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Inferring local structure from pairwise correlations.

Mahajabin Rahman¹, Ilya Nemenman²

¹Department of Physics, Emory University, Atlanta, Georgia 30322, USA.

Physical Review. E

|October 18, 2023

Summary

Pairwise correlations in complex systems, even with limited data, can reveal local structures and data dimensionality. This method aids in reconstructing scrambled data and understanding machine learning models.

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Area of Science:

Complex Systems Modeling
Machine Learning Theory
Data Analysis

Background:

Modeling complex systems requires identifying variable interactions.
Detecting local structures is crucial for understanding multivariate systems.
Modern machine learning, like attention mechanisms, shows promise in handling complexity.

Purpose of the Study:

To investigate if pairwise correlations can recover local structures in complex systems.
To determine if this approach is effective even with undersampled and noisy data.
To provide insights into the success of modern machine learning techniques.

Main Methods:

Utilized a toy model of 2D natural and synthetic images.
Analyzed pairwise correlations between variables under severe undersampling.
Assessed the ability to recover local relations and data dimensionality.

Main Results:

Pairwise correlations successfully recovered local relations and data dimensionality.
Reconstruction of pixel arrangements in scrambled images was achieved.
Effectiveness was demonstrated despite the presence of higher-order interactions.

Conclusions:

Pairwise correlations are sufficient for inferring local structures in complex systems.
This approach offers a method for modeling complex systems and explaining machine learning successes.
The findings have implications for both theoretical modeling and practical applications in AI.