The Penalized Regression and Penalized Logistic Regression of Lasso and Elastic Net Methods for High- Dimensional Data: A Modelling Approach | Chapter 03 | Innovations in Science and Technology Vol. 3

 The goal of this study is to examine parameter estimation for penalised regression and penalised logistic regression on high-dimensional data using the lasso, elastic net, adaptive lasso, and adaptive elastic net methods. In two linked variables consisting of dependent and independent variables, parameter estimation of the multiple linear regression model is a significant difficulty. Ordinary least squares provides a unique solution when the number of independent variables is smaller than the number of sample sizes. The number of independent variables, on the other hand, is more than the number of sample sizes, resulting in high-dimensional data. In the case of high-dimensional data, standard regression analysis does not estimate the answer to this problem. Penalized regression analysis is used to solve high-dimensional data in order to tackle this challenge. The penalised regression analysis section focuses on estimating the lasso, adaptive lasso, elastic net, and adaptive elastic net methods. The penalty term is added as the scaled sum of the absolute value of the coefficients using the Lasso (least absolute shrinkage and selection operator). On the penalty term, the elastic net combines ridge regression and lasso. For variable selection, the lasso and elastic net approaches can decrease the coefficients. Adaptive weights on the penalty term are used in the adaptive lasso and elastic net methods based on the lasso and elastic net estimates. The adaptive weight is proportional to the estimator's power order. Typically, these methods focus on estimating parameters in linear regression models using a continuous scale for the dependent and independent variables. Furthermore, these algorithms can categorise high-dimensional data using penalised regression based on logistic regression. The penalised logistic regression model is used to categorise categorical data for dependent variables that are dependent on the independent variables. The categorical data is treated as a binary variable, whereas the independent variables are treated as continuous variables. When the sample sizes are less than the independent variables, the independent variables are created from the normal distribution on various variances at 20, 30, 40, and 50. The average mean square error is used as a comparison criterion in penalised regression. When comparing penalised logistic regression performance, the average percentage of accuracy is employed.

Author(S) Details

Autcha Araveeporn
Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand.

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