Volume 58, Issue 1 p. 267-288

Regression Shrinkage and Selection Via the Lasso

Robert Tibshirani

Corresponding Author

Robert Tibshirani

University of Toronto, Canada

Address for correspondence: Department of Preventive Medicine and Biostatistics, and Department of Statistics, University of Toronto, 12 Queen's Park Crescent West, Toronto, Ontario, M5S 1A8, Canada. E-mail: [email protected]Search for more papers by this author


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.