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I see many people on the web assuming that R² is not an appropriate metric to select a regressor instead of another, suggesting AIC or BIC to do so. From my view, it means that its almost preferable to avoid complex models, even if they're more accurate (I'm not sure if this view is correct).

My question is what is wrong about using MSE? And to see if the model is better than "always predict the mean", just check R²?

Another reason that I insist on using them to prefer a regressor instead of another (even not sure of its appropriateness) is that sklearn does use R² as default scoring function for GridSearchCV.

Adelson Araújo
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    Also, to choose the best predictive model, you should probably rely on something like Mean Squared Predicted Error (MSPE) rather than (MSE). The difference is subtle, but very important. See here for an explanation. https://stats.stackexchange.com/questions/20741/mean-squared-error-vs-mean-squared-prediction-error – StatsStudent Feb 10 '19 at 19:24

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It is not wrong. If you want to choose simple model, mean squared error won't help you. AIC and BIC penalize models with more parameters, even if they fit slightly better, so they help you with choosing simple model that still fits well. If you want accurate predictions, choose the model that does accurate predictions as judged with some criterion for that like mean squared, or absolute, error, or something else. It depends on if you want to use the model to understand something better (then you want simple, easily interpretable model), or you are interested only in making predictions (then you choose most accurate model, while it sometimes may not matter if it's complicated, but check if it doesn't overfit).

Tim
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