Complexity as Causal Information Integration

A new measure of integrated information, Φ_{CII}, is proposed for quantifying causal connections between neurons within the Integrated Information Theory of consciousness. Unlike a prior candidate, Φ_{CIS}, which satisfies all theoretically desirable properties but lacks an intuitive graphical representation, Φ_{CII} models a common exterior influence via a latent variable and also satisfies all required conditions. It can be computed with an iterative information-geometric algorithm (the em-algorithm), enabling comparison with existing integrated information measures.

Study at a glance

Abstract

Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system and one without causal connections. Various measures have been proposed and compared in this setting. We will discuss a class of information geometric measures that aim at assessing the intrinsic causal influences in a system. One promising candidate of these measures, denoted by $Φ_{CIS}$, is based on conditional independence statements and does satisfy all of the properties that have been postulated as desirable. Unfortunately it does not have a graphical representation which makes it less intuitive and difficult to analyze. We propose an alternative approach using a latent variable which models a common exterior influence. This leads to a measure $Φ_{CII}$, Causal Information Integration, that satisfies all of the required conditions. Our measure can be calculated using an iterative information geometric algorithm, the em-algorithm. Therefore we are able to compare its behavior to existing integrated information measures.