Learning Rich Rankings
Arjun Seshadri Stephen Ragain Johan Ugander
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.