Learning classifiers from imbalanced data based on biased minimax probability machine

We consider the problem of the binary classification on imbalanced data, in which nearly all the instances are labelled as one class, while far fewer instances are labelled as the other class, usually the more important class. Traditional machine learning methods seeking an accurate performance over a full range of instances are not suitable to deal with this problem, since they tend to classify all the data into the majority, usually the less important class. Moreover, some current methods have tried to utilize some intermediate factors, e.g., the distribution of the training set, the decision thresholds or the cost matrices, to influence the bias of the classification. However, it remains uncertain whether these methods can improve the performance in a systematic way. In this paper, we propose a novel model named Biased Minimax Probability Machine. Different from previous methods, this model directly controls the worst-case real accuracy of classification of the future data to build up biased classifiers. Hence, it provides a rigorous treatment on imbalanced data. The experimental results on the novel model comparing with those of three competitive methods, i.e., the Naive Bayesian classifier, the k-Nearest Neighbor method, and the decision tree method C4.5, demonstrate the superiority of our novel model.