Density estimation with distribution element trees
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Date
2018-05
Publication Type
Journal Article
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yes
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OPEN ACCESS
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Abstract
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pairwise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators.
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Publication status
published
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Journal / series
Volume
28 (3)
Pages / Article No.
609 - 632
Publisher
Springer
Event
Edition / version
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Date collected
Date created
Subject
Nonparametric density estimation; Adaptive histogram; Kernel density estimation; Adaptive binning; Polynomial histogram; Curse of dimensionality; High dimensional; Big data; Pólya tree; Density estimation tree
Organisational unit
03644 - Jenny, Patrick / Jenny, Patrick
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.