English

Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

Machine Learning 2022-06-16 v1 Machine Learning Functional Analysis Statistics Theory Statistics Theory

Abstract

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes of kernels on Banach spaces and on metric spaces of strong negative type. The general results are used to give explicit classes of kernels on separable LpL^p spaces and on sets of measures.

Keywords

Cite

@article{arxiv.2206.07588,
  title  = {Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures},
  author = {Johanna Ziegel and David Ginsbourger and Lutz Dümbgen},
  journal= {arXiv preprint arXiv:2206.07588},
  year   = {2022}
}