Abstract: Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyze rank data, but its computational complexity has limited its use to a form based on Kendall distance. Here, new computationally tractable methods for Bayesian inference in Mallows models are developed that work with any right-invariant distance. The method performs inference on the consensus ranking of the items, also when based on partial rankings, such as top-k items or pairwise comparisons. When assessors are many or heterogeneous, a mixture model is proposed for clustering them in homogeneous subgroups, with cluster-specific consensus rankings. Approximate stochastic algorithms are introduced that allow a fully probabilistic analysis, leading to coherent quantification of uncertainties. The method can be used, for example, for making probabilistic predictions on the class membership of assessors based on their ranking of just some items, and for predicting missing individual preferences, as needed in recommendation systems.

Speaker: Elja Arjas

Affiliation: Professor (emeritus) of Mathematics and Statistics, University of Helsinki

Place of Seminar: University of Helsinki