  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--$C_p$, 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.
