The PR curve plots the precision as a function of the recall, and the AUC can be interpreted as the average precision. The ROC plots the recall as a function of the specificity. Can we interpret the AUC as the average recall?
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Not usefully.
It's the recall integrated with equal weight over all possible specificities. That's not typically an average over any well-motivated real or imaginary distribution.
answered Jun 1, 2022 at 5:56
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$\begingroup$ How is it different from interpreting the AUC ROC as the average precision? $\endgroup$– usual meCommented Jun 1, 2022 at 9:42
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$\begingroup$ @usual-me When you compute an "average" of a function $f$ that depends on a random variable $X$, you must compute the expectation value of $f$ as $\int f(x)\,p(x)\,dx$, where $p$ is the probability density of $X$. You want to replace $p(x)$ with $1/W$, where $W$ is the width of the interval over which the integration runs ($W=1$ in this particular case) which does not make much sense. This is what Thomas Lumley wanted to say in his answer. $\endgroup$– cdalitzCommented Jun 1, 2022 at 11:24