On the Robustness of Regularized Pairwise Learning Methods Based on Kernels

TL;DR

This paper investigates the robustness of regularized pairwise learning methods based on kernels, demonstrating their strong statistical robustness properties under specific loss functions and kernel choices.

Contribution

It provides a theoretical analysis showing that certain kernel-based RPL methods possess desirable robustness features, expanding understanding beyond traditional empirical risk minimization.

Findings

RPL methods with bounded, non-convex loss functions exhibit robustness.

Unbounded convex loss functions with Lipschitz conditions also lead to robustness.

The study highlights the importance of loss and kernel selection for robustness.

Abstract

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is regularized minimization of the error entropy loss which has recently attracted quite some interest from the viewpoint of consistency and learning rates. This paper shows that such RPL methods have additionally good statistical robustness properties, if the loss function and the kernel are chosen appropriately. We treat two cases of particular interest: (i) a bounded and non-convex loss function and (ii) an unbounded convex loss function satisfying a certain Lipschitz type condition.