AUC from a single precision and recall value?

Question

I found the below post to provide an answer for calculating AUC value for a single TPR and FPR.

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

Is it also possible to calculate AUC from a single Precision and Recall value? I know it is not possible to calculate AUC from just a single point but just wanted to know if there are any other theories like the one for TPR and FPR.

Thanks!

Answer 1

Well, like the link you provided says, you could always interpolate the data to get multiple TPR, FPR values. But this is of no significance because:

• The whole point is to use AUC(TPR, FPR) value to check how well your model is. Predicting both the target function as well as the means to verify it makes no sense.
• Even in this case, you need multiple values to calculate AUC, whether you interpolate or get actual values.