Unimodal Likelihood Models for Ordinal Data

Abstract

Ordinal regression (OR) is the classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the explanatory variables. In this study, we suppose the unimodality of the conditional probability distribution of the target variable given a value of the explanatory variables as a natural ordinal relation of the ordinal data. Under this supposition, unimodal likelihood models are considered to be promising for achieving good generalization performance in OR tasks. Demonstrating that previous unimodal likelihood models have a weak representation ability, we thus develop more representable unimodal likelihood models, including the most representable one. OR experiments in this study showed that the developed more representable unimodal likelihood models could yield better generalization performance for real-world ordinal data compared with previous unimodal likelihood models and popular statistical OR models having no unimodality guarantee.