REGRESSION SHRINKAGE AND SELECTION VIA THE LASSO

We propose a new method for estimation in linear models. The 'lasso' m inimizes the residual sum of squares subject to the sum of the absolut e 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 stu dies suggest that the lasso enjoys some of the favourable properties o f both subset selection and ridge regression. It produces interpretabl e models like subset selection and exhibits the stability of ridge reg ression. 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 ar e briefly described.