Improved Measures of Integrated Information

TL;DR

This paper reviews, classifies, and simplifies measures of integrated information, proposing practical formulas suitable for real-world data analysis with reduced computational complexity.

Contribution

It introduces a taxonomy of Phi-measures based on factorization, distribution comparison, and measure choice, identifying a limited set of effective measures with practical formulas.

Findings

Classified Phi-measures by factorization, distribution comparison, and measure.

Reduced hundreds of options to a few effective measures.

Derived formulas applicable to laboratory data with manageable computation.

Abstract

Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated and classified by various desirable properties. A simple taxonomy of Phi-measures is presented where they are each characterized by their choice of factorization method (5 options), choice of probability distributions to compare (3x4 options) and choice of measure for comparing probability distributions (7 options). When requiring the Phi-measures to satisfy a minimum of attractive properties, these hundreds of options reduce to a mere handful, some of which turn out to be identical. Useful exact and approximate formulas are derived that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands.