On the “ Degrees of Freedom ” of the Lasso

  • Published 2008

Abstract

We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso—a conclusion that requires no special assumption on the predictors. In addition, the unbiased estimator is shown to be asymptotically consistent. With these results on hand, various model selection criteria—Cp, AIC and BIC—are available, which, along with the LARS algorithm, provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least-squares fit.

4 Figures and Tables

0204060'06'07'08'09'10'11'12'13'14'15'16'17
Citations per Year

388 Citations

Semantic Scholar estimates that this publication has 388 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{2008OnT, title={On the “ Degrees of Freedom ” of the Lasso}, author={}, year={2008} }