Label Ranking through Nonparametric Regression

TL;DR

This paper introduces a nonparametric regression approach to Label Ranking, providing theoretical guarantees, algorithms for high-dimensional data, and empirical insights into noise effects on rankings.

Contribution

It develops a nonparametric regression framework for Label Ranking, with theoretical bounds, efficient algorithms, and experimental analysis of noise impacts.

Findings

Sample complexity bounds for noiseless and noisy settings

Efficient algorithms using decision trees and random forests

Empirical analysis of input noise effects on rankings

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, 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.