The relationship between Precision-Recall and ROC curves

TLDR

ROC curves are the standard tool for binary decision problems, but in highly skewed datasets precision‑recall curves provide a more informative performance view. The authors aim to show a deep connection between ROC and PR spaces. They prove that a curve dominates in ROC space if and only if it dominates in PR space. The authors define an achievable PR curve, analogous to the ROC convex hull, present an efficient algorithm to compute it, and show that PR space differs from ROC space: linear interpolation is invalid and optimizing AUC‑ROC does not guarantee AUC‑PR optimization.

Abstract

Receiver Operator Characteristic (ROC) curves are commonly used to present results for binary decision problems in machine learning. However, when dealing with highly skewed datasets, Precision-Recall (PR) curves give a more informative picture of an algorithm's performance. We show that a deep connection exists between ROC space and PR space, such that a curve dominates in ROC space if and only if it dominates in PR space. A corollary is the notion of an achievable PR curve, which has properties much like the convex hull in ROC space; we show an efficient algorithm for computing this curve. Finally, we also note differences in the two types of curves are significant for algorithm design. For example, in PR space it is incorrect to linearly interpolate between points. Furthermore, algorithms that optimize the area under the ROC curve are not guaranteed to optimize the area under the PR curve.