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Kernel Density Machines

Author

Listed:
  • Damir Filipović

    (École Polytechnique Fédérale de Lausanne (EPFL); Swiss Finance Institute)

  • Paul Schneider

    (University of Lugano - Institute of Finance; Swiss Finance Institute)

Abstract

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.

Suggested Citation

  • Damir Filipović & Paul Schneider, 2025. "Kernel Density Machines," Swiss Finance Institute Research Paper Series 25-53, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2553
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