Learning in the Class Imbalance Problem When Costs are Unknown for Errors and Rejects

In the context of the class imbalance problem, most existing approaches require the knowledge of costs for reaching the reasonable classification results. If the costs are unknown, some approaches can not work properly. Moreover, to our best knowledge, none of the cost-sensitive approaches is able to process the abstaining classifications when costs are unknown for errors and rejects. Therefore, the challenge above forms the motivation of this work. Based on information theory, we propose a novel cost-free learning approach which targets the maximization of normalized mutual information between the target outputs and the decision outputs of classifiers. Using the approach, we can deal with classifications with/without rejections when no cost terms are given. While the degree of class imbalance is changing, the proposed approach is able to balance the errors and rejects accordingly and automatically. Another advantage of the approach is its ability of deriving optimal reject thresholds for abstaining classification and the "equivalent" costs for binary probabilistic classification. Numerical investigation is made on several benchmark data sets and the classification results confirm the unique feature of the approach for overcoming the challenge.