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Effectiveness of the Kozachenko-Leonenko estimator for generalized entropic forms
1Unilever R&D Port Sunlight, Quarry Road East, Wirral CH63 3JW, United Kingdom. silvio.queiros@unilever.com
Summary
The Kozachenko-Leonenko entropy estimator is effective for uniform distributions but limited for others. Variable dependence, especially nonlinear, reduces estimator accuracy for Boltzmann-Gibbs-Shannon entropy.
Area of Science:
- Information Theory
- Statistical Mechanics
- Complex Systems Analysis
Background:
- The Kozachenko-Leonenko estimator is a key tool for estimating entropy in data.
- Systems exhibiting asymptotic scale invariance and dependence require generalized entropic forms.
- Understanding the limitations of entropy estimators is crucial for accurate system analysis.
Purpose of the Study:
- To evaluate the generalized Kozachenko-Leonenko entropy estimator's effectiveness.
- To investigate its performance with different entropic forms (Boltzmann-Gibbs-Shannon).
- To analyze the impact of linear and nonlinear variable dependence on estimator accuracy.
Main Methods:
- Generalization of the Kozachenko-Leonenko entropy estimator.
- Analysis of estimator performance under various data distributions (uniform and others).
- Assessment of estimator accuracy with independent and identically distributed (IID) variables.
- Investigation of the influence of linear and nonlinear dependence between variables.
Main Results:
- The estimator is effective across the entire domain only for uniformly distributed data.
- For non-uniform distributions, effectiveness is limited to the Boltzmann-Gibbs-Shannon entropy form's limit.
- Both linear and nonlinear dependence between variables reduce estimator accuracy.
- Nonlinear dependence significantly impacts the estimator's efficiency for the Boltzmann-Gibbs-Shannon form.
Conclusions:
- The generalized Kozachenko-Leonenko estimator shows limitations with non-uniform data and dependent variables.
- Careful consideration of data distribution and variable dependence is necessary when applying this estimator.
- The estimator's utility is context-dependent, particularly concerning the chosen entropic form.
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