Checking whether the best alpha is stable

Hello,

At the end of the Regularization of linear regression model lecture, after we run RidgeCV to assess the performance of different Ridge models with different values for alpha, this is mentioned:

We can check if the best alpha found is stable across the cross-validation fold.

What does “stable” mean in this context? And is this “cross-validation” the outer or the inner cross-validation?

stable will refer if the alpha is varying a lot, from non-regularized (e.g. 1e-3) to regularized (1e3). If this is the case, it means that the random change of the train/test dataset induced by the cross-validation will have a huge impact on the model and it is problematic.

It refers to the outer. The outer will change the train/test used and for this specific dataset we set an alpha (using the inner cross-validation).