Class Proportion Estimation with Application to Multiclass Anomaly Rejection

This work addresses two classification problems that fall under the heading domain adaptation, wherein the distributions of training and testing differ. The first problem studied is that of class proportion, which is the problem of estimating the class proportions in an testing data set given labeled examples of each class. Compared to work on this problem, our approach has the novel feature that it does require labeled training data from one of the classes. This property allows to address the second domain adaptation problem, namely, multiclass anomaly. Here, the goal is to design a classifier that has the option of a "reject" label, indicating that the instance did not arise from a present in the training data. We establish consistent learning strategies both of these domain adaptation problems, which to our knowledge are the of their kind. We also implement the class proportion estimation and demonstrate its performance on several benchmark data sets.