ON THE “DEGREES OF FREEDOM” OF THE LASSO

ON THE “DEGREES OF FREEDOM” OF THE LASSO

2007, Vol. 35, No. 5, 2173-2192 | BY HUI ZOU, TREVOR HASTIE AND ROBERT TIBSHIRANI
The paper by Hui Zou, Trevor Hastie, and Robert Tibshirani studies the degrees of freedom of the Lasso regression method in the context of Stein's Unbiased Risk Estimation (SURE). They show that the number of nonzero coefficients in the Lasso solution is an unbiased estimate of the degrees of freedom, which is consistent as well. This result allows for the construction of model selection criteria such as $C_p$, AIC, and BIC, which can be used to efficiently select the optimal Lasso fit with the computational effort of a single ordinary least-squares fit. The authors also provide theoretical foundations and numerical experiments to support their findings, demonstrating the effectiveness of their approach in practical scenarios.The paper by Hui Zou, Trevor Hastie, and Robert Tibshirani studies the degrees of freedom of the Lasso regression method in the context of Stein's Unbiased Risk Estimation (SURE). They show that the number of nonzero coefficients in the Lasso solution is an unbiased estimate of the degrees of freedom, which is consistent as well. This result allows for the construction of model selection criteria such as $C_p$, AIC, and BIC, which can be used to efficiently select the optimal Lasso fit with the computational effort of a single ordinary least-squares fit. The authors also provide theoretical foundations and numerical experiments to support their findings, demonstrating the effectiveness of their approach in practical scenarios.
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