On the robustness of kernel-based pairwise learning

TL;DR

This paper demonstrates that kernel-based pairwise learning methods are robust under minimal assumptions, establishing their influence function properties and qualitative robustness, and extends previous results to more general prediction functions.

Contribution

It generalizes existing robustness results for kernel-based pairwise learning to broader settings, including functions with two arguments.

Findings

Influence function exists and is bounded for these estimators

Kernel-based estimators exhibit qualitative robustness

Results hold without moment or boundedness assumptions on data

Abstract

It is shown that many results on the statistical robustness of kernel-based pairwise learning can be derived under basically no assumptions on the input and output spaces. In particular neither moment conditions on the conditional distribution of Y given X = x nor the boundedness of the output space is needed. We obtain results on the existence and boundedness of the influence function and show qualitative robustness of the kernel-based estimator. The present paper generalizes results by Christmann and Zhou (2016) by allowing the prediction function to take two arguments and can thus be applied in a variety of situations such as ranking.