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  3. Multivariate Partial Information Decomposition: Constructions, Inconsistencies, And Alternative Measures.
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  3. Multivariate Partial Information Decomposition: Constructions, Inconsistencies, And Alternative Measures.

Related Experiment Video

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Multivariate partial information decomposition: Constructions, inconsistencies, and alternative measures.

Aobo Lyu1, Andrew Clark1, Netanel Raviv2

  • 1Washington University in St. Louis, Department of Electrical and Systems Engineering, St. Louis, Missouri, USA.

Physical Review. E
|April 18, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

Partial Information Decomposition (PID) quantifies multivariate interactions. This study resolves two-source PID, proves inconsistencies for three+ sources, and proposes new measures for unique and synergistic information.

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Area of Science:

  • Information theory
  • Statistical modeling
  • Computational neuroscience

Background:

  • Mutual information quantifies dependence but lacks fine-grained detail in multivariate settings.
  • Partial Information Decomposition (PID) was developed to dissect mutual information into components like redundancy, uniqueness, and synergy.

Purpose of the Study:

  • To review the axiomatic system and properties of PID.
  • To resolve the two-source PID case with explicit formulas.
  • To demonstrate inconsistencies in PID for three or more sources and propose alternative measures.

Main Methods:

  • Derivation of closed-form formulas for two-source PID.
  • Proof of PID inconsistencies for N>=3 sources using an impossibility theorem.
  • Development of new measures for multivariate unique and synergistic information by eliminating higher-order dependencies.

Main Results:

  • Explicit closed-form formulas for two-source PID satisfying all axioms.
  • Demonstration of fundamental inconsistencies in lattice-based PID for three or more sources.
  • Novel measures for multivariate unique and synergistic information exhibiting desirable properties and strong performance.

Conclusions:

  • The standard PID framework is fundamentally inconsistent for analyzing information from three or more sources.
  • New measures are proposed to accurately quantify multivariate unique and synergistic information.
  • A new framework is needed for robust multivariate information decomposition.