From Theory to Practice: Efficient Active Cost-sensitive Classification with Expected Error Reduction

Yexun Zhang, Yanfeng Wang, Wenbin Cai, Siyuan Zhou, Ya Zhang

Abstract: In many classification tasks, the data distribution is imbalanced and different misclassifications involve different costs. In addition, the data collected are often lack in labels and it is expensive and tedious to label them manually. Motivated by these two problems, we propose a novel active cost-sensitive classification algorithm based on the Expected Error Reduction (EER) framework, aiming to selectively label examples which can directly optimize the expected misclassification costs. However, the native EER (N-EER) framework is inefficient and impractical due to the considerable requirement for model retraining. In this paper, we propose an efficient EER (E-EER) to overcome the inefficiency of N-EER with the application of cost-sensitive classification which is realized by incorporating the cost information into the expected loss calculation. We first present a formal formulation for EER, then the active cost-sensitive classification algorithm is derived. In order to achieve E-EER, we derive an efficient model update rule for logistic regression (LR) and cost-sensitive support vector machines (C-SVM), respectively, to avoid model retraining, which are employed as the base learners. Furthermore, we theoretically analyze the error bound of our algorithm to provide a guarantee for its generalization performance. Extensive experiments demonstrate the effectiveness and efficiency of our method.