Consider a situation, where there are two unbalanced classes (n1 < n2). Some standard statistical methods advise to use SMOTE (or similar) oversampling methods to balance classes and train a classifier on balanced classes.
Here is my question: how to assess properly a classification error of the trained classifier (or any other metrics, f1, etc)? Remember, the classifier is trained on the augmented dataset (balanced).
Does cross validation on the augmented dataset make sense? I was told, that assessing a performance of the classifier (which is trained on balanced data) should be done only on the original unbalanced dataset.
UPD Here is a nice paper addressing exactly the same problem of CV with SMOTE