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Measuring integrated information in complex systems is challenging due to computational limits. This study presents a feasible taxonomy of Φ-measures, offering practical formulas for real-world experimental data analysis.

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Area of Science:

  • Cognitive Science
  • Computational Neuroscience
  • Information Theory

Background:

  • Growing interest in quantifying integrated information within computational and cognitive systems.
  • Current methods for measuring integrated information are computationally intractable for practical application.

Purpose of the Study:

  • To investigate and classify existing and novel measures of integrated information.
  • To develop a feasible taxonomy of Φ-measures for practical use.
  • To derive formulas applicable to real-world experimental data.

Main Methods:

  • Classification of Φ-measures based on factorization methods, probability distribution comparisons, and distribution comparison measures.
  • Development of a taxonomy with 5 factorization options, 12 probability distribution comparison options, and 7 comparison measures.
  • Derivation of exact and approximate formulas for calculating integrated information.

Main Results:

  • A systematic taxonomy of Φ-measures is presented, reducing hundreds of options to a manageable set.
  • Identified identical Φ-measures within the proposed taxonomy.
  • Derived practical formulas for calculating integrated information from experimental data.

Conclusions:

  • The proposed taxonomy and derived formulas significantly reduce the computational burden of measuring integrated information.
  • Enables practical application of integrated information measures to real-world data from laboratory experiments.
  • Advances the field of integrated information measurement in computational and cognitive systems.