  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 $\Phi_{CIS}$, 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 $\Phi_{CII}$, 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.
