Improved Measures of Integrated Information

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 Φ-measures is presented where they are each characterized by their choice of factorization method (5 options), choice of probability distributions to compare (3 × 4 options) and choice of measure for comparing probability distributions (7 options). When requiring the Φ-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.Author Summary: How can one determine whether an unresponsive patient is conscious or not? Of all the information processing in your brain that can be measured with modern sensors, which corresponds to information that you are subjectively aware of and which is unconscious? A theory that has garnered much recent attention proposes that the answer involves measuring a quantity called integration that quantifies the extent to which information is interconnected into a unified whole rather than split into disconnected parts. Unfortunately, proposed measures of integration are too slow to compute in practice from patient data. In this paper, I explore and classify existing and novel integration measures by various desirable properties, and derive useful exact and approximate formulas that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands. This improves the prospects of making fascinating questions and theories about consciousness experimentally testable.