Label Ranking through Nonparametric Regression
This work addresses the fundamental problem of learning rankings from features for machine learning practitioners, offering incremental theoretical and algorithmic contributions.
The paper tackles the Label Ranking problem by adopting a nonparametric regression approach, providing theoretical guarantees and sample complexity bounds for learning algorithms in both noiseless and noisy settings, with experiments to analyze the impact of input noise.
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, and provide sample complexity bounds for learning algorithms in both cases. In the noiseless setting, we study the LR problem with full rankings and provide computationally efficient 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 and partial rankings from a statistical viewpoint and obtain sample complexity bounds using the One-Versus-One approach of multiclass classification. Finally, we complement our theoretical contributions with experiments, aiming to understand how the input regression noise affects the observed output.