title: Nonparametric k-nearest-neighbor entropy estimator.
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.
authors: Inria Paris-Rocquencourt, Boîte Postale 105, 78153 Le Chesnay Cedex, France; Sorbonne Universités, UPMC Université Paris 06, 4 Place Jussieu, 75252 Paris Cedex 05, France; and CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, France.
authors: Damiano
authors: D
authors: Lombardi
authors: Inria Paris-Rocquencourt, Boîte Postale 105, 78153 Le Chesnay Cedex, France; Sorbonne Universités, UPMC Université Paris 06, 4 Place Jussieu, 75252 Paris Cedex 05, France; and CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, France.
authors: Sanjay
authors: S
authors: Pant