Practical measures of integrated information for time-series data

• Published in: PLoS computational biology Vol. 7; no. 1; p. e1001052
• Main Authors: Barrett, Adam B, Seth, Anil K
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01-01-2011; Public Library of Science (PLoS)
• Subjects: Behavior; Consciousness; Experiments; Information Services; Information theory; Markov Chains; Models, Theoretical; Neural stimulation; Neuroscience/Theoretical Neuroscience; Physiological aspects; Psychological aspects; Random variables; Studies; United Kingdom; Models, Theoretical; Information Services; Markov Chains
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1001052

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.