AUC-ROC: only the order matters?

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.


Ok, here’s the answer.


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