Confidence Sets for Statistical Classification (II): Exact Confidence Sets

Abstract

Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. Liu et al. (2019) proposed a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. However, the classifier uses a conservative critical constant. In this paper, we show how to determine the exact critical constant in applications where prior knowledge about the proportions of the future objects from each class is available. As the exact critical constant is smaller than the conservative critical constant given by Liu et al. (2019), the classifier using the exact critical constant is better than the classifier by Liu et al. (2019) as expected. An example is provided to illustrate the method.