José Hernandez-Orallo, Peter Flach and Cèsar Ferri

- ROC curves can be transferred to cost space by means of a very natural threshold choice method:

- We employ a very natural threshold choice method, which
sets the decision threshold such that the proportion of positive
predictions

equals the operating condition - Using this threshold choice method we define a new curve: rate-driven curves
- The expected loss as measured by the area under these curves is linearly related to AUC

- Rate-driven curves are the genuine equivalent of ROC curves in cost space
- A decomposition of the rate-driven curves separates the loss due to the threshold choice method from the ranking loss (Kendall τ distance)
- The corresponding curve to the ROC convex hull in cost space is also derived

- More details in this paper.
- An R script for drawing Rate-Driven curves and ROC curves.