Log-Gamma Distribution Optimisation via Maximum Likelihood for Ordered Probability Estimates

Abstract

Ordinal regression considers classification problems where there exist a natural ordering between the categories. In this learning setting, thresholds models are one of the most used and successful techniques. These models are based on the idea of projecting the patterns to a line, which is thereafter divided into intervals using a set of biases or thresholds. This paper proposes a general likelihood-based optimisation framework to better fit probability distributions for ordered categories. To do so, a specific probability distribution (log-gamma) is used, which generalises three commonly used link functions (log-log, probit and complementary log-log). The experiments show that the methodology is not only useful to provide a probabilistic output of the classifier but also to improve the performance of threshold models when reformulating the prediction rule to take these probabilities into account.

This work has been subsidized by the TIN2011-22794 project of the Spanish Ministerial Commission of Science and Technology (MICYT), FEDER funds and the P11-TIC-7508 project of the “Junta de Andalucía” (Spain).