  We propose a unified theoretical framework for quantifying spatio-temporal
interactions in a stochastic dynamical system based on information geometry. In
the proposed framework, the degree of interactions is quantified by the
divergence between the actual probability distribution of the system and a
constrained probability distribution where the interactions of interest are
disconnected. This framework provides novel geometric interpretations of
various information theoretic measures of interactions, such as mutual
information, transfer entropy, and stochastic interaction in terms of how
interactions are disconnected. The framework therefore provides an intuitive
understanding of the relationships between the various quantities. By extending
the concept of transfer entropy, we propose a novel measure of integrated
information which measures causal interactions between parts of a system.
Integrated information quantifies the extent to which the whole is more than
the sum of the parts and can be potentially used as a biological measure of the
levels of consciousness.
