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Deterministic Sampling of Multivariate Densities based on Projected Cumulative Distributions

Hanebeck, Uwe D.

Abstract:
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate settings. Simple solutions are restricted to the one-dimensional case. In this paper, we propose to employ one-dimensional density projections. These are the Radon transforms of the densities. For every projection, we compute their cumulative distribution function. These Projected Cumulative Distributions (PCDs) are compared for all possible projections (or a discrete set thereof). This leads to a tractable distance measure in multivariate space. The proposed approximation method is efficient as calculating the distance measure mainly entails sorting in one dimension. It is also surprisingly simple to implement.

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Zugehörige Institution(en) am KIT Institut für Anthropomatik und Robotik (IAR)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 30.12.2019
Sprache Englisch
Identifikator KITopen-ID: 1000120241
Umfang 21 S.
Nachgewiesen in arXiv
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