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Information-Theoretic Bounds and Approximations in Neural Population Coding.

Wentao Huang1, Kechen Zhang2

  • 1Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, U.S.A., and Cognitive and Intelligent Lab and Information Science Academy of China Electronics Technology Group Corporation, Beijing 100846, China whuang21@jhmi.edu.

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Calculating mutual information for high-dimensional neural data is challenging. This study introduces accurate approximation formulas for neural population coding, enabling efficient computation even in high dimensions.

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Area of Science:

  • Computational Neuroscience
  • Information Theory
  • Machine Learning

Background:

  • Shannon's mutual information is vital but hard to compute for high-dimensional data due to the curse of dimensionality.
  • Accurate mutual information calculation is crucial for understanding neural population coding.

Purpose of the Study:

  • To develop effective approximation methods for evaluating mutual information in high-dimensional neural population coding.
  • To provide computationally efficient solutions for estimating mutual information in large neural populations.

Main Methods:

  • Derivation of information-theoretic asymptotic bounds and approximation formulas for large, finite neural populations.
  • Proof of convexity for optimizing population density distributions using approximation formulas.
  • Numerical simulations to validate the accuracy of the derived formulas.

Main Results:

  • The proposed asymptotic formulas accurately approximate mutual information in high-dimensional spaces for large neural populations.
  • Optimization of population density based on these formulas is a convex problem with efficient numerical solutions.
  • In specific scenarios, the approximation formulas yield exact mutual information values.

Conclusions:

  • The developed approximation methods offer a practical solution for calculating mutual information in high-dimensional neural population coding.
  • These methods facilitate efficient computation and analysis of information processing in neural systems.
  • Techniques for variable transformation and dimensionality reduction further enhance computational feasibility.