Kernel Density Machines

We introduce kernel density machines (KDM), a novel density ratio estimator in a reproducing kernel Hilbert space setting. KDM applies to general probability measures on countably generated measurable spaces without restrictive assumptions on continuity, or the existence of a Lebesgue density. 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.

@article{filipovic2025_2504.21419,
  title={ Kernel Density Machines },
  author={ Damir Filipovic and Paul Schneider },
  journal={arXiv preprint arXiv:2504.21419},
  year={ 2025 }
}