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Nonparametrick-nearest-neighbor entropy estimator

Damiano Lombardi, Sanjay Pant Orcid Logo

Physical Review E, Volume: 93, Issue: 1

Swansea University Author: Sanjay Pant Orcid Logo

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Abstract

A nonparametric k-nearest-neighbor-based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering nonuniform probability densities in the region of k-nearest neighbors around each sample point. It aims to improve the classical estimators in three situa...

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Published in: Physical Review E
ISSN: 2470-0045 2470-0053
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa34501
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Abstract: A nonparametric k-nearest-neighbor-based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering nonuniform probability densities in the region of k-nearest neighbors around each sample point. It aims to improve the classical estimators in three situations: first, when the dimensionality of the random variable is large; second, when near-functional relationships leading to high correlation between components of the random variable are present; and third, when the marginal variances of random variable components vary significantly with respect to each other. Heuristics on the error of the proposed and classical estimators are presented. Finally, the proposed estimator is tested for a variety of distributions in successively increasing dimensions and in the presence of a near-functional relationship. Its performance is compared with a classical estimator, and a significant improvement is demonstrated.
College: College of Engineering
Issue: 1