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Empirical Nonnegative Finite-Resolution MAR-PID for Continuous Variables.

András Telcs1

  • 1HUN-REN Wigner Research Centre for Physics, Konkoly Thege Miklós út 29-33, 1121 Budapest, Hungary.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for partial information decomposition (PID) applicable to complex variables. It enables nonnegative information summaries, improving upon methods that can conflate informational mechanisms.

Keywords:
Blackwell orderMAR-PIDcontinuous variablesempirical estimationpartial information decompositionrecursive quantile binarizationzonogons

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Area of Science:

  • Information theory
  • Computational neuroscience
  • Machine learning

Background:

  • Partial Information Decomposition (PID) quantifies information shared between variables.
  • Existing PID methods struggle with continuous or non-binary discrete variables.
  • Nonnegative Mages-Anastasiadi-Rohner (MAR)-PID is a promising but limited approach.

Purpose of the Study:

  • To develop a finite-resolution empirical framework for applying nonnegative MAR-PID to continuous and non-binary discrete variables.
  • To represent complex variables using recursive quantile binarization for balanced binary-tree structures.
  • To provide nonnegative target-relative information summaries for observed variables.

Main Methods:

  • Recursive quantile binarization to represent variables.
  • Application of MAR-PID to binary target components.
  • Conditional channel estimation and bit-level MAR-PID computation.
  • Projection and aggregation of information atoms back to original variables.

Main Results:

  • A novel framework for finite-resolution empirical MAR-PID is established.
  • Nonnegative information summaries are generated for complex variables.
  • The method successfully separates informational mechanisms, unlike signed interaction-information summaries.
  • XOR and mixed redundancy-synergy examples demonstrate the framework's efficacy.

Conclusions:

  • The developed framework offers a robust method for applying nonnegative MAR-PID to diverse variable types.
  • This approach enhances the analysis of information flow and mechanisms in complex systems.
  • Future work will explore downstream summaries like resolution-normalized PID-dimension descriptors.