Enlarged scaling ranges for the KS-entropy and the information dimension

TL;DR

This paper introduces improved methods for estimating the KS-entropy and information dimension from finite data, extending the reliable scaling ranges and demonstrating these improvements on experimental data.

Contribution

It presents a novel approach to better estimate entropy and information dimension by focusing on computable decay rates and ignoring uncomputable parts, enhancing analysis accuracy.

Findings

Extended scaling range for information dimension estimates

Improved KS-entropy estimates from finite data

Demonstrated effectiveness on experimental data

Abstract

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data.