Estimation Consistency of Group Lasso with Special Diagonal Matrix

Group Lasso is an efficient regularized least-square regression algorithm, and is now being used as a computationally feasible method to select grouped variables. In this paper, we address the issue of estimation consistency of the group Lasso with special diagonal matrix. We derive sufficient condition for the consistency of group Lasso under practical assumptions, such as model misspecification. This sufficient condition, which depends mainly on the covariance of the predictor variables, states that group Lasso selects the true model consistently if the predictors that are in and not in the true model have low correlation. Specifically, the consistency condition adopts the regularization with special kernel matrix. Experiments are carried out to provide insights and understanding of this result.