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  1. Home
  3. A Benchmark For Entropy Estimators.
  1. Home
  3. A Benchmark For Entropy Estimators.

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A Benchmark for Entropy Estimators.

Lucio M Calcagnile1, Angelo Di Garbo1,2, Stefano Galatolo3

  • 1Istituto di Biofisica, CNR, Via G. Moruzzi 1, 56124 Pisa, Italy.

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View abstract on PubMed

Summary
This summary is machine-generated.

This study benchmarks entropy estimators for time series data. Approximate Entropy and symbolic methods accurately estimated Kolmogorov-Sinai entropy, unlike Sample and Permutation Entropy.

Keywords:
Kolmogorov–Sinai entropyLyapunov exponentcomplexitytime series

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Area of Science:

  • Dynamical Systems Theory
  • Information Theory
  • Time Series Analysis

Background:

  • Estimating Kolmogorov-Sinai entropy is crucial for characterizing complex dynamical systems.
  • Existing entropy estimators vary in accuracy and robustness across different data types and system dynamics.
  • Computer-assisted proofs offer certified entropy values with rigorous error bounds for benchmarking.

Purpose of the Study:

  • To quantitatively assess and compare the performance of widely used entropy estimators.
  • To evaluate estimators on diverse one-dimensional dynamical systems with known certified entropy.
  • To identify reliable entropy estimation techniques for numerical and symbolic time series data.

Main Methods:

  • Generated long time series orbits for four classes of one-dimensional interval maps.
  • Compared certified Kolmogorov-Sinai entropy values against estimates from Approximate Entropy, Sample Entropy, Permutation Entropy, symbolic Plug-In, and Non-Sequential Recursive Pair Substitution (NSRPS) methods.
  • Utilized Grassberger-type bias correction for symbolic Plug-In and NSRPS estimators.

Main Results:

  • Approximate Entropy and symbolic methods (Plug-In, NSRPS) demonstrated consistent accuracy within rigorous error bounds across all tested systems.
  • Sample Entropy systematically underestimated the true entropy.
  • Permutation Entropy exhibited significant biases, particularly for expanding maps lacking a Markov partition.

Conclusions:

  • The study provides a quantitative benchmark for evaluating entropy estimation techniques in deterministic dynamical systems.
  • Approximate Entropy and symbolic methods are recommended for reliable entropy estimation in similar systems.
  • Further research is needed to improve the accuracy of Sample and Permutation Entropy estimators for complex dynamics.