Deep Ordinal Classification Based on the Proportional Odds Model

Abstract

This paper proposes a deep neural network model for ordinal regression problems based on the use of a probabilistic ordinal link function in the output layer. This link function reproduces the Proportional Odds Model (POM), a statistical linear model which projects each pattern into a 1-dimensional space. In our case, the projection is estimated by a non-linear deep neural network. After that, patterns are classified using a set of ordered thresholds. In order to further improve the results, we combine this link function with a loss cost that takes the distance between classes into account, based on the weighted Kappa index. The experiments are based on two ordinal classification problems, and the statistical tests confirm that our ordinal network outperforms the nominal version and other proposals considered in the literature.