A non-parametric k-nearest neighbor entropy estimator

Damiano Lombardi 1 Sanjay Pant 1
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, UPMC - Université Pierre et Marie Curie - Paris 6, Inria de Paris
Abstract : A non-parametric k-nearest neighbor based entropy estimator is proposed a. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbors around each sample point. It aims at improving 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 shown to be a significant improvement.
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Damiano Lombardi, Sanjay Pant. A non-parametric k-nearest neighbor entropy estimator. Physical Reviev E, 2016, ⟨10.1103/PhysRevE.93.013310⟩. ⟨hal-01272527⟩

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