I was looking at the arguments in the linear regularization methods with cross validation within scikit-learn. RidgeCV has an argument scoring which is None by default but one can use a custom scorer (e.g. RMSE). I noticed that no such option is given for the rest of the classes (LassoCV, LassoLarsCV, ElasticNetCV). Why is this? Is MSE used by default in all of them?
RidgeCV implements CV by
GridSearchCV, which supports custom scorer.
ElasticNetCV implement CV by
LinearModelCV, with MSE as scoring hard-coded.
LassoLarsCV impletments CV by
LarsCV, with MSE as scoring hard-coded too.
If you want to use other scorers, maybe you can use