MRA-based statistical learning from incomplete rankings

Eric Sibony (1) , Stéphan Clémençon (1) , Jérémie Jakubowicz (2, 3, 4, 5)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 METHODES-SAMOVAR - Méthodes et modèles pour les réseaux
3 TSP - RS2M - Département Réseaux et Services Multimédia Mobiles
4 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
5 CNRS - Centre National de la Recherche Scientifique

Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance

Domaines: Machine Learning [stat.ML]

Eric Sibony, Stéphan Clémençon, Jérémie Jakubowicz. MRA-based statistical learning from incomplete rankings. ICML 2015 : 32nd International Conference on Machine Learning, Jul 2015, Lille, France. pp.1432 - 1441. ⟨hal-01270543⟩