On the Robustness of Regularized Pairwise Learning Methods Based on Kernels
This work addresses robustness issues in kernel-based pairwise learning methods, which is important for practitioners in machine learning dealing with noisy or adversarial data, though it appears incremental as it extends existing theory.
The paper investigates the statistical robustness properties of regularized pairwise learning methods based on kernels, showing that they achieve good robustness when the loss function and kernel are appropriately chosen, with results covering bounded non-convex and unbounded convex loss functions under specific conditions.
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.