Pairwise network information and nonlinear correlations.

Area of Science:

• Complex Systems Analysis
• Network Science
• Information Theory

Background:

• Reconstructing structural connectivity from observed activity is crucial but challenging across disciplines.
• Determining if interactions are pairwise is a fundamental, yet often computationally intensive, first step.
• Traditional methods relying on bivariate distributions are often impractical due to estimation difficulties and high computational costs.

Purpose of the Study:

• To develop a computationally efficient method for assessing pairwise interactions in complex systems.
• To enable reliable network reconstruction by using mutual information as a proxy for bivariate distributions.
• To overcome the limitations of existing methods based on direct entropy calculations.

Main Methods:

• Introduced an approach utilizing mutual information as a proxy for bivariate probability distributions.
• Developed a novel entropy maximization scheme based on conditioning on entropies and mutual informations.
• Validated the method using oscillator networks and resting-state human brain network data.

Main Results:

• The proposed method is less computationally expensive and easier to estimate compared to traditional approaches.
• The novel entropy maximization scheme demonstrates superiority over methods based on linear approximations.
• Successful application to both synthetic (oscillator networks) and real-world (human brain) data.

Conclusions:

• The developed approach provides a practical and efficient tool for network reconstruction and connectivity analysis.
• Mutual information serves as a viable proxy, simplifying the assessment of pairwise interactions.
• This method advances the ability to model complex systems by facilitating network analysis.