Kernel Density Machines

Damir Filipovic, Paul Schneider
4/30/2025
stat.MLcs.LGmath.ST

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Abstract

We introduce kernel density machines (KDM), a nonparametric estimator of a Radon--Nikodym derivative, based on reproducing kernel Hilbert spaces. KDM applies to general probability measures on countably generated measurable spaces under minimal assumptions. For computational efficiency, we incorporate a low-rank approximation with precisely controlled error that grants scalability to large-sample settings. We provide rigorous theoretical guarantees, including asymptotic consistency, a functional central limit theorem, and finite-sample error bounds, establishing a strong foundation for practical use. Empirical results based on simulated and real data demonstrate the efficacy and precision of KDM.

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Cite this paper

@article{filipovic2025kernel,
  title  = {Kernel Density Machines},
  author = {Damir Filipovic and Paul Schneider},
  year   = {2025},
  eprint = {2504.21419},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2504.21419v2}
}

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