  This paper study sparse classification problems. We show that under
single-index models, vanilla Lasso could give good estimate of unknown
parameters. 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
train classifiers. Simulations confirm that vanilla Lasso could be used to get
a good estimation when data are generated from a logistic regression model.
