I have always always understood the diagonal of the ROC plot to represent the performance of a "random" classifier (corresponding to an AUC of 0.5). Is this still the case for highly imbalanced problems? (e.g. 10 positives vs 1000 negatives).
If not, is there any way to estimate the ROC-AUC for a "random" classifier (fully blind to features and to the proportions of positives and negatives).
What if we test against a stratified random classifier? (i.e. one that guesses positives and negatives randomly but according to the proportion of positives and negatives).
What can be said about the metric Average Precision in the same scenarios? (random and stratified random).