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The Higher-Order of Adaptive Lasso and Elastic Net Methods for Classification on High Dimensional Data

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  • Autcha Araveeporn

    (Department of Statistics, King Mongkut’s Institute of Technology Ladkrabang, School of Science, Bangkok 10520, Thailand)

Abstract

The lasso and elastic net methods are the popular technique for parameter estimation and variable selection. Moreover, the adaptive lasso and elastic net methods use the adaptive weights on the penalty function based on the lasso and elastic net estimates. The adaptive weight is related to the power order of the estimator. Normally, these methods focus to estimate parameters in terms of linear regression models that are based on the dependent variable and independent variable as a continuous scale. In this paper, we compare the lasso and elastic net methods and the higher-order of the adaptive lasso and adaptive elastic net methods for classification on high dimensional data. The classification is used to classify the categorical data for dependent variable dependent on the independent variables, which is called the logistic regression model. The categorical data are considered a binary variable, and the independent variables are used as the continuous variable. The high dimensional data are represented when the number of independent variables is higher than the sample sizes. For this research, the simulation of the logistic regression is considered as the binary dependent variable and 20, 30, 40, and 50 as the independent variables when the sample sizes are less than the number of the independent variables. The independent variables are generated from normal distribution on several variances, and the dependent variables are obtained from the probability of logit function and transforming it to predict the binary data. For application in real data, we express the classification of the type of leukemia as the dependent variables and the subset of gene expression as the independent variables. The criterion of these methods is to compare by the average percentage of predicted accuracy value. The results are found that the higher-order of adaptive lasso method is satisfied with large dispersion, but the higher-order of adaptive elastic net method outperforms on small dispersion.

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  • Autcha Araveeporn, 2021. "The Higher-Order of Adaptive Lasso and Elastic Net Methods for Classification on High Dimensional Data," Mathematics, MDPI, vol. 9(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1091-:d:553022
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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