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On the Robustness of Kernel-Based Pairwise Learning

In: Artificial Intelligence, Big Data and Data Science in Statistics

Author

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  • Patrick Gensler

    (University of Bayreuth, Department of Mathematics)

  • Andreas Christmann

    (University of Bayreuth, Department of Mathematics)

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 [11] 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.

Suggested Citation

  • Patrick Gensler & Andreas Christmann, 2022. "On the Robustness of Kernel-Based Pairwise Learning," Springer Books, in: Ansgar Steland & Kwok-Leung Tsui (ed.), Artificial Intelligence, Big Data and Data Science in Statistics, pages 111-153, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07155-3_5
    DOI: 10.1007/978-3-031-07155-3_5
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