Are FAR and FRR the same as FPR and FNR, respectively?

Question

FPR = False Positive Rate FNR = False Negative Rate

FAR = False Acceptance Rate FRR = False Rejection Rate

Are they the same? if Not, is it possible to calculate FAR and FRR from the confusion matrix?

Thank you

score 4 · Answer 1 · answered Apr 10 '17 at 18:22

4

Yes, they are the same.

So in order to calculate their values from the confusion matrix:

FAR = FPR = FP/(FP + TN)

FRR = FNR = FN/(FN + TP)

where FP: False positive
      FN: False Negative
      TN: True Negative
      TP: True Positive

answered Apr 10 '17 at 18:22

Aizzaac

1

Caveat: In statistics a "false rejection" is a Type I or $\alpha$ error, aka a false positive aka rejecting $H_{0}$ when $H_{0}$ is true. – Alexis Mar 02 '18 at 02:57
Unfortunately, this answer is wrong. Check – Tyathalae Sep 14 '22 at 13:12

score 2 · Answer 2 · answered Apr 19 '19 at 15:03

2

If you want to compute FPR and FNR (aka FAR and FRR), here is a Python code for this :

from sklearn import metrics

fpr, tpr, thresholds = metrics.roc_curve(y_true, scores)
fnr = 1-tpr

answered Apr 19 '19 at 15:03

Ismael EL ATIFI

score 0 · Answer 3 · answered Sep 25 '19 at 11:09

0

If it helps you can look at the confusion matrix as below to see that they are the same :

Action -->  Accept    Reject
          |-----------------
Genuine   |  TP    |    FN
          |-----------------
Impostor  |  FP    |    TN

answered Sep 25 '19 at 11:09

Noel

score 0 · Answer 4 · answered Apr 02 '22 at 13:08

0

Yes, they are the same. but confusion metrics can switch between positive features and negative features as we need, Biometrics can not do that.

answered Apr 02 '22 at 13:08

Tyathalae · Answer 5 · 2022-09-14T15:39:16.830

0

No, they are not the same.

FAR and FRR are calculated over all attempts, not individually over positive and negative cases. Ref1 Ref2 Ref3 Ref4

FAR = FP / (TP + FP + TN + FN)
FRR = FN / (TP + FP + TN + FN)

edited Sep 14 '22 at 15:39

answered Sep 14 '22 at 13:11

Tyathalae

5 Answers5