Practical measures of integrated information for time- series data

Abstract

A recent measure of 'integrated information', φDM, 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, φDM is defined only for discrete Markov systems, which are unusual in biology; as a result, φDM can rarely be measured in practice. Here, we describe two new measures, φE and φAR, 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. © 2011 Barrett, Seth.