Distributed Online Ordinal Regression Based on VUS Maximization

Ordinal regression (OR) is a multi-class classification problem with ordered labels. The objective functions of most OR methods are based on the misclassification error. The volume under the ROC surface (VUS) is a measure of OR that quantifies the ranking ability of OR models. It can also be used as an objective function in OR. In practice, data may be collected by multiple nodes in a distributed and online manner, and is difficult to process centrally. In this paper, we intend to develop a VUS-based distributed online OR method. Computing VUS requires a sequence of data from all categories, but the available online data may not cover all categories and the required data may distribute across different nodes. Besides, the existing approximation methods of VUS are inappropriate for using in OR. To address these issues, we first propose two new surrogate losses of the VUS in OR. We then derive their decomposed formulations and propose distributed online OR algorithms based on VUS maximization (dVMOR). The experimental results demonstrate their effectiveness.