Practical Measures of Integrated Information for Time-Series Data

Two new measures of integrated information, Φ(E) and Φ(AR), overcome limitations of the earlier Φ(DM) measure, which could rarely be applied to biological systems because it required discrete Markov dynamics. The new measures are easy to apply to time-series data, as demonstrated through simulations. They offer new opportunities for studying information integration in real and model systems and have implications for understanding consciousness and other neurocognitive processes. However, the findings also challenge theories that assign physical meaning to these measured quantities.

Study at a glance

Abstract

A recent measure of 'integrated information', Φ(DM), quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ(DM) is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ(DM) can rarely be measured in practice. Here, we describe two new measures, Φ(E) and Φ(AR), that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.