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Entropy estimation of symbol sequences.

Thomas Schurmann1, Peter Grassberger

  • 1Department of Theoretical Physics, University of Wuppertal, D-42097 Wuppertal, Germany.

Chaos (Woodbury, N.Y.)
|September 1, 1996
PubMed
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This study introduces algorithms to estimate Shannon entropy in complex data. A proposed scaling law helps predict entropy from limited data, applicable to chaotic systems and text analysis.

Area of Science:

  • Information Theory
  • Statistical Mechanics
  • Computational Linguistics

Background:

  • Estimating Shannon entropy (h) is crucial for analyzing complex data with long-range correlations.
  • Existing methods may face challenges with finite sequences and computational constraints.

Purpose of the Study:

  • To develop and analyze algorithms for estimating Shannon entropy in finite symbol sequences.
  • To investigate the convergence properties of these algorithms with increasing sequence length.
  • To propose a method for extrapolating entropy estimates from finite sample lengths.

Main Methods:

  • Algorithms estimating Shannon entropy from compression-derived code lengths.
  • Analysis of algorithm convergence assuming no limits on computational resources.

Related Experiment Videos

  • Development of a scaling law for entropy extrapolation.

    • Main Results:

    • Demonstrated convergence of entropy estimation algorithms with sequence length.
    • Validation of the proposed scaling law for extrapolation.
    • Successful application to diverse datasets including chaotic dynamical systems, cellular automata, and written English.

    Conclusions:

    • The discussed algorithms provide robust methods for Shannon entropy estimation.
    • The proposed scaling law offers an effective approach for extrapolating entropy from limited data.
    • The findings have broad applicability in analyzing complex systems and natural language.