# Understand TPR, FPR, FAR, FRR and EER Metrics in Voiceprint Recognition – Machine Learning Tutorial

By | June 21, 2022

In order to evaluate a voiceprint recognition model, we need compute eer metric. In this tutorial, we will introduce some metrics TPR, FPR, FAR, FRR to help you understand how to compute ERR.

## TPR and FPR

TPR and FPR can be computed as follows:

TPR = TP / (TP + FN)

FPR = FP / (FP + TN)

Understand TPR, FPR, Precision and Recall Metrics in Machine Learning – Machine Learning Tutorial

## FAR and FRR

This tutorial gives us some basic introduction on them.

Compute FAR, FRR and EER Metrics in TensorFlow – TensorFlow Tutorial

Here:

FAR = False Acceptance Rate

FRR = False Rejection Rate

EER  =FAR = FRR

From paper: Robust Performance Metrics for Authentication Systems, we can find:

FPR is sometimes called the false accept rate (FAR). It means FPR = FAR

The false negative rate (FNR) which is alternatively called the false reject rate (FRR). It means FNR = FRR

FNR = 1-TPR = FRR

## How to compute EER?

When FAR = FRR, we can get EER. Moreover, we can compute it by ROC curve.

ROC curve looks like:

In ROC curve, the x axis is FPR (FAR), the y axis is TPR. The line from (0, 1) and (1.0) is FRR.

Then we can compute EER easily.