A Generalization of LASSO Modeling via Bayesian Interpretation

The aim of this paper is to introduce a generalized LASSO regression model that is derived using a generalized Laplace (GL) distribution. Five different GL distributions are obtained through the T -R{Y } framework with quantile functions of standard uniform, Weibull, log-logistic, logistic, and extreme value distributions. The properties, including quantile function, mode, and Shannon entropy of these GL distributions are derived. A particular case of GL distributions called the beta-Laplace distribution is explored. Some additional components to the constraint in the ordinary LASSO regression model are obtained through the Bayesian interpretation of LASSO with beta-Laplace priors. The geometric interpretations of these additional components are presented. The effects of the parameters from beta-Laplace distribution in the generalized LASSO regression model are also discussed. Two real data sets are analyzed to illustrate the flexibility and usefulness of the generalized LASSO regression model in the process of variable selection with better prediction performance. Consequently, this research study demonstrates that more flexible statistical distributions can be used to enhance LASSO in terms of flexibility in variable selection and shrinkage with better prediction.