Approximately Unimodal Likelihood Models for Ordinal Regression

Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable. A key to successful OR models is to find a data structure `natural ordinal relation' common to many ordinal data and reflect that structure into the design of those models. A recent OR study found that many real-world ordinal data show a tendency that the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable will often be unimodal. Several previous studies thus developed unimodal likelihood models, in which a predicted CPD is guaranteed to become unimodal. However, it was also observed experimentally that many real-world ordinal data partly have values of the explanatory variable where the underlying CPD will be non-unimodal, and hence unimodal likelihood models may suffer from a bias for such a CPD. Therefore, motivated to mitigate such a bias, we propose approximately unimodal likelihood models, which can represent up to a unimodal CPD and a CPD that is close to be unimodal. We also verify experimentally that a proposed model can be effective for statistical modeling of ordinal data and OR tasks.