Label Ranking Through Nonparametric Regression

Dimitris Fotakis, Alkis Kalavasis, Eleni Psaroudaki

Abstract: Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this fundamental practical problem. We introduce a generative model for Label Ranking, in noiseless and noisy nonparametric regression settings. In the noiseless setting, we focus on the computational aspects of the LR problem with full rankings and provide guarantees for time-efficient learning algorithms using decision trees and random forests in the high-dimensional regime. In the noisy setting, we consider the more general cases of LR with incomplete rankings from a statistical viewpoint and obtain sample complexity bounds using the One-Versus-One approach of multiclass classification. Lastly, we complement our theoretical contributions with experiments, aiming to understand how the input regression noise affects the observed output.