that is additive in the rows and columns, i.e. the additive ANOVA decomposition of the mean matrix, plus a matrix of elementwise effects, and assuming that the elementwise effects may be sparse. Accordingly, the mean matrix can be estimated by solving a penalized regression problem, applying a lasso penalty to the elementwise effects. Although solving this penalized regression problem is straightforward, specifying appropriate values of the penalty parameters is not. Leveraging the posterior mode interpretation of the penalized regression problem, moment-based empirical Bayes estimators of the penalty parameters can be defined. Estimation of the mean matrix using these moment-based empirical Bayes estimators can be called LANOVA penalization, and the corresponding estimate of the mean matrix can be called the LANOVA estimate. The empirical Bayes estimators are shown to be consistent. Additionally, LANOVA penalization is extended to accommodate sparsity of row and column effects and to estimate an unknown mean tensor. The behavior of the LANOVA estimate is examined under misspecification of the distribution of the elementwise effects, and LANOVA penalization is applied to several datasets, including a matrix of microarray data, a three-way tensor of fMRI data and a three-way tensor of wheat infection data.

Suggested Citation

  • Griffin, Maryclare & Hoff, Peter D., 2019. "Lasso ANOVA decompositions for matrix and tensor data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 181-194.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:181-194
    DOI: 10.1016/j.csda.2019.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300520
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.02.005?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. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    2. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    3. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    4. Jeffrey T Leek & John D Storey, 2007. "Capturing Heterogeneity in Gene Expression Studies by Surrogate Variable Analysis," PLOS Genetics, Public Library of Science, vol. 3(9), pages 1-12, September.
    5. Saralees Nadarajah, 2006. "On the linear combination of normal and Laplace random variables," Computational Statistics, Springer, vol. 21(1), pages 63-71, March.
    6. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    7. Eloísa Díaz-Francés & José Montoya, 2008. "Correction to “On the linear combination of normal and Laplace random variables”, by Nadarajah, S., Computational Statistics, 2006, 21, 63–71," Computational Statistics, Springer, vol. 23(4), pages 661-666, October.
    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. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.

    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. Jan Schepers & Hans-Hermann Bock & Iven Mechelen, 2017. "Maximal Interaction Two-Mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 49-75, April.
    2. S. Hadasch & J. Forkman & W. A. Malik & H. P. Piepho, 2018. "Weighted Estimation of AMMI and GGE Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 255-275, June.
    3. Li, Chunyu & Lou, Chenxin & Luo, Dan & Xing, Kai, 2021. "Chinese corporate distress prediction using LASSO: The role of earnings management," International Review of Financial Analysis, Elsevier, vol. 76(C).
    4. Anne Musson & Damien Rousselière, 2020. "Exploring the effect of crisis on cooperatives: a Bayesian performance analysis of French craftsmen cooperatives," Applied Economics, Taylor & Francis Journals, vol. 52(25), pages 2657-2678, May.
    5. Prüser, Jan, 2017. "Forecasting US inflation using Markov dimension switching," Ruhr Economic Papers 710, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Armagan, Artin & Dunson, David, 2011. "Sparse variational analysis of linear mixed models for large data sets," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1056-1062, August.
    7. Wang, Hong & Forbes, Catherine S. & Fenech, Jean-Pierre & Vaz, John, 2020. "The determinants of bank loan recovery rates in good times and bad – New evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 875-897.
    8. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    9. Kastner, Gregor, 2019. "Sparse Bayesian time-varying covariance estimation in many dimensions," Journal of Econometrics, Elsevier, vol. 210(1), pages 98-115.
    10. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    11. Martin Feldkircher & Florian Huber & Gary Koop & Michael Pfarrhofer, 2022. "APPROXIMATE BAYESIAN INFERENCE AND FORECASTING IN HUGE‐DIMENSIONAL MULTICOUNTRY VARs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1625-1658, November.
    12. Eliaz, Kfir & Spiegler, Ran, 2022. "On incentive-compatible estimators," Games and Economic Behavior, Elsevier, vol. 132(C), pages 204-220.
    13. Ruixin Guo & Hongtu Zhu & Sy-Miin Chow & Joseph G. Ibrahim, 2012. "Bayesian Lasso for Semiparametric Structural Equation Models," Biometrics, The International Biometric Society, vol. 68(2), pages 567-577, June.
    14. Oguzhan Cepni & I. Ethem Guney & Norman R. Swanson, 2020. "Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 18-36, January.
    15. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    16. Young‐Geun Choi & Lawrence P. Hanrahan & Derek Norton & Ying‐Qi Zhao, 2022. "Simultaneous spatial smoothing and outlier detection using penalized regression, with application to childhood obesity surveillance from electronic health records," Biometrics, The International Biometric Society, vol. 78(1), pages 324-336, March.
    17. Francesca Caselli & Matilde Faralli & Paolo Manasse & Ugo Panizza, 2021. "On the Benefits of Repaying," IMF Working Papers 2021/233, International Monetary Fund.
    18. Mehran Aflakparast & Mathisca de Gunst & Wessel van Wieringen, 2020. "Analysis of Twitter data with the Bayesian fused graphical lasso," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-28, July.
    19. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    20. Korobilis, Dimitris, 2015. "Quantile forecasts of inflation under model uncertainty," MPRA Paper 64341, University Library of Munich, Germany.

    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:181-194. 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.