A Universal Trade-off Between the Model Size, Test Loss, and Training Loss of Linear Predictors

Ghosh, Nikhil; Belkin, Mikhail

The problem of ordinal classification occurs in a large and growing number of areas. Some of the most common source and applications of ordinal data include rating scales, medical classification scales, socio-economic scales, meaningful groupings of continuous data, facial emotional intensity, facial age estimation, etc. The problem of predicting ordinal classes is typically addressed by either performing n-1 binary classification for n ordinal classes or treating ordinal classes as continuous values for regression. However, the first strategy doesn't fully utilize the ordering information of classes and the second strategy imposes a strong continuous assumption to ordinal classes. In this paper, we propose a novel loss function called Ordinal Hyperplane Loss (OHPL) that is particularly designed for data with ordinal classes. The proposal of OHPL is a significant advancement in predicting ordinal class data, since it enables deep learning techniques to be applied to the ordinal classification problem on both structured and unstructured data. By minimizing OHPL, a deep neural network learns to map data to an optimal space where the distance between points and their class centroids are minimized while a nontrivial ordinal relationship among classes are maintained. Experimental results show that deep neural network with OHPL not only outperforms the state-of-the-art alternatives on classification accuracy but also scales well to large ordinal classification problems.

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