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Ising distribution as a latent variable model.

Adrien Wohrer1

  • 1Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000 Clermont-Ferrand, France.

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Summary
This summary is machine-generated.

The Ising distribution, while theoretically useful for correlated binary data, is often impractical. This study shows it can be replaced by the Cox distribution in many applications, particularly within the mean-field domain.

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Area of Science:

  • Statistical modeling
  • Computational neuroscience
  • Machine learning

Background:

  • The Ising distribution is a maximum entropy model for correlated binary variables, useful for observed means and covariances.
  • Numerical challenges make the Ising distribution impractical, leading to the use of alternatives like the Cox distribution in life sciences.

Purpose of the Study:

  • To explore conditions for replacing the Ising distribution with the Cox distribution.
  • To investigate the Ising distribution as a latent variable model and its quasi-normal properties.

Main Methods:

  • Treating the Ising distribution as a latent variable model.
  • Employing a variational approach to analyze the latent variable's distribution.
  • Utilizing weak coupling (Plefka) expansions and numerical tests.

Main Results:

  • Identified conditions under which the Ising distribution's latent variable approximates a normal distribution.
  • Revealed a formal link between the variational approach and classic mean-field methods (e.g., adaptive TAP).
  • Confirmed theoretical findings through numerical simulations.

Conclusions:

  • The Cox distribution can serve as a principled replacement for the Ising distribution in practical scenarios.
  • This replacement is valid when the Ising model's parameters fall within the "mean-field domain."
  • The study bridges theoretical Ising models with practical computational approaches.