Ord-MAP criterion: Extending MAP for ordinal classification
Rosario Delgado · Knowledge-Based Systems · 2025
Ordinal classification is a machine learning task where the goal is to predict labels with an inherent order. In traditional ordinal classification, the Maximum A Posteriori (MAP) criterion for assigning class labels fails to account for the ordinal structure of the target variable. We introduce Ord-MAP, a novel criterion for ordinal classification, as the most suitable extension of the binary MAP criterion to ordinal data. Unlike the usual approach, which selects the class with the highest probability — a logical choice for nominal classification — Ord-MAP identifies the first class whose cumulative probability exceeds 0.5, explicitly incorporating the class order and minimizing the expected misclassification cost under an order-sensitive loss function. This theoretical advancement addresses the fundamental limitation of existing methods by directly integrating the ordinal nature of the classes into the decision-making process. The theoretical contribution of this study is complemented by a comprehensive empirical evaluation that includes both experiments with real-world datasets and controlled simulations, showing that Ord-MAP outperforms MAP in various scenarios, achieving statistically significant improvement in prediction. Simulations further demonstrate that this improvement is particularly noticeable for centrally located classes, with symmetric gains at both extremes of the ordinal scale. Additionally, as the Shannon entropy of the predicted probability distribution increases — indicating greater uncertainty — the difference in MAE between Ord-MAP and MAP also grows, with Ord-MAP consistently outperforming MAP under moderate to high entropy. These findings highlight the practical benefits and broad applicability of the Ord-MAP criterion, positioning it as a well-founded alternative for ordinal classification tasks.