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Basics of Multivariate Analysis in Neuroimaging Data
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Generalised Measures of Multivariate Information Content.

Conor Finn1,2, Joseph T Lizier1

  • 1Centre for Complex Systems, The University of Sydney, Sydney NSW 2006, Australia.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

New multivariate information measures can be accurately represented using Venn diagrams, overcoming limitations of existing methods. This advance aids in visualizing complex information sharing across multiple random variables.

Keywords:
information contentinformation decompositioninformation measuresmultivariate mutual informationredundancysynergy

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Area of Science:

  • Information Theory
  • Probability and Statistics
  • Data Science

Background:

  • Venn diagrams commonly illustrate entropy for pairs of random variables.
  • Existing representations are misleading due to potentially negative multivariate mutual information.
  • Need for accurate visualization of information sharing among multiple variables.

Purpose of the Study:

  • Introduce novel measures for multivariate information content.
  • Enable accurate Venn diagram representation for any number of random variables.
  • Complement existing multivariate mutual information measures.

Main Methods:

  • Develop new measures based on the algebraic structure of information sharing.
  • Utilize concepts from lattice theory to model information sharing.
  • Combine algebraic structures of joint and shared information content.

Main Results:

  • New measures allow accurate Venn diagram depiction for multivariate information.
  • Demonstrate correspondence between information sharing patterns and free distributive lattice elements.
  • Independently derive the redundancy lattice from partial information decomposition.

Conclusions:

  • Proposed measures offer a reliable method for visualizing multivariate information.
  • The algebraic approach provides a robust framework for understanding information sharing.
  • This work enhances the toolkit for analyzing complex dependencies in data.