Causal Discovery: A New Framework Allowing for and Incorporating General Inseparable Interactions

Causal discovery, unraveling cause and effect in complex systems, is a rapidly developing field, especially in its application to the natural and earth sciences, such as atmospheric science. The information theoretic approach has proved very useful for causal network discovery in this field filled with nonlinear relationships. Current calculations using this framework return values that are difficult to interpret physically, and existing causal discovery methods either do not incorporate the possibility that processes combine inseparably to influence another process, or the specific form of the nonlinear interaction has to be specified. This is slightly surprising as inseparable interaction terms are a fundamental aspect of the dynamics of the atmosphere and the specific form is often unknown.

We propose a new causal discovery framework that attempts to overcome these issues by first renormalizing all variables to have equal variance in order to remove all human-imposed scaling and to have a single reference process of maximal entropy. Then the method determines what we call the latent information content of the transformed variable as well as contributions to total information in the form of mutual information with other (lagged) known processes. Furthermore, the framework accounts for inseparable causation of multiple processes on a single process, ie. terms such as xⁿ⁺¹=yⁿzⁿ+..., or even more complicated terms. Allowing for inseparable interaction of unknown form is crucial, and our new framework explicitly incorporates this, further advancing our ability to unravel cause and effect in the complex atmospheric system.

The merit of the new framework will be tested in highly nonlinear and inseparable systems that have atmospheric relevance. The pro’s and con’s will be discussed. Since the computational effort grows exponentially with the number of processes in the network special attention will be given to efficient numerical implementation of the framework.