Extension I: BMPM for Imbalanced Learning

Abstract

In this chapter, we consider the imbalanced learning problem. This problem means the task of binary classification on imbalanced data, in which nearly all the instances are labeled as one class, while far fewer instances are labeled as the other class, usually the more important class. Traditional machine learning methods seeking 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 class, usually the less important class. Moreover, many current methods have tried to utilize some intermediate factors, e.g. the distribution of the training set, the decision thresholds or the cost matrix, to impose a bias towards the important class. However, it remains uncertain whether these roundabout methods can improve the performance in a systematic way. In this chapter, we apply Biased Minimax Probability Machine, one of the special cases of Minimum Error Minimax Probability Machine to deal with the imbalanced learning tasks. Different from previous methods, this model achieves in a worst-case scenario to derive the biased classifier by directly controlling the classification accuracy on each class. More precisely, BMPM builds up an explicit connection between the classification accuracy and the bias, which thus provides a rigorous treatment on imbalanced data. We examine different models and compare BMPM with three other competitive methods, i.e. the Naive Bayesian classifier, the k-Nearest Neighbor method, and the decision tree method C4.5. The experimental results demonstrate the superiority of this model.