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A Comparative Analysis of Discrete Entropy Estimators for Large-Alphabet Problems.

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Summary
This summary is machine-generated.

This study compares 21 entropy estimators for large alphabets, finding no single best method. Performance depends on data distribution, guiding practical estimator selection.

Keywords:
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Area of Science:

  • Information Theory
  • Machine Learning
  • Statistical Inference

Background:

  • Numerous entropy estimators exist, each suited for specific data characteristics.
  • No single entropy estimator demonstrates universal superiority across all scenarios.
  • Large-alphabet entropy estimation presents unique challenges and requires careful method selection.

Purpose of the Study:

  • To conduct a comprehensive comparative analysis of twenty-one entropy estimators.
  • To evaluate estimator performance across various data distributions in a large-alphabet setting.
  • To provide data-driven recommendations for optimal entropy estimation.

Main Methods:

  • Comparative evaluation of twenty-one distinct entropy estimation techniques.
  • Categorization of underlying data distributions into three classes (uniform to degenerate).
  • Development and assessment of a sample-dependent approach for estimator selection.

Main Results:

  • Entropy estimator performance is highly contingent on the underlying data distribution.
  • Specific estimators are recommended for different distribution classes.
  • A sample-dependent framework identifies top-performing estimators tailored to data characteristics.

Conclusions:

  • The choice of entropy estimator significantly impacts accuracy in large-alphabet settings.
  • Distribution-specific and sample-dependent approaches enhance practical entropy estimation.
  • This work offers a valuable guide for selecting appropriate entropy estimators in real-world applications.