Preference-Based Rank Elicitation using Statistical Models: The Case of Mallows

We address the problem of rank elicitation assuming that the underlying data generating process is characterized by a probability distribution on the set of all rankings (total orders) of a given set of items. Instead of asking for complete rankings, however, our learner is only allowed to query pairwise preferences. Using information of that kind, the goal of the learner is to reliably predict properties of the distribution, such as the most probable top-item, the most probable ranking, or the distribution itself. More specifically, learning is done in an online manner, and the goal is to minimize sample complexity while guaranteeing a certain level of confidence.