Vanilla Lasso for sparse classification under single index models

This paper study sparse classification problems. We show that under single-index models, vanilla Lasso could give good classifiers. With this result, we see that even if the model is not linear, and even if the response is not continuous, we could still use vanilla Lasso to give good classifiers. Simulations confirm that vanilla Lasso could be used to get a good estimation when data are generated from a logistic regression model.