Valeria Vitelli: Probabilistic preference learning with the Mallows rank model

Abstract:

The analysis and modelling of rank data has received renewed interest in the era of almost full availability of internet, when recruited or volunteer assessors compare and rank objects to facilitate decision making in disparate areas, from politics to entertainment, from education to marketing. The Mallows rank model is among the most successful approaches, but for computational convenience its use has been limited to a particular form based on the Kendall distance. We develop computationally tractable methods for Bayesian inference in Mallows models with any right-invariant metric, allowing for greatly extended flexibility. Our method performs inferences on the consensus rankings of the considered items, also when based just on partial rankings, such as top-k or pairwise comparisons. We prove that items which none of the assessors have ranked do not influence any a posteriori statement about the consensus ranking, and can therefore be ignored. If the assumption of an underlying common true ranking for all assessors is unrealistic, we can cluster assessors in more homogeneous subgroups and consider consensus rankings within each. We develop a series of approximate stochastic algorithms that allow a fully probabilistic analysis, leading to coherent quantifications of uncertainties. Our method can be used for making probabilistic predictions on the classification of assessors based on their ranking of some items, and on individual preferences based only on partial information. The performance of the approach is studied using several experimental and benchmark datasets.