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Exact Partial Information Decompositions for Gaussian Systems Based on Dependency Constraints.

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Summary
This summary is machine-generated.

This study extends Partial Information Decomposition (PID) to Gaussian systems using the I dep method. The I dep approach provides more intuitive results for information sharing compared to the I mmi method.

Keywords:
Gaussian graphical modelsdependency constraintsmaximum entropymutual informationpartial information decompositionunique information

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Area of Science:

  • Information Theory
  • Statistical Modeling
  • Machine Learning

Background:

  • Partial Information Decomposition (PID) quantifies multivariate information sharing.
  • The I dep method was recently developed for discrete systems.
  • Gaussian systems present unique challenges for information decomposition.

Purpose of the Study:

  • To apply the I dep PID method to Gaussian systems.
  • To derive closed-form solutions for I dep in Gaussian settings.
  • To compare I dep with existing methods like I mmi.

Main Methods:

  • Constructing maximum entropy probability models based on marginal dependency constraints.
  • Applying these models to Gaussian graphical models.
  • Deriving closed-form solutions for I dep in univariate and multivariate Gaussian systems.

Main Results:

  • Closed-form solutions for I dep PID in Gaussian systems were successfully derived.
  • The I dep method yielded more intuitive results than I mmi.
  • I dep generally produced smaller estimates of redundancy and synergy compared to I mmi.

Conclusions:

  • The I dep method is a viable and intuitive approach for PID in Gaussian systems.
  • I dep offers advantages over I mmi in quantifying information sharing.
  • Gaussian graphical models and deviance tests are useful tools for analyzing information decomposition.