Assessing classifiers in terms of the partial area under the ROC curve

Assessing classifiers using the partial area under the ROC curve (PAUC) (or its equivalent, “separability”, that is a function of the chosen threshold of the decision variable) is considered. The population properties of the “separability” as a function only of the trained classifier and the selected threshold are derived. Next, the nonparametric estimation of the “separability” and its mean, for which we assume the availability of only one dataset, using the leave-pair-out bootstrap-based estimator is considered. In addition, the influence function approach to estimate the uncertainty of that estimate is used. The major contributions are the inclusion of the effect of the training set on the properties of the “separability”, and also on its nonparametric estimator, in both the mean and the variance; this is a key difference from the PAUC literature and its use in medical community. The mathematical properties are confirmed by a set of experiments using simulated and real datasets. Finally, the true performance (not its estimate) of classifiers measured in “separability” may vary significantly with varying the training set, while its estimate yet has a small estimated variance. This accounts for having “good” estimate for “bad” performance.