When dealing with a binary classification problem, where the decision function threshold is being varied from 0 to 1 at step 0.1:
When calculating the Area Under the Curve (AUC) for a ROC Curve plot (x: FPR, y: TPR) is the result AUC value equal for both classes?
When calculating the Area Under the Curve (AUC) for a PR (Precision-Recall) Curve plot (x: TPR, y: PPV) is the result AUC value equal for both classes?
I am not asking about any specific framework or method of calculation, just whether to expect the same AUC values for each class or not when using ROC AUC or PR AUC?
Best Answer
You have several misconceptions about ROC and PR curves.
First, ROC and PR curves indicate how well a binary classifier separate positive and negative examples. Hence, you have a single AUC per classifier, not per class.
Second, the following assertion is incorrect:
where the decision function threshold is being varied from 0 to 1 at step 0.1
The ROC and PR curves show how the classifier performs on all thresholds. Depending on the output of your classifier that could mean between $-infty$ to $+infty$. There is no stepping, though in practice you will only test the thresholds you observed, effectively making steps.
I suggest you check out the following question and answer for a more thorough overview of ROC curves : Understanding ROC curve.
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