We live in an increasingly interconnected world and, unfortunately, our understanding of interdependency is still limited. As a matter of fact, while bivariated relationships are at the core of most of our data analysis methods, there is still no principled theory to account for the different types of interactions that can occur between three or more variables. This talk explores the vast and largely unexplored territory of multivariate complexity, and discusses information-theoretic approaches that have been introduced to fill this important knowledge gap.

The first part of the talk is devoted to synergistic phenomena, which correspond to statistical regularities that affect the whole but not the parts. We explain how synergy can be effectively captured by information-theoretic measures inspired in the nature of high brain functions, and how these measures allow us to map complex interdependencies into hypergraphs. The second part of the talk focuses on a new theory of what constitutes causal emergence, and how it can be measured from time series data. This theory enables a formal, quantitative account of downward causation, and introduces “causal decoupling” as a complementary modality of emergence. Importantly, this not only establishes conceptual tools to frame conjectures about emergence rigorously, but also provides practical procedures to test them on data. We illustrate the considered analysis tools on different case studies, including cellular automata, baroque music, flocking models, and neuroimaging datasets.