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Model selection is a problem of judging which model from some set performs best. Popular methods include $R^2$, AIC and BIC criteria, test sets, and cross-validation. To some extent, feature selection is a subproblem of model selection.

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How to get both MSE and R2 from a sklearn GridSearchCV?

You can for example create a scorer that computes MSE score and R2 score and choose which one you're gonna use in the GridSearch, however you will be able to see the two scores, if you insert a print …
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