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Abstaining classificaiton aims to reject to classify the easily misclassifiedexamples, so it is an effective approach to increase the clasificaitonreliability and reduce the misclassification risk in the cost-sensitiveapplications. In such applications, different types of errors (false positiveor false negative) usaully have unequal costs. And the error costs, whichdepend on specific applications, are usually unknown. However, currentabstaining classification methods either do not distinguish the error types, orthey need the cost information of misclassification and rejection, which arerealized in the framework of cost-sensitive learning. In this paper, we proposea bounded-abstention method with two constraints of reject rates (BA2), whichperforms abstaining classification when error costs are unequal and unknown.BA2 aims to obtain the optimal area under the ROC curve (AUC) by constrainingthe reject rates of the positive and negative classes respectively.Specifically, we construct the receiver operating characteristic (ROC) curve,and stepwise search the optimal reject thresholds from both ends of the curve,untill the two constraints are satisfied. Experimental results show that BA2obtains higher AUC and lower total cost than the state-of-the-art abstainingclassification methods. Meanwhile, BA2 achieves controllable reject rates ofthe positive and negative classes.

Abstaining Classification When Error Costs are Unequal and Unknown