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A Novel Approach to the Partial Information Decomposition.

Artemy Kolchinsky1

  • 1Santa Fe Institute, Santa Fe, NM 87501, USA.

Entropy (Basel, Switzerland)
|March 25, 2022
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Summary

This study introduces a new framework for partial information decomposition (PID) to break down information from multiple sources about a target variable. The approach uses set theory analogies and ordering relations, offering a more robust method for analyzing information components.

Keywords:
partial information decompositionredundancysynergy

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Area of Science:

  • Information Theory
  • Probability Theory
  • Computer Science

Background:

  • The partial information decomposition (PID) problem seeks to partition information from source variables about a target variable.
  • Existing PID methods face challenges in providing a comprehensive and consistent decomposition into redundant, synergistic, union, and unique components.

Purpose of the Study:

  • To propose a general framework for constructing a multivariate partial information decomposition (PID).
  • To define a PID using the Blackwell order, offering a fundamental operational interpretation.
  • To address and overcome limitations of previous PID proposals.

Main Methods:

  • Developed a general framework for multivariate PID based on formal analogies with set theory (intersection, union).
  • Introduced an ordering relation to compare information informativeness between sources.
  • Applied the framework to define PID using the Blackwell order for operational interpretation.

Main Results:

  • Successfully constructed a general framework for multivariate partial information decomposition.
  • Demonstrated the framework's ability to define PID using the Blackwell order.
  • Showcased the proposed approach's effectiveness on various examples, highlighting its advantages over prior methods.

Conclusions:

  • The proposed general framework offers a robust and axiomatically motivated approach to partial information decomposition.
  • The integration with the Blackwell order provides an operationally meaningful interpretation of information components.
  • This work advances the field of information theory by providing a more effective tool for analyzing complex information relationships.