Sign-based Shrinkage Based on an Asymmetric LASSO Penalty

Journal of Data Science

article

Eric S. Kawaguchi¹  Burcu F. Darst¹  Kan Wang²  David V. Conti¹ 

[1] Department of Preventive Medicine, Keck School of Medicine, University of Southern California;Google

关键词: asymmetric Laplace distribution;    high-dimensional statistics;    penalized regression;    quantile regularization;    variable selection;   

DOI  :  10.6339/21-JDS1015

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

Penalized regression provides an automated approach to preform simultaneous variable selection and parameter estimation and is a popular method to analyze high-dimensional data. Since the conception of the LASSO in the mid-to-late 1990s, extensive research has been done to improve penalized regression. The LASSO, and several of its variations, performs penalization symmetrically around zero. Thus, variables with the same magnitude are shrunk the same regardless of the direction of effect. To the best of our knowledge, sign-based shrinkage, preferential shrinkage based on the sign of the coefficients, has yet to be explored under the LASSO framework. We propose a generalization to the LASSO, asymmetric LASSO, that performs sign-based shrinkage. Our method is motivated by placing an asymmetric Laplace prior on the regression coefficients, rather than a symmetric Laplace prior. This corresponds to an asymmetric ${\ell _{1}}$ penalty under the penalized regression framework. In doing so, preferential shrinkage can be performed through an auxiliary tuning parameter that controls the degree of asymmetry. Our numerical studies indicate that the asymmetric LASSO performs better than the LASSO when effect sizes are sign skewed. Furthermore, in the presence of positively-skewed effects, the asymmetric LASSO is comparable to the non-negative LASSO without the need to place ana prioriconstraint on the effect estimates and outperforms the non-negative LASSO when negative effects are also present in the model. A real data example using the breast cancer gene expression data from The Cancer Genome Atlas is also provided, where the asymmetric LASSO identifies two potentially novel gene expressions that are associated withBRCA1with a minor improvement in prediction performance over the LASSO and non-negative LASSO.

【 授权许可】

CC BY