AI RESEARCH
On the Geometry of Receiver Operating Characteristic and Precision-Recall Curves
arXiv CS.AI
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ArXi:2504.02169v3 Announce Type: replace-cross We study the geometry of Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves in binary classification problems. The key finding is that many of the most commonly used binary classification metrics are merely functions of the composition function $G:= F_p \circ F_n^{-1}$, where $F_p(\cdot)$ and $F_n(\cdot)$ are the class-conditional cumulative distribution functions of the classifier scores in the positive and negative classes, respectively.