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Is there a main reference/publication suggesting to use cross-validation in order to choose the regularization parameter in Lasso?

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    $\begingroup$ The original Lasso paper by Tibshirani discusses using cross-validation to choose the regularisation parameter in Section 4. $\endgroup$
    – David R
    Sep 29, 2016 at 15:40

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You can try sec. 6.2.3 of James/Witten/Hastie/Tibshirani, Introduction to Statistical Learning

... implementing ridge regression and the lasso requires a method for selecting a value for the tuning parameter λ ... Cross-validation provides a simple way to tackle this problem. We choose a grid of λ values, and compute the cross-validation error for each value of λ ... We then select the tuning parameter value for which the cross-validation error is smallest. (p. 227)

The canonical text for Lasso is probably Hastie/Tibshirani/Friedman, Elements of Statistical Learning, but ISLR is a good place to start for non-PhD level.

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