Vanilla Lasso for sparse classification under single index models

TL;DR

This paper demonstrates that vanilla Lasso can effectively estimate parameters and train classifiers in sparse single-index models, even when the model is non-linear or responses are non-continuous, with simulations confirming its practical utility.

Contribution

It shows that vanilla Lasso is effective for sparse classification under single-index models, extending its applicability beyond linear models.

Findings

Vanilla Lasso provides good parameter estimates in single-index models.

Lasso can be used for classification even with non-linear models.

Simulations confirm effectiveness in logistic regression scenarios.

Abstract

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.