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PrecisionRecallGain Curves: PR Analysis Done Right
Peter Flach · Meelis Kull
PrecisionRecall analysis abounds in applications of binary classification where true negatives do not add value and hence should not affect assessment of the classifier's performance. Perhaps inspired by the many advantages of receiver operating characteristic (ROC) curves and the area under such curves for accuracybased performance assessment, many researchers have taken to report PrecisionRecall (PR) curves and associated areas as performance metric. We demonstrate in this paper that this practice is fraught with difficulties, mainly because of incoherent scale assumptions  e.g., the area under a PR curve takes the arithmetic mean of precision values whereas the $F_{\beta}$ score applies the harmonic mean. We show how to fix this by plotting PR curves in a different coordinate system, and demonstrate that the new PrecisionRecallGain curves inherit all key advantages of ROC curves. In particular, the area under PrecisionRecallGain curves conveys an expected $F_1$ score on a harmonic scale, and the convex hull of a PrecisionRecallGain curve allows us to calibrate the classifier's scores so as to determine, for each operating point on the convex hull, the interval of $\beta$ values for which the point optimises $F_{\beta}$. We demonstrate experimentally that the area under traditional PR curves can easily favour models with lower expected $F_1$ score than others, and so the use of PrecisionRecallGain curves will result in better model selection.
Author Information
Peter Flach (University of Bristol)
Meelis Kull (University of Bristol)
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