Asymmetric Horseshoe+ Prior for high Dimensional Quantile Regression with Variational Bayes

High-dimensional data analysis necessitates variable selection, and Bayesian quantile regression proves to be an effective method for modeling complex data. Common variable selection approaches often overlook potential patterns or asymmetries in regression coeffcients. This paper introduces the asymmetric Horseshoe+ prior, addressing computational effciency issues in Bayesian quantile regression by employing the Variational Bayes (VB) algorithm for parameter estimation and variable selection. Results from simulation studies and real world data analyses highlight the superiority of the asymmetric Horseshoe+ prior over the symmetric Horseshoe+ prior when there are potential patterns or asymmetries in regression coeffcients or covariates.