Ordinal Choquistic Regression

We propose an extension of choquistic regression from the case of binary to the case of ordinal classification. Choquistic regression itself has been introduced recently as a generalization of conventional logistic regression. The basic idea of this method is to replace the linear function of predictor variables in the logistic regression model by the Choquet integral. Thus, it becomes possible to capture nonlinear dependencies and interactions among predictor variables while preserving two important properties of logistic regression, namely the comprehensibility of the model and the possibility to ensure its monotonicity in individual predictors. In experimental studies, choquistic regression consistently improves upon standard logistic regression in terms of predictive accuracy, especially when being combined with a novel regularization technique that prevents from exceeding the required level of nonadditivity.