Institute of Mathematics


Modul:   STA671  Kolloquium über anwendungsorientierte Statisik

Probabilistic preference learning from incomplete rank data

Talk by Prof. Dr. Arnoldo Frigessi

Date: 11.04.24  Time: 15.15 - 16.15  Room: ETH HG G 19.1

Ranking data are ubiquitous: we rank items as citizens, as consumers, as scientists, and we are collectively characterised, individually classified and recommended, based on estimates of our preferences. Preference data occur when we express comparative opinions about a set of items, by rating, ranking, pair comparing, liking, choosing or clicking, usually in an incomplete and possibly inconsistent way. The purpose of preference learning is to i) infer on the shared consensus preference of a group of users, or ii) estimate for each user their individual ranking of the items, when the user indicates only incomplete preferences; the latter is an important part of recommender systems. I present a Bayesian preference-​learning framework based on the Mallows rank model with any right-​invariant distance, to infer on the consensus ranking of a group of users, and to estimate the complete ranking of the items for each user. MCMC based inference is possible, by importance-​sampling approximation of the normalising function, but mixing can be slow. We propose a Variational Bayes approach to performing posterior inference, based on a pseudo-​marginal approximating distribution on the set of permutations of the items. The approach scales well and has useful theoretical properties. Partial rankings and non-​transitive pair-​comparisons are solved by Bayesian augmentation. The Bayes-​Mallows approach produces well-​calibrated uncertainty quantification of estimated preferences, which are useful for recommendation, leading to excellent accuracy and increased diversity, compared for example to matrix factorisation. Simulations and real-​world applications help illustrate the method. This talk is based on joint work with Elja Arjas, Marta Crispino, Qinghua Liu, Ida Scheel, Øystein Sørensen, and Valeria Vitelli.