Learning Acceptance Regions for Many Classes with Anomaly Detection

In multicategory classification, traditional methods return a single class label as the prediction without a confidence measure attached. For points near the classification boundary where the classes overlap, these methods may misclassify with high probability. As classification and machine learning in general have played a more and more significant role in high stake domains, these mistakes can incur severe consequences. To avoid making mistakes when they are likely to happen, set-valued classification methods have emerged (Herbei and Wegkamp, 2006; Shafer and Vovk, 2008; Dümbgen et al., 2008; Denis and Hebiri, 2017; Wang and Qiao, 2018; Zhang et al., 2018; Sadinle et al., 2019). A set-valued classifier may return multiple class labels as the prediction for each observation. Specifically, those near the boundary between classes may receive multiple labels as the prediction. Herbei and Wegkamp (2006), Bartlett and Wegkamp (2008), Ramaswamy et al. (2015) and Zhang et al. (2018) proposed and developed Classification with a Reject Option (CRO) by training a classifier and a rejector at the same time. A rejector determines when to refuse to make a classification for ambiguous points (i.e.