Article
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Collision Entropy Estimation in a One-Line Formula
Version 1
: Received: 18 May 2023 / Approved: 19 May 2023 / Online: 19 May 2023 (11:19:36 CEST)
Version 2 : Received: 23 May 2023 / Approved: 24 May 2023 / Online: 24 May 2023 (04:45:46 CEST)
Version 2 : Received: 23 May 2023 / Approved: 24 May 2023 / Online: 24 May 2023 (04:45:46 CEST)
How to cite: Gecchele, A. Collision Entropy Estimation in a One-Line Formula. Preprints 2023, 2023051438. https://doi.org/10.20944/preprints202305.1438.v2 Gecchele, A. Collision Entropy Estimation in a One-Line Formula. Preprints 2023, 2023051438. https://doi.org/10.20944/preprints202305.1438.v2
Abstract
We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost.
Keywords
Rényi entropies; collision entropy estimation; collision entropy rate estimation
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Alessandro Gecchele
Commenter's Conflict of Interests: Author
Modification of figure 3 by making the upper diagram as tall and wide as the lower diagram.
Modification of some sentences of the paper.
Spelling correction.