Regression Shrinkage and Selection Via the Lasso

TLDR

The work relates to recent adaptive function estimation by Donoho and Johnstone. The paper proposes a new estimation method for linear models. The method uses the lasso, minimizing residual sum of squares with an L1 penalty that forces some coefficients to zero, yielding interpretable models and extending to various statistical frameworks. Simulations show the lasso combines subset‑selection interpretability with ridge‑regression stability.

Abstract

SUMMARY We propose a new method for estimation in linear models. The ‘lasso’ minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.