Model-Based Learning from Preference Data

Preference data occur when assessors express comparative opinions about a set of items, by rating, ranking, pair comparing, liking, or clicking. The purpose of preference learning is to (a) infer on the shared consensus preference of a group of users, sometimes called rank aggregation, or (b) estimate for each user her individual ranking of the items, when the user indicates only incomplete preferences; the latter is an important part of recommender systems. We provide an overview of probabilistic approaches to preference learning, including the Mallows, Plackett-Luce, and Bradley-Terry models and collaborative filtering, and some of their variations. We illustrate, compare, and discuss the use of these methods by means of an experiment in which assessors rank potatoes, and with a simulation. The purpose of this article is not to recommend the use of one best method but to present a palette of different possibilities for different questions and different types of data.