Semi-Supervised Ordinal Regression Based on Empirical Risk Minimization
This work addresses the lack of metric-aware, flexible, and theoretically sound methods for semi-supervised ordinal regression, which is incremental in improving existing approaches.
The authors tackled the problem of semi-supervised ordinal regression by proposing a novel framework based on empirical risk minimization, which is applicable to various metrics, offers flexible model choices, and provides theoretical guarantees, with experiments demonstrating its usefulness.
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absolute error, mean zero-one error, and mean squared error. However, the existing studies do not take the evaluation metric into account, have a restriction on the model choice, and have no theoretical guarantee. To overcome these problems, we propose a novel generic framework for semi-supervised ordinal regression based on the empirical risk minimization principle that is applicable to optimizing all of the metrics mentioned above. Besides, our framework has flexible choices of models, surrogate losses, and optimization algorithms without the common geometric assumption on unlabeled data such as the cluster assumption or manifold assumption. We further provide an estimation error bound to show that our risk estimator is consistent. Finally, we conduct experiments to show the usefulness of our framework.