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In https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html, it says that LassoCV defaults to 5 folds.

In https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeCV.html, it says that RidgeCV defaults to leave one out ($n$ folds).

Why are the two different? Is there any theoretical or practical justification for not using LOOCV for Lasso?

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There are at least two possible contributing reasons

  1. The non-smoothness of the lasso makes some statisticians nervous about leave-one-out operations (even though there are now results for the lasso)
  2. For ridge regression the LOOCV can be computed rapidly using the Sherman-Morrison-Woodbury formula for single-row updates. For the lasso, you need to actually refit the model, which is slow if you do it $n$ times.
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