A power-controlled reliability assessment for multi-class probabilistic classifiers

In multi-class classification, the output of a probabilistic classifier is a probability distribution of the classes. In this work, we focus on a statistical assessment of the reliability of probabilistic classifiers for multi-class problems. Our approach generates a Pearson \(\chi ^2\) statistic based on the k-nearest-neighbors in the prediction space. Further, we develop a Bayesian approach for estimating the expected power of the reliability test that can be used for an appropriate sample size k. We propose a sampling algorithm and demonstrate that this algorithm obtains a valid prior distribution. The effectiveness of the proposed reliability test and expected power is evaluated through a simulation study. We also provide illustrative examples of the proposed methods with practical applications.