  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.
