  Abstaining classificaiton aims to reject to classify the easily misclassified
examples, so it is an effective approach to increase the clasificaiton
reliability and reduce the misclassification risk in the cost-sensitive
applications. In such applications, different types of errors (false positive
or false negative) usaully have unequal costs. And the error costs, which
depend on specific applications, are usually unknown. However, current
abstaining classification methods either do not distinguish the error types, or
they need the cost information of misclassification and rejection, which are
realized in the framework of cost-sensitive learning. In this paper, we propose
a bounded-abstention method with two constraints of reject rates (BA2), which
performs abstaining classification when error costs are unequal and unknown.
BA2 aims to obtain the optimal area under the ROC curve (AUC) by constraining
the 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 BA2
obtains higher AUC and lower total cost than the state-of-the-art abstaining
classification methods. Meanwhile, BA2 achieves controllable reject rates of
the positive and negative classes.
