# On the Robustness of Regularized Pairwise Learning Methods Based on Kernels

arXiv: https://arxiv.org/abs/1510.03267 · HTML: https://mlsanity.com/paper/1510.03267/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2015.

## Built on by (most cited first, 4 of 4)

- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Dimension Free Generalization Bounds for Non Linear Metric Learning](https://mlsanity.com/paper/2102.03802/) (2021)
- [Bootstrap SGD: Algorithmic Stability and Robustness](https://mlsanity.com/paper/2409.01074/) (2024)
- [Stability-based Generalization Analysis of Randomized Coordinate Descent for Pairwise Learning](https://mlsanity.com/paper/2503.01530/) (2025)

## Abstract (arXiv)

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.