About the project
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. Recommender systems rely on estimating the preferences of users to propose next items; search algorithms estimate what the user is looking for and ranks possible items; decision making algorithms use features of the items to rank them according to given measures. The purpose of preference learning is to (a) infer on the shared consensus preference of a group of users, or (b) estimate for each user their individual ranking of the items, when the user indicates only incomplete preferences.We develop 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. This is why we work on Variational Bayes approaches to performing posterior inference, using pseudo-marginal approximating distributions on the set of permutations of the items. The approach scales well, and has useful theoretical properties. We treat partial rankings and non-transitive pair-comparisons by Bayesian augmentation, and heterogeneity of the assessors by a mixture of Mallows models. 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. Current research focuses on using features of the assessors (humans or algorithms) to cluster the assessors in unsupervised settings and on partial ranking. Simulations and real-world applications help understand the methods.
Project team
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Professor Arnoldo Frigessi, University of Oslo
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Associate Professor Valeria Vitelli, University of Oslo, Institute of Basic Medical Sciences
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Associate Professor Ida Scheel, University of Oslo, Department of Mathematics
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Professor Øystein Sørensen, University of Oslo, Department of Psychology