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.

采用基于选择建模的上下文重复选择（CRS）模型，结合多模态模型，提供了生成丰富的排名空间的工具，同时使用结构相关的尾部风险和期望风险界限，对该模型的最大似然估计提供了严格的理论保证，并且在多项式逻辑选择模型（MNL）和 Plackett-Luce（PL）排名模型的预期风险以及 PL 排名模型的尾部风险方面也提供了前所未有的紧密界限。该 CRS 模型在各种场景下明显优于现有的排名数据建模方法，包括比赛和排名投票。