Assumptionless consistency of the Lasso

TL;DR

This paper demonstrates that the Lasso estimator is consistent with minimal assumptions on the data, emphasizing its robustness in high-dimensional linear regression.

Contribution

It reveals that the Lasso's consistency does not require strong assumptions, highlighting its fundamental robustness in statistical modeling.

Findings

Lasso is consistent under very weak conditions

Minimal assumptions suffice for Lasso consistency

Reinforces Lasso's robustness in high-dimensional settings

Abstract

The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The purpose of this note is to highlight the simple fact (noted in a number of earlier papers in various guises) that for the loss function considered in Tibshirani's original paper, the Lasso is consistent under almost no assumptions at all.