Learning Rich Rankings

Abstract: Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total ordering. Explicit mixture models have provided some tools for modelling multimodal ranking data, though learning such models from data is often difficult. In this work, we contribute a contextual repeated selection (CRS) model that leverages recent advances in choice modeling to bring a natural multimodality and richness to the rankings space. We provide rigorous theoretical guarantees for maximum likelihood estimation under the model through structure-dependent tail risk and expected risk bounds. As a by-product, we also furnish the first tight bounds on the expected risk of maximum likelihood estimators for the multinomial logit (MNL) choice model and the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on the PL ranking model. The CRS model significantly outperforms existing methods for modeling real world ranking data in a variety of settings, from racing to rank choice voting.