| Summary: | 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 cross-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 cross-influences in a system. One promising candidate of these measures, denoted by <inline-formula><math display="inline"><semantics><msub><mi mathvariant="sans-serif">Φ</mi><mrow><mi>C</mi><mi>I</mi><mi>S</mi></mrow></msub></semantics></math></inline-formula>, 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 <inline-formula><math display="inline"><semantics><msub><mi mathvariant="sans-serif">Φ</mi><mrow><mi>C</mi><mi>I</mi><mi>I</mi></mrow></msub></semantics></math></inline-formula>, 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.
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