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?
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.
$\begingroup$ How is it different from interpreting the AUC ROC as the average precision? $\endgroup$– usual meJun 1, 2022 at 9:42
$\begingroup$ @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. $\endgroup$– cdalitzJun 1, 2022 at 11:24