Statistical models and learning algorithms for ordinal regression problems

In this study, we propose a learning algorithm for ordinal regression problems. In most existing learning algorithms, the threshold or location model is assumed to be the statistical model. For estimation of conditional probability of labels for a given covariate vector, we extended the location model to apply ordinal regressions. We present this learning algorithm using the squared-loss function with the location-scale models for estimating conditional probability. We prove that the estimated conditional probability satisfies the monotonicity of the distribution function. Furthermore, we have conducted numerical experiments to compare these proposed methods with existing approaches. We found that, in its ability to predict labels, our method may not have an advantage over existing approaches. However, for estimating conditional probabilities, it does outperform the learning algorithm using location models.