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The group lasso for logistic regression

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  • Lukas Meier
  • Sara van de Geer
  • Peter Bühlmann
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    Abstract

    The group lasso is an extension of the lasso to do variable selection on (predefined) groups of variables in linear regression models. The estimates have the attractive property of being invariant under groupwise orthogonal reparameterizations. We extend the group lasso to logistic regression models and present an efficient algorithm, that is especially suitable for high dimensional problems, which can also be applied to generalized linear models to solve the corresponding convex optimization problem. The group lasso estimator for logistic regression is shown to be statistically consistent even if the number of predictors is much larger than sample size but with sparse true underlying structure. We further use a two-stage procedure which aims for sparser models than the group lasso, leading to improved prediction performance for some cases. Moreover, owing to the two-stage nature, the estimates can be constructed to be hierarchical. The methods are used on simulated and real data sets about splice site detection in DNA sequences. Copyright 2008 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 70 (2008)
    Issue (Month): 1 ()
    Pages: 53-71

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    Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:53-71

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    Cited by:
    1. Hess, Wolfgang & Persson, Maria & Rubenbauer, Stephanie & Gertheiss, Jan, 2013. "Using Lasso-Type Penalties to Model Time-Varying Covariate Effects in Panel Data Regressions - A Novel Approach Illustrated by the 'Death of Distance' in International Trade," Working Papers 2013:5, Lund University, Department of Economics.
    2. Fellinghauer, Bernd & Bühlmann, Peter & Ryffel, Martin & von Rhein, Michael & Reinhardt, Jan D., 2013. "Stable graphical model estimation with Random Forests for discrete, continuous, and mixed variables," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 132-152.
    3. Silvia Villa & Lorenzo Rosasco & Sofia Mosci & Alessandro Verri, 2014. "Proximal methods for the latent group lasso penalty," Computational Optimization and Applications, Springer, vol. 58(2), pages 381-407, June.
    4. Choi, Hosik & Yeo, Donghwa & Kwon, Sunghoon & Kim, Yongdai, 2011. "Gene selection and prediction for cancer classification using support vector machines with a reject option," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1897-1908, May.
    5. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," Advances in Data Analysis and Classification, Springer, vol. 7(4), pages 393-416, December.
    6. Jerome H. Friedman & Trevor Hastie & Rob Tibshirani, . "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, American Statistical Association, vol. 33(i01).
    7. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    8. A. Antoniadis & I. Gijbels & S. Lambert-Lacroix, 2014. "Penalized estimation in additive varying coefficient models using grouped regularization," Statistical Papers, Springer, vol. 55(3), pages 727-750, August.
    9. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    10. Wolfgang Hess & Maria Persson, 2012. "The duration of trade revisited," Empirical Economics, Springer, vol. 43(3), pages 1083-1107, December.
    11. Nicolas Städler & Peter Bühlmann & Sara Geer, 2010. "ℓ 1 -penalization for mixture regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(2), pages 209-256, August.
    12. 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.
    13. Michele Lalla & Davide Ferrari & Patrizio Frederic, 2012. "Unit nonresponse errors in income surveys: a case study," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(6), pages 1769-1794, October.
    14. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer, vol. 97(4), pages 349-385, October.
    15. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    16. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Centre de Recherche en Economie et Statistique.
    17. Toshio Honda & Wolfgang Karl Härdle, 2012. "Variable selection in Cox regression models with varying coefficients," SFB 649 Discussion Papers SFB649DP2012-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. Wei, Fengrong & Zhu, Hongxiao, 2012. "Group coordinate descent algorithms for nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 316-326.

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