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?

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#### 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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