Distributed Robust Support Vector Ordinal Regression under Label Noise

Ordinal regression (OR) methods are designed for a type of classification problems where data labels have natural orders. In practice, data may be corrupted by label noise, which affects the training process thus degrading the generalization performance of OR methods. In OR, data are usually assumed to have latent variables underlying the ordinal labels, and label noise exhibits a special characteristic that it usually causes large latent variable value deviations. However, there are few existing works on OR considering label noise, and the existing works do not utilize the above-mentioned characteristic. Besides, most of the existing OR methods are centralized, which are inapplicable in some realistic distributed applications. In this paper, we utilize the characteristic of label noise in OR to develop a distributed robust support vector ordinal regression method (dRSVOR) under label noise. Specifically, after analyzing the characteristic of label noise in OR, we take the form of SVOR with explicit constraints to achieve robustness to one type of mislabeled samples. Then, we adopt correntropy, an information-theoretic measure, to achieve robustness to the other type of mislabeled samples. Theoretically, we analyze the consensus and convergence of dRSVOR. Experimentally, we conduct experiments on both synthetic data and real OR datasets to illustrate the effectiveness of the proposed method. The results show that the centralized version of dRSVOR outperforms several state-of-the-art OR methods considering label noise in centralized circumstances with label noise, and dRSVOR could approach the performance of the centralized version despite additional constraints in distributed scenarios.