A New Strategy of Cost-Free Learning in the Class Imbalance Problem

In this work, we define cost-free learning (CFL) formally in comparison with cost-sensitive learning (CSL). The main difference between them is that a CFL approach seeks optimal classification results without requiring any cost information, even in the class imbalance problem. In fact, several CFL approaches exist in the related studies, such as sampling and some criteria-based pproaches. However, to our best knowledge, none of the existing CFL and CSL approaches are able to process the abstaining classifications properly when no information is given about errors and rejects. Based on information theory, we propose a novel CFL which seeks to maximize normalized mutual information of the targets and the decision outputs of classifiers. Using the strategy, we can deal with binary/multi-class classifications with/without abstaining. Significant features are observed from the new strategy. While the degree of class imbalance is changing, the proposed strategy is able to balance the errors and rejects accordingly and automatically. Another advantage of the strategy is its ability of deriving optimal rejection thresholds for abstaining classifications and the "equivalent" costs in binary classifications. The connection between rejection thresholds and ROC curve is explored. Empirical investigation is made on several benchmark data sets in comparison with other existing approaches. The classification results demonstrate a promising perspective of the strategy in machine learning.