Multi-resolution analysis of ranking data.

Summary This theme introduces a multi-resolution analysis framework for ranking data. Initiated in the 18th century in the context of elections, ranking data analysis has attracted major interest in many areas of scientific literature: psychometrics, statistics, economics, operations research, machine learning or computational social choice among others. It has also been revitalized by modern applications such as recommender systems, where the goal is to inform the preferences of users to offer them the best personalized suggestions. In these contexts, users express their preferences only on small subsets of objects varying within a large catalog. However, the analysis of such incomplete rankings poses an important challenge, both from a statistical and computational point of view, pushing industrial actors to use methods that exploit only a part of the available information. This theme introduces a new representation for the data, which overcomes by construction this double challenge. Although it is based on combinatorics and algebraic topology results, its numerous analogies with multiresolution analysis make it a natural and efficient framework for the analysis of incomplete classifications. Since it makes no assumptions on the data, it already provides state-of-the-art estimators for small catalogs of objects and can be combined with many regularization procedures for large catalogs. For all these reasons, we believe that this multi-resolution representation opens the way to many future developments and applications.