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Ising model for neural data: model quality and approximate methods for extracting functional connectivity.

Yasser Roudi1, Joanna Tyrcha, John Hertz

  • 1NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
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We developed accurate methods to determine neuron network couplings in pairwise Ising models. These models effectively describe multineuron spike train statistics but require higher-order correlations for large networks.

Area of Science:

  • Computational neuroscience
  • Statistical physics

Background:

  • Pairwise Ising models are used to describe the statistics of multineuron spike trains.
  • Understanding network couplings is crucial for analyzing neural activity.

Purpose of the Study:

  • To explore efficient methods for finding optimal couplings in pairwise Ising models.
  • To examine the statistical properties of these couplings and model performance.

Main Methods:

  • Utilizing Boltzmann learning to extract optimal couplings for neuron subsets.
  • Comparing exact couplings with results from approximate methods like Thouless-Anderson-Palmer and Sessak-Monasson approximations.
  • Analyzing the impact of subset size on coupling estimation and model fit quality.

Main Results:

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  • Two approximate methods (Thouless-Anderson-Palmer and Sessak-Monasson) show remarkable accuracy.
  • Estimating couplings from smaller subsets systematically overestimates their magnitude.
  • Pairwise coupling variation reflects intrinsic network properties, outweighing global input effects.
  • Model fit quality deteriorates for larger subsets, indicating the need for higher-order correlations.

Conclusions:

  • Accurate methods for determining couplings in pairwise Ising models have been identified.
  • Subset-based analysis reveals systematic biases in coupling estimation.
  • Pairwise Ising models are effective for small networks but require extensions for larger systems.