Using ROC can miss the low precision where FP > TP
because ROC only look at TPR and FPR. I think what we need to ask is:
- Will
FP > TP
happen with your data and the model. - Does
FP > TP
matter for your business problem.
If the answer is yes for both, then ROC only is not fit for use.
If the problem is identifying shoplifters and FP
will alarm the police. Almost all the shop customers are honest, then catching more honest customers as shoplifters than real ones will cause angry customers and police. Then looking at only ROC will not be a good idea to measure the model.
If the problem is identifying potentially fatal food for toddlers, FP > TP
may not be a big issue because there will be so many safe food (TN
) as long as TPR is really high. Then ROC will be fit for use to measure the model.
FP: False Positive
TP: True Positive
FPR: False Positive Rate
TPR: True Positive Rate
Suppose I am running a risky loan business where manymajority of the customers can beare risky. If I evaluate the business performance with ROC only, I think the performance is good because TPR
is high and FPR
is low, although actually the business is losing money because of FP > TP
. By looking at PR, it will tell the low precision and I will understand the business performance is bad as I am looking money.