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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Network Inference and Maximum Entropy Estimation on Information Diagrams.

Elliot A Martin1, Jaroslav Hlinka2,3, Alexander Meinke1

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Summary
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This study introduces a novel maximum entropy method for network connectivity inference. The approach accurately estimates direct network connections, outperforming existing methods, especially in complex systems and undersampled data.

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Area of Science:

  • Information theory
  • Network science
  • Statistical inference

Background:

  • Maximum entropy estimation is crucial for system property inference across disciplines.
  • Existing methods for network connectivity estimation have limitations, particularly in undersampled regimes.

Purpose of the Study:

  • To develop an advanced maximum entropy estimation technique for inferring direct network connectivity.
  • To propose a nonparametric method for assessing network description explanatory power.
  • To generalize the approach for continuous variables and diverse information-theoretic quantities.

Main Methods:

  • Utilizing a novel technique for maximum entropy estimation conditioned on bivariate mutual informations and univariate entropies.
  • Applying the method to phase oscillators and resting-state human brain networks.
  • Developing a nonparametric formulation of connected informations.

Main Results:

  • The proposed method accurately estimates direct network connectivity, outperforming simple mutual information approaches.
  • The nonparametric connected informations formulation aligns with parametric methods and shows advantages in brain network analysis.
  • The generalized approach demonstrates superior performance in undersampled conditions and offers computational efficiency for high-cardinality variables.

Conclusions:

  • The new maximum entropy method provides a robust and efficient tool for network connectivity inference.
  • This approach enhances the analysis of complex systems, including biological networks.
  • Significant advantages over existing methods are established, particularly concerning data limitations and computational cost.