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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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    6. Max H. Farrell, 2013. "Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations," Papers 1309.4686, arXiv.org, revised Feb 2018.
    7. Didier Nibbering, 2023. "A High-dimensional Multinomial Logit Model," Monash Econometrics and Business Statistics Working Papers 19/23, Monash University, Department of Econometrics and Business Statistics.
    8. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    9. Stolbov, Mikhail & Shchepeleva, Maria, 2020. "What predicts the legal status of cryptocurrencies?," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 273-291.
    10. Park, Beomjin & Park, Changyi, 2023. "Multiclass Laplacian support vector machine with functional analysis of variance decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    11. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    12. Hai-Bin Zhang & Jiao-Jiao Jiang & Yun-Bin Zhao, 2015. "On the proximal Landweber Newton method for a class of nonsmooth convex problems," Computational Optimization and Applications, Springer, vol. 61(1), pages 79-99, May.
    13. Piotr Swierkowski & Adrian Barnett, 2018. "Identification of hospital cost drivers using sparse group lasso," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.

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