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Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy

João V R Izzi1, Ricardo F Ferreira1, Victor A Girardi1

  • 1Department of Statistics, Federal University of São Carlos, São Carlos 13565-905, SP, Brazil.

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Summary

This study introduces transfer entropy to measure information flow in neuronal systems. The method effectively determines neuronal connectivity by analyzing causal relationships in time series data.

Keywords:
causalityconditional independenceeffective connectivityhypothesis testinginteracting variable-length Markov chainstransfer entropy

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Area of Science:

  • Neuroscience
  • Information Theory
  • Computational Neuroscience

Background:

  • Information theory provides frameworks for understanding information encoding and transmission.
  • Neuronal systems process information through interconnected neurons transmitting electrical signals.
  • Effective neuronal connectivity is crucial for understanding brain function.

Purpose of the Study:

  • To apply transfer entropy for quantifying information flow between neuronal sequences.
  • To develop a hypothesis test for determining effective neuronal connectivity based on information transfer.
  • To analyze causal relationships in discrete time series representing neuronal activity.

Main Methods:

  • Utilized transfer entropy to measure directed information flow between binary time series.
  • Developed a hypothesis test for zero transfer entropy rate, indicating no causal influence.
  • Employed a plug-in estimator based on log-likelihood ratios, with an asymptotic chi-squared distribution for p-value calculation.
  • Simulated data from a neuronal network model with stochastic neurons and variable-length memory.

Main Results:

  • Demonstrated that zero transfer entropy rate signifies no causal influence under specific conditions (jointly stationary ergodic variable-length Markov chain).
  • The plug-in estimator follows an asymptotic chi-squared distribution, enabling empirical p-value calculation.
  • The hypothesis test successfully identified biologically relevant information in simulated neuronal network data.

Conclusions:

  • Transfer entropy provides a robust method for assessing effective neuronal connectivity.
  • The developed hypothesis test is effective in identifying causal relationships and information flow in neuronal systems.
  • This approach offers a valuable tool for advancing our understanding of neural information processing.