Loss Functions for Preference Levels: Regression with Discrete Ordered Labels

We consider different types of loss functions for discrete ordinal regression, i.e. fitting labels that may take one of several discrete, but ordered, values. These types of labels arise when preferences are specified by selecting, for each item, one of several rating “levels”, e.g. one through five stars. We present two general threshold-based constructions which can be used to generalize loss functions for binary labels, such as the logistic and hinge loss, and another generalization of the logistic loss based on a probabilistic model for discrete ordered labels. Experiments on the 1 Million MovieLens data set indicate that one of our construction is a significant improvement over previous classificationand regression-based approaches.