Abstract/Summary

Many frameworks exist to infer cause and effect relations in complex nonlinear systems, but a complete theory is lacking. A new framework is presented that is fully nonlinear, provides a complete information theoretic disentanglement of causal processes, allows for nonlinear interactions between causes, identifies the causal strength of missing or unknown processes, and can analyze systems that cannot be represented on directed acyclic graphs. The basic building blocks are information theoretic measures such as (conditional) mutual information and a new concept called certainty that monotonically increases with the information available about the target process. The framework is presented in detail and compared with other existing frameworks, and the treatment of confounders is discussed. While there are systems with structures that the framework cannot disentangle, it is argued that any causal framework that is based on integrated quantities will miss out potentially important information of the underlying probability density functions. The framework is tested on several highly simplified stochastic processes to demonstrate how blocking and gateways are handled and on the chaotic Lorentz 1963 system. We show that the framework provides information on the local dynamics but also reveals information on the larger scale structure of the underlying attractor. Furthermore, by applying it to real observations related to the El-Nino–Southern-Oscillation system, we demonstrate its power and advantage over other methodologies. Unraveling cause and effect in complex systems is one of the fundamental tasks of science. This becomes a considerable challenge in systems where interventions are not possible and our only sources of information are time series of the processes of interest. Huge progress has been made for systems in which the underlying causal structure can be represented on a standard graph, in which each process is represented by a node and causal links by arrows from one node to another. However, there are many systems where the causal structure is too rich to be represented on such graphs. We developed the first complete causal discovery network for such systems, decomposing the causal influence of each driver into its direct contribution to a target process and its contribution with any other driver, any two other drivers, etc. Furthermore, we are able to quantify the influence of unknown driver processes so that we know how accurate our causal decomposition is. The usefulness is demonstrated via many examples. The new framework allows for new insights into complex systems for which often only time series are available, such as the atmosphere and the ocean and climate, astrophysics, the human brain, etc.