Learning Rich Rankings

Arjun Seshadri, Stephen Ragain, Johan Ugander

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.