FEERCI: A Package for Fast Non-Parametric Confidence Intervals for Equal Error Rates in Amortized O(m log n)

Abstract

Equal Error Rates (EERs), or other weighted relations between False Match and Non- Match Rates (FMR/FNMR), are often used as a performance metric for biometric systems. Confidence Intervals (CIs) are used to denote the uncertainty underlying these EERs, with many methods existing to estimate said CIs in both parametric and non-parametric ways. These confidence intervals provide, foremost, a method of comparing scoring/ranking functions. Non-parametric methods often suffer from high computational costs, but do not make assumptions as to the shape of the EERand score distributions. For both EERs and CIs, contemporary open-source toolkits leave room for improvement in terms of computational efficiency. In this paper, we introduce the Fast EER (FEER) algorithm that calculates an EER in O(logn) on a sorted score list, we show how to adapt the FEER algorithm to calculate non-parametric, bootstrapped EER CIs (FEERCI) in O(mlogn) given m resamplings, and we introduce an opinionated open-source package named feerci that provides implementations of the FEER and FEERCI algorithm.We provide speed and accuracy benchmarks for the feerci package, comparing it against the most-used methods of calculating EERs in Python and show how it is able to calculate EERs and CIs on very large score lists faster than contemporary toolkits can calculate a single EER.