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Estimation of the entropy based on its polynomial representation.
Martin Vinck1, Francesco P Battaglia, Vladimir B Balakirsky
1Cognitive and Systems Neuroscience Group, Center for Neuroscience, University of Amsterdam, The Netherlands.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study introduces a novel method for estimating entropy from finite data, reducing statistical bias. The new approach combines polynomial approximation and Bayesian estimation for more accurate results in information theory and statistical analysis.
Area of Science:
- Information Theory
- Statistical Analysis
- Computational Statistics
Background:
- Estimating entropy from finite empirical samples is crucial but suffers from statistical bias.
- Accurate entropy estimation is vital for analyzing complex statistical systems.
Purpose of the Study:
- To develop an unbiased entropy estimator for finite sample sizes.
- To reduce the intrinsic statistical bias in entropy estimation.
Main Methods:
- Decomposition of the entropy function into polynomial approximation and remainder functions.
- Utilizing Taylor expansion of the logarithm for the approximation.
- Employing nonlinear Bayesian estimation with a flat prior for the remainder.
Main Results:
- An unbiased, linear estimate for the first n power series terms of entropy was derived.
- The combined estimator demonstrated reduced bias compared to existing methods in simulations.
Conclusions:
- The novel entropy estimation method offers improved accuracy by mitigating statistical bias.
- This technique is valuable for information theory and the analysis of complex systems.
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