Practical Measures of Integrated Information for Time-Series Data

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.

Author Summary

A key feature of the human brain is its ability to represent a vast amount of information, and to integrate this information in order to produce specific and selective behaviour, as well as a stream of unified conscious scenes. Attempts have been made to quantify so-called ‘integrated information’ by formalizing in mathematics the extent to which a system as a whole generates more information than the sum of its parts. However, so far, the resulting measures have turned out to be inapplicable to real neural systems. In this paper we introduce two new measures that can be applied to both realistic neural models and to time-series data garnered from a broad range of neuroimaging and electrophysiological methods. Our work provides new opportunities for examining the role of integrated information in cognition and consciousness, and indeed in the function of any complex biological system. However, our results also pose challenges for theories that ascribe a direct physical meaning to any version of integrated information so far described.