Group Lasso for Zero-Inflated Bernoulli Regression Model

Abstract

Group Lasso is an extension of the Lasso regularization method that selects variables in predefined groups within regression models. In this study, we adapt Group Lasso to the Bernoulli regression model with zero inflation and introduce an efficient algorithm designed for high-dimensional problems, solving the related convex optimization task. The resulting Group Lasso estimator is proven to be statistically consistent and asymptotically Gaussian, even when the number of predictors greatly exceeds the sample size, provided the true underlying structure is sparse.