Kernel Density Machines

Andrea Della Vecchia; Damir Filipovic; Paul Schneider

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arXiv · 2504.21419

Kernel Density Machines

Andrea Della Vecchia·Damir Filipovic·Paul Schneider

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Abstract

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids the structural requirements common in classical nonparametric density estimators. We construct a sample estimator and prove its consistency and a functional central limit theorem. To enable scalability, we develop Nystrom-type low-rank approximations and derive optimal error rates, filling a gap in the literature where such guarantees for density learning have been missing. We demonstrate the versatility of KDM through applications to kernel-based two-sample testing and conditional distribution estimation, the latter enjoying dimension-free guarantees beyond those of locally smoothed methods. Experiments on simulated and real data show that KDM is accurate, scalable, and competitive across a range of tasks.

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BibTeX RIS

Andrea Della Vecchia, Damir Filipovic, Paul Schneider. 2025-04-30. Kernel Density Machines. https://arxiv.org/abs/2504.21419

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