The vast majority of real world classification problems are imbalanced,
meaning there are far fewer data from the class of interest (the positive
class) than from other classes. We propose two machine learning algorithms to
handle highly imbalanced classification problems. The classifiers constructed
by both methods are created as unions of parallel axis rectangles around the
positive examples, and thus have the benefit of being interpretable. The first
algorithm uses mixed integer programming to optimize a weighted balance between
positive and negative class accuracies. Regularization is introduced to improve
generalization performance. The second method uses an approximation in order to
assist with scalability. Specifically, it follows a \textit{characterize then
discriminate} approach, where the positive class is characterized first by
boxes, and then each box boundary becomes a separate discriminative classifier.
This method has the computational advantages that it can be easily
parallelized, and considers only the relevant regions of feature space