Preference learning refers to the learning of latent patterns from ranking and preference data of different kinds. Typical aims of preference learning are to infer a shared consensus ranking, to learn individual-level preferences, and to perform unsupervised clustering. The Mallows model is among the few approaches that can achieve all these objectives jointly. Previous work has developed computationally tractable methods for Bayesian inference based on a MCMC Metropolis-Hastings scheme, where clustering is performed via a finite mixture of Mallows models. Inference on the number of clusters is then conducted a posteriori. Here we propose a Bayesian nonparametric Mallows model, based on a Dirichlet process mixture model. This allows joint inference on the number of non-empty clusters and on the clustering allocation, as well as posterior inference on cluster-specific parameters. The implementation of the proposed sampling algorithm is integrated into the existing R package BayesMallows, which also supports data in the form of incomplete rankings and pairwise comparisons. Simulated data show good performance of the nonparametric model compared to a finite mixture model in terms of recovery of the correct number of clusters, while empirical data on movie ratings show the model's effectiveness in providing personalized movie recommendations on discarded ratings.

翻译：偏好学习是指从不同类型的排序和偏好数据中学习潜在模式的过程。其典型目标包括推断共享共识排序、学习个体层面偏好以及执行无监督聚类。Mallows模型是为数不多能够同时实现所有这些目标的方法之一。以往研究基于MCMC Metropolis-Hastings方案开发了可计算可行的贝叶斯推断方法，其中通过Mallows模型的有限混合实现聚类，并在后验阶段对聚类数量进行推断。本文提出基于狄利克雷过程混合模型的贝叶斯非参数Mallows模型，该模型可对非空聚类数量与聚类分配进行联合推断，同时对聚类特定参数进行后验推断。所提出的采样算法实现已集成至现有R包BayesMallows中，该包同时支持不完整排序和成对比较数据格式。模拟数据显示，与有限混合模型相比，非参数模型在恢复正确聚类数量方面表现更优；电影评分实证数据则表明，该模型在基于丢弃评分的个性化电影推荐中具有有效性。