Can balancing of the majority and minority classes (RUS/SMOTE/...) improve AUC of a binary classifier?

Question

Given that AUC is a threshold independent measure, can undersampling or oversampling of the majority/minority class during training improve the performance of a binary classifier?

In my experience balancing the classes has the same effect as changing the threshold when making predictions. I believe that you can achieve any desired sensitivity or precision (not simultaneously of course) just by playing with the threshold.

If I am correct, I do not see the value of those sampling techniques. Perhaps they are more important for multiclass problems?

Could someone shed some light on this? Thank you.

Related: Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? And our Meta thread on imbalanced data with many more links. — Stephan Kolassa, Aug 01 '22 at 13:33
If changing the training data changes the model predictions, then the ROC AUC can change. If the predictions are fixed and you append copies of prediction, label tuples to the data and compute the AUC, then the AUC will be unchanged. https://stats.stackexchange.com/questions/346184/what-is-the-expected-value-of-aurocc-for-random-predictions/346185#346185 — Sycorax, Aug 01 '22 at 13:35

Can balancing of the majority and minority classes (RUS/SMOTE/...) improve AUC of a binary classifier?

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