Oracle inequalities for weighted group Lasso in high-dimensional Poisson regression model

Abstract

This article considers the problem of estimating the high-dimensional Poisson regression model with group sparsity in the parameter vector using the weighted group Lasso method. Non asymptotic oracle inequalities measuring the convergence rate of the estimation and prediction errors are given, provided that the true regression coefficients and the covariates satisfy suitable conditions. The non asymptotic oracle inequalities imply that the weighted group lasso estimator is consistent. A comparison of the performance of our proposed weights with other adaptive weights in simulated data shows that the weighted group Lasso estimator provides a good sparse approximation to the true parameters.