Multinomial Regression with Elastic Net Penalty and Its Grouping Effect in Gene Selection

Chen, Liuyuan; Yang, Jie; Li, Juntao; Wang, Xiaoyu

doi:10.1155/2014/569501

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Simon et al (2013) applied the group LASSO (Yuan and Lin, 2006) by treating the parameters in each class as grouped parameters in the group LASSO. Chen et al (2014) adapted the elastic net (Zou and Hastie, 2005) for imposing group effects on the input variables which often serves to improve prediction accuracy. Tutz et al (2015) developed a category-specific group LASSO for cases when a set of category-specific predictors are available (Tutz, 2011).…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for the non-convex penalized multinomial logistic regression

Kwon

Kim

Lee

2020

CSAM

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In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.

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