A non-parametric k-nearest neighbour entropy estimator
For researchers needing accurate entropy estimation in high-dimensional or correlated data, this method offers a practical improvement over existing non-parametric estimators.
The paper proposes a non-parametric k-nearest neighbour entropy estimator that improves on the Kozachenko-Leonenko estimator by accounting for non-uniform densities in the k-nearest neighbour region. It demonstrates significant improvement over the classical estimator across various distributions, especially in high dimensions and with near-functional relationships.
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.