IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v033i01.html
   My bibliography  Save this article

Regularization Paths for Generalized Linear Models via Coordinate Descent

Author

Listed:
  • Friedman, Jerome H.
  • Hastie, Trevor
  • Tibshirani, Rob

Abstract

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multi- nomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Suggested Citation

  • 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).
  • Handle: RePEc:jss:jstsof:v:033:i01
    DOI: http://hdl.handle.net/10.18637/jss.v033.i01
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v033i01/v33i01.pdf
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/glmnet_1.1-4.tar.gz
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/v33i01.R
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/v33i01-timings.zip
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/InternetAd.RData
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/Leukemia.RData
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/NewsGroup.RData
    Download Restriction: no

    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v033i01/Ramaswamy.RData
    Download Restriction: no

    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v033.i01?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
    ---><---

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    3. 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)

    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. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. repec:jss:jstsof:33:i01 is not listed on IDEAS
    3. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.
    4. Yang, Yanlin & Hu, Xuemei & Jiang, Huifeng, 2022. "Group penalized logistic regressions predict up and down trends for stock prices," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    5. Yuan Jiang & Yunxiao He & Heping Zhang, 2016. "Variable Selection With Prior Information for Generalized Linear Models via the Prior LASSO Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 355-376, March.
    6. Zanhua Yin, 2020. "Variable selection for sparse logistic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 821-836, October.
    7. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    8. Yanfang Zhang & Chuanhua Wei & Xiaolin Liu, 2022. "Group Logistic Regression Models with l p,q Regularization," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    9. Young Joo Yoon & Cheolwoo Park & Erik Hofmeister & Sangwook Kang, 2012. "Group variable selection in cardiopulmonary cerebral resuscitation data for veterinary patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1605-1621, January.
    10. Xiaoping Liu & Xiao-Bai Li & Sumit Sarkar, 2023. "Cost-Restricted Feature Selection for Data Acquisition," Management Science, INFORMS, vol. 69(7), pages 3976-3992, July.
    11. Haibin Zhang & Juan Wei & Meixia Li & Jie Zhou & Miantao Chao, 2014. "On proximal gradient method for the convex problems regularized with the group reproducing kernel norm," Journal of Global Optimization, Springer, vol. 58(1), pages 169-188, January.
    12. Chen, Ya & Tsionas, Mike G. & Zelenyuk, Valentin, 2021. "LASSO+DEA for small and big wide data," Omega, Elsevier, vol. 102(C).
    13. Matthew Hindman, 2015. "Building Better Models," The ANNALS of the American Academy of Political and Social Science, , vol. 659(1), pages 48-62, May.
    14. Ya Chen & Mike Tsionas & Valentin Zelenyuk, 2020. "LASSO DEA for small and big data," CEPA Working Papers Series WP092020, School of Economics, University of Queensland, Australia.
    15. Hendrik van der Wurp & Andreas Groll, 2023. "Introducing LASSO-type penalisation to generalised joint regression modelling for count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 127-151, March.
    16. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    17. Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    18. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    19. Yang, Hu & Yi, Danhui, 2015. "Studies of the adaptive network-constrained linear regression and its application," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 40-52.
    20. Wanling Xie & Hu Yang, 2023. "Group sparse recovery via group square-root elastic net and the iterative multivariate thresholding-based algorithm," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 469-507, September.
    21. Mingqiu Wang & Guo-Liang Tian, 2016. "Robust group non-convex estimations for high-dimensional partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 49-67, March.

    More about this item

    Statistics

    Access and download statistics

    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:jss:jstsof:v:033:i01. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.