On the robustness of kernel-based pairwise learning
This work provides theoretical robustness guarantees for kernel-based methods in pairwise learning, which is incremental as it generalizes prior results to broader applications like ranking.
The paper tackles the problem of establishing statistical robustness for kernel-based pairwise learning without requiring assumptions on input/output spaces, such as moment conditions or boundedness, and demonstrates the existence and boundedness of the influence function along with qualitative robustness of the estimator.
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 (2016) by allowing the prediction function to take two arguments and can thus be applied in a variety of situations such as ranking.