Semisupervised Ordinal Regression Based on Empirical Risk Minimization

Abstract

Ordinal regression is aimed at predicting an ordinal class label. In this letter, we consider its semisupervised 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, restrict model choice, and have no theoretical guarantee. To overcome these problems, we propose a novel generic framework for semisupervised ordinal regression based on the empirical risk minimization principle that is applicable to optimizing all of the metrics mentioned above. In addition, 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 provide an estimation error bound to show that our risk estimator is consistent. Finally, we conduct experiments to show the usefulness of our framework.

Don't fear the unlabelled: safe deep semi-supervised learning via simple debiasing

“…The method is designed only for binary classification and has not been tested in a deep learning setting. It has extended to ordinal regression in a follow-up work (Tsuchiya et al, 2021).In the context of kernel machines, Liu and Goldberg (2020) used an unbiased estimate of risk, similar to ours, for a specific choice of H. Guo et al (2020) proposed DS 3 L, a method safe that needs to approximately solve a bi-level optimisation problem. In particular, the method is designed for a different setting, not under the MCAR assumptiom, where there is a class mismatch between labelled and unlabelled data.…”

“…The idea is to use unlabelled data to better evaluate the risk for both negative and positive samples in order to reduce its variance. In follow-up work (Tsuchiya et al, 2021) proposed a similar approach based on an unbiased risk estimate for ordinal regression, and demonstrated the Fisher consistency of their method, as well as other theoretical properties. Older works have already proposed safe methods.…”