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Approximations of Shannon Mutual Information for Discrete Variables with Applications to Neural Population Coding.
Wentao Huang1,2, Kechen Zhang2
1Key Laboratory of Cognition and Intelligence and Information Science Academy of China Electronics Technology Group Corporation, Beijing 100086, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces new, accurate methods to approximate Shannon mutual information for neural population coding. These formulas work for both discrete and continuous variables, simplifying complex information theory calculations.
Area of Science:
- Computational neuroscience
- Information theory
- Statistical signal processing
Background:
- Shannon mutual information is crucial but difficult to compute for neural data.
- Existing methods like Fisher information are limited to continuous variables.
Purpose of the Study:
- Develop novel information metrics to approximate Shannon mutual information.
- Address limitations of current methods in neural population coding.
Main Methods:
- Utilized Kullback-Leibler and Rényi divergences for approximations.
- Developed asymptotic formulas applicable to discrete variables.
- Validated a universally applicable formula for discrete and continuous variables.
Main Results:
- Proposed several accurate information metrics for approximating mutual information.
- Demonstrated consistent high accuracy for a key formula across variable types.
- Numerical simulations confirmed accuracy in large neural populations.
Conclusions:
- The new approximation formulas offer practical solutions for calculating mutual information.
- These methods enhance the application of information theory in neuroscience and other fields.
Keywords:
Chernoff divergenceKullback-Leibler divergenceRényi divergenceapproximationdiscrete variablesmutual informationneural population codingMore Related Videos
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