Extending previous work on quantile classifiers (q-classifiers) we propose the q*-classifier for the class imbalance problem. The classifier assigns a sample to the minority class if the minority class conditional probability exceeds 0 < q* < 1, where q* equals the unconditional probability of observing a minority class sample. The motivation for q*-classification stems from a density-based approach and leads to the useful property that the q*-classifier maximizes the sum of the true positive and true negative rates. Moreover, because the procedure can be equivalently expressed as a cost-weighted Bayes classifier, it also minimizes weighted risk. Because of this dual optimization, the q*-classifier can achieve near zero risk in imbalance problems, while simultaneously optimizing true positive and true negative rates. We use random forests to apply q*-classification. This new method which we call RFQ is shown to outperform or is competitive with existing techniques with respect to tt-mean performance and variable selection. Extensions to the multiclass imbalanced setting are also considered.
Keywords: Class Imbalance; Minority Class; Random Forests; Response-based Sampling; Weighted Bayes Classifier.