Estimating the Arc Length of the Optimal ROC Curve and Lower Bounding the Maximal AUC. (arXiv:2110.09651v2 [math.ST] UPDATED)

We show that when the data likelihood ratio is used as the score function,
the arc length of the corresponding ROC curve gives rise to a novel
$f$-divergence which measures differences between the positive and negative
data distributions. This $f$-divergence can be expressed using a variational
objective and estimated only using samples from the positive and negative
\emph{data} distributions. We show the empirical version of this variational
objective is also a consistent estimator for the arctangent likelihood ratio
with a …

arxiv auc math roc