F1 from ROC curve

Question

Given ROC curve (http://en.wikipedia.org/wiki/Receiver_operating_characteristic), how do you read the maximum F1? (if it is possible)

Answer 1

The coordinates of points on the ROC curve are true positive rate (TPR) and false positive rate (TPR). These are given by: $$ TPR=TP/(TP+FN)$$ and $$ FPR=TP/(TP+FP)$$ The F1 score is given by: $$F_1=2*precision*recall/(precision + recall)$$ where $recall=TPR$ and $precision=1-FPR$.

So in order to calculate the maximum $F_1$ score, you have to calculate it at every point on the curve, where you take the $TPR$ value for $recall$ and the $FPR$ value for $1-precision$.