Beyond integrated information: A taxonomy of information dynamics phenomena

Most information dynamics and statistical causal analysis frameworks rely on the common intuition that causal interactions are intrinsically pairwise -- every 'cause' variable has an associated 'effect' variable, so that a 'causal arrow' can be drawn between them. However, analyses that depict interdependencies as directed graphs fail to discriminate the rich variety of modes of information flow that can coexist within a system. This, in turn, creates problems with attempts to operationalise the concepts of 'dynamical complexity' or `integrated information.' To address this shortcoming, we combine concepts of partial information decomposition and integrated information, and obtain what we call Integrated Information Decomposition, or PhiID. We show how PhiID paves the way for more detailed analyses of interdependencies in multivariate time series, and sheds light on collective modes of information dynamics that have not been reported before. Additionally, PhiID reveals that what is typically referred to as 'integration' is actually an aggregate of several heterogeneous phenomena. Furthermore, PhiID can be used to formulate new, tailored measures of integrated information, as well as to understand and alleviate the limitations of existing measures.