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An approximate method for Bayesian entropy estimation for a discrete random variable.

Yasunari Yokota1

  • 1Dept. of Information Sci., Faculty of Engineering, Gifu Univ., Japan.

Conference Proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference
|February 3, 2007
PubMed
Summary

This study introduces an improved Bayesian entropy estimator for discrete random variables. The novel method uses Taylor series approximation, significantly enhancing precision and reducing computational cost for complex variables.

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Area of Science:

  • Information Theory
  • Statistical Inference
  • Machine Learning

Background:

  • Entropy estimation is crucial for understanding discrete random variables.
  • Traditional Bayesian estimators can be computationally intensive for variables with many values.
  • Existing methods may lack precision in complex scenarios.

Purpose of the Study:

  • To develop a computationally efficient Bayesian entropy estimator.
  • To improve the precision of entropy estimation for discrete random variables.
  • To address the high computational cost of existing Bayesian methods.

Main Methods:

  • Proposed an approximated Bayesian entropy estimator.
  • Utilized Bayesian estimation for occurrence probabilities.
  • Applied truncated Taylor series approximation to the entropy function.

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Main Results:

  • Achieved least square error in the Bayesian entropy estimator.
  • Demonstrated significant improvement in estimation precision compared to conventional methods.
  • The Taylor series approximation offers a practical computational approach.

Conclusions:

  • The approximated Bayesian entropy estimator provides a practical and precise solution.
  • The method is particularly beneficial for discrete random variables with numerous values.
  • This approach enhances the efficiency and accuracy of entropy estimation in statistical analysis.