Hi ML enthusiasts. Would some please check my understanding of the ROC-AUC metric?
Suppose (just hypothetically of course) you are submitting a test set to Kaggle consisting of images and their probabilities of being in a class.
It seems that you should be able to stretch, squeeze, or otherwise alter the probabilities with any strictly increasing function. Then the ROC-AUC score will remain unaffected, as long as the images remain in the same order of probabilities.
Is this right? And if not, please tell me what invariant I am trying to see here.