Practical measures of integrated information for stationary systems

Document Type: 
ASSC Conference Item
Article Type: 
Theory of Consciousness
Integrated information theory ** Measures of consciousness ** Conscious level ** Time-series analysis
Deposited by: 
Adam Barrett
Contact email:
Date of Issue: 
Adam B. Barrett, Anil K. Seth
Event Dates: 
24-27 Jun 2010
Event Location: 
Toronto, Canada
Event Title: 
14th annual meeting of the Association for the Scientific Study of Consciousness
Event Type: 
ASSC Conference
Presentation Type: 
Number of Pages: 
Publish status: 
Integrated information theory (IIT) has recently gained prominence as a theory of consciousness. IIT posits that any physical system has the potential to generate consciousness, and that the quantity of consciousness present corresponds to the integrated information generated [1]. Integrated information, PHI, is computed by quantifying the extent to which the system as a whole generates more information than the sum of its parts. However, in its present form [1], PHI cannot be measured for real neural systems, undermining its scientific utility. We present a new measure of integrated information, stationary PHI (SPHI), which is measurable for real neural systems. Defined for any system whose states are statistically stationary, SPHI measures information as reduction in uncertainty from the stationary distribution. By contrast, the formulation in Ref. [1] takes information as reduction in uncertainty from the maximum entropy distribution. Use of the stationary distribution, instead of the maximum entropy distribution, gives rise to two key features that enable SPHI to be measurable from time-series data. First, it is well-defined for systems whose states may vary continuously. Second, it can be measured purely through observation, without recourse to perturbation of system subsets. When states are Gaussian distributed, SPHI can be computed directly from empirical covariance matrices, and can in fact be expressed in terms of linear regressions, which further enhances its practical application. The latter property also motivates a second measure, ARPHI (autoregressive PHI), defined directly from regression errors. ARPHI is equivalent to SPHI for Gaussian systems, whereas for non-Gaussian systems it provides a pragmatic alternative to SPHI. ARPHI (and SPHI for Gaussian systems) are state-independent. Therefore, to the extent that they are considered as measures of consciousness, they predict that (i) conscious level is constant during each stationary epoch in brain activity, and (ii) conscious level changes when functional connectivity changes, modifying the stationary statistics. To better understand the relations between structural connectivity, functional connectivity and integrated information, we present results from optimizing SPHI across a variety of simulation models, as well as comparisons with related measures such as ‘causal density’ and ‘neural complexity’. [1] Balduzzi, Tononi 2008.
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