Probability Estimation for Multi-class Classification Based on Label Ranking

We consider the problem of probability estimation in the setting of multi-class classification. While this problem has already been addressed in the literature, we tackle it from a novel perspective. Exploiting the close connection between probability estimation and ranking, our idea is to solve the former on the basis of the latter, taking advantage of recently developed methods for label ranking. More specifically, we argue that the Plackett-Luce ranking model is a very natural choice in this context, especially as it can be seen as a multinomial extension of the Bradley-Terry model. The latter provides the basis of pairwise coupling techniques, which arguably constitute the state-of-the-art in multi-class probability estimation. We explore the relationship between the pairwise and the ranking-based approach to probability estimation, both formally and empirically. Using synthetic and real-world data, we show that our method does not only enjoy nice theoretical properties, but is also competitive in terms of accuracy and efficiency.