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This study introduces novel methods for inferring network couplings using the Ising model and continuous time Glauber dynamics. The developed algorithms efficiently estimate network parameters from spin trajectories, even for complex biological networks.

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Area of Science:

  • Computational Neuroscience
  • Statistical Physics
  • Machine Learning

Background:

  • The inverse Ising problem is crucial for understanding complex network interactions from observed data.
  • Continuous time Glauber dynamics are often used to model spin systems, but inference can be challenging.

Purpose of the Study:

  • To develop efficient algorithms for inferring network couplings in the context of the inverse Ising problem.
  • To adapt these methods for continuous time Glauber dynamics and handle sparse network structures.

Main Methods:

  • Introduced auxiliary latent variables (Poisson and Pólya-Gamma) to simplify the likelihood function.
  • Derived an expectation-maximization (EM) algorithm for maximum likelihood estimation of network parameters.
  • Extended the EM algorithm with L1 regularization for sparse couplings and developed a variational Bayesian inference approach.

Main Results:

  • Demonstrated the performance of the developed algorithms on simulated data from Ising models.
  • Showed that the Ising model effectively captures low-order statistics of spiking neuron network data.
  • Established a relationship between inferred Ising couplings and the underlying synaptic structure of biological networks.

Conclusions:

  • The proposed methods provide an efficient and robust framework for solving the inverse Ising problem with continuous time Glauber dynamics.
  • These algorithms are applicable to both synthetic and biologically realistic network data, offering insights into neural connectivity.