Variable Selection for Sparse Logistic Regression with Grouped Variables

We present a new penalized method for estimation in sparse logistic regression models with a group structure. Group sparsity implies that we should consider the Group Lasso penalty. In contrast to penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting the group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.