A non-parametric k-nearest neighbour entropy estimator

TL;DR

This paper introduces a non-parametric k-nearest neighbor entropy estimator that improves accuracy over classical methods, especially in high-dimensional, highly correlated, or heteroscedastic data scenarios.

Contribution

It extends the classical Kozachenko-Leonenko estimator by accounting for non-uniform densities, enhancing entropy estimation in complex data conditions.

Findings

Significant improvement over classical estimators in high dimensions.

Effective in the presence of near-functional relationships.

Performs well with varying marginal variances.

Abstract

A non-parametric k-nearest neighbour based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbours 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.