On the Robustness of Kernel-Based Pairwise Learning

Titelangaben

Gensler, Patrick ; Christmann, Andreas:
On the Robustness of Kernel-Based Pairwise Learning.
In: Steland, Ansgar ; Tsui, Kwok-Leung (Hrsg.): Artificial Intelligence, Big Data and Data Science in Statistics : Challenges and Solutions in Environmetrics, the Natural Sciences and Technology. - Cham : Springer , 2022 . - S. 111-153
ISBN 978-3-031-07154-6
DOI: https://doi.org/10.1007/978-3-031-07155-3_5

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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 by allowing the prediction function to take two arguments and can thus be applied in a variety of situations such as ranking, similarity learning and distance metric learning.