Reviews: Calibration tests in multi-class classification: A unifying framework

Summary The paper presents a novel unified theoretical framework and new measures for the calibration properties of multi-class classifiers, which generalize commonly used ones. Estimators for the proposed measures, based on vector-valued RKHS, are then proposed. The statistical properties of such estimators are theoretically characterized (including proofs), and statistical tests associated to the estimators are presented. Finally, the properties of the proposed estimators are exhaustively validated in supporting simulated experiments. Originality The proposed ideas are novel in the context of calibrated multi-class classification.