Using theoretical ROC curves for analysing machine learning binary classifiers.

Abstract

Most binary classifiers work by processing the input to produce a scalar response and comparing it to a threshold value. The various measures of classifier performance assume, explicitly or implicitly, probability distributions Ps and Pn of the response belonging to either class, probability distributions for the cost of each type of misclassification, and compute a performance score from the expected cost. In machine learning, classifier responses are obtained experimentally and performance scores are computed directly from them, without any assumptions on Ps and Pn. Here, we argue that the omitted step of estimating theoretical distributions for Ps and Pn can be useful. In a biometric security example, we fit beta distributions to the responses of two classifiers, one based on logistic regression and one on ANNs, and use them to establish a categorisation into a small number of classes with different extremal behaviours at the ends of the ROC curves.