Out of a hundred trials, how many errors does your speaker verifier make?

Out of a hundred trials, how many errors does your speaker verifier make? For the user this is an important, practical question, but researchers and vendors typically sidestep it and supply instead the conditional error-rates that are given by the ROC/DET curve. We posit that the user's question is answered by the Bayes error-rate. We present a tutorial to show how to compute the error-rate that results when making Bayes decisions with calibrated likelihood ratios, supplied by the verifier, and an hypothesis prior, supplied by the user. For perfect calibration, the Bayes error-rate is upper bounded by min(EER,P,1-P), where EER is the equal-error-rate and P, 1-P are the prior probabilities of the competing hypotheses. The EER represents the accuracy of the verifier, while min(P,1-P) represents the hardness of the classification problem. We further show how the Bayes error-rate can be computed also for non-perfect calibration and how to generalize from error-rate to expected cost. We offer some criticism of decisions made by direct score thresholding. Finally, we demonstrate by analyzing error-rates of the recently published DCA-PLDA speaker verifier.

Automated summary

This article discusses the calculation of error rate of speaker verifier, emphasizing the importance of Bayes error rate to users. It demonstrates how to calculate the error rate obtained by Bayes decisions through a tutorial, showing the impact of EER and prior probabilities on the Bayes error rate.