IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v31y2016i3d10.1007_s00180-016-0658-2.html
   My bibliography  Save this article

Random Subspace Method for high-dimensional regression with the R package regRSM

Author

Listed:
  • Paweł Teisseyre

    (Polish Academy of Sciences)

  • Robert A. Kłopotek

    (Polish Academy of Sciences)

  • Jan Mielniczuk

    (Polish Academy of Sciences
    Warsaw University of Technology)

Abstract

Model selection and variable importance assessment in high-dimensional regression are among the most important tasks in contemporary applied statistics. In our procedure, implemented in the package regRSM, the Random Subspace Method (RSM) is used to construct a variable importance measure. The variables are ordered with respect to the measures computed in the first step using the RSM and then, from the hierarchical list of models given by the ordering, the final subset of variables is chosen using information criteria or validation set. Modifications of the original method such as the weighted Random Subspace Method and the version with initial screening of redundant variables are discussed. We developed parallel implementations which enable to reduce the computation time significantly. In this paper, we give a brief overview of the methodology, demonstrate the package’s functionality and present a comparative study of the proposed algorithm and the competitive methods like lasso or CAR scores. In the performance tests the computational times for parallel implementations are compared.

Suggested Citation

  • Paweł Teisseyre & Robert A. Kłopotek & Jan Mielniczuk, 2016. "Random Subspace Method for high-dimensional regression with the R package regRSM," Computational Statistics, Springer, vol. 31(3), pages 943-972, September.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:3:d:10.1007_s00180-016-0658-2
    DOI: 10.1007/s00180-016-0658-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0658-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-016-0658-2?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. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    3. Mielniczuk, Jan & Teisseyre, Paweł, 2014. "Using random subspace method for prediction and variable importance assessment in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 725-742.
    4. Kuhn, Max, 2008. "Building Predictive Models in R Using the caret Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i05).
    5. Zuber Verena & Strimmer Korbinian, 2011. "High-Dimensional Regression and Variable Selection Using CAR Scores," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, July.
    6. Ian T. Jolliffe, 1982. "A Note on the Use of Principal Components in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 300-303, November.
    7. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    8. Yingying Fan & Cheng Yong Tang, 2013. "Tuning parameter selection in high dimensional penalized likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 531-552, June.
    9. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    10. Jie Cheng & Elizaveta Levina & Pei Wang & Ji Zhu, 2014. "A sparse ising model with covariates," Biometrics, The International Biometric Society, vol. 70(4), pages 943-953, December.
    11. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    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. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    2. Tomasz Górecki & Łukasz Smaga, 2019. "fdANOVA: an R software package for analysis of variance for univariate and multivariate functional data," Computational Statistics, Springer, vol. 34(2), pages 571-597, June.

    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. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    2. She, Yiyuan, 2012. "An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2976-2990.
    3. Zhihua Sun & Yi Liu & Kani Chen & Gang Li, 2022. "Broken adaptive ridge regression for right-censored survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 69-91, February.
    4. Jian Huang & Yuling Jiao & Lican Kang & Jin Liu & Yanyan Liu & Xiliang Lu, 2022. "GSDAR: a fast Newton algorithm for $$\ell _0$$ ℓ 0 regularized generalized linear models with statistical guarantee," Computational Statistics, Springer, vol. 37(1), pages 507-533, March.
    5. Štefan Lyócsa & Petra Vašaničová & Branka Hadji Misheva & Marko Dávid Vateha, 2022. "Default or profit scoring credit systems? Evidence from European and US peer-to-peer lending markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    6. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    7. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2015. "Sparse principal component regression with adaptive loading," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 192-203.
    8. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    9. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    10. Zeng, Yaohui & Yang, Tianbao & Breheny, Patrick, 2021. "Hybrid safe–strong rules for efficient optimization in lasso-type problems," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    11. Kimia Keshanian & Daniel Zantedeschi & Kaushik Dutta, 2022. "Features Selection as a Nash-Bargaining Solution: Applications in Online Advertising and Information Systems," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2485-2501, September.
    12. Achim Ahrens & Christian B. Hansen & Mark E. Schaffer, 2020. "lassopack: Model selection and prediction with regularized regression in Stata," Stata Journal, StataCorp LP, vol. 20(1), pages 176-235, March.
    13. Mishra, Aditya & Dey, Dipak K. & Chen, Yong & Chen, Kun, 2021. "Generalized co-sparse factor regression," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    14. Zakariya Yahya Algamal & Muhammad Hisyam Lee, 2019. "A two-stage sparse logistic regression for optimal gene selection in high-dimensional microarray data classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 753-771, September.
    15. Soyeon Kim & Veerabhadran Baladandayuthapani & J. Jack Lee, 2017. "Prediction-Oriented Marker Selection (PROMISE): With Application to High-Dimensional Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 217-245, June.
    16. Ruggieri, Eric & Lawrence, Charles E., 2012. "On efficient calculations for Bayesian variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1319-1332.
    17. Armin Rauschenberger & Iuliana Ciocănea-Teodorescu & Marianne A. Jonker & Renée X. Menezes & Mark A. Wiel, 2020. "Sparse classification with paired covariates," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 571-588, September.
    18. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    20. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.

    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:spr:compst:v:31:y:2016:i:3:d:10.1007_s00180-016-0658-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.