A Probabilistic Classifier Model with Adaptive Rejection Option

Lately the topic of rejecting decisions in a classification scenario became attention, e. g. in medical data analysis, since not only the decision itself but also the certainty of the decision is important. While often a reject option is used on top of a trained model, recent approaches include it directly in the objective function of the desired model, e. g. for learning vector quantization. Following this trend, we propose a theoretical framework for probabilistic models, e. g. Gaussian mixture models, which includes costs for wrong classification as well as costs for rejection in its objective function. Further the rejection threshold is optimised during the training phase of the model. The proposed method follows the ideas of C. K. Chows paper: On optimum recognition error and reject tradeoff (1970). This article describes the new model in detail including the derivatives of the objective function.