Kernel Density Machines

Damir Filipović and Paul Schneider
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Damir Filipović: École Polytechnique Fédérale de Lausanne (EPFL); Swiss Finance Institute
Paul Schneider: University of Lugano - Institute of Finance; Swiss Finance Institute

No 25-53, Swiss Finance Institute Research Paper Series from 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.

Keywords: density ratio estimation; reproducing kernel Hilbert space (RKHS); low-rank approximation; finite-sample guarantees (search for similar items in EconPapers)
Pages: 43 pages
Date: 2025-05
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2553

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