Regression Shrinkage and Selection via the Lasso

Abstract

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 coeecients being less than a constant. Because of the nature of this constraint it tends to produce some coeecients that are exactly zero 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 brieey described.

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@inproceedings{Tibshirani1994RegressionSA, title={Regression Shrinkage and Selection via the Lasso}, author={Robert Tibshirani and ROBERT TIBSHIRANIt}, year={1994} }