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Sparse group lasso and high dimensional multinomial classification

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  • Vincent, Martin
  • Hansen, Niels Richard

Abstract

The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifier. On three different real data examples the multinomial group lasso clearly outperforms multinomial lasso in terms of achieved classification error rate and in terms of including fewer features for the classification. An implementation of the multinomial sparse group lasso algorithm is available in the R package msgl. Its performance scales well with the problem size as illustrated by one of the examples considered—a 50 class classification problem with 10 k features, which amounts to estimating 500 k parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:771-786
    DOI: 10.1016/j.csda.2013.06.004
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    1. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    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. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    4. 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).
    5. Kim, Yongdai & Kwon, Sunghoon & Heun Song, Seuck, 2006. "Multiclass sparse logistic regression for classification of multiple cancer types using gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1643-1655, December.
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